SUPPLEMENTARY MATERIALS
SP1. Analyses of MD Simulations (RMSD, Evaluation of Protein–Ligand Interactions
and H-Bond Statistics)
For each trajectory, the root-mean-square deviation (RMSD) values from the initial
structure of the backbone atoms of the transporter were monitored. The average RMSD
values for all simulations were approximately 1.6–2.1 Å for the entire structure. The
RMSD values for the core region forming the binding pocket of WT-LeuT were smaller,
fluctuating around a mean of 1.3–1.6 Å. Replacement of three side-chains in the core
domain led to higher RMSD values of 1.9–2.2 Å. Nevertheless, the protein backbone
RMSD for wild-type and mutant structures were similar to those reported for simulations
of a variety of other proteins1. The trajectories obtained from MD simulations were used
to perform analyses of H-bond statistics. H-bond statistics were obtained for every
transporter–substrate complex by computing the average distance and angle between a
light or heavy donor and heavy acceptor from 30 ns of the simulation. An H-bond was
defined by a heavy donor–heavy acceptor distance of 3.5 Å, a light donor–heavy
acceptor distance of 3.5 Å, and the allowed deviation from linearity was 60° (in
accordance with previously reported algorithms2).
The decomposition of protein–ligand interactions (EAA,int) into specific electrostatic and
non-electrostatic contributions can be used for indirect measurement on the role of the
specific residue in the substrate binding. Furthermore, adjustments of the contributions
of specific residues (EAA,int) to different substrates relative to the native substrate
offers an opportunity to understand the mechanism of substrate specificity at the atomic
level. The average difference in the transporter–substrate interaction energies between
native substrate (leucine) and two other ligands presented in the living cell (glycine and
alanine) from MD simulations can be expressed as:
N res
Eint   E AA,int
(1 )
1
vdW
vdW
Elec
Elect
E AA,int  ( E AA
,Substrate  E AA,Leu )  ( E AA,Substrate  E AA,Leu ) ( 2 )
where EAA,int is the interaction free energy between the bound substrate and a specific residue in the
transporter, and Nres is the total number of residues. EAA,int can be further decomposed to the
electrostatic contribution ( EAA,elec) and the van der Waals contribution (EAA,vdW) to the transporter–
substrate interaction energies.
Equation 2 assumes similar conformational changes in addition to similar entropy
changes of leucine, alanine and glycine binding to LeuT. In the following,  refers to the
absolute free energies or differences in protein-substrate bound and substrate-free
states, and  represents the transporter–substrate thermodynamic properties
(interaction energies or binding free energies) relative to the transporter–native ligand
(leucine) complex. Based on the MD trajectories for wild-type and mutant forms of
LeuT–substrate complexes, the changes in the van der Waals and electrostatic
interaction energies upon binding were calculated with unit dielectric constant and
SP1
infinite cut-offs. This analysis is similar to the well-developed method combining
molecular mechanics (MM) with approaches based on continuum electrostatic
approaches (Poisson-Boltzman (PB) or generalized Born (GB)) and solvent accessible
area (SA), generally known as MM/PBSA algorithm. This approach consists of
averaging the results of PB and MM computations over an ensemble of snapshots
generated by MD simulations3. It was shown than MM/PBSA can efficiently evaluate
protein–ligand interaction energies and, thus, provides an excellent tool for monitoring
adjustments in the interaction caused by a specific ligand. However, the accurate
estimation for the remaining contributions such as, for example, the orientational
dynamics of a ligand in the binding pocket and changes in the ligand conformation upon
transfer from the bulk phase to the binding pocket, represents a challenge within the
canonical MM/PBSA scheme. A convenient alternative, although it is computationally
expensive, is to use free-energy-simulation techniques together with the results from
equilibrium MD simulations.
SP2. Absolute Binding Free Energy: Theory
The present study is the first report of the application of combined MD and FEP
simulations for the study of absolute free energy of substrate binding to a membrane
transporter with a known high-resolution structure. Detailed theoretical foundations for
evaluation of equilibrium binding constants and standard binding free energies were
elaborated by Deng and Roux4, and Wang et al.5. Under the assumption of low ligand
concentration in solution, the equilibrium binding constant Kb can be expressed as:
Kb 


bulk
site
d ( L ) d ( X )e U
d ( L ) ( rL  r* ) d ( X )e U
; (3)
where L is the coordinates of the ligand, X is a collective coordinate of solvent and protein atoms, U is the
total potential energy of the system, rL is the position of the centre-of-mass of the ligand and r* is the
arbitrary position in the bulk solution. Subscript ‘site’ and ‘bulk’ indicate that this integration accounts only
for configurations in which the ligand is either bound or free in bulk solution.
It can be shown that the reversible work for the entire association and dissociation
process can be broken down into eight sequential steps by turning interactions on or off
(i.e. electrostatic, van der Waals and orientational restraints) between the substrate and
receptor. The use of an extensive set of constraints is unavoidable to ensure that the
ligand is kept to selected average conformations. The key assumption of this method is
that relatively small conformational changes occur upon ligand transfer from bulk phase
to the protein-binding pocket. Restraining the ligand around experimentally derived
geometry helps to focus on the contribution from the most relevant binding
conformations to the absolute binding free energy. The biasing constraints acting on the
system can be removed rigorously in the post-simulation analysis.
This theoretical approach to protein–ligand association is based on the early theory
developed by Hermans and Shankar6,7, which gave rise to a variety of modern methods.
The evaluation of binding free energies with FEP simulations allows explicit
SP2
quantification of substrate and receptor dynamics, and exhibits computational
advantages, for example, many steps (or windows) can be run simultaneously on multiprocessor clusters.
The resulting absolute free energy of binding can be given as:
0
site
Gbind
 Gcsite  Gtsite  Grsite  Gint
 k BT ln( Fr ) 
hydration
k BT ln( Ft C 0 )  Gint
 Gchydration
(4)
where Gcsite corresponds to the reversible work in the presence of the conformation-constraining
potential uc applied to the fully interacting ligand in the binding site, Gtsite is determined similarly to uc but
the potential ut acts on a centre-of-mass to maintain its relative position in the binding site, Grsite is the
reversible work due to the rotational restraints applied on the substrate. Gintsite is the reversible work in
which all interactions between the ligand and the binding site are turned off while all restraints are acting
on the system. Grsite and Gintsite correspond to the standard free energy of hydration for the ligand in
bulk solution. Fr and Ft rotational and translational factors evaluated by the integration over relevant
degrees of freedom. C0 is a conversion factor to the standard concentration = 1M or 1/1661 A°3).
Every term, with the exception of the translational and orientational factors of the ligand,
can be estimated using FEP simulations, and the effect of the biasing potential is
removed at post-analysis using a weighted histogram method8,9. The constant C0
ensures the use of the standard state concentration.
It is advantageous to the understanding of this complex approach to re-write equation 2
in another form:
G 0
 G  G  G 0  Gr ,
(5)
bind
int
c
t
where Gint  Gsiteint  Gbulkint corresponds to the free energy differences in the
interactions of the ligand with site or bulk solutions. Got  Gsitet  kBTln (FtCo), and
Got  Gsiter  kBT ln(Fr) corresponds to the conformational, translational and
orientational restrictions of the ligand upon binding.
The physical meaning of the absolute free energy decomposition is a genuine concern
for any free energy simulation. Although, the free-energy decomposition of the nonbond interactions depends on the order in which these contributions are activated or
deactivated, the mathematical definition for every term must be rigorously
unambiguous. Furthermore, it should be emphasized that the arbitrary free energy
decomposition does not affect the absolute free energy of binding, which is a pathindependent property. Unlike classical thermodynamical integration schemes, the
method used here computes the reversible work needed for insertion of the ligand in a
step-by-step process: first, the repulsive LJ part; second, the attractive dispersive part of
van der Waals; and third, the electrostatics. The physical meaning of each step is clear,
but the quantities determined hereare only for shedding light on the analysis of the
molecular determinants of tight binding. Any decomposition is somewhat arbitrary, but
the evaluation that reversible work is undertaken in a step-wise manner is physically
sound5. The analysis of different contributions to the free energy should be undertaken
SP3
with care. In this work, the notions of electrostatic, van-der-Waals and spatial
contributions refer readily to the choice of the path used to obtain the term, that is,
charging or uncharging, WCA decomposition and scaling of the spatial constraints.
Therefore, the decomposition of the absolute free energy in this paper is used only to
provide qualitative concepts such as general importance of the relative change in the
non-bond interactions upon binding.
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SP4