Large Scale Simulation and Analysis to
Understand Enzymatic Chemical Mechanisms
ARCHIR
by
Ishan Satish Patel
MASSACHSETTS INSTITUTE
OF TECHNOLOGY
B.S. Chemistry
NOV 0 9 2015
Boston University, 2008
LIBRARIES
SUBMITTED TO THE DEPARTMENT OF CHEMISTRY
IN PARTIAL FULMILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 2015
0 2015 Massachusetts Institute of Technology. All rights reserved.
A
A1-
Signature redacted
Signature of Author:
Department of Chemistry
August 12, 2015
Al
Certified by:
Signature redacted
Bruce Tidor
Professor of Biological Engineering and Computer Science
Thesis Supervisor
Accepted by:
Signature redacted_
i
Robert W. Field
Robert T. Haslam and Bradley Dewey Professor of Chemistry
Chairman, Departmental Committee on Graduate Students
This doctoral thesis has been examined by a Committee of the Department of Chemistry as
follows:
Signature redacted
Jianshu Cao
Professor of Chemistry
Chairman of Thesis Committee
Signature redacted
Robert W. Field
Professor of Chemistry
Thesis Committee Member
Signature redacted
Ii,
Bruce Tidor
Professor of Biological Engineering and Computer Science
Thesis Supervisor
Large Scale Simulation and Analysis to
Understand Enzymatic Chemical Mechanisms
by
Ishan Satish Patel
Submitted to the Department of Chemistry
on August 12, 2015 in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
ABSTRACT
The full stack approach, from Biochemical Network Simulation to Quantum Mechanics,
is developed and utilized to understand in this thesis to understand enzymatic mechanism. The
story falls into two segments that highlight two different aspects of enzymatic mechanisms. The
first is the determination of the kinetic complexity of one full enzymatic turnover can affect the
system in ways that cannot be predicted by simplistic simulations, as evidenced by differential
hydrolysis rates of VX and Paraoxon in the enzyme PTE. Over 4M CPU hours of
thermodynamic integration simulations were performed to obtain free energy profiles, as a
function of up to 6 dimensions, along a reaction path determined through a combination of
knowledge from physical organic chemistry, local energetic optimizations, and experimental
information. The activation barriers were converted to reaction rates and simulated with mass
action kinetics. The results show the slow-down in one turnover for the enzyme is not exactly
the one with the "highest barrier" but is instead the result of non-preferential product-facing
equilibrium. We also show that active site poisoning by VX opens up new pathways that are an
overall detriment to the enzyme. The second is the uncovering of the drivers of enzymatic
reactivity for a purely electronic Claisen rearrangement of Chorismate in CM, CM mutants, 1 F7
antibody, Solvent, and Vacuum. Utilizing Transition Path Sampling (TPS), we performed large
scale simulations totaling over I OM CPU hours and 1000 TB of storage space to arrive at an
understanding of the causation behind differential reactivity from a quantum mechanical orbital
point of view. Our results suggest differential catalytic capacity is driven by, and correlates with,
greater capacity to generate the forming bond, and for faster enzymes, greater capacity to disrupt
the breaking bond. Further orbital level decompositions were performed that demonstrated
disruption of the breaking bond allows greater catalytic gains because orbital symmetry prevents
strong intermolecular electronic delocalization of the breaking bond electrons. Our evidence
suggests a combination of catalyzing the departure from the reactant basin and the transport
through the transition region are both reasons why the WT CM is an extremely capable catalyst.
Thesis Supervisor: Bruce Tidor
Title: Professor of Biological Engineering and Computer Science
3
4
CONTENTS
Acknow ledgem ents ........................................................................................................................................
6
Mechanistic Investigation of Fast and Slow Substrate Hydrolysis by Phosphotriesterase .........................
7
In tro d u ctio n ................................................................................................................................................
M e th o d s ....................................................................................................................................................
7
14
Coordinate Preparation for PTE M ichaelis Com plex ........................................................................
15
Potential Energy Function ....................................................................................................................
16
M olecular Dynam ics Sim ulations: General Setup .............................................................................
17
Generation of Bim olecular Com plexes .............................................................................................
18
Solvent-M ediated Protonation Events .............................................................................................
18
Potential of M ea n Force .......................................................................................................................
19
Kinetic M ass Action M odeling of System Behavior ..........................................................................
19
Results and D iscussion .............................................................................................................................
22
Overall Pathway Description ................................................................................................................
26
Calculated kcat from M ass Action sim ulations, and its decom position ............................................
27
Dependence of Product KD on Calculated Rates for Paraoxon and VX.............................................
40
Concluding Rem arks .................................................................................................................................
40
The Diversity of Methods Utilized in QM/MM Reaction Mechanism Discovery of Chorismate Mutase ... 45
Large Scale Analysis of Chorsim ate Rearrangement Reaction Drivers ...................................................
58
Intro d u ctio n ..............................................................................................................................................
58
M e th o d s ...................................................................................................................................................
60
Coordinate Preparation for the Chorism ate-Bound M ichaelis Com plex..........................................
61
Potential Energy Function ....................................................................................................................
63
Um brella Sam pling Setup .....................................................................................................................
64
TPS Seed Trajectory Finding .................................................................................................................
65
Transition Path Sam pling Setup..........................................................................................................
65
Chem om etric Analysis of Trajectories Obtained from TPS...............................................................
67
Results and Discussion .............................................................................................................................
67
Um brella Sam pling ...............................................................................................................................
68
Transition Path Sam pling ......................................................................................................................
70
Catalytic m echanism of Wild Type Chorismate M utase Rearrangem ent ..........................................
72
Elucidation of Reaction Drivers from Probability Factor Trajectories ..............................................
83
C o n c lu sio n ..............................................................................................................................................
101
B ib lio g ra p hy ...............................................................................................................................................
10 4
A p p e n d ix ....................................................................................................................................................
1 10
5
ACKNOWLEDGEMENTS
I can't begin to emphasize how important my fellow lab members have been in encouraging and supporting
me both personally and academically in accomplishing this thesis. I have to give very special thanks to Brian Bonk
and Raja Srinivas, without whom, this thesis would have been very different, or potentially non-existent. I will miss
my long post-decaf dialogues with David Flowers, coffee-dealing and talking about the latest tweaks and
technologies with Andrew Homing, conversing with David Hagen about economics and statistics, Nirmala Paudel's
cheeky comments, and discussions about clever ways to leverage every ounce of computing power from our cluster
with Kevin Shi. I especially have to thank Sally Guthrie for letting me advisor her, who was an astoundingly astute
student who probably could've written a PhD thesis in the time she was researching in our lab. Of course, I will
forever be grateful to Nate Silver, Bracken King, Yuan Yuan Cui, Gil Kwak, Yang Shen and Filipe Gracio, who
have been both fantastic teachers and friends. I am grateful that Natasha Seelam, James Weiss, and Ishan Arora
have decided to join the lab. I know for sure they will carry forward the amazing atmosphere that I've been lucky to
be involved.
I also have to thank the community of people around me that have been very supportive, both academic and
personal. My academic connections from Boston University, John Straub, Lawrence Ziegler, Linda Doerrer, and
Katinka Csigi, all created, supported, and sustained an environment which allowed me to explore my interests. The
trajectory I've been on has been heavily influenced by these four amazing souls. I've been lucky that I'm a local
and I have friends who were supportive throughout this tough period. The support from Jeff Martell, Derek McGee,
Raj Manoharan, Tong Yin, Sachit Bakshi and Jewoo Yu is the reason why I tried to be better, to excel, and to learn
how to be a proper scientist. I also have to thank Professor Jianshu Cao, Professor Robert Field, and Professor
Catherine Drennan for serving on my thesis committees. They all have been very kind and helpful in shaping the
research in my thesis.
I have to definitely thank Dr. Ge and the Department of Energy - Office of Science Graduate Fellowship
for all their support, both financial and academic. From this program, I have made a lifelong group of friends and
colleagues.
My family has been an incredible source of support and they were always there for both the bad and good
days. Of course, I have to thank my 7 month old niece, Shaley, for putting everything in perspective and giving me
the encouragement to finish and defend this thesis! March 3 rd, 2013 has been the one of the most pivotal dates in my
life, where I've met my lifelong partner, Mary Orczykowski. She is a fantastic source of ideas, support, and
encouragement. Without her, I sincerely do doubt this thesis would be where it is or present. I can't wait to help her
out as she goes through her PhD program and ends up where I am now!
Last, but definitely the greatest, is Bruce. He has been very encouraging, and been a constant voice of
selfless personal and scientific guidance and mentorship. I knew he was the one when he called me apologizing that
he could not make it to our second meeting on December 2 3 rd, 2009 given the tribulations he went through to make
the phone call! Since I joined his lab, it's been a story of constant growth, and he has changed the way I perceive
and understand the world. This has spilled over into other aspects of my life and has enhanced my abilities to solve
problems across all aspects of my life. I did not expect the PhD to be such a transformative experience, and I have
to thank Bruce's influences and support in doing so! I can only hope that I will be able to reciprocate as much as
possible to him as he has unconditionally given to me.. .which is an immeasurable amount!
6
MECHANISTIC INVESTIGATION OF FAST AND SLOW SUBSTRATE
HYDROLYSIS BY PHOSPHOTRIESTERASE
Abstract
Nerve agent deactivation is of importance to national security and defense.
Phosphotriesterase (PTE) may be of use for this purposes, since it exhibits broad spectrum, but
slow, hydrolytic activity towards various organophosphates. We performed QM/MM Free
Energy simulations over one full turnover of the PTE catalyzed hydrolysis of VX Nerve Agent
and the 10,000 fold faster organophosphate pesticide Paraoxon. The resulting free energy
profiles were then utilized to generate kinetic mass action networks that were simulated to obtain
the ensemble behavior of PTE. Our results show that PTE is slower at catalyzing VX because
the resulting hydrolysis thiol product requires protonation to reset the enzyme. In contrast, the
PTE catalysis of Paraoxon is fast because the resulting hydrolysis p-nitrophenolate only requires
displacement by environmental water. Our results indicate that hydrolysis is not the rate-limiting
step, and instead, product departure from active site largely causes the calculated rate.
Introduction
Organophosphorus compounds have been developed for their ability to inhibit
acetylcholinesterase, which enables their usage in pesticide and insecticides. These class of
molecules can also be utilized as nerve agents to target humans, hence there is interest in
developing safe and efficacious methods to detoxify such compounds'. The enzyme
Phosphotriesterase (PTE, EC 3.1.8.1) has shown broad spectrum activities against multiple
classes of such compounds and shows promise as a means for nerve agent remediation.
7
With this broad array of substrates also comes a wide array of degradation rates that are
affected by both the pKa of the leaving group (LG)
2 and
the bond type being hydrolyzed with
phosphotriesters (P-O) being fastest and phosphothiolesters (P-S) being slowest 3. One of the
fastest substrates is the phosphotriester paraoxon (kcal = 2400 s-1 and kcat / Km = 3 x 107 M-1 s-1 ) 4,
which operates at the PTE hydrolysis diffusion limit 2. In contrast, PTE shows much lower
catalytic ability for phosphonothioate neurotoxins, such as acephate (kcat=2.8 s- 1) and especially
the human nerve agent VX (kcat = 0.6 s-I and kcat/Km= 1 x 10- 3 M-Is-1) 3. The promise of
improving PTE activity, especially for bioremediation purposes, has attracted multiple directed
evolution studies to alter substrate stereoselectivity and improve degradation rate -. While
these studies have found a variety of mutations that increase catalytic rate, knowledge about the
mechanistic steps within PTE to facilitate the hydrolysis reaction would help bolster future
directed evolution studies. Previous attempts to elucidate mechanism have focused on fitting
experimental rate kinetics to generalized enzyme kinetic schemes
2,10,
crystal structures with
substrate analogs 113, chemical species modification or spectroscopy 14-16, QM/MM simulations
of the hydrolysis step 1,17, QM/MM simulations of a subset of potential enzymatic mechanistic
steps 18, and MD simulations to elucidate various structural aspects of active site structure 19-24
In contrast to previous work in which a small subset of the mechanistic steps were studied with
great detail, we use QM/MM simulations to model and detail all the mechanistic steps that PTE
could follow in performing one full turnover during the hydrolysis of both an efficient and a poor
substrate, with paraoxon and VX as model exemplars of such substrates, respectively, with the
scheme shown in Figure 1. To connect the mechanistic steps to a macroscopic behavior of PTE,
8
we will employ kinetic mass action simulations that will be used to show which subset of paths
in the turnover pathway most directly determine whether a substrate is efficient or poor.
Structure and ExperimentalRate Data
The three dimensional structure of PTE from Pseudomonas diminuta was determined by
X-ray crystallographic diffraction ".
Each monomer of the C 2 symmetry-related homodimer
consists of 329 amino acids and folds into an (ap)s barrel motif The active site, as shown in
Figure 2, contains a binuclear metal center consisting of two Zn(II) ions. Zn(II)-a is less solvent
exposed and is bound exclusively by His 55, His 57, and Asp 301. Zn(II)-p is more solvent
exposed and is bound exclusively by His 201 and His 230. Both Zn(II) ions share the posttranslationally carboxylated Lys 169 and a bridging hydroxide
0
16.
There exist several solved
0
OH
O
O' -
O*OEt
H 20
0P
PTE
h
dEt
N
_
0-
hydrogen phosphate (DHP)
Sdiethyl
p-nitrophenolate (pNP)
O
H 20
EtO
PTE
HOH
+
0
Paraoxon
ethyl hydrogen methylphosphonate (EHMP)
VX Nerve Agent
2-(diisopropylamino)ethane-1-thio (DIPET)
Figure 1: The overall reaction scheme catalyzed by the enzyme Phosphotriesterase
structures of PTE, namely PTE from Pseudomonas diminuta at its resting state 25,26, with various
bound substrate analogs
11,12,27
, and binuclear metal ion identities
28
site directed mutated
structures from directed evolution studies of the PTE of Pseudomonas diminuta 5,29, and wild
type and mutated structures from Agrobacterium radiobacter13,30,31
9
PTE has the ability to hydrolyze a broad variety of substrates
to bind both the substrate and its
H
0
N%
HNs 5
zna2+
supposed transition state
'Znp2+---
------
N
Hishas
N
N
which is thought to
arise from the enzyme's ability
Asp 301
His 5 7
32,5,
Lys1 69
H
I
His 230
33
This lack of substrate specificity
been utilized in several
His2N1
experimental studies to better
HN
understand P. diminuta PTE
Figure 2: The Phosphotriesterase active site
substrate stereochemistry 32,7,12
and reaction mechanism 32,2,7,10,14. Bronsted plots of paraoxon-like substrates demonstrated a
robust logarithmic growth in the rate ofp-nitrophenolate (or similar) appearance with decreasing
pKa's of the leaving group of the substrate. The rate of appearance of the p-nitrophenolate (or
similar) reporter is unchanged for substrates with leaving group pKa's less than 7 2,10
ProposedMechanisms
Several hypothesis have been proposed for the reaction mechanism of PTE catalyzed
degradation of organophosphate species. Aubert et al utilized a multitude of experimental
techniques to elucidate the mechanism. To summarize, a fit of a minimal kinetic model to
experimental data demonstrated the presence of a rate-limiting step post-appearance ofpnitrophenol (or similar), pH rate profiles indicated that the protonation of active site hydroxyl
reduces p-nitrophenol appearance rate (further supported by a later study 16), significant
Asp233(Ala/Asn) and His254(Ala/Asn) mutagenesis rate effects implied an importance at these
two positions to catalysis, and the observation of inverse thio effects suggests the existence of an
interaction between the phosphoryl oxygen and an active site metal ".
10
A)
.00H
i
structural data 11,12,25,28, the authors proposed the
suba te
H
Using these experimental data and previous
Xr
*O7%o
first phase of the mechanism , shown in Figure
3B, to be in which the substrate first binds to
Zn(II)-p via its phosphoryl oxygen by displacing
a previously Zn(II)-p water, followed by attack
rN
I
heH
0
R
4
h
of the active site hydroxide concomitant with the
abstraction of the hydroxide proton via Asp 301
(and subsequent coordination with His254), then
alI.P
.eA hw h
rpse
ehns
o
the departure of the leaving group (pnitrophenolate for paraoxon) that leaves the
phosphate bridging Zn(II)-a and Zn(II)-p. The
proton on Asp 301 was postulated to be shuttled
.
enzyme resetting and Panel B shows the proposed
mechanism of phosphotriester hydrolysis. Figure
taken from ref10
out of the active site via His 254 and Asp 233.
The proposed reaction mechanism was supported
with later QM calculations that provided reasonable energetics for the deprotonation of the
hydroxide proton via Asp 301 17 and an X-ray crystal structure with a soaked product mimic,
diethyl phosphate, that showed its capable of bridging both activie site Zn(II) 27. The second
phase of the mechanism, shown in Figure 3A, which comprises the rate limiting step for
paraoxon, is the subsequent slow departure of the deprotonated phosphate with displacement by
solvent water, followed by generation of the active site hydroxide and neutralization of His 254
to restore back the active site 0.
Wong and Gao, by computational QM/MM studies of the initial hydrolysis step and by
utilizing additional DFT calculations, proposed a similar hydroxide attack step to that proposed
11
by Aubert et al, but they differ in that the
.H
resulting product is found as a neutral
Asp300
oe
phosphate, dissociated p-nitrophenol, and
0
\S,~
Et
'
2.
HOPOEI
no phosphate bridge, as shown in Figure 4.
Additional simulations of this resting state
Hiss
N
H
H
-NH
Hs254
showed a water enter the active site and
H'0Et
E0H5E
exhibit potential proton transfer interactions
H2 ®o'r
AsX.
\N
e
y715
H
y
with His 254, which led them to
additionally conclude that the mechanism
ends with hydroxide generation via His 254
1
Figure 4: The mechanism proposed by Wong and Gao
through the use of QM/MM simulations. Figure taken
from ref. 1
mechanism ends by a restoration of the active site via departure of all product species
.
or solvent-mediated proton abstraction. The
Overview of Our Study
These two experimental and computational studies have focused on providing only one
major pathway in which PTE operates. Another computational study has focused on expanding
on work done by Wong and Gao by calculating activation free energies for rational steps that
occur before and after the hydrolysis step 18. In this study, we will explore, with computational
modeling, all the possible pathways that PTE could take in performing one turnover for both an
efficient and poor substrate. There are several features in the mechanisms we arrive at that
consist of subsets, ideas, and themes from the mechanisms proposed by Aubert et al and Wong
and Gao.
Taking the pathway holistically, we will utilize kinetic mass action simulations to
simulate the enzyme starting in its resting state, going through all the chemical steps to hydrolyze
12
one substrate molecule, and performing the necessary steps to restore back the resting state. We
demonstrate the feasibility of the Asp 301 - His 254 - Asp 233 proton extraction pathway 10 via
direct calculation of free energy barriers along with incorporation of a potential for solvent
mediated (de)protonation events via implementation in kinetic mass action simulations. We
additionally show that our kinetic scheme does in fact show burst kinetics for substrates in which
the release of reporter is rate limiting, and we show that our calculated Vmax for both the efficient
and poor substrate are properly ranked. Flux analysis of the kinetic pathway shows that the poor
substrate has a leaving group that tightly, but reversibly, binds to Zn(II)-P, hence inhibiting
further enzyme turnovers. Finally, we show that the calculated kcat doesn't necessarily
correspond to the step in the pathway with the highest energetic barrier.
13
Methods
To fully investigate the causation for differential rates between paraoxon and VX, we utilized
Molecular Dynamics (MD) simulations, combined
03
C4
1
Quantum Mechanical and Molecular Mechanical
.O
C7
(QM/MM) methods, and Kinetic Mass Action
DII
Simulations to elucidate the mechanistic steps and its
oz
0
CS
OZ
/L-Pf
11
respective relative weight in the overall enzyme
OT
op
turnover. Starting from the reactant state, multiple
rational mechanistic steps with shown precedence in
---
N+
Enzymology and Organic Chemistry were propagated
0
forwards by thermodynamic integration with umbrella
Paraoxon
sampling. After each successful mechanistic step and
Y
N
~I
Cs
0z
I
N L P1
1
CP
VX
Figure 5: The atom naming utilized for the
investigation of the simulation results, the enzyme state
was propagated forward even more until the enzyme
was restored back to its resting state and the reactant
was successfully hydrolyzed into product.
mapping of atoms in Paraoxon and VX to the
Dii inhibitor found in the crystai structureG.
Because of the complexity of the enzyme, and
it's relatively labile and mobile active site groups, uni-dimensional umbrella sampling wasn't
sufficient to generate a continuous path (i.e. one in which non-reaction coordinate controlled
degrees of freedom didn't show a large change between windows). Hence, each mechanistic
step required 2, 3, or 4 dimensional umbrella sampling. This high dimensionality allowed us to
explore more possible mechanistic pathways. Overall, 30 and 18 mechanistic steps were
simulated for VX and Paraoxon hydrolysis, respectively, for a total of 1.2 pts of QM/MM
simulation sampling time.
14
Kinetic mass action simulations, where individual mechanistic steps are treated as 1st or
2 nd
order reactions, were utilized to understand the interactions between individual species in the
network composing one enzymatic turnover. While these simulations are computationally
inexpensive, they provide important network dynamics that correlate directly to experimental
observables. By treating our QM/MM pathway with kinetic mass action simulations, we are
capable of capturing the dynamics of individual states in a catalytic pathway by better
13)
A)
Figure 6: The structure of A) Paraoxon and B) VX after placement into the active site of PTE utilizing a crystalstructure bound inhibitor as a template.
understanding the flux and population of various species. With these results, we provide insight
into pre-steady state kinetics, dominant enzymatic states, and dominant reaction paths.
CoordinatePreparationforPTE Michaelis Complex
The 1.9 A X-ray crystal structure of PTE bound to the substrate analog methylphosphonic
acid diisopropyl ester (DII) was obtained from the Protein Data Bank (identifier 1 EZ2) and used
as a starting point to construct two enzyme-substrate complexes, one with paraoxon and one with
VX bound 26 . The atomic coordinates for the enzyme were extracted together with
crystallographic water oxygen atom coordinates. The neighbors of all Asp, Glu, Arg, and Lys
side chains were examined and the local hydrogen bonding network analyzed to determine
protonation state. All instances were left charged in these four residue types. Similarly, the
neighbors for each His residue were examined and titration states were set to maximize hydrogen
15
bonding interactions: His 123, 201, 254, and 257 were protonated at the epsilon position; His 55,
57 and 230 were protonated at the delta position; and none were positively charged. Hydrogenatom positions were calculated with the HBUILD facility of the molecular mechanics package
CHARMM. DII was used as template to situate paraoxon and VX in the active site, with the DII
P1, 01, 02, 03, C4, and C7 atoms used as corresponding positions for VX P, OT, SL, Oz, Cs,
and Cp and paraoxon P1, OT, OL, Oz, Cs, and Op in a fitting procedure, as shown in Figure 5.
The structure of VX and paraoxon with enzyme residues fixed underwent 250 rounds of
Newton-Raphson energy minimization to better situate the substrate. The resulting locations of
both VX and paraoxon in the active site are shown in Figure 6. The enzyme, with no positions
fixed, underwent 250 more rounds of Newton-Raphson energy minimization to minimize large
unfavorable interactions.
PotentialEnergy Function
To simultaneously model both the bond breaking and forming reactions along with the
enzyme dynamics, a hybrid QM/MM approach was utilized. Asp 301, His 55, His 57, His 201,
His 230, both Zn2 ions, bridging hydroxide, carboxylated Lys 169, and the substrate were
treated with the AM I level of semi-empirical quantum mechanics via the SQUANTM module in
CHARMM c36al and the rest of the protein was treated with the CHARMM27 molecular
mechanical force field. When involved in reactions, His 254 and Asp 233 were also included in
the quantum region. The C, of Asp 301, His 55, His 57, His 201, His 230, His 254, and Asp 233
and C6 of Lys 169 were treated with the Generalized Hybrid Orbital method to define the
boundary between the QM and MM region. A total of 110 to 140 atoms were included in the
quantum region.
16
Molecular Dynamics Simulations: General Setup
MD simulations were carried out in vacuo with a Langevin integrator (friction coefficient
of 5 ps') at 300 K with l-fs time steps. Non-bonded interactions were truncated using a
switching function between 10 to 12
A. The Michaelis complex, constructed as described, was
subject to umbrella sampling constraints that led the system along defined potential reaction
pathways. To initiate a simulation at a given umbrella-sampling window, the system was pushed
linearly towards the sampling position by sequential steps of size 0.1 reaction coordinate units
(generally
A), with 250 fs of equilibration at each step. This initial positioning was followed by
at least 10 ps of equilibration and 40 ps of production dynamics at the given umbrella window.
The actual duration for the equilibration and production times were selected based on observed
convergence properties of the simulations, requiring that an additional 5 ps of sampling produced
a change in free energy of less than 5%. A sufficient number of umbrella-sampling windows
were simulated to ensure that each window had at least 15% population overlap with adjacent
windows. Typically, one-dimensional umbrella sampling consisted of 30 windows, twodimensional of 300 windows, and three-dimensional of 1200 windows. The last frame of the
MD trajectory situated in the product state was used as the starting structure for subsequent
umbrella sampling runs. The structures were propagated forward until one full turnover was
performed, i.e. the enzyme active site was restored and the substrate was full degraded.
Aggregated over all the windows in this study, over 1 is of total sampling time was simulated in
this work.
17
Generationof Bimolecular Complexes
Certain reactions generate a bimolecular complex, in which the product and enzyme are
non-covalently bound together. However, the active site needs to expel this product in order to
return to its resting state. To model the unimolecular dissociation, the complex was subject to
reaction coordinates that separated the complex into two entities until the dissociation of the
product from the enzyme would be diffusion driven, i.e. there is no change in free energy as the
distance between the two complexes is increased. The
0"H
complex was considered dissociated when the free energy
H
change was less than 0.25 kcal/mol per 1
H
-''
'0'
H'I
H
H
0
.H
H
H
H
H
A increase in
separation. The association of the product and enzyme is
still unimolecular due to the proximity of the product and
enzyme, which permits the usage of TST to obtain a first
order rate constant from activation free energies.
Figure 7: The scheme utilized for
hydronium catalyzed protonation of
base
Solvent-Mediated ProtonationEvents
In the VX reaction pathway, a solvent mediated Zn-bound thiol protonation pathway was
develope
in wiUC
a Eige
catIonic hyru
m complex sr
Us the storage medium for the
excess proton with its transfer occurring via a fifth water in a Zundel-like transfer of protons to
the destination thiol. The H 1305' complex was generated via the <source> model and positioned
in the active site such that proton transfer would be mediated through water positioned between
the base and proton source, as shown in Figure 7. To maintain the structure of the hydronium
complex, NOE constraints were placed on all hydrogen bonds in the complex with an rmin of 0
kmin of 0 kcal/A 2, rmax of 3
A,
A, and kmax of 200 kcal/A 2 . Additional NOE constraints were placed
18
between all H-O bonds with a rmin of 0 A, kmin of 0 kcal/A 2, rmax of 1.2 A, and kmax of 200
.
kcal/A 2
Potentialof Mean Force
The free energy profiles (FEPs) were calculated from the collected distribution of
reaction coordinates in umbrella sampling simulations via the Weighted Histogram Analysis
Method (WHAM) 4 . Each window was divided into 7 histogram bins centered on the window
mean and the WHAM equations were iteratively solved until the maximal difference in energy in
a histogram bin was less than 0.01 kcal/mol per iteration. The Boltzmann weighted onedimensional free energy profile for different paths in a non-unidimensional FEPs was obtained
by integration over all the bins that are on the desired path:
F(L)
F(r) e -F(r)
=
f
.)-flF(r)
(L=f (r)
L=f (r)
Where
(L
is 1/RT, F(L) is the free energy as a function of L, which is the value of the reaction
coordinate, r, after they're operated on by linear combination defined by a function f(r). For
example, if two distances di and d2 were used as order parameters in a two-dimensional potential
of mean force, then it might be reduced to a one-dimensional PMF using only di, only d 2 , or the
difference d 2-di.
Kinetic Mass Action Modeling of System Behavior
The enzymatic pathway mapping generates a multitude of pathways connected that
compose the kinetic complexity of the enzyme. While traditional kinetic pathways have linear
models, our model is a network of reactions that describe one complete turnover. The forward
19
and reverse kinetic rate constants between each state was determined from the forward and
35
reverse activation free energies by the Eyring-Polanyi relation:
k =
kIBT AG*
e RT
h
The kinetic system was modeled in the Kronecker software package with the ordinary
differential equations numerically integrated with mass action rate laws with the ode 15s stiff
differential equation integrator in MATLAB. The starting concentration for enzyme, substrate,
and H 3 0 was I nM, 1 M, and 100 nM (concentration at pH 7). The two resting states of the
enzyme are differentiated by the protonation state of the active site water, which experimental
evidence suggests has a pKa of 6.1. A rapid equilibrium between the two protonation states was
assumed, with ionization assumed possible only before substrate binding due to solvent
exclusion. The equilibrium was modeled with an ionization (deprotonation) rate constant of 1012
and a deionization (protonation) rate constant of 1011, which are magnitudes in accord with
proton exchange rates in water. These ratio of rate constants yield a 10:1 preference in
concentration for the OH- over the H20 species in the active site, in accordance with equilibrium
concentrations of an acid with a pKa of 6.1.
The association rates. kon, for substrate to enzyme was reasoned from the k-+ and kc,+/KM
values for Paraoxon and VX. Since KM = ( kr + kcat )/kf, paraoxon's k0 n is lower bounded by 108
and upper bounded by the diffusion limit of 10' M-' s-'. Paraoxon's koff approaches 0 s-' if k0 n is
108 M 1 s-1, which is unrealistic. However, the computed kcat of Paraoxon is insensitive to the
substrate koff, when kon is 108 M-' s-', as shown in Figure SI. Hence, for all simulations,
Paraoxon's kon was set to be 108 M-1 s- which was determined to be the lower bound from
experimental KM values. The koff value was set to be 10 3 S-1, which is a place holder value for the
sake of reversibility in the binding process even though it has no effect on the simulation
dynamics and results. The kcat associated with PTE catalyzed degradation of VX is low enough
20
such that Km approximates KD. Any range of k.n from 103 to 10' M-1 s- would allow proper
fitting of KM. All values of the koff/kon pair that equate to KM = 10-3 M give the same overall
network result, as shown in Figure S2. Hence, the k0 n of to 10 9 M-1 s-I from the Paraoxon
simulation was utilized with the corresponding koff to 106 S1.
For all product species, at a constant equilibrium constant for diffusion-only dissociation,
KDiffision, changing kon from the 10 3 to 10 9 M-'s-1 does not affect results, hence the product
species binding and unbinding were treated as if they were an equilibrium process with the kon
being set to that of Paraoxon and VX's 108 M- 1 s-1. The choice of KDiffusion does affect the
magnitude of rate constants in our simulations, but it does not change intrinsic properties such as
the dominant pathways. The observed dissociation constant, KD, is actually a product of two
equilibrium constants originating from two separate steps 1) Kseparation, the product departs the
active site and breaks all intramolecular interactions and 2) KDiffusion, the product dissociates
away from the enzyme. Hence, the
KDiffusion
because KD
where Kseparation is generally less than 1.
KDiffusion X
Kseparation,
will lower than experimentally measured KD
explicitly computed by umbrella sampling whereas
KDiffusiion
Kseparation
is
is bounded by the diffusion
controlled dissociation rate. Since the diffusion controlled dissociation rate isn't available, a
weak binder's KD Of 10 mM was utilized, which would set koff in the
KDiffusion
to be 107 M'S~'.
The sensitivity of the simulation results to the koff will be discussed in the results.
The simulated kcat was determined by simulating each system at steady state at saturating
fixed concentrations of substrate, which was easily reachable at [S]> 103 [E]. The rate of free
thiol and nitrophenol formation, for VX and paraoxon, divided by overall enzyme concentration
(1 nM) was plotted as a function of time. The effective enzyme turnover number was calculated
from the slope of this plot. To further understand the causation behind calculated kcat, different
21
reactions were accelerated or decelerated by magnification or reduction of the affiliated rate
constant. The rates of production of species were further understood by flux analysis.
Results and Discussion
We studied a variety of conceivable mechanisms for the PTE catalyzed hydrolysis of VX
and paraoxon to evaluate their feasibility through an energetic analysis. The overall reaction
scheme consists of the reaction of water with substrate to yield hydrolyzed substrate and the
leaving group of VX or paraoxon, in their respective protonation state at neutral pH. To
elucidate the mechanistic steps that compose one full PTE turnover, we chose to investigate two
starting points, both initiating from the available crystal structure, but one in which the zincbound species is treated as a hydroxide, as is typically done by others 1 8, and the other in which
it is treated as a water (1) where the crystal structure is the starting point for hydrolysis of the
substrate and (2) where the crystal structure was taken as the starting point for the binding of
substrate and generation of the active site hydroxide.
Each starting point was simulated through plausible mechanistic steps with umbrella
samplingVVII
1 QMM
Dsmuainw Ichprvided Structural Inf-Ormation and free energy
profiles. This information was used, in turn, to refine or redirect the mechanistic steps in
directions that reduce free energy barriers and increase the fidelity to knowledge obtained from
experimental data. To differentiate why PTE hydrolyzes paraoxon and VX differentially, the
reaction pathways for both substrates were subject to the identical reaction coordinates for a
subset of the paths. The resulting reaction paths for VX and paraoxon are shown in Figures 8
and 9, respectively. With these pathways in hand, we simulated the mechanistic steps during the
catalysis of VX and Paraoxon through PTE by mass action simulations.
22
We will first present high level results of the pathway, followed by its mass action
simulations to illustrate network dynamics. The kcat will be decomposed to understand the rate
limiting steps and network branches. Using this knowledge of rate limiting steps, we will
discuss pivotal microscopic steps within one turnover and their implications in affecting the
observed kcat.
23
.
ANW
11.99.1
HH-
VII
20-014.g
V12 -ThioIH
V12
HIM
*0
HHA*
ViO
VIIP-Th 1i
H'"
H-
S
H H
N
VII P
A
H
H
C',
0 111
c~H'
16 .514.2:
0'
L?
y9
61
VIO-ThIoIH
9.011
17 242.6
"
-
-
H
V7Phos
zH-
V7
/
V7-Th~oIH
V8
V8-Thiol
HW.
H
H
Deprotona ted PTE Pathway
Protonat ed PTE Pathway
-V
am-
0
'0
N.
.-
V6
V5 -Phos
VS
S
VIP
"A"
VI Phos
V3-Thio
C9
-
*
-
I--
so
*
VIA
V3
060
H
W4A
V2A
VI
HP~H H.~
O 4.16.9
4 31.
7B
*
1
P0
SH
-
0
---
W..
-
H
14.814 7
-5'724.0
V2
1.741
13.760
15.731.6
VIB
V2B
Figure 8: The calculated reaction pathway of VX hydrolysis derived from an ensemble of umbrella sampling simulations
24
Hb
-
-%.
0
HN
%
H-H0
33
44
e
H
0
.-
MI..
ASP-
H
H
- W
.-.-o
16.991
H
H
0H.H
P2A
'-N
-
P
H
LM
H
16.8
H
4'-Ly4'.
+H
,_..
.
H
513.4
3.36.
H
0$
P2N
HP
P1
22.07A 4N
H H
A 4-
HH
H
*
P2B
4'-
A"--
ho*
-
P1A-Phos -
H
16.09,
P4A-NP--
-
-
%
0
12.00
P3A
Hs
0, 63 6
P4A
-b
.Hi.
N
070
H
0
-/'
H-
W
f
4)
MO/H
P4B-PhoS
P3
a
P3B-NP 18.68.5
.
*
HHH
H
H
H
,
NO
A---
..
-W
16.24A4'
10.727.8
PIB
H.H
AM
Z4'
b
4,~M
8.917.1
H0
1C IA
4%.W
H
P2
65.1
-.
9.90.7--
ONN
N'O-H P3B
P4B
ft"
AW.
4'.,
0- H
Hi~
H"
s'
20.68.3
18.027.7
H
"H
H
4
M*0
0
'I
SO
H
0H
H
13.7148
H
0
H
0
H.4P
0/
S
WA-
P5E
-
Mi.-
4'W-
4'-.
* N
- S
P6
P5
P7
Figure 9: The reaction pathway for Paraoxon hydrolysis as computed from umbrella sampling simulations
25
Pe
Overall Pathway Description
The calculated pathway for VX and Paraoxon hydrolysis by PTE is shown in Figure 8
and 9. An enzyme turnover for both substrates begins with 2 PTE resting states which differ by
the ionization state of the active site water. At pH=7, there are 10 fold more PTE coordinating
an OH- over H 2 0. After substrate binding, PTE follows a multitude of paths towards the
product. Any integration over the path will decompose one substrate molecule to exactly one
phosphate and one leaving group species (DIPET or p-nitrophenol). Both pathways end with
PTE at either of the two aforementioned resting states. VX and Paraoxon share the exact same
resting states, but differ in the steps required to expel the products from the active site. The
phosphates from both VX and Paraoxon hydrolysis can be ejected from the active site without
the need for chemical modification i.e. no ionization state changes are required.
The necessity of ionization changes in the second LG of VX differentiates the two
pathways. Paraoxon's p-nitrophenol LG, since it does not require protonation to depart the
active site, can be expelled from the active site without any chemical modification. In contrast,
VX's DIPET LG demonstrated an overwhelming necessity to be protonated before departure.
Atte11pts. LUY JVL Ie L I fr0m thle active siLe exhiiULed activation energies oi at least 28.0
kcal/mol with no discernible product well (pulling the VX further from the active site caused it to
exhibit erroneous behavior). Due to the necessity of protonation of DIPET to restore the
enzyme, more states that could potentially perform this function become accessible. These states
concern either the shuttling of protons within active site residues or from the solvent to the PTE
active site via solvent-mediated protonation events and/or water. First, high level results from
kinetic mass action simulations will be presented, followed by a mechanism-based breakdown of
reactions affecting the observed kcat.
26
Substrate
Calculated kcat
Absolute (s-')
Relative
Experimental kcat
Absolute (s-1)
Relative
(s-1)
Effective AG*
(kcal/mol)
2400'1
275
20.3
8.98 x 10-3
Paraoxon
23.6
0.33
VX
3.26 x 10-'
1
Table 1: The kcat observed in the kinetic mass action simulations for Paraoxon and VX
8000
1
Effective AG*
(kcal/mol)
12.9
18.2
Calculatedkcatfrom Mass Action simulations, and its decomposition
The calculated kcat for Paraoxon and VX is summarized in Table 1. While the calculated
kcat is 107 lower than the experimental value, the relative kcat agrees with experimental
observations. The effective AGI, which is a measure of the activation energy if the entire
reaction were restricted by one rate limiting step, for Paraoxon and VX is 23.6 kcal/mol and 26.4
kcal/mol. Inspection of the energy landscape of the pathways in Figures 8 and 9 shows that the
effective AGI is actually greater than the path with the lowest barrier. The fastest path in VX
shows a maximum AGI of 15.7 kcal/mol (V2B 4 V4 transition). Yet, the fastest path in
Paraoxon overcomes a maximum AGI of 16.9 kcal/mol (P2A 4 P3 transition). If these
activation barriers were the rate determining steps, VX hydrolysis would exhibit a greater
calculated kcat than Paraoxon, which is not in accordance with actual network analysis results.
Hence, a decomposition of what determines the kcat will be performed to better understand how
kinetic complexity affects PTE turnover rate.
27
Paraoxon - Pathway
Factorsslowing down the pathway
The kcat was computed by measuring the change in free pNP concentration per unit time.
A flux-analysis breakdown of all species that generate and consume [pNP] is shown in Table 2.
There is only one source for the generating species for each reaction that generates pNP, hence
Generating Reaction
Sources
Forward Flux (nM s-1)
Reverse Flux (nM s-')
1 (from P3A)
1.19 x 101
1.19 x 101
P4A-NP4 P4A
P3-NP4 P3B
5.71 x 10 7
1 (from P3)
5.50 x 10-7
1.19 x 101
1.19 x 101
Total
Table 2: Flux analysis breakdown of all species that generate and consume [pNP]
Net Flux (nM s-1)
8.98 x 10-3
2.03 x 10-8
8.98 x 10-3
no further decomposition is required. The majority of [pNP] is generated between the P3A 4
P4A transition. However, the reverse transition, P4A4P3A also consumes the majority of
[pNP]. The net difference shows an overall [pNP] production rate, normalized against enzyme
concentration, of 8.98 x 10-3 s-I that exclusively dominates observed kcat. Net minor
consumption of 2.03 x 10-8 s-1 by the P34P3B reaction offsets [pNP] production to yield the
observed rate of 8.98 x 10-3 s-1 (effective AGI of 20.3 kcal/mol). To understand potential
Modification
P3, P3B, P4B Removal
Removal of reverse rates in P3A
-*P4A-)P1A
Remove of reversal rates in
P3A -)P4A-*P1A and
P3 *P3BA P4B P1A
Remove of reversal rates in
P2A- P3,
P3A - P4A-*P1A, and
P3-- P3B-- P4B4P1A
Forward
Reverse Flux
Net Flux
FI.x
IIUA (nMA
tImmVI s1)
a
,
(nIIv
(MA VI
sf-1)
-1)
I a Idcal IIU11
Effective AG*
(k/L
m-1)
1.20 x 10'
1.20 x 10'
8.99 x 10-3
20.3
1.22 x 10-1
4.42 x 10-
1.18 x 10-1
18.8
1.24 x 10-'
4.92 x 10 -
1.24 x 10 -
18.7
1.99
0.61
1.38
17.3
Table 3: The experiments performed to probe causation behind the observed deviance of kcat value from that
obtained by the lowest "barrier"
28
contributions to the increase of effective AGI from 16.9 kcal/mol to 20.3 kcal/mol, several
experiments were performed as shown in Table 3. The first experiment was removal of the P3
-P3B4P4B
pathway because it showed minor pNP consumption. The resulting kcat was not
different: 8.98 x 10-3 s-1 (20.3 kcal/mol). Decomposition of flux contributors showed that P3A
generated and consumed most of the pNP.
To minimize P3A consumption of pNP, the P3->P3B-P4B pathway was restored and
the mass action simulations were performed again with removal of the reverse rate terms in the
P3A-P4A-P1A pathway. The resulting kcat was 1.18 x 10-1 s-1 (18.8 kcal/mol) with 1.22 x 10s-I and 4.42 x 10-3 pNP generation and consumption. This result suggests that the overall rate of
pNP production can be increased by slowing the reverse reactions that occur upstream of pNP
generation. To determine if the P34P3B4P4B pathway has any importance, the next
experiment was the removal all reverse rate terms in both the P34P3B4P4B and
P3A-P4A4P1A pathway. The calculated kcat increased marginally to 1.24 x 10-1 s-1 (18.7
kcal/mol), with 0.124 s-1 and 4.92 x 10- consumed and generated pNP flux.
29
Source
Species
Fs-1
Flux Generation (nM
2.03
P2A
1.76 x 10-8
P2B
8.78 x 10-2
P3A
2.38 x 10-7
P3B-NP
species flux sources
P3
the
of
breakdown
Table 4: Further
P3
Flux Consumption
(nM s-1)
2.02
4.62 x 10-14
9.68 x 10-2
2.58 x 10-1
Net Flux (nM s1)
8.98 x 10-3
1.76 x 10-8
-8.98 x 10-3
-2.03 x 10-8
From these results, it is apparent the favorability of the reverse reactions is decreasing
PTE's ability to recover itself to the resting state. This results in a slower kcat. To extend this
concept further, we took the above simulation where the reversal rates on both pathways were
removed and removed an additional reverse rate term from the P2A-P3 transition. This
transition was chosen because it has both an equilibrium preference towards the reactant and that
Flux Dependence on Rate
106
-
P3A -- P4A-NP
--P4A-NP -+ P3A
-P4A -+ PlA-Phos
--- P1A-Phos -+P4A
1 04
Nm
m
102
0)
C:
4%mI
10
0
LL
I
I%
"
1 0-2
10-4
~
1u
10-6
1040
10 0
102
104
1 06
Fold Change of Original Rate
Figure 10: The rate limiting step decomposition of the Paraoxon hydrolysis pathway
it generates 5 x 105 more P3 than P2B, as shown in Table 4. The resulting kcat increased 10-fold
30
to 1.38 s- 1 (17.3 kcal/mol), which is only -0.4 kcal/mol greater than maximum barrier of the
fastest path.
Origin of species producingpNP
From above, the major source of pNP is from the P3*P3A-P4A pathway. P3A is
generated by the P1 4P3-P3A and P54P6 routes, with P1 having water and P5 having
hydroxide in the active site of PTE. The net P3A fluxes between P3, P4A-NP, and P6 were 8.98
x
10-3 nM s-, -8.98 x 10- 3 nM s-1, and 0 nM s 1 at a steady state P3A concentration of 3.61 x 10-2
nM. To test the importance of either state, first the P54P6 states were deleted from the system
and the system was again simulated. The results were identical, except for the lack of flux
between the P6 and P3A states. Deletion of the other route, P1 -P34P3A,
x
10-2 S-1 with P3A fluxes between P4A-NP and P6 of 2.61 x 10-2nM s- and
-
higher kcat of 2.61
yields a slightly
2.61 x 10-2 nM s-1. Hence, the system shows little dependence of kcat on the existence of either
P1 P3-P3A or P5-P6 route. This result can arise from two possibilities 1) the two routes are
identical in their macro behavior or 2) neither are the rate limiting step. For the first possibility,
we know that the results differ slightly if one or the other route is exclusively utilized, but the
difference is very marginal. To test the second hypothesis, we replaced both paths we equated
both the P1 and P5 state to the P3A state, which shunts the P3 and P6 states. The kcat was
marginally changed to 2.74 x 10-2 S-1. We conclude that the rate limiting step occurs at parts of
the pathway that occur past P3A.
Rate limiting step ofpNP production
Our results have already suggested the rate limiting step occurs within the transformation
of the system from P3A to the resting state enzyme. To further probe which mechanistic step
causes the problem, the forward and reverse rate constants for the P3A 4 P4A-NP and P4A
4PIA -Phos reactions were amplified or reduced by 106. The shunted model described above
31
was utilized such that the flux dependence can be calculated without the influence of other
network effects. The flux, as a function of either of the four rate constants, was calculated to
ascertain the sensitivity of pNP production rates. The results are shown in Figure 10. From the
figure, it's evident that any increase or decrease of the forward or reverse rate in P3A-P4A-NP
causes marginal increases in flux at values near the simulation value. However, the forward or
reverse rate in P4A4PlA Phos correlates strongly with the overall flux of pNP. Increasing the
forward reaction rate and/or decreasing the reverse reaction rate directly increases the flux.
Therefore, the P4A-PIA -Phos step is the rate limiting step. The P4A4P1A-Phos step isn't
rate limiting because of the activation barrier moving forwards: if that were the case, the flux
would be sensitive only to forward rate. The flux is sensitive instead to both the forward and
reverse rates. This suggests the P4A4P1A-Phos step limits the rate because the equilibrium
between the two states is favored towards the reactant direction, and not the product direction.
This step isn't involved with release of pNP, which follows experimental evidence that the rate
limiting step in paraoxon hydrolysis by PTE is not the chemical release of pNP.
VX
-
Pathway
32
Factorsslowing down the rate
The kcat was computed by measuring the change in free DIPET concentration per unit
time. DIPET Flux analysis breakdown like that for paraoxon was performed for the VX
pathway, as shown in Table 5. The majority of DIPET is generated from V3P-Thiol, VlP Thiol,
VI P-Thiol. Of the four thiol-generating species (TGS), three of them, VIP, V8, and
VI IP-Thiol originate from 8 previous species. These three multi-sourced TGS were each put
Generating
Reaction
Sources
Flux Generation
(nM s-1)
Flux Consumption
(nM s-1)
Net Flux (nM s-1)
V3-Thiol 4V3
1 (from V4A)
3.16 x 10-7
1.16 x 10-10
3.16 x
VlP-Thiol -V1P
3
3.21 x 10-
9.93 x 10-14
3.21 x 10-5
V8-Thiol-*V11P
VlP-ThiolMV11P
3
4
1.84 x 10-14
1.71 x 10-7
3.14 x 10-1
9.93 x 10-13
-3.14 x 10-11
1.71 x 10-7
1.49 x 10-10
3.26 x 10-s
Total
Table 5: The DIPET flux analysis breakdown for the VX hydrolysis pathway
10-7
3.25 x 10-5
through another round of flux analysis and the results are shown in Table 6. Flux analysis of the
reactions that generate the TGS do not exhibit the ideal scenario in which only one reaction
generates TGS and only the thiol-releasing reaction consumes TGS. Instead, the scenario is
quite different: non thiol-releasing reactions consume and generate TGS, with the net remnant
being directed towards generating thiol. An example is found in Table 6 for V IP-Thiol: V7
adds 5.59 x 10- nM s-1 to V1IP-Thiol, but V10 and V12-ThiolH consume all but 1.71 x 10-7 nM
s-1. The remaining 1.71 x 10-7 nM s- 1 of the flux is actually contributed to generating product. A
similar case is observed for the other two TGS in Table 6. While paraoxon was slowed by
33
Generating
Reaction
Source
V1P-Thiol
_____ ____
V5
Flux Generation
(nM s1)
1.34 x 10 4
Flux Consumption
(nM s')
5.40 x 10 7
V7-ThiolH
ViP +
7.34 x 10-2
9.93 x 10"
7.35 x 10-2
3.21 x 10-5
___rce
____
V8-Thiol
V11P-Thiol
Thiol
_
_
_
_
_
_
Net Flux (nM
s1)
1.33 x 10-4
-3.20 x 10-1.01 x 10-4
1.16 x 10-9
1.03 x 10-'
V10ThiolH
V8 + Thiol
V7
V10
8.52 x 1010
2.05 x 10-
1.16 x 10-9
-1.19 x 10-
3.14 x 10-"
5.59 x 10-s
5.28 x 10-6
1.84 x 10-14
3.79 x 10-10
5.15 x 10-5
3.13 x 10-11
5.59 x 10-4.62 x 10-5
Th1
V12--2
+o
1
-1.01
10-4
x
_
V5
V12ThiolH
Sum of Net
Flux
X10-210-6
4.42 x 102
4.42 x 10-2
-9.52 x 10-6
9.93 x 10-9
1.71 x 1i-7
-1.71 x 10-7
-3.13 x 10-"
3.13 x 10-"
1.71 x
10-7
-1.71 x 1i-7
Table 6: Further flux analysis breakdown of the thiol generating species
equilibrium preference towards reactant, VX may be slowed by competing reactions that
consume TGS' before they get the opportunity to release DIPET. However, while Paraoxon
didn't operate exclusively off either ionization state of PTE, the results from VlP-Thiol suggest
the V5 state (protonated PTE pathway) generates 1.33 x 10-4 M s-1 of flux, while V7-ThiolH
(deprotonated PTE pathway) consumes 3.20 x 10-5 M s-1 of that flux. It may be that the
Pathway
Calculated kcit (s')
Effective AG*
(kcal/mol)
Percent of Net Flux that
Generates DIPET
Protonated
7.54 x 10-4
21.7
100%
Deprotonated
1.63 x 10-7
26.9
0.3% [only generated from V7]
Table 7: The pathway breakdown of the two potential branches in the VX reaction pathway
deprotonated PTE pathway, even though it's slower, may consume the TGS made from the
protonated PTE pathway.
To better understand how the protonated and deprotonated PTE pathway would function
if they weren't connected, both pathways were simulated individually with all connecting
reactions deleted, with results shown in Table 7. The protonated pathway exhibits a kcat of 7.54x
10-4 s-1, with TGS being produced from V3 and VlP-Thiol. The deprotonated pathway shows a
kcat of 1.63 x 10-7 s-1, with TGS being produced from V8 and VI P-Thiol. In simulations of the
34
combined pathway, the protonated pathway's V3 and VlP-Thiol generate 10 4 less thiol than if
done separately. In contrast, the deprotonated pathway's V8 and Vi P-Thiol generate thiol at
the same rate whether it is functioning independently of or together with the protonated pathway.
Reaction
Removed
Total Thiol Flux (nM
s-') = kcat
Flux From
Protonated
Pathway (nM s')
Flux from
Deprotonated
Pathway (nM s-1)
Percent Flux
From
Protonated
Pathway
99.5
99.5
99.7
99.6
100.0%
None
3.26 x 10-s
3.24 x 10-1
1.71 x 10-7
V54V8
3.26 x 10-1
3.24 x 101.71 x 10V5-*V7
5.48 x 10-1
5.46 x 10-1
1.45 x 10-7
V4->V6
4.17 x 10-5
4.15 x 10-5
1.60 x 10-7
V5->V8, V54V7,
1.83 x 10-4
1.82 x 10-4
6.55 x 10-10
V44V6
V1P-Thiol4 V79.56 x 10'
9.54 x 10-1
1.81 x 10-7
99.8%
ThiolH
V54V8, V5-V7,
7.42 x 10-4
7.42 x 10-4
2.34 x 10-9
100.0%
V4+V6,
V1P-Thiol4V7ThiolH
V54V8, V5-V7,
7.42 x 10~4
7.42 x 10-4
0
100.0%
V44V6,
V1P-Thiol4 V7ThiolH,
V1P->V11P
Table 8: The experiments performed in trying to better understand the causation behind the kcat for VX hydrolysis
These results suggest the thiol generating capacity of the protonated PTE pathway is diminished
when operating in conjunction with the deprotonated PTE pathway, potentially because of
conversion of protonated pathway states to deprotonated pathway states.
Reactions that convert states from the protonated PTE pathway to states in the
deprotonated PTE pathway were removed to understand the cause of the diminished thiol
generating capacity of the protonated PTE pathway. The results, shown in Table 8, demonstrate
that sequential removal of reactions that connect protonated PTE pathway states to deprotonated
PTE pathway states increase the overall kcat of the combined system by shifting production to the
protonated PTE pathway. As all potential connections from the protonated to the deprotonated
pathway are removed, DIPET production rate approaches the DIPET production rate of just
35
protonated PTE pathway. Hence, our simulations suggest that VX hydrolysis is slowed by state
diversion into less productive pathways.
Origin of species producing DIPET
Given we know that state diversion causes VX h ydrolysis to be slowed from its optimal
Originating
Species
V5
Generating Species
Net Flux (nM s-1)
V5-Phosphate
-9.70 x 10-2
-1.33 x 10.4
9.71 x 10-2
1.16 x 10-1
9.69 x 10-2
-9.71 x 10-2
1.01 x 10-4
5.54 x 10-1
-5.59 x 10-1
9.69 x 10-2
-9.69 x 10-2
9.69 x 10-2
-9.69 x 10-2
5.65 x 10-10
3.25 x 107.33 x 10-1
-3.15 x 10-7
9.69 x 10-2
-9.69 x 10-2
3.26 x 10-5
-3.26 x 10-5
6.11 x 10-6
2.64 x 10-3.26 x 10-1
-7.33 x 10-11
2.64 x 10-5
-2.64 x 10-1
VIP-Thiol
V7
V8-Thiol
V7-Phosphate
V5
V7
V6
V4
V2A
V7-ThiolH
V9
V11P-Thiol
V6
V7 + Phosphate
V4
V7-Phosphate
Vi
V2A
V2B
V4A
V5_Phosphate
V6
V2
V4
ViA
V
V11B
V2A
V2B
Vi1
V1
V2
Table 9: The breakdown of the most important contributors to
reaction flux in the VX hydrolysis pathway
rate, flux analysis was performed to
elucidate the dominant pathway(s)
that produce DIPET. Table 5 shows
that that -99% of DIPET is generated
from the V1P- Thiol-*V1P reaction.
Further decomposition of the species
generating V1P-Thiol, in Table 6,
shows state V5 to be the primary
producer of VIP-Thiol. This method
was propagated forwards until the VI
or V 1 state was reached, the results
of which are shown in Table 9. The
poath most traveled towards
generation of the Thiol is S + VIP 4
VI -V1B4V2-*V2A-4V4-*
V6 4 V7-Phosphate 4 V7 4 V5 4
VIP-Thiol 4 VIP + Thiol. Hence, the most dominant path actually includes traveling through
both the deprotonated and protonated PTE pathways.
36
Rate limiting step of DIPETproduction
We tested the response of kcat to changing all the rate constants individually, and have
shown the three that affect the reaction rate the most, without changing the dominant pathway, in
Figure 11. Rate largely depends on the V5 -)V1P-Thiol transformation, and its acceleration
results in the greatest increase in DIPET production rate. The V74V5 and V7-ThiolH
4VIP-ThiolH transitions also showed tendencies to increase DIPET production rate with
increasing forward rate constants; the former acts by increasing the reactant concentration in the
V5 4 VIP-Thiol transition, and the latter acts by directly increasing DIPET production in the
V7-ThiolH 4V1P-ThiolH transition. Hence, for the dominant pathway, we conclude the V5 4
VIP-Thiol is the rate limiting step.
37
In our analysis, we noticed that slowing the rate of V3-Thiol *V4A transformation by
10~10 generously increased DIPET production rates to 8.47 x 10-2 s-', which surpasses the rate of
DIPET production with just the protonated pathway. In addition to this change, removing just
the V4 -- V6 reaction caused the pathway to increase DIPET production to 11.1 nM s-1 (16.1
kcal/mol effective barrier) that closely matches rates obtained from the lowest barrier 21.8 nM s
Flux Dependence on Rate
10
-
V5 --+ VlP-Thiol
--
VIP-Thiol -4 V5
--
V7 -+V5
---
V5 -+ V7
--
--
104
V7-ThiolH
V1P-Thiol
-* V1P-Thiol
-> V7-ThioIH
102
C
a)
C
LL
-
-
-
-
--
s- s-
-
10
100
10-
10 -6
10~4
I
I
III
10-2
100
102
106
104
Fold Change of Original Rate
Figure 11: The rate limiting step decomposition for the VX hydrolysis pathway
1(15.7
kcal/mol). This transformation causes all pathway density to flow from V4
V3 Thiol
+
V3
+
+
V4A 4
VI -Phos + VIP. Just as observed in paraoxon, decreasing the reverse rate
constant for specific processes can greatly increase the pathway kcat.
38
100
10-
2
4
10~
0
6
10-
C
10-8
CU
10
1012
I"""""Rate(s)
P4A-NP
P38-NP
- 14
-9
10
1
6
10
100
10-3
Product K
(M)
kcatfor paraoxon
Figure 12: The effect of Ko on the calculated contribution of each species to the
10-2
10-6
-
-
10~4
0
100
~
12
0
Ca
10-16
(s')
1018 -Rate
-
VIP-Thicl
----
-V11P-Thiol
V8- Thiol
1020 -V5-Thiol
10-9
10-3
10-6
Product KDiffuson (M)
39
100
Figure 13: The effect of KD on the calculated contribution of each species to the kcet for VX.
Dependence ofProduct KD on CalculatedRatesfor Paraoxonand VX
Figures 13 and 14 show the contributions of each product generating species to the
computed kcat for the Paraoxon and VX pathway as a function of the product
KDiffusion,
which is
pNP and DIPET, respectively. Inspection of the figures show that the rate is dominated by
preliminarily one generating species, P4A-NP for Paraoxon and VlP-Thiol for VX. As the
product KDiffusion is decreased, the kcat scales downwards but there is no evident change of the
dominant rate-generating species. Additionally, the overall discussed trends do not change.
Hence, our simulations and their results are valid in the sensible ranges of product KDiffusion. The
only segments where results would not correlate with experiment would be in regions where
Paraoxon was degraded slower than VX. Such a case is observed only when KD
<
I
PM
for
Paraoxon products and when KD> 30 mM for VX products. This kind of scenario is
improbable, given that the strongest inhibitors of PTE exhibit a KD of 2.8 IM and that the
product KDiffusion only captures the diffusion linked aspect of the overall product KD.
C
eTma
Inspection of the chemistry of the microscopic steps shows paraoxon follows a path in
which paraoxon binds to yield P1, active site water is deprotonated to yield P2, and bound
paraoxon is hydrolyzed to yield P3. The P3 state is a branch point where pNP, Phosphate, and
His254 proton shuttling can occur in different orders. The dominating branch is one in which the
His254 proton shuttling occurs first, followed by pNP departure (via pentacoordinate paraoxon
collapse), and then phosphate departure, which constitute the P3 -
P3A -
P4A 4
PiE
pathway. Though the His254 proton shuttling may seem inconsequential to the catalysis of
40
Paraoxon, it is of importance to VX which was found to necessitate protonation of the DIPET
leaving group in order to restore the enzyme resting state.
Reaction mutation studies, as summarized in Table 4, and kcat sensitivity analysis, as
shown in Figure 10, suggest the disfavored equilibrium from P3A to PIE is the reason why it
exhibits a kcat with an effective AGI of 20.3 kcal/mol not matching that of the highest barrier of
16.8 kcal/mol in the dominant path. The two equilibrium steps, which if adjusted to be product
favoring, caused the effective barrier to decrease to 18.8 kcal/mol. The two non-product
favoring steps are the expulsion of pNP from the pentacoordinate phosphorous (P3A 4P4A)
followed by water displacement of the resulting phosphate (P4A4P1E). Additional pathway
flux decomposition found that promoting the favorability of the P2A 4P3, proton shuttling from
Asp233 to His254, reaction increased the effective AGI to 17.3 kcal/mol.
The 5 x 105 more populous P2A 4P3 than P2B4P3 transition highlights the importance
of pathway dynamics in understanding the drivers of catalytic rate. It may seem like the latter
transition should be more dominant because it has a substantially lower barrier, but the
importance of that step in the kinetics of the enzyme is convolved by the concentrations of the
species in each reaction. P2A and P2B stem from the same reactant, P2, but while P2B may
have a lower barrier in converting itself to P3, P2A has a lower barrier to be converted from P2.
Because of this rate difference, the steady-state [P2A] is 0.706 nM, whereas the steady-state
[P2B] is substantially lower at 1.73 x 10-1 nM. Even though the hydrolysis step is performed
with a lower barrier of 10.7 kcal/mol for P2B than for the barrier of 16.8 kcal/mol for P2A, the
hydrolysis in P2B 4P3 occurs at 1.76 x 10-8 nM/s whereas the hydrolysis in P24P2A occurs at
9.01
x
10- nM/s. This example highlights the problems kinetic-control can cause to enzymatic
reaction pathways. The enzyme has the capacity to perform the main reaction, the hydrolysis of
Paraoxon, in a very efficient manner with an activation barrier of only 10.7 kcal/mol. Due to
41
kinetic-control of steps preceding the hydrolysis, it instead performs the hydrolysis in a less
favorable way with a greater activation barrier. Hence, the observed mechanism for PTE may be
globally optimal for performing a complete turnovers, but may not follow the locally optimal
route in performing each individual reaction within a turnover.
The pathway for VX hydrolysis, as shown in Figure 8, shows that the initial microscopic
steps taken by PTE in catalyzing the hydrolysis of VX are very similar to that of Paraoxon until
hydrolysis occurs. Whereas the Paraoxon's pNP leaving group stays bonded to the phosphorous
and does not require protonation to depart, VX's DIPET leaving group breaks away from its
phosphorous and instead binds to the active site Zn+2 . Our simulations, corroborated by higher
level QM calculations at the B3LYP/6-3 I G(d) level, showed the dissociation energy of DIPET
from Zn+2 to be greater than 28 kcal/mol. This was the highest dissociation energy we obtained
before the simulations resulted in nonsensical geometries. Protonation is the only feasible
solution to remove DIPET from the PTE active site and to restore catalytic activity.
We discovered two feasible sources of protons for DIPET: solvent H 30' and His254'.
The former is supported by crystallographic studies showing that the bound reactant is exposed
to solvent1 1 and the latter supported by mutagenesis swuies supporting His254' s role in being a
proton shuttle from Asp301 to Asp233
'.
Overall, there are three opportunities for DIPET to
gain a proton: 1) from any solvent-mediated protonation event, such as V7-V7ThiolH4VI P-Thiol 2) from His254+, where the His254 proton originated from the water that
hydrolyzes VX as in the V1B-4V24V2B transition, and 3) from His254', where the Hist254
proton originated from the water that displaces the phosphate product (EHMP) as in the
V74V94V1O transition. Opportunity #2 is diminished by proton shuttling towards Asp233.
The combinatorial expansion resulting from differential timing of these three opportunities
42
causes the kinetic complexity of VX hydrolysis, with each unique reaction type highlighted by a
different color and line style in Figure 8.
Our results indicate several interesting chemical features of the pathway. The response of
overall kcat to changes to both forward and reverse reaction rate changes in V5->V7 transition
changes suggests that proton shuttling serves to deplete the amount of reactive species available.
With the removal of this branch, as shown in Table #R7, the network showed subsequent
redirection of the pathway dynamics towards utilizing His254' as a proton source via the
protonated pathway. The importance of equilibrium and its effect on intermediate species
concentrations is evident by the speed up of kcat upon removal of the V3.Thiol -V4A
transformation. However, these unfavorable equilibrations serve to diminish overall catalytic
capacity, especially when they act on species in the dominant network and/or at the rate limiting
step. The rate limiting step of the VX hydrolysis pathway is also product departure, as observed
for Paraoxon. Whereas Paraoxon's phosphate departure is a disruption of non-bonded
interactions, the DIPET from VX instead requires a protonation event in order to facilitate its
release.
43
Additional Figures
10
10
(D
2
2
-
.510-3
102
100
1010
108
106
kof
10
-
S1: The independence of Paraoxon hydrolysis calculated kcat from koff
Figure
10'
10.2
10
0
106
10,-
101,104
102,100
3
6
10 ,10
1
1
k 0 ,k. (s- , M's
4
10
,10
7
10.10
8
106.109
)
100,103
Figure S2: The independence of VX hydrolysis calculated kc.t from any Ko preserving koff/kon pair
44
THE DIVERSITY OF METHODS UTILIZED IN QM/MM
REACTION MECHANISM DISCOVERY OF CHORISMATE
MUTASE
The advent of structural biology and computational modeling tools has led to the
development of computational biophysics as a tool to understand atomic-level details behind
enzyme mechanism. Bacillus subtilis Chorismate mutase (BsCM) has been the subject of
numerous experimental and computational studies, in part because it catalyzes a unimolecular
rearrangement with no intermolecular covalently bonded intermediates. Of key computational
interest is understanding the dominant perturbations the enzyme makes in accelerating the
reaction by 106 in comparison to solvent. The quest to understand this has been the subject of
numerous studies utilizing considerably creative methods to give a multitude of possible
explanations behind BsCM's catalytic prowess.
0-
0)
0
0
0/
00
0
0
____
0
0
0
Scheme 1: The chorismate to prephenate reaction catalyzed by Chorismate mutase
45
Transition State
Transition State
i
B)
A)
Near Attack
05
E
Conformation
Li
GTS
C
U-
AGU
LL
W5
AGNAC
Reactant
Reactant
Prodt
Product
Reaction Progress (Arbitrary Units)
Figure 2: The two proposed energetic rationales for BsCM catalysis
The reaction catalyzed by Chorismate mutase is summarized in Scheme 1 with a diagram
of the BsCM active site, with the spectroscopically observed chorismate conformation shown in
Figure 136. This CHAIR conformation, which does not exist in solvent, subsequently led to
debate in the community about the origin of Chorismate catalytic capabili3 7 . Two groups of
thought began to form: the first which postulated that the active site performed transition state
stabilization (TST) and the second which hypothesized that the enzyme stabilizes a pre-TS
intermediate structure termed the "near attack conformation" (NAC). Before introducing the
methods utilized in trying to understand the catalytic mechanism, we first will discuss the
differences between these two arguments.
Figure 2 A and B highlight the energetic differences between the two arguments
presented for differential catalytic activity. Figure 2A is the traditional rationale behind catalytic
activity. The blue line denotes an uncatalyzed reaction. The orange dotted line is the energetic
46
path a catalysts causes the reaction to take. It's important to note that the substrate absolute free
energy stays unperturbed and only the transition state energy is decreased. This causes the
activation energy, AG: to decrease, hence, increasing the reaction rate. Figure 2B highlights the
NAC argument in the red line. The system, instead of stabilizing the transition state, instead
promotes the formation of an intermediate along the path, which causes the effective AGI to be
the sum of the AGNAC and AGTs at saturating substrate concentrations. If the system is better at
stabilizing this pre-TS intermediate, then the effective AGI would decrease, hence causing an
increase in catalytic rate. Uniting the two schools of thought was experimental evidence
suggesting that both the catalyzed and uncatalyzed reaction went through a CHAIR-like
transition state3 8 ,39
Guo et al. utilized molecular dynamics simulations to develop an understanding of how
the populations
System
Water
1F7
BsCM R90Cit
BsCM E52A
BsCM WT
EcCM WT
AG*
24.2
21.3
21.2
18.2
15.4
15.2
-
AGNAC
AGTS
8.1
5.5
4.1
1.3
0.3
0.1
16.1
Table 1: The calculated AGrs values taken after subtracting the simulation
1
experimental AG*. All values taken from ref.
15.8
17.1
16.9
15.1
15.1
AGNAcfrom
of the various
conformers
chorismate
change with
catalytic
environment.
While no active chair conformation chorismate was observed in simulations of the solvent, the
authors discovered that Yeast CM was capable of binding a non-reactive conformer and
converting into the more active CHAIR form, which subsequently passes through a CHAIR-like
transition state to generate the prephenate product. This study suggest that CM enzymes can
accommodate and convert substrate into the CHAIR substrate conformer and don't pluck only
the (non-existent) CHAIR conformers out of solution.
47
ION
C
B1
Al
6
= L
.
1
-250
50
-50
-150
E.
......
...... ...
150 250 -150
-50
50
150-250
-150
-50
50 150
dihi (degree)
Figure 2: The free energy profile of Chorismate conformational change in the A) water B) EcCM WT C) BsCM WT D)
1F7 E) BsCM E52A and F) BsCM R90Cit. Due to ambiguity in dihi structure, the pink bars represent the free energy
4
change in bringing the system to the proper conformation. Figure taken from ref. 1
Hur and Bruice further explored this idea that an enzyme causes a change in substrate
41
conformation to understand the origin of activity in a multitude of systems . Utilizing AM]
QM/MM molecular dynamics, the authors utilized thermodynamic integration methods to
discover the change in free energy difference from non-CHAIR substrate binding to conversion
to the CHAIR conformer in the active sites of
24
water
EcCM, BsCM, BsCM E52A, BsCM R90Cit,
R90Cit
22
1F7 antibody, and water. Utilizing a
1F7
20
definition of NAC contingent on distance
E52A
0
18
16 .
between the atoms in the forming bond and
w-BsCM
-
.. C
0
two angle defined by each atom's normal
.
14
Y =15.7+ 1.1 X
R=0.97
-
6
2
4
AGN*
(kcal/mol)
8
10
vector to that of the forming bond vector, the
authors computed a free energy profile,
Figure 3: The plot of the data in Table 1 shows a linear
dependence and suggests the importance of NAC formation
energy on the actual activation energy. Figure taken from
ref.41
shown in Figure 2, that is a function of one of
these two angles. Due to the structural
48
ambiguity in the free energy projection onto only
200-
Ar
150-
Reactant
Arg7
a"
-
Arg3
3rn
Arg90
one of the three NAC definitions, the pink bars
correspond to the free energy of bringing the
Li~imI~,
-
50
0
substrate to a reactive NAC. Of interest in later
CD
wJ
parts of this thesis, are the breadth of the wells
as
-50-100-
@Asp1 18
-150-
observed in each system.
0
so
100
200
1SO
2;0
300
350
Residue Number
After integrating several sources of
Transition State
200-
Arg7
1501
experimental information together, the study
Arg63
"
*Arg9O
100-
compiled the final energetic tally, as shown in
0
so-
-4
0-
Table 1, with a plot shown in Figure 3. Their
W
results suggest the differences in chorismate
-
-100
Asp118
-150-
rearrangement rate observed amongst different
C
50
200
150
100
250
300
35
Residue Number
systems may result more from changes in energetic
Transition State - Reactan
*Arg90
10
stabilization of the pre-TS intermediate, then in the
Arg7
differential transition state stabilization, hence
-0
E
Glu78
4-U
2-
supporting that the dominant mechanism of
TJ8 a
chorismate rearrangement is the one driven by
-0 0
-2-
NAC formation, as shown in Figure 2B. The 1:1
* AspI18
-8-
0
50
100
1;0
200
250
300
350
Residue number
correlation between the NAC free energy and
Figure 4: The observed interaction energies for
chorismate with active site BsCM residues in a)
reactant b) transition state and c) the difference.
43
Figure taken from ref
activation energy, as shown in Figure 3, was
utilized as further evidence indicating the
dependence of this energy component on the overall activation barrier.
42
Guimaries et al. published a study at the same time stating the opposite . Their
computed AGNAC demonstrated a net negative value of -0.9 and -9.0 kcal/mol in both water and
49
.
BsCM WT, which is in contrast to those largely positive values computed by Hur and Bruice4 1
With the assumption of rapid equilibrium of Chorismate to the NAC form, the authors justify
these values, because they are both negative, would cause sufficient population of the NAC
chorismate state such that the rate limiting step is the transformation of the system through the
transition state to prephenate.
In performing these simulations, the authors also developed a thermodynamic cycle to
understand the binding capacity of different conformations of chorismate in both the solvent and
CM environment. Their cycle spanned three states: NAC, a compressed NAC, and transition
state. Interestingly, the compressed NAC was favored by 8.8 kcal/mol to be bound in CM than
water, with the transition state being favored by 0.9 kcal/mol. Hence, utilizing this data, the
authors concluded that BsCM causes NAC compression more than it causes transition state
stabilization. This hypothesis does fall under the broader category of transition state
stabilization, but instead clarifies the system is better at stabilizing the structures preceding the
transition state. This is in contrast to the NAC hypothesis, by Hur and Bruice, because no stable
intermediate state is formed.
A thematic element across these studies is the utilization of creative methods to
decompose energetic tendencies that may hint at the enzymatic mechanism. Lee et al. utilized
QM/MM minimum energy paths with molecular mechanical energy decomposition to understand
differential enzymatic contributions. 43 A QM/MM force field was utilized to map out the
minimum energy path, with chorismate being treated with HF/4-31G and the rest of the protein
being treated with CHARMm22 molecular mechanics force field.
50
After performing the minimum energy path scan, the authors then calculated the
difference in energy between the simulated complex and an artificial complex which has zero
charge on the atoms of a single residue. The results of this calculation are shown in Figure 3. At
the reactant and transition state, Arg7, Glu78, Arg90, and Aspi 18 exhibit high interaction energy
values. The difference of the two, highlights Arg90 showing an astounding 10 kcal/mol
stabilization, Arg7 and Glu78 showing about 4 kcal/mol, and Asp] 18 showing -5 kcal/mol
destabilization. The authors then concluded the dominant effect is electrostatic interactions on
the transition state, without precluding the NAC effect.
2
0
-2
-4
CuC
AMP 2 ~
l
ASCF
-8
A(1)
EL -----
-10 -
0J
0=
L
-12 -_I
I
EP
I
<l U~)
I
I
I
I
I
I
I
I
I
UC)
>
x<
<0
54
Figure 5: The observed stabilization energies, relative to reactant, under different levels of quantum
mechanical theory. AEL is the first order electrostatic term, AM) is the first order HL term, ASCF is the HartreeFock term, and AMP2 is the MP2 level term. The arrows correspond to the differential electronic behavior each
level accounts for: exchange (A() - AEL), delocalization (ASCF _&(1), and correlation (AMP2 - ASCF). Figure taken from
ref 45
51
-
To expand upon this interaction energy analysis, Szefczyk et al. utilized multi-level
quantum mechanical calculations to understand how each residue around the substrates affects
the energy as three quantum mechanical terms are added: exchange, delocalization, and
20
E
(a)
correlation, with the addition of each term
exponentially increasing the computational
10
0
complexity of the problem. By utilizing a
Sr
-10
*partitioning
-20-
scheme" that computes the
4)-20-
W
-30
20.
E
change in quantum mechanical energy as
_301_
-2
-1
0
2
1
two molecules are brought from infinitely
(b)
far away to the actual configuration, the
authors computed the interaction energy
10
0
CD
(-20
C
W
between all relevant residues and the
-10
_30
chorismate substrate.
The authors computed this
_
-2
-1
0
2
1
Reaction Coordinate (A)
interaction energy at different levels of
theory to understand the role of three
.
Figure 6: The calculated minimum energy path resulting
from an ensemble of QM/MM MD sampled structures in
A) BsCM and B) solvent. Figure taken from ref4 7
important quantum mechanical terms, and is
shown in figure 4. Their results, from which the electrostatic term match the results from
Guimaries et al., show Arg90, Arg7, and Glu78 to be the largest contributors of stabilization to
52
M
the transition state. Their study also used the most expansive basis set, 6-31 G(d), in comparison
to all papers preceding it. With differential treatment of the basis set, the author demonstrate
that, although the addition of electronic
,
15-
exchange, delocalization, and correlation
(a)
A.'I,
10-
does change the calculated magnitude of
1~,
I
5.
0-
observed stabilization energies, the greater
0
I
-5
-10-
trends are approximated with a much
CO
-1 N
-2
simpler, and computationally inexpensive,
electrostatic treatment of the interactions
15-
0
between the active site and substrate 45 . The
E 10-
exact changes observed for each energy
(D
1
0
-1
Reaction Coordinate (A)
2
(b)
50-
C
term are shown in figure 4.
a
-10-
Another approach to understand the
-2
C
stabilization energy was put forward by the
Reaction Coordinate (A)
16
more study that evaluated how the
a
ensembles of minimum energy paths4
w
.
14
interaction energy would vary with
2
*
0 2018'
18
same research group, which published two
1
0
-1
12A
10
8
61
A long semi-empirical QM/MM molecular
2
0
2
4
6
8
10 12
Stabilization Energy (kcal/mol)
dynamics run with a structure of chorismate
.
both in water and in the BsCM active site,
Figure 7: The stabilization energy of chorismate in A)
BsCM and B) water. The plot of stabilization energy vs
energy barrier C) shows a linear dependence, with
triangles as BsCM and grey circles as solvent47
from which 16 transition state structures
were collected and placed through minimum energy path scans with B3LYP/6-3 I G(d) for the
substrate and CHARMM27 for the rest of the protein.
53
The energy profiles of these scans in BsCM and water are shown in Figure 5 A and B.
The authors observed an average reaction barrier of 11.3 + 1.8 kcal/mol and 17.4
1.9 kcal/mol
for BsCM and solvent, respectively. Utilizing a previously discussed technique 46 , the authors
determined the interaction energy of the environment on the quantum mechanical treatment by
calculating the difference in energy of the quantum subsystem in the relevant system (as charge
embedding in the quantum system) and vacuum. Hence, this calculation measures the change in
the quantum energy upon introduction of the substrate environment.
These calculated differences are shown in Figure 6 A and B for BsCM and Water. Both
systems exhibit a rise in stabilization energy near the transition state, as the charges grow greater
in magnitude on the substrate. The authors then plotted the energy barrier as a function of
stabilization energy, shown in Figure 6 C, to highlight the importance of transition state
stabilization in performing the reaction. This figure resembles Figure 3, which was utilized by
Hur and Bruice to show a linear relationship between NAC energy and activation barrier.
Hence, these two studies are at odds with each other, because the one discussed earlier concludes
differential catalytic ability arises from differences in NAC stability, whereas this study
concludes differences in transition state stabilization are the driving factor.
Multiple other computational studies have yielded results supporting transition state
stabilization
48-50
through similar frameworks. Ishida published an exhaustive, elegant, and
conclusive study that sought to unite and create a definitive answer for NACs and Transition
state stabilization5 utilizing the conclusions from the author's previous works2 5, 3 . The study
54
30
(U
E
C,
20
10
- - 7-
0
0
-_-
_
-10
-- *-model reference reaction
-30
-
0
-1
2
-
enzymatic reaction
-20
02
20
E
-"0
10
(b)
--
0
C
wild-type
-10
~~~
- ys90-mu tant-cit90-mutant-
-20
~
gi78,5mutant
lys7-mutant
-30
-2-1
12
0
Reaction coordinate (angstrom)
.
Figure 8: The computed free energy profile by the QM/MM MD-FEP method. In a) is
the comparison of the free energy profile of enzymatic Wild Type BsCM with that of
solvent, termed the model reference reaction. In b) is the comparison of free energy
1 3
profile of the mutants investigated in this study. Figure taken from refs-
followed a multi-layered approach. First, free energy profiles for a multitude of mutants were
obtained. Next, the electronic structure along the minimum energy path was computed through
all-electron QM calculations for the entire protein complex. This was followed by analysis of
the trajectories to search for any wide-spread geometric changes in the complex for different
mutants of BsCM.
55
10
10
5
5
0
0
-5
-s
w
-10
-10
V
C
-15
-15
10
10
CD1
- --
Cl)
Cl)
Ici)
ci)
--
i-V.---
5
0
.0
-5
~1)
C.)
C -10
0
L.
0 -15
-
-
.-a-)-
5
0
-5
I-
Inn
-10
-15
V
__--1
10
I...
ci)C
0
C
0
C.)
CU
I0
C
5
0
10
-
-5
--1----
4c)
-L
---
-7
5
0
-5
1ILI{
-10
-15
~
-
0
50
100
-10
-15
37
87
20
70
120
0
so
100
37
87
20
70
120
Amino residue serial number
Amino residue serial number
Figure 9: The interaction energy difference between the TS and ES complex determined by FMO2-MP2/6-31G*
calculations for WT mutants at the following sites a) Arg90 b) Lys90 c) Cit90 d) Asp78 e) Gln78 f) Lys7.
The approach taken by Ishida to obtain a free energy profile was different than others and
utilized insight from Szefczyk et al. that the electrostatic energy was sufficient in describing the
interaction between the active site residues and substrate45 . To make the problem
computationally feasible, free energy perturbation was performed with SHAKE-fixed ab initio
QM-derived geometries and ESP charges. Hence, instead of having to perform the
computationally expensive SCF procedure at every integration step, the substrate was reduced
down to a molecular mechanics model with QM derived charges and geometries that, given the
study by Szefcyk et al., should be accurate enough to emulate QM treatment to the entire system.
The energy decomposition, similar to Szefczyk et al. 45,50 was performed by Ishida.
Instead of using electrostatic energy, which is simply a sum of Coulombic and van der Waals
56
energy terms, Ishida instead utilized the interaction energy between the quantum mechanical
partitions of each segment in the full enzyme QM calculation through the Frontier Molecular
Orbital framework. Ishida further evaluated the tertiary CM changes upon introduction of
mutants to show the lack of conformational changes that may be utilized to justify reduction in
catalytic activity in mutants 51
Taken collectively, the literature behind Chorismate Mutase QM/MM simulations has
utilized a multitude of creative approaches to better understand this mechanism. The quantum
calculation has ranged from treatment of just the substrate with a semi-empirical QM to the
treatment of the entire enzyme with FMO2-MP2-6-31G*.
Different regions of the underlying
free energy profile were probed with thermodynamic integration techniques to yield evidence
that elucidates any part of the profiles observed in Figure 2. The consensus in the field points
heavily towards electrostatic stabilization with some conformational biasing towards the
transition state as the dominant mechanism for WT CM catalysis.
57
LARGE SCALE ANALYSIS OF CHORSIMATE
REARRANGEMENT REACTION DRIVERS
Introduction
The enzyme Chorismate mutase from Bacillus subtilis has been the subject of numerous
studies studied through creative ways, which were described in the aforementioned chapter. The
reaction catalyzed by this enzyme is the Claisen rearrangement of chorismate to prephenate, as
shown in Scheme 1.
0
CJICT
0
(o~
:F2
0
______
H
0O
'0
CJ
B~
CT
C2
0
0
Prephenate
Chorismate
Scheme 1: The reaction converting substrate chorismate to product prephenate catalyzed by chorismate mutase, with
the proposed mechanistic arrows. The atom numbering scheme utilized in this study is also shown.
The aim of this study is to take a novel approach to the study of this reaction. Instead of
utilizing electrostatic interaction energies fit to a framework of transition state theory, our
objective will be to utilize a dynamics driven, non-free energy integration based method, without
prior assumption of the nature of the interaction occurring between the active site and enzyme.
Hence, transition path sampling (TPS) will be utilized54'55 to study the Chorismate rearrangement
through the use of a Quantum Mechanical / Molecular Mechanical (QM/MM) framework. We
will utilize Natural Bonding Orbitals (NBO)5 6 to transform the electron density into electronic
energy based estimators of the actual interactions occurring in the active site. This allows
58
interpretation of the electronic density into a framework that is more rationalized through the
body of work performed previously by physical organic chemists.
A)
B)
/Argy
HN
HN
Tyr1 08
H 2N
Argso
HO
0
yr, 08
NH 2
H 2N
NH2
/Arg7
H
0
00
NH
00
0
0
HS
H2
0
00
H
0
NH
Arg 116
H2N
Arg 1 16
H '0
0 0D
CysYS
75
GIU7 8
~
Lys 8 8 gNH 3
H2 N
0
/
H2NH
&NH
GIu 78
HS
CysS
75
0
D)
C)
/Arg 7
HN
H2 N
NH2
CitNH
0
Asp
O'H
H
HO
Arg95
NH
H2 N
00
0
2
0
H 2N
H' 0
0
Glu7 8
0
D
HS
H0
HO
Arg 1 16
0
H
Tyr9 4
O
o
O
H 20
00
H20
0
0
0
H
20
o
H2 0
HO
F)
H20
0
H2 0
0
00
Asn 33
E)
H 20
0
H2N-<4
(DNH 2
tNH
CysYS
75
H20
- Asn50
0-0
NH
NH~
7
Tyr1 08
WO
H2 0
H2 0
Figure 1: The various environments in which the simulation of Chorismate rearrangement was performed: A) WT
CM B) C88K/R90S CM C) R90Cit CM D) 1F7 Catalytic antibody E) Bulk Solvent and F) in vacuo.
The question we seek to answer is one about the exact orbital interactions that occur in
order to facilitate the reaction. Hence, we will decompose the results of simulations of a
59
combination of mutants and alternative systems that exhibit differential reactivity. More
specifically B. subtilis, Wild Type Chorismate Mutase (WT CM) and two of its mutants,
C88K/R90S and R90Cit, will be utilized. These, hereafter, will be termed the true-enzymes.
Additionally, the catalytically active 1 F7 antibody 37 will also be utilized in addition to a
simulation in bulk solvent. A simulation of the Chorismate rearrangement in vacuo will be
performed to serve as a control. Figure 1 shows the diagrammatic summary of the environment
in each one of these six environments.
Methods
To elucidate the role of dynamics behind the chorismate rearrangement, we performed
QM/MM potential of mean force and Transition Path Sampling (TPS) to gather trajectories and
compute rates. We then examined especially the TPS trajectories in greater detail using multiple
feature transformation frameworks to understand more thoroughly the reactions from a physical
organic chemistry perspective. The TPS simulations were initiated using trajectories from the
PMF calculations; perturbation of PMF trajectories from the region of the transition state with
full shooting moves was used to generate seed traiectories. From a seed, approximately 100,000
reactive trajectories (for the frequency calculation) and 1,000,000 reaction-coordinate spanning
trajectories (for the probability factor) were harvested. We utilized Chemometric and Natural
Bond Orbital localization approaches to study and compare the reaction as observed in our
calculations to geometric and quantum mechanical arguments found in physical organic
chemistry literature. With these results, we demonstrate important geometric and electronic
features that are important for the chorismate rearrangement mechanism and driving the system
towards the product state, and we compare differences among wild-type and mutant enzymes,
the catalytic antibody, and the uncatalyzed reaction.
60
Coordinate Preparationforthe Chorismate-BoundMichaelis Complex
All structures for the true enzymes were derived from one starting WT CM structure.
After inspection of and experimentation with the multitude of chorismate mutase structures in
the literature, we decided to utilize the 2.2 A X-ray crystal structure of (IR,3S,5S,8R)-8Hydroxy-2-oxabicyclo[3.3.1]non-6-ene-3,5-dicarboxylic acid, henceforth referred to as oxybridged prephenic acid, bound to wild-type B. subtilis chorismate mutase, which was obtained
from the Protein Data Bank (identifier 2CHT)5 7. While other structures were similar to that of
the one used in this study, 2CHT demonstrated the best electrostatic arrangement to catalyze
chorismate rearrangement. The first of four trimers in the structure of 2CHT was utilized, from
which we filled in the missing chain terminal residues of each subunit through copying of the
dihedral angles from the 1.3 A X-ray crystal structure of unbound wild-type B. subtilis
.
chorismate mutase, which was also obtained from the Protein Data Bank (identifier 1DBF)s8
The neighbors of all Asp, Glu, Arg, and Lys side chains were examined and the local hydrogen
bonding network analyzed to determine protonation state, with all instances being left charged.
Similarly, the neighbors for each His residue were examined and titration states were set to
maximize hydrogen-bonding interactions. Hydrogen-atom positions were computed with the
.
HBUILD facility of the molecular mechanics package CHARMM 5 9 6 0
The oxy-bridged prephenic acid co-crystallized with wild-type chorismate mutase was
used as a template structure for the chorismate anion57 . Atoms OB, CI, C3, and C5 from the
chorismate anion (atom naming shown in Scheme 1) were aligned to minimize the root mean
squared displacement with the analogous atoms from the TSA. Chorismate doesn't precisely
match TSA's structure, because of differences in Cj and CT hybridization57 . Hence, we
performed 50 rounds of adopted basis Newton-Raphson (ABNR) 6 1 energy minimization of
chorismate while holding the enzyme fixed. This was followed by a 250 more rounds of ABNR
energy minimization on the entire complex in order to minimize large unfavorable interactions.
61
We then solvated the complex in a pre-equilibrated rhombic dodecahedron box of TIP3P water
molecules with a 90-A edge length. The subsequent solvated complex was then neutralized with
9 positively charged potassium ions (K') through Monte Carlo water replacement 62 . This
neutralized complex was heated with Leap-Verlet molecular dynamics from 100 K to 298 K in
2500-fs steps with I -fs integration step size and NOE restraints that penalized every polar
contact between the substrate and active site if it exceeded 4 A. The heated complex was then
subject to CPT equilibration for 200 ns with 1-fs integration step size at 298 K, with the NOE
constraints still turned on. The final equilibrated complex structure was used as input for
umbrella sampling. The NOE constraints were kept in place for the umbrella sampling
simulations presented here, and they were removed for all of the TPS simulations presented.
The structure of R90Cit CM was obtained by replacing Arg90 with Cit90 in structure of
the neutralized, pre-heating wild-type complex. We performed analysis on the orientation of
Cit9O, and found the previously proposed conformation was optimal6 3 . We substituted three
potassium ions in place of three water molecules to restore neutrality. This structure was placed
through the same heating and equilibration routine utilized for the wild-type complex. During
our study, Burschowsky et. al released the crystal structure of R90Cit bound to TSA (PDB
Identifier Code: 3ZOP) 6 4 , which we compared with the equilibrated structure we used in our
studies. We found variations of up to only about 0.1 A in the positioning of atoms in the active
site, fully consistent with the structure we obtained through modeling.
In the absence of crystal structures of C88K/R90S in complex with TSA, we initially
repositioned active-site residues and placed chorismate in a similar conformation to that in the
wild-type complex but in the crystal structure of unbound C88K/R90S (Protein Data Bank Code:
1FNK); however, this wasn't sufficient to replicate the environment of WT CM65 . Hence, we
modified our pre-heating wild-type structure by mutating Cys88 and Arg90 to Lys88 and Ser90.
62
We then replicated the dihedral angles found in the aforementioned crystal structure of
C88K/R90S. To better situate these two residues, we fixed all but K88 and S90, and performed
250 rounds of ABNR minimization. This was followed by the same heating and equilibration
routine used for the wild-type complex.
.
The structure for 1 F7 with TSA bound was used from the Protein Data Bank (ID I FIG)6 6
The same chorismate placement and minimization procedures utilized for the wild-type complex
were used for 1F7. The structure was placed in a pre-equilibrated 67 x 79 x 100 A orthorhombic
water box with 900 angles, which was then neutralized with 3 C- ions through Monte Carlo
replacement. The same heating and equilibration procedure was used for I F7. The geometrical
distance values in Table I highlight the closeness between the CM structure used in this study
and that found in the crystal structure.
Distance
R90-NH2 ----- CHR OB
R90-NE ----- CHR OB
R7-NH2 ----- CHR OB2
R7-NH1---- CHR OB1
Y108-OH ----- CHR OB1
E78-OE2 ----- CHR OR
C75-SG ----- CHR OR
R63-NH1 ---- CHR OA2
WT CM
Simulation
2.99 0.16
2.93 0.12
2.91 0.12
3.00 0.11
3.21 0.30
3.66 0.25
3.60 0.34
3.38 0.32
2CHT (Chain E)
3.17
3.20
2.76
3.11
2.91
2.71
3.57
3.14
57
R90Cit CM
Simulation
3.09 0.15
3.18 0.25
2.96 0.13
3.08 0.15
3.26 0.29
3.54 0.21
3.30 0.33
2.76 0.32
3ZP4 64
2.82
3.06
2.49
2.58
3.26
2.90
3.68
2.80
Table 1: A comparison of the distance between electrostatic interactions between the structures resulting from
the model in this study and that from the crystal structure.
PotentialEnergy Function
The CHARMM27 force field was utilized to treat all non-QM atoms60 . Molecular
mechanical parameters for chorismate and citrulline (Cit), needed during initial structure
parameters were obtained through existing parameters in the CHARMM27 force field,
vibrational mode analysis with the PARAMTOOL interface in VMD 67 for missing parameters,
and RESP fitting using Guassian03, minimization at the HF/g-3 1 G(d) level, and constraints on
63
backbone and C, partial atomic charges of citrulline to match those of arginine 68 ,69 . For the
wild-type complex, chorismate, Wat237, Wat236, Arg63, Cys75, Arg90, Arg7, Argl 16, and
Tyrl08 were treated with the AMI semi-empirical QM force field. We chose semi-empirical
QM over ab initio QM because it enables us to perform Transition Path Sampling with adequate
sampling in a reasonable time. To perform ab initio QM, we could've chosen to treat only the
substrate molecule in quantum mechanical detail, but that focus would manifest the active site as
a mesh of charge, which would preclude investigation of active-site electronic and chargetransfer contributions to catalysis. Semi-empirical QM methods were then explored because
they offer a better balance of computational cost versus qualitative accuracy. Semi-empirical
methods available for use with CHARMM, include but are not limited to AMI, PM3, SCCDFTB, SCC-DFTB3, AMI(d)-PhoT 70- 7 3 . AMI was chosen because for its balance of
computational speed, self-consistent-field convergence rates, and qualitative accuracy. The link
atom method was utilized to interface the QM and MM regions, with placement occurring along
the CA-CB bond of all residueS 74 . This was chosen over the generalized hybrid orbital method
because it allows calculation of the density matrix in programs not containing this
functionality 75. Electrostatics were computed with Particle Mesh Ewald summation with a real
.
space cutoff of 14-A with 1 A grid spacing 76
Umbrella Sampling Setup
MD simulations for umbrella sampling were carried out with a Constant Pressure and
Leapfrog Integrator under Hoover temperature control at a temperature of 298 K and 1 atm
pressure. Each variant of the system was subject to umbrella sampling constraints that led the
system along defined potential reaction pathways. We chose the reaction coordinate to be the
length of the breaking bond (C3-OB) minus that of the forming bond (C 1 -Ci). The NOE
constraints used in the equilibration and heating steps were implemented in the umbrella
64
sampling simulations to bias the system towards sampling energetically proper configurations.
We found that the sum of all NOE restraints resulted in an average energy of 0.1 kcal mol' in
each window because the majority of the sampling positions weren't near the position of the
starting structure, the system was pushed linearly towards the sampling position in reaction
coordinate step sizes of 0.1
A, with 250 fs of equilibration at each step until it reached the
sampling position. This combination of step size and equilibration time was judged to be
sufficiently small and large, respectively, because when trial simulations were run with finer step
size and longer equilibration time, the calculated free energy changed only negligibly. The
system was further equilibrated for an additional 10 ps, followed by 40 ps of production
dynamics at each umbrella window, with convergence judged similarly to the equilibrations
above. Each system was subject to umbrella windows from -4 A to 4 A in steps of 0.05 A. The
probability distributions of the reaction coordinates at all windows were subject to the Weighted
Histogram Analysis Method to construct a free energy profile.
TPS Seed Trajectory Finding
To construct a seed trajectory, we utilized the collection of all structures from all
umbrella windows within 0.2
A of the transition-state window. To each structure, random
velocities from a Gaussian distribution were assigned at T=298 K. The resulting coordinates and
momenta were propagated with Leapfrog NVE dynamics forwards and backwards in time for
1000 steps of I fs each". We retained individual trajectories that connected reactant to product
basin, as defined below in the TPS setup. At end of this procedure, we typically had on the order
of 25 trajectories from which to select. A single trajectory was selected to seed the TPS based on
the common set of interactions seen in crystal structures with bound transition-state analog.
Transition Path Sampling Setup
65
The order parameter was chosen to be the length of the breaking bond (C3-OB) minus
that of the forming bond (C 1 -C 1 ) because this best captured and represented the basins, which
were defined from inspection of the free energy profile. The maximum value of the reactant
basin was chosen to be the point at which the system is 6 kcal/mol below and before the
transition state. The minimum value of the product basin was chosen to be the point at which the
system is 6 kcal/mol below and after the transition state. A value of 6 kcal/mol was chosen
because after that point, the system has a 105 fold greater attraction to end in the nearest basin as
opposed to traversing the transition state and ending at the further basin. This criterion is
important, because it is generally understood that to make effective use of TPS each basin should
be a strong attractor5
4
55.
The reactant and product basins, hence, were defined to be -oo<kR<-0.5
A and O<kp<oo, respectively, where X is the order parameter that used for TPS and that was used
to filter out trajectories in the trajectory finding procedure. At each TPS step, full shoot, half
shoot, forward shift, or reverse shift moves were chosen randomly. The trajectories were
allowed to full or half shoot from any point in the trajectory that was %/to
3/4
way through (50 fs
to 150 fs for frequency factor, 25 fs to 75 fs for probability factor trajectories). For either
forward or reverse shifts, the trajectories were allowed to shift up to /4 of the trajectory length
(50 fs for frequency factor, 25 fs for probability factor).
A Langevin integrator was utilized with a coupling constant of 5 s-. For the frequency
factor trajectories, 100 repetitions of 2000 trajectories with a length of 201 fs were performed, in
which the first 1000 trajectories were utilized for equilibration, even though approximately 200
trajectories appeared sufficient to properly equilibrate the system. For the probability factor
simulations, 5 repetitions of 200 trajectories with a length of 101 fs were performed for each of
the 405 windows. Windows with a width of 0.1 spanning k--2 A to k=2 A, in increments of
X=0.05 A, were utilized. Hence, each window has a 0.05-A order parameter overlap with both
the preceding and proceeding window. This span was deemed sufficient, because an additional
66
window added to either end was computed to change the P-factor by less than 0.1%.
The
trajectory end-point probability distributions were collected in each window after sampling 1000
equilibration trajectories. Starting with the window with the lowest k, the proceeding window's
probability distribution was weighted to equate the two window's total probabilities in the
overlapping region. The reweighted windows were combined to generate the overall probability
distribution, P(X). The resulting P(X) was normalized, and the probability factor value was
computed by integration over all values in the product basin. During the TPS simulations, the
position and velocities of the QM atoms were kept for later analysis.
Chemometric Analysis of Trajectories Obtainedfrom TPS
The appropriate geometric descriptors were computed with standard procedures in
MATLAB. Natural Bond Orbital calculations were performed with NBO6 with the Density and
Hartree-Fock matrix resulting from calculations using MOPAC2012, with appropriate extraction
of descriptors from the resulting output files 5 6,77. The descriptors were plotted as a function of
time after departure of the reactant basin. That is, at t=0 fs, the system was at the last integration
step before departing the reactant basin. At values of t<0 fs and t>0 fs, the system was Itl time
steps before and after, respectively, departure from the reactant basin.
Results and Discussion
A combined QM/MM approach was used to study the Claisen rearrangement of
chorismate from the perspective of energetics, dynamics, quantum mechanics, and electronic
environment, and the reaction was analyzed for multiple, related systems (wild type B. subtilis
67
enzyme, the two mutants C88K/R90S and R90Cit, and the catalytic antibody 1 F7) to compare
how changes in environment affect reactivity. We used an umbrella sampling approach to
generate the potentials of mean force (PMFs) for crossing the reaction barrier and additionally
analyzed rate from a transition-state theory framework, and we compared this to results of TPS
calculations that compute reaction rate from a kinetic framework. Analysis of the both sets of
calculations was made with a focus on geometric and energetic properties of different states
along the reaction pathway, and how they differ among the different species studied. Kinetic
features unique to the TPS calculations were also analyzed, as were orbital descriptions of the
electronic drivers of reaction.
Umbrella Sampling
Umbrella sampling simulations of each system were carried out using the onedimensional reaction coordinate (R) of the length of the breaking bond minus that of the forming
bond for all of the enzymatic reactions. For the reaction occurring free in solution with no
enzyme, the two-dimensional reaction coordinates of the breaking bond and the forming bond
treated independently were used. The resulting two-dimensional PMF was integrated to produce
a one-dimensional PMF corresponding to the enzyme-catalyzed reactions.
68
-WT
-C88K/R90S
50
-R90Cit
40
-
1F7
-
Solvent
-
Vacuum
30
-
20
U_ 10-
0
-10
-20
Rictant
-3
-2
-1
;Produc
0
1
2
3
Reaction Coordinate Value
Figure 2: Free energy profile for the systems investigated in this study, computed as a potential of mean force from
umbrella sampling simulations. The dotted vertical lines at reaction coordinate values of -0.5 and 0.0 A correspond to
the maximum value of the reactant basin and minimum value of the product basin, respectively. The triangles represent
the location of the reactant state minimum free energy, whereas the inverted triangles mark the location of the product
state minimum free energy.
The PMFs across all systems are smooth and all exhibit a peak corresponding to the
transition state at essentially the same value of the reaction coordinate, R=-0.25 A (Figure 2).
locations in each system (from lowest to highest reaction coordinate value, at -2.84, -2.17,
-
The reactant wells have different curvatures and their minima occur at somewhat different
2.03, and -2.01 A for 1F7, WT, R90Cit, and C88K/R90S, respectively), indicating different
reactant-bound geometries for the different catalytic systems). Similarly, the product wells have
some differences in curvature and place the well at different locations, also indicating different
modes of holding and binding the product; however, the three true enzymes exhibit extremely
69
similar product wells and it is the catalytic antibody that is dramatically different. The computed
activation barriers (AGI) range from 38 to 42 kcal/mol, which form a relatively tight grouping; as
found in other computational studies7 8 - 80 , these values are systematically greater than
experimentally inferred values by roughly 20 kcal/mol (Table 2). Encouragingly, the ranking of
calculated Eyring rates for the CM enzymes matches that found by experiment. The computed
free energy of reaction (AG) is between --15 and -16 kcal/mol for the three true enzymes but
only -7 kcal/mol for the catalytic antibody, suggesting that the bound product is relatively less
stabilized than the bound reactant on the antibody as compared to the true enzymes.
Calculated Umbrella Sampling
System
AGa
AG*
kcatb
(Erying)
Transition Path Sampling
kcat / kcat,WTC
vb
Experimental
kcatb
kcat / kcat,WTc
kcatb
kcat / kcat,WTC
1.36 x 10-8
1.00
4689
1.0
2.31 x 10-10
1.70 x 10-2
0.3265
0.32
1.47 x 10-11
1.08 x 10-3
0.002665
5.7 x 10-5
1.02 x 10-16
7.50 x 10-9
0.001266
2.6 x 10-5
PC
WT CM
-16.1
37.9
1.14 x 10-11
1.00
C88K/R90S CM
-15.1
38.6
3.50 x 10-16
0.0307
R90Cit CM
-15.0
41.9
1.33 x 10-18
1.20 x 10-3
5.96 x 1012
2.28 x 10-21
5.88 x 1012
3
3.93 x 10-23
5.99 x 1012
2.45 x 10-24
1F7
-7.2
41.8
1.57 x 10-18
1.38 x 10-3
5.95 x 1012
1 7? v1 n-29
Table 2: The summary of values related to the experimentally observed kinetics computed from umbrella sampling and transition
path sampling. Units are specified as ') kcal mo[- 1 b) s1 ) unitless.
TransitionPath Sampling
TPS provides ensembles of trajectories that together can be used to compute the reaction
rate as a product of a frequency factor (v) and a probability (P) 55 8' 1 . The v-factor is a measure of
the frequency with which trajectories enter the product basin, averaged over an ensemble of
reactive trajectories. The P-factor is calculated from a procedure similar to thermodynamic
70
integration that yields trajectories that start in the reactant basin with end points spanning the
entire order parameter space. Integration over the probabilities in the product basin yields the Pfactor value. The probability factor gives the probability that a trajectory starting in the reactant
well will proceed to the product well in a small time window. The product of v and P yields a
computed value of kcat.
The results of the TPS calculations of the chorismate rearrangement in true enzymes, 1F7
antibody, solvent, and vacuum environments are shown in Table 2, together with experimental
rates. The overall calculated rates are significantly faster as computed by TPS than by umbrella
sampling with Eyring theory, which brings them closer to experiment but still substantially
slower. Comparing computed TPS rates relative to WT between TPS and experiment show
relatively good agreement, with the correct ordering, but R90Cit computed to be a little more
active than observed and 1F7 significantly less so. This level of agreement motivates our interest
to understand the properties responsible for the decreased reactivity of the mutant enzymes and
the catalytic antibody as compared to the wild type enzyme.
Of the two terms that contribute to the calculated
kcat,
the frequency factor varies less
than 2% among the different reactions studied here, and it is the probability factor that accounts
for the differences in computed rates. A simple geometric argument based on the linear growth
in the number of reactive trajectories with simulation time allows one to approximate v as
(Ttrajectory - Tavg. transition time)- 1 ,
where the length of trajectories Ttrajectory is user defined and was
chosen to have the same value for all reactions here, and
Tavg. transition time
is the time to transition
from reactant to product basin and depends here on the C3-OB vibrational frequency, which is not
expected to change by orders of magnitude for different catalysts. Thus, it is not surprising that
the frequency factor is relatively constant for these calculations, and it may be a relatively
common occurrence for different catalysts for the same reaction.
71
Based on these observations of v and P values, in the presentation that follows, we focus
first on results of frequency factor simulations to analyze the WT reaction. Then we examine
differences evident primarily in the P-value simulations leading to different reactivity of mutants
and 1F7 compared to WT.
Catalyticmechanism of Wild Type ChorismateMutase Rearrangement
Bond Length, Velocity, and Applied Force
Wild-type chorismate mutase. The calculation of the WT frequency factor was done with
a collection of 1,000,000 simulations of length 201 fs each that started in the reactant well and
progressed to the product well. For the purposes of this analysis, these simulations were shifted
in time so that each departed the reactant well (defined as an order parameter value of -0.5) at
time t=O fs. The aligned ensemble of trajectories was analyzed for geometric, energetic, and
other properties, as described here, focusing initially on the breaking bond (C3-OB). Property
trajectories will be generally be shown as a contour plot of the distribution of the property value
as a function of time, with the density of grey stippling indicating the frequency of that value
(darker for more populated values) and a solid line indicating the trajectory of the average value
of the property. The average length of the breaking bond before t=0 (Figure 3A) exhibits a
forced harmonic-oscillator motion with some growth in amplitude, driven by an oscillation with
a period of 30 fs (1000 cm-), which can be attributed to a C-O bond stretch. The velocity of the
bond length and force applied across the bond before t=0 are also approximately harmonic with a
similarly growing amplitude (Figure 3 B,C). All three trajectories of the breaking bond
properties show remarkable coherence as demonstrated through a relatively tight distribution.
The trajectories exhibit a final compression occurring at t=-1 5 fs. At this compression, the
velocity is near 0 A fs-', with a force of +300 kcal mol' A' (with a positive sign indicating a
72
force acting to stretch or break the bond). From this point onward the behavior departs from
oscillatory. The bond length expands through t=O (leaving the reactant well) and continues to
grow through the region corresponding to the transition state until the product well is reached.
The velocity slows continuously until after leaving the reactant well but then reverses direction
and increases again in the region of the transition state and remains positive in nearly all of the
reactive trajectories. The force decreases dramatically in amplitude and is within 50 kcal mol-
A' throughout most of the transition region. Thus, upon leaving the reactant well, the breaking
bond expands continuously with very little force exerted across its constituent atoms.
Forming Bond
The average length of the forming bond (Figure 3D) decreases from approximately 3.0
A
at t <-50 fs through 2.25 A at t = 0 fs to an equilibrium 1.6 A at t > 50 fs. The length changes
relatively gradually for t <0 fs compared to the more rapid forced-oscillator motion observed in
the breaking bond. The forming bond velocity (Figure 3E) increases irregularly to a maximum
rate of shortening of about -0.022 A s- 1 at t=-10 fs, and -0.030 A s- 1 near t=35 fs, thereafter
oscillating with some sinusoidal regularity.
73
Change inBreIln Dond Length per rim
B)
A)
C)
O4
0
0
Qo
H'0
In-
T:...,S,.,. t.,
Bond Lentg
Change
E)
D)
F)
0
-
0
Fwft*v BWW Length w Tine
"
Fwr
I.T.
ilk
0
I
L,
I
L,
I
L
Figure 3: The geometrical descriptors of the breaking bond (top row) and forming bond (bottom row). The first, second, and third columns correspond to
length, velocity, and applied force, respectively
74
The forming bond exhibits a maximum absolute velocity of 0.022 A s-' which is 68% of
the breaking bond's 0.032 A s-1 at t < 0 fs. However, in contrast to the breaking bond, the
maximal force (Figure 3F) is only 35 kcal mol-' A-', which is only 13% of the breaking bond's
275 kcal mol-1 A-'.
Atomic Hybridizations
Breaking Bond
We probed the geometry and electron distribution adjacent to the breaking bond to
understand in more detail the structural changes related to bond breaking. Hybridization changes
are frequently utilized as probes in enzymology to understand vibrations important to the
chemical transformation of interest2-8 5 . Figure 4A shows the trajectory distribution of the
improper dihedral about C3 (the breaking bond is OB-C3). The value of the improper dihedral is
near pyramidal (60') in the substrate due to C3's sp3 hybridization in chorismate and moves to
near planer (00) in the product due to that atom's sp 2 hybridization in prephenate (Scheme 1).
The improper dihedral changes around C 3 show an oscillation with a mean of 50', an amplitude
of 18', and a period of 30 fs in the reactant well (before t=0 fs; in phase with and similar to the
motions of the breaking bond). The improper dihedral reaches a minimum t=-30 fs of4l , when
the bond is at its maximal length before breaking; the proceeding maxima occurs of 570 at t--1 6
fs. As the system approaches t=0 fs to leave the reactant well, the C 3 improper dihedral crosses
through 32'. At t>100, the C 3 improper is at 7' and without clear oscillatory character.
75
o
A)
C)
B)
0
eo
EO
0
0
_
H'x
A:
H'
EO__
-V
IM
1W.1"
Figure 4: The geometrical improper angle computed for C3,
!it
CT,
i
1
W
1n
and C1 that serves as a marker for hybridization. A value of 0* indicates sp2 while a value of 60*
indicates sp3 like character
76
We also computed the partial atomic charge, using natural population analysis8 6 , assigned
to C3 during the reaction (Figure SI), which is somewhat negative (-0.05e to -0.15e) in the
reactant well and transitions to sharply more negative in the product well (-0.25e to -0.30e).
Taken together, these observations are consistent with a picture in which as the molecule exits
the reactant state, electrons in the CI-C 2 E system begin donating into the C 2-C
increasing the double-bond character of C 2 -C
3
3
D system,
and starting to break the C3-OB bond while
concomitantly pushing C 3 toward sp 2 hybridization geometry.
Forming Bond
Similar observations were made on the improper dihedrals monitoring the geometric
consequences of orbital hybridization and on the computed partial atomic charges on the atoms
of the forming bond
(CT-Cl).
Figure 4 B,C shows trajectories of the improper dihedral around
3
C 1 and C 1, respectively. Both undergo a hybridization change from sp 2 to sp , which correspond
to a change in the ideal improper dihedral from 0' to 60'. The
CT
dihedral exhibits minor
oscillatory behavior in the region of 70 to 14' before t=0 fs, and the CI dihedral samples small
positive values below 150 before t=0 fs, with an unusual excursion that peaks at 19' at t=-58 fs.
At about t--5 fs both dihedrals large monotonic movements that are still below 200 at t=O but
reach greater than 500 by 50 fs, consistent with the product hybridization. Just before leaving the
reactant well,
CT
appears to accept electron density and C I appears to remain essentially neutral,
as judged by their computed partial atomic charges.
CT
becomes progressively more negative
(from -0.1 8e to -0.28e in the timeframe between t<-5 fs and t=0 fs), and C1 goes from 0.05e at
t=-58 fs to -0.03e at t-5
fs to 0.Oe at t=0 fs.
77
A)
B)
SC
S
4C
C O.C
C2 .C
.
C,C,"r
CC
40 -
/P
C26
X
00
015
oK7)
~~0
0e00
0
10i
0,
11 i11t
2
A~
rM
n
Tm
H
ty
M11t10121,1
1t-222
'
H',
Figure 5: The energetic estimates of bond-antibond interactions calculated with NB06 as a function of trajectory
integration step. In A) are the singular interaction energy terms, with a negative energy for electron flows
opposite that in Scheme 1. Results in B) show the summation of the bond-antibond interactions corresponding to
one bonding pair, and yields an estimate of the net energetic tendency for the electrons to interact in the direction
of electron flow indicated in Scheme 1.
.n.3
B)
A)
06-
0.5 C.,irC, C,, NLMO
C-C. - NLMO
015'S
o-0,45
.0.8
-0,5
- - -, --
- - - -
- - -
- - - -
- -
-
-
Cta
-77
0 75
5,0
Figure 6: The pz orbital phases of the six involved atoms from the three bonds involved in the rearrangement. In A)
are the pz orbital phases of atoms composing the primary bonding partners and B) contains the pz orbital phases of
the atoms proximal to the bond where density can delocalize towards.
78
JO
Quantum Mechanical Bond Energies and Polarizations
Breaking Bond
The manifestations of the breaking bond dynamics on the quantum mechanics were first
probed by investigation of the breaking bond quantum mechanical energy and its polarization.
The Hartree-Fock AMI calculation yielded strongly delocalized molecular orbitals that weren't
indicative of localized bonding structure. To address the electronic structure affiliated with the
breaking bond, the delocalized MOs were transformed into localized natural bond orbitals
(NBO) by NB06
6
)B)
A)
p2olrztotoadOBwrexrceananlzdwihterslssoniFiue7Th
breaking ~ ~ ~ ~
2 bodeeg7olw5h bevd3-spridfre-siltrbhvo bevdi
th. emtia4acltin0rmt00t
-
5ftebn
nryosiltosicesdi
amplitue. Theminimumenergyoccurre at t- 5 fswhcwaprmtyfloebyn
aitde
ThDiiumeegacre
engynre
at
=1
s
hc
a
rmtyfloe
ya
as e of NB nrgy 175 al cleant/bond from the equiliium enepolrgyi cofrrepondiyng t ownag
Fnrgymcteae ocalized NB75 kth/e quantm mheailrmenergy,ofr respkning o andrg
79
increase in the distance between the previously bonded atoms. The breaking bond equilibrium
energy has no skew. The polarization of the breaking bond OB also exhibited oscillations that
grew in magnitude from t=-80 to -15 fs, with consistent polarization with greater shared electron
density at OB rather than C 3 (roughly 60%). After t=-1 5 fs, the OB polarization continued to rise
and reached 69% at t=+1 5 fs. The phase between oscillations in energy and polarization is such
that the breaking bond energy decreased when electronic density grew on OB.
Phases and Energetic Interactions of pz Phases
All bonds involved in the Claisen rearrangement
The pz projections of the orbitals involved in the rearrangement were studied to
understand if the breaking bond energy oscillations correlate with necessary orbital
rearrangements in performing the reaction. The productive pz orbital arrangements in a Claisen
rearrangement is frequently conceptualized as one in which the C 3-C 2-C LUMO receives
electron density from the OB-CJ-CT HOM0
87 .
Here, we decompose the orbitals further, and
consider the interplay between HOMO's and LUMO's of the three electron pairs involved in the
rearrangement: OB-C3
U
, CJ-CT 7E/7*, C l-C2 71/7t*.
We define a positive pz phase as one in
which the vector from the negative to the positive lobe of pz points in roughly the same direction
as the vector from the mean of {C 1, C2, C 3} to the mean of {OB, CJ, CT} positions. Orbitals of the
same sign have the capacity to overlap and form interactions, with interactions between bonding
orbitals allowing possible delocalization and interactions between bonding/antibonding orbitals
allowing bonding electron-pair driven bond disruption of the antibonding orbital's bonding
variant 8. Additionally, given two orbitals, A and B, an A-1B* interaction not only promotes
cleavage of the B bond, but also the withdrawal of density from A. In Figure 6 A and B, the
80
orbital phases of pz of the n and
2*
are plotted for each of the six atoms involved in the Claisen
rearrangement.
In the reactant state, the projection of the occupied pz of each atom in either CJ-C121 or
C I-C 2
7 has the same sign, as expected for participants in a n bond. The atomic pz of OB and C3
in OB-C3 cy show opposite sign consistent with the symmetry of an sp-hybridized cY bond. This
trend is observed throughout all time steps in Figure 6. For times before -10 fs, OB pz has
positive phase, while the other five atoms have negative phase (Figure 6A). Because C 3 gains
negative charge while electrons are being removed through the breaking bond, the allylic bond is
the logical source of these additional electrons. This electron donation may be supported by the
common phase of the C3-C 2-C1 Pz moiety.
The arrangement of pz orbitals for t<-l 0 fs would allow electron density in Cl-CT
7E
to
donate to CI-C 2 7E* (or vice versa). Throughout the trajectory, the orbital alignment enables
breakage of the OB-C3 cF bond via donation to its antibond from Ci-C2 n with this interaction
being capable of counteracted during bond stretches. During bond compression and stretching,
the orbitals enable density withdrawal from OB-C3 Yand C]-C 2i7 bond into C 3-C
1 2*,
respectively, hence enabling the cleaving and forming of the bonds important to this reaction
during compression and expansion. At t >-I 0 fs, the phase of Cl-CT
71
switches, allowing bond
formation with Ci and electron delocalization with OB. OB pz and C 2 pz magnitudes oscillate in
phase, which would allow better C 2 delocalization into C 3 . The Ci pz orbital grows smaller in
size, which would discourage the formation of constructive overlap between the forming bond
atoms.
To complement the pz orbital level analyses above, we also analyzed the interaction
energy between the mixing of each bonding and antibonding natural bond orbital. The net
81
energetic tendency for each electron pair shift was computed for each of the three electron pairs
-
that migrate in the Claisen rearrangement. For example, the energetic tendency of C3-OB G
CJ-CT 7t* is computed as the energy of mixing of C3-OB G with CJ-C 1
itminus
CJ-C1 n with
C3-OB G*. A positive energetic tendency would show the C3-OB G orbital has greater tendency
to donate into Cj-C1 a*, then for the C 1-C 1 7E to donate into C3-OB G*. Hence, the C3-OB
y
natural localized molecular orbital (NLMO, of which the additive sum of all matches the
electronic energy) would show more CJ-C 1 R* character, which suggests that the electron pair in
C3-OB a has greater propensity to flow in the direction of CJ-CT.
The energetic tendencies for each of the three orbital interactions are show in Figure 5.
Both the C3-OB a
-
CJ-CT
and C 1-C
n*
2
E 4 C3-OB
G*
interactions vary in-phase with the
breaking bond length. After t > -10 fs, the latter interaction rises to a higher energy than the
former, which suggests that as the C3-OB bond approaches cleavage, the energetic tendency to
reverse the C 3-OB bond expansion (by the reverse C3-OB
7E -C 1 -C 2 7t*
interaction) is
outweighed by the energetic tendency towards cleaving the C3-OB bond through C3-OB n
CI-
C2 7r*. The energetic tendency acting in the forward direction grows from 5 kcal mol 1 to 40
kcal/mol, whereas in the reverse direction, the tendency grows significantly less from -2 kcal
mol- 1 to -10 kcal/mol. The C3-OB G energies as that of Ci-C2
-
C3-OB
G*.
R 4
CJ-CT
t* forward interaction term rises to as high
C3-OB a*, but the reverse term grows more than that of CI-C2
7E
Hence, the net propensity of the C3-OB G - CJ-CT 7t* transition is not as
substantial as for the CI-C2
it 4
C3-OB a*. However, the net positive energetic proclivities for
each of the two interaction show electron directional tendencies suggest flow in the clockwise
direction, from C I-C 2 it to C3-OB a*, and from C3-OB G to CJ-CT
82
7E.
The CJ-CT 7E*Ci-C2 n* remains largely at zero, with both its constituent terms being
zero until t > -20 fs, when the interaction becomes increasingly reverse-favored until peaking at
t=0 fs and returning to zero at t = 10 fs. The interaction energy of the forward Cl-CT n to Ci-C2
7*
grows slower than the reverse. Given the other two's tendencies for electron donation
occurring in the clockwise direction, the negative sign of the Cl-CT
R4-C
I-C2
t*
proclivity
suggests it may act against the overall reaction, but this energetic proclivity quickly drops to
zero, negating its effect.
These results provide support for a few physical organic chemistry scenarios. A strong
increase in C3-OB G
4
CJ-CT
E*
may be driven by liberation of the OB from its bond, but that
was not observed. One possibility is that the electronic environment surrounding OB may be
electron withdrawing enough such that it may emulate a bond, and prevent donation to the C1-CT
2t*
orbital. This electron withdrawing environment on OB can also cause the CI-C2
G*
interaction to be weak in the reverse direction, because of a lack of OB electrons being
n 4
C3-OB
available to interact with C 1 -C 2 7r, which may cause the observed the rise from 5 kcal/mol to 40
kcal/mol. The CJ-C1 n4CI-C2 n* interaction may be weak because of withdrawal of electron
density from C1 through OB'S pull. Additionally, the lack of interaction from C3-OB G to CI-C 2
7*
would increase Ci-C 2 n character, which would further discourage the CJ-CT 7E-C -C
2
7*
interaction.
Elucidationof Reaction Driversfrom ProbabilityFactor Trajectories
The Probability factor gives the probability that a trajectory starting in the reactant well
will reach the product well during the time span of our 201-fs trajectories. These values are
dramatically less than unity for wild-type and mutant chorismate mutates, as well as for
83
simulations carried out for isolated substrate in vacuum and in solvent. This "probability loss"
can be understood as some loss because not all unbiased simulations starting in the reactant well
will depart the reactant well and enter the transition region (order parameter passing from less
than to greater than -0.5), more loss because not all of those entering the transition region will
depart it and enter the product well (order parameter greater than 0.0), and a final loss because
not all of those entering the product well will reach the actual To capture this effect for all
species.. .(Table #R9). Overall differences in the Probability Factor cover eight orders of
magnitude, with wild-type chorismate mutase having the greatest value and vacuum the lowest.
This difference is dominated by effects in the reactant basin (six orders of magnitude),
with another 50 fold coming from the transition region and just 2 fold from the product region.
Moreover, although the mutants and the catalytic antibody are overall less proficient that wild
type as reported by the Probability Factor, some species are actually more proficient that wild
type in certain regions. Specifically, the catalytic antibody I F7 has a greater probability of
successfully traversing the transition region than wild type and all other species, and R90 has a
greater probability of successfully traversing the product well to reach the product. Interestingly,
C88K/R90S CM would actually befaster WT CM if it had WT CM's reactant basin profile.
Species
Probability of Leaving
Reactant Basin
Probability of Entering
Probability Factor
Product Basin After
Leaving Reactant Basin
WT
4.13 x 10-19
5.53 x 10-3
2.28 x 10-1
9.50 x 10-3
8.22 x 10-23
8.73 x 10-21
C88K/R90S
2.45 x 10-24
2.68 x 10-3
9.13 x 10-22
R90Cit
1F7
6.58 x 10-26
2.61 x 10-4
1.72 x 10-29
3.48 x 10-28
3.56 x 10-3
Solvent
9.77 x 10-26
Vacuum
2.77 x 10-26
8.50 x 10-4
2.35 x 1029
Table 3: The summary of the calculated probability factors when viewed as a product of transition probabilities.
These results show that C88K/R90S is better at performing the transition through the intermediate region than the
WT CM.
84
Figure 8 shows the probability factor trace as a function of trajectory ending order parameter
value. Different systems exhibit different ending points. The true-enzymes show probable
trajectory end points that are closer to the edge of the reactant basin then the non-true enzymes.
WT shows the greatest tendency to have trajectories end nearer to the reactant basin edge,
followed by R90Cit and then C88K/R90S. Of the non-true enzymes, 1F7 has the most favorable
trajectory end point closest to the reactant basin, followed by solvent, and vacuum.
To understand the catalytic effort each system performs in the reactant basin, we
analyzed the trajectories resulting from the Probability Factor calculation. Due to the nature of
the calculation,
-10,000
trajectories were collected at each value of order parameter end point,
for a total of about -5,000,000 trajectories. These trajectories are both dependent on time and on
ending order parameter value. To present data as a function of trajectory ending order parameter
value, at each window, the metric value of trajectories at a specified time were calculated and
then subsequently averaged with calculation of the middle 50% ranges. The time points utilized
were between t--1 00 fs to 0 fs. In that time point span, the ones most relevant to the metric and
behavior of the system in the reactant basin were selected, with the selected time point given in
the title.
85
10 0-WT
5 .---
-
Vacuum
-C88K/R90S
R90Cit
1F7
Solvent
C 10
C
uJ
L
o 10'
15
U
10-
20
4-
0
10-25
.0
0-
030
13
'
-3
'
-2
R
ctant
Produc
0
1
Order Parameter Value (A)
-1
2
3
Figure 8: The probability factor plot as a function of order parameter value. Note the differences amongst
systems in the most probable order parameter value in the reactant basin
The alignment of the trajectories utilized in the plots that follow is different than the ones
utilized previously. For trajectories that end at X>-0.5, the alignment procedure is still the same,
t=O fs corresponds to the point in the trajectory when it departs the reactant basin, which itself
ends at X=-0.5.
For trajectories that end at X<-0.5, they are aligned such that the last point
closest to their sampling window is at t=Ofs. Hence, in the proceeding plots, the catalytic actions
taken by the species to make a trajectory reactive are evident by reading the plot from X=-3 to
X=3. While the profiles of each species at X=-0.5 show roughly the same probability of being
86
reactive, it is the transition from k=-3 to k--0.5 that has differential probability and highlights
the catalytic actions each system takes in performing the reaction.
TPS: Reaction Drivers: Bond Length, Velocity, and Applied Force
Figure 9 shows the per-system ensemble maximal breaking bond lengths, velocities, and
forces and the minimal forming bond lengths, velocities, and forces. The breaking bond length,
velocity, and force is larger for trajectories that end at greater order parameter values. The true
enzymes, over the non-true enzymatic systems, exhibit a greater breaking bond length, velocity,
and force. The forming bond length, velocity, and force are smaller (velocity and force grow
greater in absolute value) for trajectories that end at greater order parameter values. The forming
bond length is smaller for non-true enzymatic systems. Forming bond compression velocities are
higher in slower systems. There is no clear trend on forming bond force.
87
C)
B)
A)
41
\10
0
W~BS..114-44
0
#A- F
D)
qS-
E)
f
F)
i
/.
o
0
0
Figure 9: The geometrical descriptors of the breaking bond (top row) and forming bond (bottom row) as a function of trajectory ending order parameter value.
The first, second, and third columns correspond to length, velocity, and applied force, respectively. The change in the geometric descriptor as trajectories end
further towards the product basin is indicative of the changes that occur in performing the rearrangement.
88
B)
A)
C)
Ho
0
o
H 0
H
Figure 10: The geometrical improper angle for each species as a function of trajectory ending order parameter value for A) C3 B) Cr and C) C1. This metric
serves as a marker for hybridization; a value of 0' indicates sp2 while a value of 600 indicates sp 3 like character.
89
Atomic Hybridizations
To further investigate how the dynamics of the breaking and forming bond play a role in
perturbing the system towards the product state, we looked at the hybridization observed at t=O fs
of all involved atoms with geometrically probe-able hybridizations, C3, CT, and C (Figure 10).
Trajectories for wild type, R90Cit, and C88K/R90S that successfully reached the product basin
tended to greater sp 2 character about C 3 (more planar improper dihedral angle on this atom in the
breaking bond, roughly 25-350) when leaving the reactant well than for the slower reactions
(1F7, solvent, and vacuum, which had more pyramidal values around 35-45'). For the forming
bond, the true enzymes exhibited relatively planar geometries about both Ci and CT (maximum
value of about 20') as compared to the slower reactions (maximum value of 25-35'). That is, the
true enzymes show early development of product character upon leaving the reactant well for the
breaking but not the forming bond (both are relatively more sp2-like), but the slower reactions
show less development of the breaking bond and more development of the forming one (both are
relatively more sp 3-like).
90
C3-09 u NBO Energy
Percentage
O of C3 O
NBO
B)
A)
-1
-015
0
0.5
1
i
-'6
2
-1
-06
0.5
a
.
Figure 11: The breaking bond energy (A) and polarization towards the ether oxygen (B) for each species as a
56
function of ending trajectory order parameter value. These values were calculated with NB06
Quantum Mechanical Bond Energies and Polarizations
Differences in the natural bond orbital level decomposition were analyzed to understand
better differences in reactivity (Figure 11). The C3-OB a energy, at t = -15 fs, decreases as
trajectories end at higher values of the order parameter, except for 1F7, which instead shows a
reversal. WT and C88K/R90S show identical bond energies, with R9OCit and 1F7 showing bond
energies 50 and 175 kcal mol' higher. The solvent system, in comparison to the vacuum, shows
greater destabilization of breaking bond. Figure 11 B shows the affiliated breaking bond
polarization at t = -1
fs. Trajectories with greater polarization towards OB end up at greater
values of the order parameter. The true enzymes show a large change in polarization of 9%, 8%,
and 4% for WT, C88K/R90S, and R90Cit, respectively. The solvated and vacuum simulations
exhibit lesser polarization with a 2% change. 1 F7, interestingly, exhibits only a 1% change in
polarization. For trajectories ending in the product basin, C88K/R90S and WT exhibit
equivalent polarization of near 69%, followed by R90Cit at 66%, at the time they left the
91
reactant basin. The solvated, I F7, and vacuum systems exhibit a polarization of about 60%.
The change in polarization for increasing final order parameter, with the polarization for
trajectories that end in the product basin suggest three insights:
(1) WT and C88K/R90S are both equally capable of polarizing the breaking bond, but
R90Cit, though it may have a similar polarization to that of WT in the reactant basin, is
not capable of polarization as great as that of WT and C88K/R90S.
(2) The solvated and vacuum systems exhibit almost equivalent amounts of polarization,
though it's still less than that of the true enzymes.
(3) 1 F7 shows the least change in polarization, suggesting it may be incapable of doing so, or
may not utilize polarization to cause the reaction.
(4) Systems capable of greater changes in polarization exhibit faster computed kcat values.
Energetic tendencies of orbital bonding/antibonding interaction
The relevant net energetic tendencies for each bonding/antibonding orbital pair were
considered and are shown in Figure 12, with the orbital interaction of interest shown in each
subpanel. There are three interactions considered: (1) breaking bond donation into the Cl-CT 21*,
(2) CJ-C 1 n donation into the lower ring Ci-C2 n*, and (3) CI-C2n donation into the breaking
bond a*. In the ideal scenario, energetic tendencies of each orbital interaction would be a
positive value in the directionality of electron flow. However, our results suggest that's not the
case for all interactions, and that deficiencies in one interaction are balanced by proficiencies in
another interaction.
In the first keto-forming interaction, the breaking bond shows greater
interaction energies towards donating to the Cl-CT n* (which would cause cleavage of the CJ-CT
7c
bond) with greater ending order parameter window in the true enzymes.
92
C
A)
*a
CQ
Cr*
Energy - C.Cr w -+ C3 -
C.Cy
f* Energy
B)
I
-+ C C2 e Energy - C-C, v
CC 2
C C. ;r' Energy
C-O
*Energy - C3-0,
-+ CC2 w* Energy
C) I[
1wJ
2D
0
Figure 12: The net energetic tendencies for each bond/anti-bond interacting pair, for each species, at t = -1 fs, as a function of trajectory ending order
parameter value. A positive value indicates favorability for electrons to delocalize in the direction indicated by the arrow in the chorismate diagram in each
panel
93
R90Cit and C88K/R90S show a net interaction energy of 12 kcal mol', while WT shows
a slightly less energy of 7 kcal/mol. For the other three systems, I F7, solvent, and vacuum,
trajectories ending at greater order parameter values exhibit near zero energetic tendency. This
is consistent with other results, above, showing that the true enzymes promote cleavage of the
breaking bond while still in the reactant well, but the other species do not do so to the same
extent, if at all.
This inability of the non-true enzymatic systems to funnel breaking bond electron density
into the CJ-C1
R*
is compensated by their greater proclivities in the CJ-CT
R
4CI-C 2
R*
interaction. The true enzymes show a net negative energy of interaction with increasing
trajectory progress, though a less negative energetic tendency of this interaction ranks with
greater kinetic proficiency. The non-true enzyme systems show increasing trajectory progress
with greater energetic tendencies for this interaction. The interaction energy ranks with the
speed of the non-true enzymes. The solvated, vacuum, and 1F7 systems exhibit a net interaction
energy of 20, 11, and 5 kcal mol', respectively.
C2
i
i
bond, but the non-true enzymatic systems appear better at breaking the C1
-
breaking the Cl-CT
Hence, the true enzymes may be better at
bond. The former would serve to create orbital vacancies for the breaking bond to deposit
its electrons, while the latter serves to create orbital vacancies so electron density can be
developed to generate the forming bond.
The third interaction is the allylic rearrangement that manifests as double bond migration
from CI-C2 to C2-C 3. This rearrangement requires the development of a C3 orbital vacancy,
hence, the CI-C 2 n to C3-OB
(T*
interaction was considered. All systems exhibit a greater
interaction energy with increasing trajectory ending order parameter value. The fastest two
systems, WT and C88K/R90S, show the greatest interaction energy of 22 kcal mol-', R90Cit
94
shows a milder 15 kcal mol' energy, and the non-true enzymes exhibit lower interaction
.
energies of 7 to 10 kcal mol- 1
The magnitude of interaction energies between the three bonds may signify the dominant
mechanism of which how system performs the reaction. Within the true enzymes, the magnitude
of the allylic rearrangement interaction matches the observed breaking polarization. A greater
interaction energy has the potential to allow greater delocalization of the Ci-C2 n bond into the
orbitals occupied by the OB-C3 c. This interaction may cause displacement of the OB-C3
electrons, which in turn may cause greater interaction in the OB-C3
n
0
with the C--C1 7r*. The
lack of WT interaction energy could be attributed to diversion of electron density to hydrogen
bonding with Arg90, as shown in Figure 14. These two interaction energies highlight the
capacity of the true enzymes to cause breaking bond cleavage, with a ranking of C88K/R90S,
WT, and then R90Cit. This may manifest as greater breaking bond lengths, as observed in
Figure 9. The ranking matches that of the enzymatic system transition probabilities through the
reactant to product basin (Table 3).
The differential catalytic rates amongst the non-true enzyme systems rank with greater
CJ-CT1 -
Ci-C 2 7* interaction energy, which serves to generate orbital vacancies to facilitate
forming bond formation. Since the non-true enzymes have equivalent allylic rearrangement and
keto-formation energy of interactions, the capacity of the non-true enzymatic systems may be
governed by their capacity in generating the forming bond. The solvated system shows the best
forming bond capacity, followed by vacuum, and then 1F7. Within the true enzymes, the
capacity to disrupt the breaking bond correlates well with catalytic capacity. The non-true
enzymes have catalytic rates correlating with their capacity to generate the forming bond.
95
O
p. from C-0
a NLMO
-C r NLMO
C .fo
B)
A)
C)
CYp
from C
-C
r NLMO
- 0
0
HO
CH2
0OH2
CH2
CO
HO
HOk
0
H0
C02-
CO2
0
0CH2
0
H2
HOk 'CO2
HOA
r
NLMO
C, p
from C 1-C2 r NLMO
C p
0
D)
01CH 2
HO
E)
'ICOj
C02
from CgC2 r NLMO
CH 2
. ....O
CH2
HO
?-CO2
F)
SCH2
~OA2
CO2
.
C3 p from C3Os
"
Sr
Figure 13: The pz orbital phases of the primary atoms involved in the bond, for each species, as a function of trajectory ending order parameter value, at
t = -1 fs. The structures in each panel visually indicate the phase. For Ci and CT, in panels B and C, the two structures in each panel indicate a change in sign,
with the curly brackets indicating over which y-axis range that structure is more dominant.
96
C67
Sum at C -O, a Lone Pakr kntrscdon
Energims
7
A)
SUM Of 0
Lonm Pair Interaction Energies
B)
Figure 14: Interaction energy of Arg90 between A) C3-OB G or B) OB lone pairs. For C88K/R90S, R90Cit, and 1F7,
the homologous Lys88, Cit90, and ArgH95H are utilized in place of Arg90. For Solvent and Vacuum, there are no
1
homologous residues or entities, hence, they are plotted as 0 kcal mol- . Even with the presence of a homologous
Arg90, 1F7 (line overlapping with vacuum) shows an interaction energy of 0 kcal mol-1 across all trajectory ending
window values.
The differential energetic tendencies for each of the three electron interactions for each
studied system suggests that each system performs the reaction through intrinsically different
electronic states. When cast onto a transition state theory framework, these results suggest that
the systems may not follow the same transition state as suggested by previous studies, or at least
it may suggest differences among the transition states.
Orbital delocalizations resulting from orbital bonding/antibonding interaction
Figure 13 exhibits the molecular orbital delocalization resulting from the
bonding/antibonding interactions discussed previously. Faster variants exhibit greater
delocalization of the breaking bond electrons into the upper ring Cj with lesser delocalization
into the lower ring C2. Slower systems have greater CJ-CT 71 bond electron delocalization into
the surrounding Ci and OB, with solvent showing the most delocalization from the top to the
97
.. .............
...
bottom, and vacuum and I F7 showing greater delocalization the other way around. The allylic
shift of the Ci-C2 bond shows higher delocalization into C3 for faster variants, with almost equal
delocalization into the CT.
For the true enzymes, faster variants exhibit greater delocalization into C3 from the Ci-C2
bond. For the non-true enzymes, their rate correlates with their capacity to delocalize the C1
CTn
-
21
bond into the forming bond's C 1. 1F7 also shows greater delocalization of the allylic C i-C 2
bond into CT, however, it also has greater delocalization for the breaking bond (in the reverse
direction) into the C2 pz. Hence, I F7 may be good at generating the forming bond, but doing say
may be detriment its capacity to disrupt the breaking bond.
Casualty behind orbital delocalizations
Figure 15 and 17 show the pz orbital component of each atom in the bonding and
antibonding orbitals, respectively, and may elucidate why species that are better at disrupting the
breaking bond are more catalytically efficient than species which are better in generating the
forming bond. The phases and magnitudes of the interaction between pz and pz* orbitals on
different atoms are indicative of the aforementioned energy differences and the delocalizations.
The forward proclivity of the allylic shift may be driven by differential pz signs, with same phase
indicating overlap. Analysis of the phase of the C2 and C 3 pz shows that the forward C 2 pz 4C3
pz* interaction is possible but the reverse is not. Additionally, faster enzymes have larger C 3 pz*
orbitals, which may serve to further increase C2 pz's donation into the breaking bond C 3 pz*. The
bond forming interaction, between the CT and C 1 pz, shows bidirectional interaction capacity that
may explain the lesser net energy proclivities observed for the faster enzymes.
98
)- CH2
fX LMO'
CJ P. fMMe
-F
CSp .fram C-C 2 WNLMO
-0
0
-
A)
C)
Cp.fruuCCir MUM
B)
-
0o
-C0
0
U2
C02
Hgb
CO2
elmni-
OCH2
HOA
C 2 P frM
D)
C37
CO2
LMOD
Clor
O
P. Irm
Ci.Co
C 7 p from C 7-Cs 7L0O
NL.MO
F)
E)
0
0CC
CH 2
HO*
COi
CH 2
HO
0
2
C02
H
CO~i
in each panel visually indicates the
Figure 15: The pz orbital phases of proximal atoms from the red bond in the drawing in each panel. The orbital diagram
value is indicative of greater
A
greater
value
phase. These phases are plotted per species, at t = -1 fs, as a function of trajectory ending order parameter
delocalization of the bond into the proximal atom pz.
99
....
..
..............
.........
...........
. ...
..
A)
C)
B)
,fr,..C4
C p. ki
.TSO
CJCr
CT p. fraM
' NW
CgCJ
o
3
OL
00
ICH2
Xb
CO
HO
- "H
2
CZpPn.Cm C
C, P. M C0 ,O* NW
NMO
D)R
C
*-Ca
F)
E)
H
pr
C'.C 2
W
'4
o
HOA
CH2
OCH2
'CO
0 CH2
HOCOi
HO
CO
Figure 16: The pz* orbital phases of atoms in the bond indicated in the drawing in each panel. The orbital diagram in each panel visually indicates the phase.
These phases are plotted per species, at t = -1 fs, as a function of trajectory ending order parameter value. A greater orbital phase magnitude is indicative of
greater capacity to receive electrons from nearby electron donors.
100
..........
It is of note that the CT pz experiences a sign flip for trajectories that end at greater order
parameter values. This sign flip would put CT in phase with the C1 pz*. The development of this
interaction may be counteracted by the increase in Cpz* size.
The allylic shift and the bond forming interaction show clear bonding/antibonding orbital
interactions that may stabilize electrons while they are in flux. The bond breaking orbital
electrons, however, have no pz antibonding orbitals that could serve are places to dump density;
the C 3 Pz
4
C 2 pz* and the OB pz
Cj pz* electronic interactions are both symmetry forbidden.
This inability to deposit electrons during the chemical reaction may explain why greater
efficiency in disrupting the breaking bond causes the system to be more catalytically proficient,
while the methylene electrons have the capacity to donate to the allylic double bond with or
without intermolecular influences. This hypothesis is supported by previous work concluding
that the mechanism for disrupting the breaking bond in WT and C88K/R90S CM is driven by
their capacity to stabilize the OB through positively charged residues. Our results show that this
catalytic strategy works because it addresses the greatest issue with this reaction: the breaking
bond electrons have no intramolecular sink.
Conclusion
Our study has shown there exists a clear stratification of catalytic capacity based off the
bond breaking/forming capacities of each system. The WT CM is the fastest of the six systems
studied because it not only holds the reactant closer to the product well, but it also is catalytically
effective at pushing the system towards the product well. C88K/R90S, even though it shows
greater ability than WT CM to transition a system from the edge of the reactant basin to the
101
product basin, is held back by its relative inability to promote the departure of the system from
the reactant basin. R90Cit, though it may be better at retaining the reactant at a place nearer the
transition region, shows the poorest capacity in catalyzing the departure of the reactant from the
reactant basin. Solvent shows the greatest capacity to generate the forming bond, followed by
Vacuum, then 1F7 and may reflect directly in their overall calculated kcat due to the lack of
differentiation in breaking bond capacity. The transition probabilities presented in Table 3 and
the net energetic tendencies in Figure 12 were utilized in supporting this argument.
We then further decomposed the source of these net energetic tendencies. An analysis of
the phases of the pz orbital suggests a greater bond breaking/forming capacity manifests as
greater delocalization into the relevant proximal atoms. Furthermore, we uncovered evidence of
the potential causality behind the observed effectiveness of being competent at the disruption of
the breaking bond over the forming bond.
In comparison to previous studies, we utilized an
entirely different framework that does not rely on projection onto reduced dimensionality
through thermodynamic integration. While we cannot make statements about the dominance of
transition state stabilization versus near-attack-conformers (NACs) in the catalytic mechanism,
we have showed evidence of how the mechanisms of catalysis permeate through dynamical
markers. For the chorismate rearrangement, faster enzymes are faster because they cause actions
to coax disruption of the breaking bond, while the slower systems can be partially redeemed by
being better at encouraging the forming bond.
102
103
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APPENDIX
Code
All 200,000 lines of MATLAB, Python, Java, and BASH code utilized in this body of work
will befound underthe
y
i
Simulation Setup Files for Chorismate simulations (generates calculations via custom code
posted above)
WT CM
[setup]
pmew=1
crystal=1
crystaltype=rhdo
usenewdynawrite=1
startcrd=cm. crd
quantumatoms= C:J, C:X 1:237, C:Y 1:236, C:A 1:63 T:GLINK, C:A 1:75
T:GLINK, C:B 1:78 T:GLINK, C:B 1:90 T:GLINK, C:B 1:7 T:GLINK, C:B 1:116
T:GLINK, C:B 1:108 T:GLINK,
qmcharge=1
dontuseoldrand=1
plotcolor=[0 1 0]
quantumtype=sqm2
quantumpdbwrite=0
charmmvatom= #skip#
charmm nprint = 1
noloops = 1
overlapbins = 2
[umbrella-setup]
dynamicstype=CPT
lineinserts=41,noecons.inp
[umbrella-descriptions]
kumb_r1=150
start_rl=-4
gradient rl=0.05
end_rl=4
[findtraj-setup]
usecharmmwriter=1
charmmwriterexe=charmmdftb
tsrange=[-0.45, -0.05]
reacfilter=[-10 -0.5]
prodfilter=[0 10]
[tps-setup]
basinreac=[-10 -0.5]
basinprod=[0 10]
targetlength=200
charmmtpsexe=charmmsqm
110
[tps-getv]
sampleamount=100
trajlength=200
[tps-getp]
sampleamount=5
trajlength=100
windowstart=-2
windowend=2
windowwidth=0.1
ignorewhamresults=1
C88K/R90S CM
[setup]
pmew=1
crystal=1
crystaltype=rhdo
usenewdynawrite=1
startcrd=mutant.crd
quantumatoms= C:J, C:X 1:237, C:Y 1:236, C:A 1:63 T:GLINK, C:A 1:75
T:GLINK, C:B 1:78 T:GLINK, C:B 1:88 T:GLINK, C:B 1:7 T:GLINK, C:B 1:116
T:GLINK, C:B 1:108 T:GLINK,
qmcharge=1
overlapbins = 2
dontuseoldrand=1
plotcolor=[0 1 0]
overlapbins=2
quantumtype=sqm2
quantumpdbwrite=0
charmmvatom= #skip
charmm-nprint = 1
noloops = 1
[umbrella-setup]
dynamicstype=CPT
lineinserts=41,noecons.inp
[umbrella-descriptions]
kumb_rl=150
start_rl=-4
gradient rl=0.05
end_rl=4
[findtraj-setup]
usecharmmwriter=1
charmmwriterexe=charmmdftb
tsrange=[-0.4, -0.2]
reacfilter=[-10 -0.5]
prodfilter=[0 10]
[tps-setup]
basinreac=[-10 -0.5]
basinprod=[0 10]
111
targetlength=200
charmmtpsexe=charmm-sqm
[tps-getv]
sampleamount=100
[tps-getp]
sampleamount=5
trajlength=100
windowstart=-2
windowend=2
windowwidth=G.1
ignorewhamresults=1
R90Cit CM
[setup]
pmew=1
crystal=1
crystaltype=rhdo
usenewdynawrite=1
startcrd=cm.crd
quantumatoms= C:J, C:X 1:237, C:Y 1:236, C:A 1:63 T:GLINK,C:A 1:75
T:GLINK, C:B 1:78 T:GLINK, C:B 1:90 T:GLINK, C:B 1:7 T:GLINK, C:B 1:108
T:GLINK, C:B 1:116 T:GLINK
qmcharge=0
overlapbins = 2
dontuseoldrand=1
noloops=1
plotcolor=[1,1,0]
quantumtype=sqm2
quantumpdbwrite=0
charmmvatom= #skip#
charmmnprint = 1
[umbrella-setup]
dynamicstype=CPT
lineinserts=41,noecons.inp
[umbrella-descriptions]
kumb_rl=150
start_rl=-4
gradient_rl=0.05
end_r1=4
[findtraj-setup]
usecharmmwriter=1
charmmwriterexe=charmmdftb
tsrange=[-0.5, -.1]
reacfilter=[-10 -0.5]
prodfilter=[0 10]
[tps-setup]
basinreac=[-10 -0.5]
basinprod=[0 10]
112
targetlength=200
charmmtpsexe=charmmsqm
sampleamount=100
[tps-getp]
sampleamount=5
trajlength=100
windowstart=-2
windowend=2
windowwidth=0.1
ignorewhamresults=1
[tps-getv]
trajlength=200
1F7
[setup]
pmew=1
crystal=1
crystaltype=orth
usenewdynawrite=1
startcrd=anti.crd
quantumatoms= C:C I:432, C:B 1:314 T:GLINK, C:B 1:250 T:GLINK, C:B 1:248
T:STD, C:B 1:247 T:CTERM, C:B 1:249 T:NTERM, C:B 1:318 T:STD, C:B 1:317
T:CTERM, C:B 1:319 T:NTERM
qmcharge=-1
usecharmmwriter=0
quantumpdbwrite=0
sccfftx=96
sccffty=96
sccfftz=64
dontuseoldrand=1
plotcolor=[1,0,0]
crysdim=[100.0 79.0 67.0]
noloops=1
quantumtype=sqm2
charmmvatom= #skip#
charmm-nprint = 1
[umbrella-setup]
lineinserts=41,noecons.inp
dynamicstype=CPT
[umbrella-descriptions]
kumb_rl=150
start_rl=-4
gradient rl=0.05
end_rl=4
[findtraj-setup]
tsrange=[-0.5, 0]
reacfilter=[-10 -0.5]
113
prodfilter=[0 10]
usecharmmwriter=1
charmmwriterexe=charmmdftb
[tps-setup]
basin_reac=[-10 -0.5]
basinprod=[0 10]
targetlength=200
charmmtpsexe=charmm-sqm
sampleamount=100
[tps-getp]
sampleamount=5
trajlength=100
windowstart=-2
windowend=2
windowwidth=0.1
ignorewhamresults=1
simfoldname=tpsgetp
Solvent
[setup]
pmew=1
crystal=1
crystaltype=cubi
usenewdynawrite=1
crysdim=26.5
startcrd=bulk.crd
quantumatoms= C:J
qmcharge=-2
dontuseoldrand=1
plotcolor=[0.5 0 1]
quantumtype=sqm2
quantumpdbwrite=0
charmnvatom=
#skip4
charmmnprint = 1
noloops = 0
[umbrella-setup]
dynamicstype=CPT
inpscriptloc=/data/isp03/cm/bulk/template/umbsamp.inp
regionexclude=[2.05 Inf; 2.3 Inf]
projectcomb=[1 -1]
projectvec=-4:0.05:4
tolerance=0.05
[umbrella-descriptions]
kumb_rl=[150,150, 250]
start_rl=[2.6 1.4 1.4 ]
gradientr1=[0.10 0.10 0.05 ]
end_rl=[10 2.0 2.5]
114
kumb-r2=[150,150,250]
startr2=[1.4 2.6 1.4]
gradientr2=[0.10 0.10 0.05]
endr2=[2.0 10 2.5]
[findtraj-setup]
usecharmmwriter=1
charmmwriterexe=charmmdftb
ts_range=[1.4, 1.8; 1.4 1.8]
reacfilter=[1 3; 3 5]
prodfilter=[3 5; 1 3]
trackalldimensions=1
[tps-setup]
trajbasinreac=[1 2.5; 3 40]
trajbasinprod=[3 40; 1 2.5]
basinreac=[-10 -0.5]
basinprod=[0 10]
ndimlcrxncoor=[-1 1]
targetlength=200
charmmtpsexe=charmmsqm
rxncoordeffile=tpsdef.def
[tps-getv]
sampleamount=100
[tps-getp]
sampleamount=5
trajlength=100
windowstart=-2
windowend=2
windowwidth=0.1
ignorewhamresults=1
Vacuum
[setup]
pmew=0
crystal=0
usenewdynawrite=1
startcrd=vacuum.crd
quantumatoms= C:J
qmcharge=-2
dontuseoldrand=1
plotcolor=[0.5 0 1]
overlapbins = 2
quantumtype=sqm2
quantumpdbwrite=0
charmmvatom= #skip#
charmm nprint = 1
noloops = 1
[umbrella-descriptions]
kumb_rl=150
start_rl=-4
gradient rl=0.05
end_rl=4
115
[findtraj-setup]
usecharmmwriter=1
charmmwriterexe=charmmdftb
tsrange=[-0.45, -0.05]
reacfilter=[-10 -0.5]
prodfilter=[0 10]
[tps-setup]
basin_reac=[-10 -0.5]
basin_prod=[0 10]
targetlength=200
charmmtpsexe=charmm-sqm
[tps-getv]
sampleamount=100
[tps-getp]
sampleamount=5
trajlength=100
windowstart=-2
windowend=2
windowwidth=0.1
ignorewhamresults=1
CHR
CR5
CR2
CR1
CR6
HR5
CA
CA
CA
CA
HP
ATOM
HR2
HP
ATOM HR6
ATOM CR4
ATOM HR4
ATOM CR3
ATOM HR3
ATOM ORH
ATOM HRH
ATOM ORB
ATOM CBJ
ATOM CBA
ATOM OBI
ATOM OB2
ATOM CET
ATOM HETI
ATOM HET2
ATOM CRA
ATOM OR1
ATOM OR2
BOND CR5
HP
CT1
HA
CT1
HA
ONI
H
ONI
CA
CC
OC
OC
CE2
HA
HA
CC
OC
OC
CR6
-0.34361
!
-0.22510
!
-0.00645
!
-0.04921
!
0.11919
0.13257
0.09192
0.17701
0.15896
0.09494
0.12009
-0.66090 !
0.38546
-0.36498 !
0.21181
0.76460
-0.79447
-0.77116
-0.54958
0.15448
0.17026 !
0.79456 !
-0.79741
-0.81299
CR5 HR5
CR5
C5
C2
C1
C6
H5
H2
H6
C4
H4
C3
H3
OR
HR
OB
CJ
CB
OB1
_B1
OB2
T
OB
HT2
H5
I
H4
\C-- L;5
HR--OR
\
C3
/ -"C-'-C 1 -l,
H3
/
H2
OB2
CT
HT1
HT2
CA
OA1
OA2
CR4
CB
/
-2.000
RESI
GROUP
ATOM
ATOM
ATOM
ATOM
ATOM
!
CHARMM Topology Parameters for Chorismate
CR2
116
CR1
2
OA2
CA
OA1
BOND CR2 HR2
CR2 CR3
CR1 CR6
CR1 CRA
BOND CR6 HR6
CR4 CR3
CR4 HR4
CR4 ORH
BOND CR3 HR3
CR3 ORB
ORH HRH
ORB CBJ
BOND CBJ CBA
CBA OB1
CBJ CET
CBA OB2
BOND CET HETI
CET HET2
CRA OR1
CRA OR2
ANGLE CR6 CR5 HR5
CR6 CR5 CR4
HR5 CR5 CR4
ANGLE CR1 CR2 HR2
CR1 CR2 CR3
HR2 CR2 CR3
CR2 CR1 CRA
ANGLE CR2 CR1 CR6
CR6 CR1 CRA
ANGLE CR5 CR6 CR1
CR5 CR6 HR6
CR1 CR6 HR6
ANGLE CR5 CR4 HR4
CR5 CR4 ORH
CR5 CR4 CR3
ANGLE HR4 CR4 CR3
HR4 CR4 ORH
CR3 CR4 ORH
CR2 CR3 ORB
ANGLE CR2 CR3 CR4
CR2 CR3 HR3
ANGLE CR4 CR3 HR3
CR4 CR3 ORB
HR3 CR3 ORB
ANGLE CR4 ORH HRH
CR3 ORB CBJ
ORB CBJ CBA
ANGLE ORB CBJ CET
CBA CBJ CET
CBJ CBA OB1
ANGLE CBJ CBA OB2
OB1 CBA OB2
CBJ CET HETI
CR1 CRA ORI
ANGLE CBJ CET HET2
HET1 CET HET2
ANGLE CR1 CRA OR2
ORI CRA OR2
DIHED HR5 CR5 CR6 CR1
HR5 CR5 CR6 HR6
DIHED CR4 CR5 CR6 CR1
CR4 CR5 CR6 HR6
CR6 CR5 CR4 CR3
DIHED CR6 CR5 CR4 HR4
DIHED CR6 CR5 CR4 ORH
HR5 CR5 CR4 HR4
DIHED HR5 CR5 CR4 CR3
HRS CR5 CR4 ORH
DIHED HR2 CR2 CR1 CR6
HR2 CR2 CR1 CRA
DIHED CR3 CR2 CR1 CR6
CR3 CR2 CR1 CRA
CR1 CR2 CR3 HR3
DIHED CR1 CR2 CR3 CR4
DIHED CR1 CR2 CR3 ORB
HR2 CR2 CR3 CR4
DIHED HR2 CR2 CR3 HR3
HR2 CR2 CR3 ORB
DIHED CR2 CR1 CR6 CR5
CR2 CR1 CR6 HR6
DIHED CRA CR1 CR6 CR5
CRA CR1 CR6 HR6
DIHED CR2 CR1 CRA ORI
CR2 CR1 CRA OR2
DIHED CR6 CR1 CRA OR1
CR6 CR1 CRA OR2
DIHED CR5 CR4 CR3 CR2
CR5 CR4 CR3 HR3
HR4 CR4 CR3 CR2
DIHED CR5 CR4 CR3 ORB
DIHED HR4 CR4 CR3 HR3
HR4 CR4 CR3 ORB
ORH CR4 CR3 HR3
DIHED ORH CR4 CR3 CR2
DIHED ORH CR4 CR3 ORB
CR5 CR4 ORH HRH
DIHED HR4 CR4 ORH HRH
CR3 CR4 ORH HRH
DIHED CR2 CR3 ORB CBJ
CR4 CR3 ORB CBJ
DIHED HR3 CR3 ORB CBJ
CR3 ORB CBJ CBA
DIHED CR3 ORB CBJ CET
ORB CBJ CBA OB1
DIHED ORB CBJ CBA OB2
CET CBJ CBA OB1
ORB CBJ CET HETi
DIHED CET CBJ CBA OB2
CBA CBJ CET HETI
DIHED ORB CBJ CET HET2
DIHED CBA CBJ CET HET2
CR2 CR1 HR2 CR3
IMPR CR6 CR5 CR1 HR6
IMPR CET CBJ HETI HET2
1.079 121.32 -178.66 121.74
IC HR5 CR5 CR6 CR1
1.079 121.32
0.52 122.17
IC HR5 CR5 CR6 HR6
-3.89 121.74
IC CR4 CR5 CR6 CR1
1.510 120.10
1.510 120.10 175.29 122.17
IC CR4 CR5 CR6 HR6
1.325 120.10 152.99 112.92
IC CR6 CR5 CR4 HR4
1.325 120.10
32.36 111.71
IC CR6 CR5 CR4 CR3
IC CR6 CR5 CR4 ORH
1.325 120.10 -89.56 109.04
IC HR5 CR5 CR4 HR4
1.079 118.37 -32.09 112.92
117
1.483
1.074
1.483
1.074
1.077
1.529
1.425
1.077
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
HR5
HR5
HR2
HR2
CR3
CR3
CR1
CR1
CR1
HR2
HR2
HR2
CR2
CR2
CRA
CRA
CR2
CR2
CR6
CR6
CR5
CR5
CR5
HR4
HR4
HR4
ORH
ORH
ORH
CR5
HR4
CR3
CR2
CR4
HR3
CR3
CR3
IC
APR
IC
IC
IC
IC
IC
IC
IC
IC
IC
IC
ORB
CET
CET
ORB
ORB
CBA
CBA
CR5
CR1
CBJ
CR4
1.079 118.37 -152.71 111.71 1.529
1.079 118.37
85.37 109.04 1.425
CR1
1.075 118.92 -177.73 118.75 1.483
CR1
1.075 118.92
1.44 122.78 1.545
CR1
1.517 121.96
0.30 118.75 1.483
CR1
1.517 121.96 179.47 122.78 1.545
CR3
1.329 121.96
28.04 111.58 1.529
CR3
1.329 121.96 146.91 110.90 1.080
CR3
1.329 121.96 -92.04 109.47 1.419
CR3
1.075 119.09 -153.94 111.58 1.529
1.075 119.09 -35.07 110.90 1.080
CR3
1.075 119.09
85.99 109.47 1.419
CR3
CR6
1.329 118.75 -14.02 121.74 1.325
CR6
1.329 118.75 166.75 116.08 1.074
CR6
1.545 118.46 166.78 121.74 1.325
CR6
1.545 118.46 -12.45 116.08 1.074
CRA
1.329 122.78 -174.93 114.85 1.238
OR2 1.329 122.78
5.53 116.30 1.232
CRA
OR1 1.483 118.46
CRA
4.24 114.85 1.238
CRA
OR2 1.483 118.46 -175.30 116.30 1.232
CR3 CR2
1.510 111.71 -42.21 111.58 1.517
CR3 HR3
1.510 111.71 -163.52 106.75 1.080
CR3 ORB
1.510 111.71
78.45 108.47 1.419
1.077 106.97 -166.25 111.58 1.517
CR3 CR2
1.077 106.97
CR3 HR3
72.44 106.75 1.080
1.077 106.97 -45.59 108.47 1.419
CR3 ORB
1.425 110.10
79.09 111.58 1.517
CR3 CR2
CR3 HR3
1.425 110.10 -42.22 106.75 1.080
CR3 ORB
1.425 110.10 -160.24 108.47 1.419
ORH HRH
1.510 109.04
53.74 106.60 0.949
ORH HRH
1.077 105.93 175.53 106.60 0.949
ORH HRH
1.529 110.10 -69.15 106.60 0.949
ORB CBJ
1.517 109.47 -108.48 118.63 1.365
ORB CBJ
1.529 108.47 129.56 118.63 1.365
1.080 109.60
13.36 118.63 1.365
ORB CBJ
1.419 118.63 -65.09 118.63 1.551
CBJ CBA
1.419 118.63 119.75 118.72 1.322
CBJ CET
9
170
1.23
11 .0a
CBA
OB1 1.365 11.6
Crp
CBJ CBA
OB2 1.365 118.63
-1.65 115.51 1.232
CBJ CBA
OBI 1.322 122.46
-5.95 115.09 1.233
CBJ CBA
OB2 1.322 122.46 173.32 115.51 1.232
CBJ CET HETI 1.365 118.72 175.88 119.45 1.072
CBJ CET HET2 1.365 118.72
-3.55 120.95 1.077
CBJ CET HET1 1.551 122.46
0.93 119.45 1.072
CBJ CET HET2 1.551 122.46 -178.51 120.95 1.077
CR1 *CR6
HR6
1.325 121.74
-0.44 116.08 1.074
HR2 *CR2
CR3
1.329 118.92
-1.23 119.09 1.517
HETI *CET
HET2 1.322 119.45
0.32 119.60 1.077
CR5
CR5
CR2
CR2
CR2
CR2
CR2
CR2
CR2
CR2
CR2
CR2
CR1
CR1
CR1
CR1
CR1
CR1
CR1
CR1
CR4
CR4
CR4
CR4
CR4
CR4
CR4
CR4
CR4
CR4
CR4
CR4
CR3
CR3
CR3
ORB
ORB
CR4
CR3
ORH
CR6
CRA
CR6
CRA
CR4
HR3
ORB
CR4
HR3
ORB
CR5
HR6
CR5
HR6
ORI
CHARMM Topology Parameters for Citrulline
RESI CIT
GROUP
ATOM N
0.00
NH1
Citrulline
-0.47
118
ATOM HN
H
0.31
ATOM CA
CT1
0.07
ATOM HA
HB
0.09
GROUP
ATOM CB
CT2
-0.18
ATOM HB1 HA
0.09
ATOM HB2 HA
0.09
GROUP
ATOM CG
CT2
-0.18
ATOM HG1 HA
0.09
ATOM HG2 HA
0.09
GROUP
ATOM CD
CT2
0.20
ATOM HD1 HA
0.09
ATOM HD2 HA
0.09
ATOM NE
NC2
-0.70
ATOM HE
HC
0.44
ATOM CZ
C
0.63
ATOM OH2 0
-0.75
ATOM NH2 NC2
-0.60
ATOM HH21 HC
0.30
ATOM HH22 HC
0.30
GROUP
ATOM C
C
0.51
ATOM 0
0
-0.51
BOND CB CA CG CB CD CG NE CD CZ NE
BOND NH2 CZ N HN N CA
CA C +N CA HA CB HB1
BOND C
BOND CB HB2 CG HG1 CG HG2 CD HD1 CD HD2
BOND NE HE NH2 HH21 NH2 HH22
DOUBLE 0 C
CZ OH2
IMPR N -C CA HN
C CA +N O
IMPR CZ OH2 NH2 NE
DONOR HN N
DONOR HE NE
DONOR HH21 NH2
DONOR HH22 NH2
ACCEPTOR 0 C
119