Molecular Control Engineering
From Enzyme Design to Quantum Control
Raj Chakrabarti
School of Chemical Engineering
Purdue University
What is Molecular Control Engineering?
Control engineering: Manipulation of system dynamics through nonequilibrium
modeling and optimization. Inputs and outputs are macroscopic variables.
Molecular control engineering: Control of chemical phenomena through microscopic
inputs and chemical physics modeling. Adapts to changes in the laws of Nature at
these length and time scales.
Aims



Reaching ultimate limits on product selectivity
Reaching ultimate limits on sustainability
Emulation of and improvement upon Nature’s strategies
Approaches to Molecular Optimization and Control
Static Optimization
Dynamic Control
milliseconds,
micrometers
Control of Biochemical
Reaction Networks
Molecular Structure/Function
Optimization: Enzyme Design
picoseconds,
nanometers
[protein pic]
femtoseconds,
angstroms
ms
Coherent Control of
Chemical Reaction Dynamics
How enzymes work
How to design them?
What makes them optimal for catalysis,
and how to improve?
Problem: hyperastronomical sequence
space
Catalytic Mechanisms of Enzymes
General acid/base
Y159
Electrostatic stabilizer
Lys65
Catalytic nucleophile
Glu-299
Catalytic
Nucleophile Ser62
DD-peptidase
General acid/base
Glu-200
b-gal
A model fitness measure for enzyme sequence optimization
slack variable
N 1 N

J seq   Gbind seq    ij rij,hbond  rij seq    ij2

i 1 j 1
Enzyme-substrate
binding affinity
Catalytic constraint: interatomic
distances rij < hbond dist
• Minimize J over sequence space
• Represent dynamical constraint with requirement that total energy of complex
minimized for any sequence
• Omits selection pressure for product release
The physics in the model: sequence optimization requires accurate
energy functions and solvation models
S-GB continuum solvation
10o resolution rotamer library (297 proteins)
Xiang, Z. and Honig, B. (2001) J. Mol. Biol. 311: 421-430.
Ghosh, A., Rapp, C.S. & Friesner, R.A. (1998)
J. Phys Chem. B 102, 10983-10990.
OPLS-AA molecular mechanics force field + Glidescore semiempirical binding affinity scoring function
Friesner, R.A, Banks, J.L., Murphy, R.B., Halgren, T.A. et al. (2004) J. Med. Chem. 47, 1739-1749.
Jacobson, M.P., Kaminski, G.A. Rapp, C.S. & Friesner, R.A. (2002) J. Phys. Chem. B 106, 11673-11680.
Computational sequence optimization correctly predicts most residues in
ligand-binding sites and enzyme active sites
Streptavidin
kcal/mol
Native –10.04
CO2- is covalent attachment site
for biomolecules
9 / 10 residues predicted correctly in top 0.5 kcal/mol of sequences
Chakrabarti, R., Klibanov, A.M. and Friesner, R.A. Computational prediction of native protein ligand-binding and enzyme
active site sequences. PNAS, 2005.
Computed amino acid distributions contain
detailed evolutionary information
0.6
Native –8.81
Glucose-binding protein
0.5
Observed
(sequence alignment)
Frequency
kcal/mol
0.4
0.3
0.2
0.1
0
Epimeric
promiscuity
Anomeric promiscuity
0.6
DA F R S Q E Y H I L K N G T WV M
0.5
Computed
Frequency
0.4
OH
0.3
0.2
0.1
OH
0
D A F R S Q E Y H I
L K N G T W V M
• Computed residue frequencies often mirror
natural frequencies
Chakrabarti, R., Klibanov, A.M. and Friesner, R.A. PNAS, 2005.
Catalytic constraints shift sequence distributions
and are associated with “evolutionary temperatures”
0.45
Fraction of total
sequences
0.4
+2 kcal/mol
0.35
0.3
+ 1 kcal/mol
0.25
0.2
0.15
Constrained
0.1
0.05
0
0
1
2
3
4
5
6
0 1
7
2
3 4
5
6 7
8
9 10
Number of residues correctly predicted
Max entropy distributions
~ single moment, evolutionary T
1
S  ln Z  seq  
Gbind  seq   Gbind ,opt
T0
multiple moments, evolutionary T’s
N 1 N
1
1
S  ln Z  seq  
Gbind  seq   Gbind ,opt  
rij  seq   rhbond
T0
T
i 1 j 1 ij
N 1 N
 1

 1

1
Z   exp  Gbind seq   Gbind,opt dseq Z   exp    Gbind  seq   Gbind ,opt    rij  seq   rhbond dseq
i 1 j 1 Tij
 T0

 T0

DD-peptidase
b-gal
High-resolution sequence optimization is robust across diverse functional families
Peptide
Nucleotide
Sugar
Computational active site optimization is structurally accurate
to near-crystallographic resolution
Rmsd to native (A)
1.2
1
0.8
0.6
0.4
0.2
0
Phe120 Asn161 Trp233 Arg285 Thr299
Ser326
Ser62
Lys65
Tyr159
Reviews on Computational Sequence Optimization and Designability of Enzymes
Nature Chemical Biology Volume 4 Number 5 May 2008:
“In a study by Chakrabarti et al. it was suggested that different enzyme active sites in
natural proteins vary in their designability – that is, the number of sequences that are
compatible with a specified structure and function.”
Chakrabarti R. Klibanov AM, Friesner RA. Sequence optimization and
designability of enzyme active sites. Proc Natl Acad Sci USA 102:1203512040, 2005
Current Opinion in Biotechnology Volume 18 2007:
•“ …Chakrabarti et al. found that they could recover the majority of wild type enzyme
sequences by optimizing enzyme-substrate binding affinity while imposing geometric
constraints on catalytic side-chain conformations.”
• “…Work by Chakrabarti et al. May also be useful for guiding the search for protein
scaffolds suitable for introduction of de novo activity.”
“Of Outstanding Interest”: Chakrabarti R, Klibanov AM, Friesner RA.
Computational prediction of native protein-ligand binding and enzyme
active site sequences. Proc Natl Acad Sci USA 102: 10153-10158, 2005.
Sirtuin enzymes and regulation of age-related physiology
2008: GSK acquires
Sirtris Pharmaceuticals for
US $700 M
2010: Pfizer contests efficacy
of drug leads from Sirtris
experimental screening
Sinclair DA. (2005) Mech. Ageing Dev. 126:987–1002
Brooks CL, Gu W. (2008) Cancer Cell 13:377–78
Brooks CL, Gu W. (2009) Nat. Rev. Cancer 9:123–28
Luo J, Nikolaev AY, Imai S, Chen D, Su F, et al. (2001) Cell 107:137–48
Vaziri H, Dessain SK, Eaton EN, Imai SI, Frye RA, et al. (2001) Cell 107:149–59
2010: GSK terminates drug
development of several
sirtuin activators
Sirtuin enzymatic activities
 Sirtuins control metabolic
pathways and aging through
amino acid deacetylation
 Feedback regulated by their
reaction byproducts
Michan S and Sinclair D (2007) Biochem J 404, 1-13.
Computational sequence optimization and experimental mutagenesis of Sirtuins
Example of screening focused
library of sequence variants
3 permissible mutations identified by
modeling at a target position
3 positions subject to mutagenesis
43 mutation combinations
= 64 sequence variations
Synthetic gene assembly and variant
library construction via DNA synthesis
0.4
0.7
0.35
0.6
0.3
0.5
0.25
0.3
0.35
0.25
0.4
0.2
0.15
0.3
0.15
0.1
0.2
0.1
0.05
0.1
0.05
0.2
0
D A
F
R
S
N
E Y
H
I
L
K
N G
T W V
C
0
Biological selection of variant library
0
D A F R S N E Y H I L K N G T W V C
D A F R S N E Y H I L K N G T W V
New enzymes Improved catalytic turnover
Altered substrate selectivity
From Enzyme Design to Dynamic Bionetwork Control
•
Maximizing kcat/Km of a given enzyme does not always maximize the fitness of a
network of enzymes and substrates
•
More generally, modulate enzyme activities in real time to achieve maximal
fitness or selectivity of chemical products
•
Lessons for control of metabolic networks via drug dosage (e.g. sirtuin inhibitors)
The Polymerase Chain Reaction: An example of
bionetwork control
Nobel Prize in Chemistry 1994; one of the
most cited papers in Science (12757 citations
in Science alone)
Produce millions of DNA molecules starting
from one
Used every day in every Biochemistry and
Molecular Biology lab ( Diagnosis, Genome
Sequencing, Gene Expression, etc.)
March 2005: Roche Molecular Diagnostics PCR patents expire
2008-2012: Celera and New England Biolabs License Chemical
PCR Patents; Roche negotiates for Chemical PCR Patents
Single Strand
– Primer
Duplex
Extension
D  S1  S2
k1m , k2m
DNA Melting
DNA Melting
Again
S1  P1  S1P1
k11 ,k21
k1 ,k2
S2  P2 
 S2 P2
2
2
Primer
Annealing
ke ,k  e
SP  E 
 E.SP
k n , k n
E.SP  N 
[ E.SP.N ] kcat
 E.D1
k n , k n
E.D1  N 
[ E.D1.N ] kcat
 E.D2
.
E.DN kcat

 E  DNA
'
k11t ,k21 t
S1  S2  DNA
3/19/2016
School of Chemical Engineering, Purdue
University
19
PCR and Disease Diagnostics
Trinucleotide Repeat Diseases



Huntington’s Disease
Muscular Dystrophy
Fragile X (Autism’s leading cause)
Race for Diagnostic Methods: Standard PCR generally fails due to
nonspecific amplification. First FDA-compliant Fragile X test based on
Chemical PCR
Chemical PCR: uses solvent engineering of PCR reaction media, to alter
kinetic parameters of the reaction network and enable sequencing of
untractable genomic DNA
R. Chakrabarti and C.E. Schutt, Nucleic Acids Res., 2001
R. Chakrabarti and C.E. Schutt, Gene 2002
R. Chakrabarti, in PCR Technology: Current Innovations, 2003
R. Chakrabarti and C.E. Schutt, Chemical PCR: Compositions for enhancing polynucleotide
amplification reactions. US Patent 7.772.383, issued 8-10-10.
R. Chakrabarti and C.E. Schutt, Compositions and methods for improving polynucleotide amplification
reactions using amides, sulfones and sulfoxides: II. US Patent 7.276,357, issued 10-2-07.
R.Chakrabarti and C.E. Schutt, US Patent 6,949,368, issued 9-27-05.
Parallel Parking and Bionetwork Control
 Stepping on gas not enough: can’t move directly in direction of interest
 Must change directions repeatedly
 Left, Forward + Right, Reverse enough in most situations
 Tight spots: Move perpendicular to curb through sequences composed
of Left, Forward + Left, Reverse + Right, Forward + Right, Reverse
The DNA Amplification Control Problem and Cancer Diagnostics
Wild Type
DNA
Mutated
DNA
 Can’t maximize concentration of target DNA sequence by maximizing any individual kinetic
parameter
 Analogy between a) exiting a tight parking spot
b) maximizing the concentration of one DNA sequence in the presence of
single nucleotide polymorphisms
Optimal Control of DNA Amplification

Min C DNA t f   C
T (t )

max 2
DNA
dx
 f  x, T 
dt
x  CS1 , CS 2 ,.....C E . D1 .....C DNA
st


Tr
For N nucleotide template –
2N + 4 state equations
Typically N ~ 103
R. Chakrabarti et al. Optimal Control of Evolutionary Dynamics, Phys. Rev. Lett., 2008
K. Marimuthu and R. Chakrabarti, Optimally Controlled DNA amplification, in preparation
From bionetwork control to coherent control of chemical
processes
 FMO photosynthetic protein complex transports solar energy with ~100% efficiency
 Phase coherent oscillations in excitonic transport: exploit wave interference
 Biology exploits changes in the laws of nature in control strategy: can we?
Coherent Control versus Catalysis
 Potential Energy Surface
with two competing
reaction channels
 Saddle points separate
products from reactants
 Dynamically reshape
the wavepacket traveling on the
PES to maximize the probability
of a transition into the desired
product channel
probability
density
time
interatomic
distance
C. Brif, R. Chakrabarti and H. Rabitz, New J. Physics, 2010.
C. Brif, R. Chakrabarti and H. Rabitz, Control of Quantum Phenomena.
Advances in Chemical Physics, 2011.
Femtosecond Quantum Control Laser Setup
2011: An NSF funded quantum control experiment collaboration between
Purdue’s Andy Weiner (a founder of fs pulse shaping) and Chakrabarti Group
Coherent Control of State Transitions in Atomic Rubidium
R. Chakrabarti, R. Wu and H. Rabitz, Quantum Multiobservable Control. Phys. Rev. A, 2008.
R. Chakrabarti, R. Wu and H. Rabitz, Quantum Pareto Optimal Control. Phys. Rev. A, 2008.
Few-Parameter Control of Quantum Dynamics
 Conventional strategies based on
excitation with resonant frequencies fails to
achieve maximal population transfer to
desired channels
 Selectivity is poor; more directions of
motion are needed to avoid undesired
states
Optimal Control of Quantum Dynamics
 Shaped laser pulse generates all
directions necessary for steering system
toward target state
 Exploits wave-particle duality to achieve
maximal selectivity, like coherent control
of photosynthesis
A Foundation for Quantum System Control
K. Moore, R. Chakrabarti, G. Riviello and H. Rabitz, Search Complexity and Resource Scaling
for Quantum Control of Unitary Transformations. Phys. Rev. A, 2010
R. Wu, R. Chakrabarti and H. Rabitz, Critical Topology for Optimization on the Symplectic
Group. J Opt. Theory, 2009
R. Chakrabarti and H. Rabitz, Quantum Control Landscapes, Int. Rev. Phys. Chem., 2007
R. Chakrabarti, Notions of Local Controllability and Optimal Feedforward Control for Quantum
Systems. J. Physics A: Mathematical and Theoretical, 2011.
R. Chakrabarti and A. Ghosh. Optimal State Estimation of Controllable Quantum Dynamical
Systems. Phys. Rev. A, 2012.
.
Summary
• Can reach ultimate limits in sustainable and selective chemical
engineering through advanced dynamical control strategies at
the nanoscale
• Requires balance of systems strategies and chemical physics
• New approaches to the integration of computational and
experimental design are being developed
Reviews of our work
Protein Design and Bionetwork Control

“Progress in Computational Protein Design”, Curr. Opin. Biotech., 2007

“Do-it-yourself-enzymes”, Nature Chem. Biol., 2008

R. Chakrabarti in PCR Technology: Current Innovations, CRC Press, 2003.

Media Coverage of Evolutionary Control Theory: The Scientist, 2008.
Princeton U Press Releases
Quantum control

R. Chakrabarti and H. Rabitz, “Quantum Control Landscapes”, Int. Rev. Phys. Chem.,
2007

C. Brif, R. Chakrabarti and H. Rabitz, “Control of Quantum Phenomena”
New Journal of Physics, 2010; Advances in Chemical Physics, 2011

R. Chakrabarti and H. Rabitz, Quantum Control and Quantum Estimation Theory,
Invited Book, Taylor and Francis, 2013.