Can free energy perturbation simulations coupled with replica-exchange molecular dynamics study ligands with distributed binding sites?

Abstract

Free energy perturbation coupled with replica-exchange with solute tempering (FEP/REST) offers a rigorous approach to compute relative free energy changes for ligands. To determine the applicability of FEP/REST for the ligands with distributed binding poses, we considered two alchemical transformations involving three putative inhibitors I0, I1, and I2 of the Venezuelan equine encephalitis virus nuclear localization signal sequence binding to importin-$\alpha$ $\left(\mathrm{i}\mathrm{m}\mathrm{p}\alpha \right)$ transporter protein. I0→I1 and I0→I2 transformations respectively increase or decrease the polarity of the parent molecule. Our objective was three-fold - (i) to verify FEP/REST technical performance and convergence, (ii) to estimate changes in binding free energy $\mathrm{\Delta }\Delta G$, and (iii) to determine the utility of FEP/REST simulations for conformational binding analysis. Our results are as follows. First, our FEP/REST implementation properly follows FEP/REST formalism and produce converged $\Delta \Delta G$ estimates. Due to ligand inherent unbinding the better FEP/REST strategy lies in performing multiple independent trajectories rather than extending their length. Second, I0→I1 and I0→I2 transformations result in overall minor changes in inhibitor binding free energy, slightly strengthening the affinity of I1 and weakening that of I2. Electrostatic interactions dominate binding interactions determining the enthalpic changes. The two transformations cause opposite entropic changes, which ultimately govern binding affinities. Importantly, we confirm the validity of FEP/REST free energy estimates by comparing them with our previous REST simulations directly probing binding of three ligands to $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$. Third, we established that FEP/REST simulations can sample binding ensembles of ligands. Thus, FEP/REST can be applied to (i) study the energetics of the ligands binding without defined poses and showing minor differences in affinities $\left|\Delta \Delta G\right|\lesssim 0.5\mathrm{k}\mathrm{c}\mathrm{a}\mathrm{l}/\mathrm{m}\mathrm{o}\mathrm{l}$ and (ii) to collect ligand binding conformational ensembles.

Introduction

Evaluating the binding free energy $\Delta G$ of a ligand to a protein target is a critically important step in computer-aided drug design and medicinal chemistry in general.¹ These computations guide the development of small molecule inhibitors that affect protein function, induce desired protein conformational changes, or play a central role in assessing protein-protein or protein-nucleic acid interactions. Free energy perturbation (FEP) is a theoretically rigorous method for computing $\Delta G$, which traces its roots to the Zwanzig formalism from the 1950s.² As a rule, FEP applications utilize all-atom explicit solvent models and molecular dynamics simulations. The first FEP simulations were reported more than 40 years ago,³ and since that time, due to continuous advances in biomolecular force fields, sampling algorithms, data processing, and not the least computational power, FEP has become a standard tool in drug development, particularly in lead optimization efforts.⁴ FEP simulations may estimate the absolute free energy of binding, namely $\Delta G$, or compute the relative changes in binding free energy $\Delta \Delta G$.^4,5 The latter is methodologically simpler and can be directly applied in lead optimization efforts. In principle, FEP can significantly reduce the time required for pharmaceutical drug development thus explaining the attention to this methodology in industry.

One of the principal, long-standing challenges in FEP application is conformational sampling.^6,7 If a ligand assumes a well-defined binding pose and its alchemical transformation involves few heavy atoms, then one may expect a limited impact of the transformation on the binding pose. In this case, the traditional FEP implementation may suffice, which relies on producing a continuous molecular dynamics trajectory sampling the alchemical transformation of a ligand at a constant temperature. However, limited overlap between the states collected at adjacent alchemical strata may render even this simple transformation challenging to converge⁷ skewing the evaluation of $\Delta \Delta G$. If a ligand changes binding poses or the protein undergoes conformational changes, the traditional FEP strategy likely becomes inadequate. This problem is further compounded if a ligand exhibits multiple binding sites and/or its binding site is distributed lacking a specific pose. To address such cases, FEP methodology was coupled with replica exchange with solute tempering (REST), as pioneered in the development of commercial FEP + platform.⁸ Combination of FEP with REST allows one to enhance conformational sampling by tempering the region affected by alchemical transformation. In FEP/REST simulations, multiple replicas of the simulation system are created, each featuring a unique combination of coupling parameter $\lambda$ governing alchemical transformation and temperature $T$. Depending on the specific version of REST, $T$ can be used to perform “targeted” heating of a ligand and, possibly, adjacent protein amino acids by scaling down their interactions thus effectively implementing Hamiltonian-like replica exchange.^8–10 For computational efficiency, the arrangement of FEP/REST replicas is typically one-dimensional, in which $T$ assumes physiological value at $\lambda =0$ and 1, while exponentially increasing in the interval $0<\lambda \le 0.5$ and exponentially decreasing at $0.5<\lambda <1$. Because FEP/REST simulates multiple replicas in parallel, it requires significantly more computational resources than traditional FEP, but in return FEP/REST can reduce errors in $\Delta \Delta G$ down to 1 kcal/mol.¹¹ The successes and challenges in using FEP/REST simulations for drug development have been recently reviewed.¹²

Although FEP/REST offers a considerable enhancement in conformational sampling, its implementation is not straightforward. One of main issues is sampling convergence, which has received surprisingly little attention in the literature. A typical sampling time in FEP/REST per replica is about 5 ns,¹¹ but there have been few systematic studies checking the adequacy of this timescale for converged $\Delta \Delta G$ estimates.¹³ The issue of FEP/REST timescales is exacerbated by the following circumstance. FEP/REST simulations differ conceptually from non-FEP simulations, because the former are inherently expected to sample exclusively bound or exclusively unbound states, whereas the latter do not face such restrictions. With a brute-force increase in the length of FEP/REST trajectories, ligands will inevitably unbind violating FEP premises. Another, closely related issue is associated with the scope of FEP/REST conformational sampling. Does the simulation sample all relevant ligand bound states? This question is particularly serious if the ligand adopts multiple bound poses and it is a priori unclear if all of them are adequately sampled by FEP/REST or if they should be evaluated by separate FEP/REST simulations and then processed according to multiple binding site formalism.^14,15 A third issue arises for the ligands binding without adopting well-defined binding sites.¹⁶ Incidently, this case would be particularly difficult for a standard FEP protocol due to the requirement for extensive and exhaustive conformational sampling of distributed poses. FEP/REST simulations executing an equilibrium walk of such ligands over all their binding locations can potentially provide an unbiased binding free energy, but close monitoring of simulation convergence is critical.

In this paper, we investigate some of these issues in FEP/REST implementation by selecting small ligand inhibitors of Venezuelan equine encephalitis virus (VEEV). This virus has been shown to interfere with nucleocytoplasmic trafficking.¹⁷ Specifically, its capsid protein contains a nuclear localization signal (NLS) recognizing the nuclear transport protein importin-$\alpha$ $\left(\mathrm{i}\mathrm{m}\mathrm{p}\alpha \right)$ and a nuclear export signal (NES) binding to the nuclear export protein CRM1.^18,19 Together with these proteins and importin-$\beta$ VEEV capsid forms a complex, which obstructs nucleocytoplasmic trafficking through a nuclear pore channel.¹⁹ Consequently, weakening the binding of VEEV capsid NLS to $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$ may represent a viable therapeutic strategy.^20–22 Implementing this approach the CL6662 scaffold ligands from the Queensland Compound Library Open Scaffolds collection²³ have been considered as VEEV inhibitors.²⁴ In particular, the compound G281–1485 denoted as I0 in Fig. 1a exhibits a good inhibition with half-maximum inhibitory and effective concentrations ${\mathrm{I}\mathrm{C}}_{50}=12\mu \mathrm{M}$ and ${\mathrm{E}\mathrm{C}}_{50}=7.5\mu \mathrm{M}$, respectively. Another related, more polar compound G281–1564 (I1 in Fig. 1a) has moderate inhibition with ${\mathrm{I}\mathrm{C}}_{50}=25\mu \mathrm{M}$ and ${\mathrm{E}\mathrm{C}}_{50}=10.8\mu \mathrm{M}$. One of the putative mechanisms of their antiviral activity involves direct binding of these ligands to major NLS binding site on $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$²⁵ (see discussion in Supporting Information (SI)). To investigate this putative inhibitory mechanism, our previous study used REST simulations to probe I0, I1 and their hydrophobic derivative I2 (Fig. 1a) binding to $\mathrm{i}\mathrm{m}\mathrm{p}\alpha .$²⁶ We showed that none of these ligands adopt a single, high affinity binding pose in the proximity of major NLS binding site. Instead these compounds exhibit a distributed binding, albeit each to different extent, around the VEEV NLS binding site. Consequently, I0–I2 compounds appear as good candidates for testing the FEP/REST protocol against the ligands lacking well-defined binding sites. To this end, we considered here two inhibitor alchemical transformations (Fig. 1b), for which we performed multiple FEP/REST simulations allowing us to probe the convergence of $\Delta \Delta G$ values, quantify the energetics of inhibitor binding, and assess binding sampling. The accuracy of FEP/REST simulations is further assessed by comparing with our previous unbiased REST simulations probing binding of the same inhibitors to $\mathrm{i}\mathrm{m}\mathrm{p}\alpha .$²⁶ Thus, the main objective of this paper is a systematic assessment of the performance of FEP/REST applied to the ligands with distributed binding sites.

Figure 1:

(a) Inhibitors considered in this study. Arrows show the modifications in I0 structure, I0→I1 and I0→I2. The differences in I1 and I2 compared to I0 are highlighted in yellow. I1 is more polar than I0 due to two fewer carbons, whereas I2 is more hydrophobic due to N to C substitution. (b) Thermodynamic cycle showing the transformation from wild-type ligand I0 into mutant $\mathrm{I}X$. Plus and colon represent unbound and bound states. (c) A snapshot of the ligand bound to $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$. The blue spheres indicate carbons annihilated upon I0→I1 transformation, whereas the orange sphere marks the removed nitrogen in I0→I2 transformation. MinNLS $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$ amino acids (see Model and Methods) are shown in dark grey with the rest of protein structure being in cartoon representation. This image was generated with ChimeraX.²⁹

Model and Methods

Simulation systems

We used all-atom isobaric-isothermal replica-exchange with solute tempering (REST) simulations coupled with free energy perturbation (FEP) to compute the change in binding free energy $\Delta \Delta G$ for the inhibitors binding to importin-$\alpha$ $\left(\mathrm{i}\mathrm{m}\mathrm{p}\alpha \right)$. We studied three ligands based off the G281 series available from the Queensland Compound Library’s Open Scaffolds collection.²³ These ligands shown in Fig. 1a include I0 (G281–1485, an octanol-water partition coefficient^27,28 $\mathit{\text{log}}P=5.1$), a less-hydrophobic variant with two fewer carbons I1 (G281–1564, $\mathit{\text{log}}P=4.4$), and a novel ligand derivative I2 with increased hydrophobicity due to a nitrogen to carbon substitution $(\mathit{\text{log}}P=5.7)$.²⁶

For our FEP/REST simulations, the CHARMM36 protein force field³⁰ was used to model $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$, and the CHARMM General Force Field³¹ (CGenFF force field v4.4 with v2.4 of the CGenFF program) was used to produce ligand force field parameters. Water was represented with the CHARMM-modified TIP3 model.^32,33 Initial structures of the inhibitors complexed with $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$ were taken from our previous study, which used unbiased REST simulations to examine their binding.²⁶ Murine $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$ structure was taken from PDB ID 3VE6 and truncated at the residue 211 to reduce computational costs but to retain the residues involved in the VEEV NLS binding. Therefore, after truncation the inhibitors still interact with the $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$ major NLS binding site, which is a plausible mode of their VEEV inhibitory effect.²⁴ Inhibitor-$\mathrm{i}\mathrm{m}\mathrm{p}\alpha$ complexes were solvated in 7715 water molecules, and the unbound systems with only the inhibitors included 8715 water molecules. In all systems, to set salt concentration at 150 mM 27 NaCl molecules were introduced, but five chloride ions were removed in protein-bound systems to keep their zero net charge. For all systems, the simulation box was initially set to the dimensions 59.6 Å × 59.6 Å × 79.1 Å.

FEP/REST protocol

The change of binding free energy $\Delta \Delta G$ is measured with respect to I0, i.e, it is treated as reference. To compute $\Delta \Delta G$ occurring upon I0→I1 or I0→I2, we used the thermodynamic cycle in Fig. 1b and express $\Delta \Delta G$ as

$$\Delta \Delta G=\Delta G_{\mathit{\text{bind}}}\left(IX\right)-\Delta G_{\mathit{\text{bind}}}\left(I0\right)=\Delta G_{\mathit{\text{bound}}}\left(I0\to IX\right)-\Delta G_{\mathit{\text{unbound}}}\left(I0\to IX\right),$$ (1)

where $\Delta G_{\mathit{\text{bound}}}$ and $\Delta G_{\mathit{\text{unbound}}}$ refer to the free energy differences upon mutating inhibitor I0 to $\mathrm{I}X$ in the bound and unbound states, respectively, $\Delta G_{\mathit{\text{bind}}}$ is the binding free energy, and $X=1$ or 2. Importantly, $\Delta G$ in either bound or unbound states can be decomposed into enthalpic and entropic contributions, i.e., $\Delta G=\Delta H-T\Delta S$. Computation of $\Delta G_{\mathit{\text{bound}}}$ or $\Delta G_{\mathit{\text{unbound}}}$ was performed using the dual topology method,³⁴ which represents both “wild-type” I0 and “mutant” $\mathrm{I}X$ within the same simulation system. For each inhibitor transformation two sets of simulations must be performed, either with the ligand bound to $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$ or in protein-free solvent.

In its traditional implementation,³⁵ replica exchange simulations evaluate $R$ replicas of a molecular system at different temperatures $T_r$. Periodic exchanges are attempted between neighboring temperatures to accelerate the exploration of conformational space within a thermodynamic ensemble. REST is an adaptation of traditional replica exchange, which, via Hamiltonian scaling, tempers a portion of the system, whereas the rest is kept “cold”. REST reduces the number of degrees of freedom subjected to exchange and thus reduces the number of replicas required to cover the wide temperature range while maintaining acceptable exchange rates. Several versions of REST scaling factors have been proposed, including those by Wang et al.¹⁰ and a reformulation utilized by Best et al.³⁰ and us.³⁶ In this work, we utilize the Wang et al. factors ${\beta }_r/{\beta }_0$, where ${\beta }_r=1/\left(R_g{T}_r\right)$ and $R_g$ is the gas constant, which scales solute energies. The advantage of Wang et al. approach is that the entire system is simulated at $T_0$, while solute is tempered to $T_r$ through scaling. Taking FEP and REST together, we write the system enthalpy

$$H_r=\left(1-{\lambda }_r\right)\frac{{\beta }_r}{{\beta }_0}{E}_{I0}+\left(1-{\lambda }_r\right)\sqrt{\frac{{\beta }_r}{{\beta }_0}}{E}_{I0,\mathit{\text{env}}}+{\lambda }_r\frac{{\beta }_r}{{\beta }_0}{E}_{IX}+{\lambda }_r\sqrt{\frac{{\beta }_r}{{\beta }_0}}{E}_{IX,env}+E_{env}+PV,$$ (2)

where ${\lambda }_r$ is the coupling parameter $\left(0\le {\lambda }_r\le 1\right)$ controlling the presence of inhibitor I0 or $\mathrm{I}X$ in the system enthalpy. When $r=0$ and ${\lambda }_0=0$, the energy of inhibitor $\mathrm{I}X{E}_{IX}$ and its interaction energy with the environment, namely, protein, water, and ions, $E_{IX,\mathit{\text{env}}}$ is removed. Similarly, when $r=R-1$ and ${\lambda }_{R-1}=1$, the energy terms associated with $I0$ vanish from Eq. (2). When $\lambda$ is between 0 and 1, the inhibitors I0 and $\mathrm{I}X$ coexist without interacting each other. The energy attributed to the environment, including protein, water, and ions, $E_{\mathit{\text{env}}}$, is not affected by ${\lambda }_r$. The scaling factor ${\beta }_r/{\beta }_0$ is applied to the inhibitor internal energies $E_{I0}$ and $E_{IX}$ effectively raising their temperature to $T_r$, whereas the interactions between inhibitors and the environment $E_{I0,\mathit{\text{env}}}$ and $E_{IX,\mathit{\text{env}}}$ are scaled by ${\left({\beta }_r/{\beta }_0\right)}^{1/2}$. The energy of the environment $E_{\mathit{\text{env}}}$ is not scaled by REST. Thus, Eq.(2) represents the enthalpy of the system at the condition $\left({\lambda }_r,T_r\right)$. According to the Metropolis criterion, replicas $m$ and $m+1$ at the conditions $\left({\lambda }_r,T_r\right)$ and $\left({\lambda }_{r+1},T_{r+1}\right)$, respectively, are exchanged with the probability $\omega =\mathit{m}\mathit{i}\mathit{n}\left(1,e^{-\Delta }\right)$, where $\Delta ={\beta }_0\left(H_r\left(x_{m+1}\right)-H_r\left(x_m\right)+H_{r+1}\left(x_m\right)-H_{r+1}\left(x_{m+1}\right)\right),x_m$ and $x_{m+1}$ are the coordinates of replicas $m$ and $m+1$. As a result, FEP/REST simulations perform a random walk of replicas over the conditions $\left({\lambda }_r,T_r\right)$.

FEP/REST simulations were executed using the program NAMD3, which implements a multicopy REST algorithm and was recently updated to permit FEP evaluation utilizing GPUs.³⁷ Temperature was controlled using Langevin dynamics with a damping coefficient of 5 ps⁻¹ and $T_0=310\mathrm{K}$. Pressure was set with the Langevin piston method keeping $P$ at 1 atm. Van der Waals interactions were slowly switched off in the interval from 8 to 12 Å, and electrostatics was computed with Ewald summation. To preserve integrator stability and accuracy of free energy evaluations, the integration step was set to 1 fs. Hydrogen associated covalent bonds were constrained with the ShakeH algorithm. In all, $R=16$ replicas were considered with FEP ${\lambda }_r$ varying linearly from 0 to 1 with the increment of 1/15 and REST scaling factors geometrically distributed in the range from $T_0=310$ to $T_7=1000\mathrm{K}$ for the first 8 replicas and from $T_8=1000$ to $T_{R-1}=310\mathrm{K}$ for the last 8 replicas (see SI for details). The electrostatic interactions of I0 were annihilated in the interval $0\le {\lambda }_r\le 0.5$, where those of $\mathrm{I}X$ were ignited at $0.5\le {\lambda }_r\le 1.0$. Van der Waals interactions of I0 and $\mathrm{I}X$ were scaled over the entire range of ${\lambda }_r$. A soft-core van der Waals shifting coefficient of 5 Ų was used to prevent atom overlap of alchemical atoms.³⁸ Importantly, according to the schedule $\left({\lambda }_r,T_r\right)$ shown in SI Table S1, the inhibitors I0 and $\mathrm{I}X$ are “fully expressed” at physiologically relevant conditions in the first $(r=0)$ and last $(r=R-1)$ replicas as required for proper evaluation of $\Delta G$. Replica exchanges were attempted every 2 ps. We have generated $N=10$ FEP/REST trajectories for bound simulations and $N=5$ for unbound simulations. In total, $3.2\mu \mathrm{s}$ was generated for each I0→IX bound simulations and $1.6\mu \mathrm{s}$ for each water simulation.

Computation of structural probes

Structural quantities were computed using VMD.³⁹ A contact between an inhibitor and an $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$ residue is formed if at least one pair of their heavy atoms occurs at a distance less than 4.5 Å apart. A ligand is bound to $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$ amino acid if there is at least one contact between them. The minNLS binding site⁴⁰ is defined in a similar way to include all $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$ residues bound to VEEV capsid protein NLS fragment KKPK in the PDB 3VE6 structure. With this definition, the minNLS binding site in Fig. 1c is composed of Ser35, Phe68, Trp72, Thr75, Asn76, Ala78, Ser79, Gly80, Thr81, Ser82, Thr85, Gln111, Trp114, Asn118, Asp122, Asn158, and Trp161. The ligand is considered bound, if it forms at least one contact with the minNLS binding site. Other definitions of binding are explored in SI. To quantify binding at intermediate $\lambda (0<\lambda <1)$, we used the range $\lambda <0.5$ for I0 and $\lambda >0.5$ for $\mathrm{I}X$.

Thermodynamic quantities, including the changes in free energy $\Delta G$, enthalpy $\Delta H$, and entropy $\Delta S$, were computed using the Multistate Bennett Acceptance Ratio (MBAR) methodology via pymbar 3.1.⁴¹ For bound simulation systems, the calculation of thermodynamic quantities was restricted to inhibitors located within the distance of less than 18Å from the center of mass of minNLS binding site. SI shows that restricting the inhibitors to those bound to minNLS amino acids or including all their poses even unbound have a negligible impact on thermodynamic quantities. Unless noted otherwise, simulation sampling errors are presented as the standard error of the mean, where each trajectory is used as an independent sample.

Results and Discussion

To estimate the change in free energy $\Delta \Delta G$ of inhibitor binding to $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$, we employed replica-exchange simulations with solute tempering (REST) coupled with free energy perturbation (FEP). In total, three inhibitors, I0, I1, and I2, were considered allowing us to evaluate two alchemical transformations I0→I1 and I0→I2 and compute $\Delta \Delta G$ for each.

Performance and convergence of FEP/REST simulations

In total, we generated ten FEP/REST trajectories of inhibitors bound to $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$ and five FEP/REST trajectories of inhibitors in water. Each trajectory performed 20 ns sampling per replica (see Model and Methods). The immediate question pertains to FEP/REST technical performance: Do the simulations adhere to FEP/REST formalism producing a random walk of replicas over conditions? To answer it, we considered several FEP/REST metrics.

In replica exchange simulations, the walk of individual replicas across conditions, represented in our case by $\left({\lambda }_r,T_r\right)$, can be visualized.³⁶ In principle, individual replicas should randomly walk across the conditions without lingering at any. If replicas are detained at any condition, it violates the prerequisite for equilibrium sampling. Fig. 2 illustrates replica walk across the conditions in FEP/REST simulations. The well-mixed color mosaic indicates that replica exchanges occur randomly without significant trapping. Similar plots are generated for other I0→I1 and I0→I2 simulations.

Figure 2:

A walk of replicas across the conditions $\left({\lambda }_r,T_r\right)$ in a FEP/REST trajectory: (a) bound I0→I1, (b) bound I0→I2, (c) unbound I0→I1, and (d) unbound I0→I2 simulations. The color scale on the right indicates the initial assignment of replicas to $\left({\lambda }_r,T_r\right)$. Replica configurations were taken at an interval of 100 exchange attempts.

The replica mixing parameter introduced by Han and Hansmann⁴² quantifies the random walk by replicas. They defined the parameter $h\left(r\right)=1-\frac{\sqrt{{\sum }_{m=0}^{R-1} t_m^2}}{\sqrt{{\sum }_{m=0}^{R-1} t_m}}$, where $t_m$ is the time spent at $\left({\lambda }_r,T_r\right)$ by replica $m$. With $R=16,h\left(r\right)$ should approach a theoretical maximum of $1-1/R^{1/2}=0.75$ for all $r$ assuming that all replicas evenly visit the conditions $\left({\lambda }_r,T_r\right)$. Fig. 3 shows that $h\left(r\right)$ is close to this maximum across all replicas, albeit at terminal conditions $r=0$ or $R-1$ there is some inefficiency due to boundary effects. The value of $h\left(r\right)$ averaged over all $r$ and trajectories is ≈ 0.70 for all FEP/REST simulation systems, indicating an approach of FEP/REST to optimum mixing. To our knowledge, the measures presented in Figs. 2 and 3 have not been previously applied to FEP/REST systems.

Figure 3:

The replica mixing parameter $h\left(r\right)$ averaged across all trajectories of bound I0→I1 (solid blue), bound I0→I2 (solid orange), unbound I0→I1 (dashed blue), and unbound I0→I2 (dashed orange) FEP/REST simulations. The theoretical maximum, $h=0.75$, is represented by a horizontal dashed black line. The standard error of the mean over trajectories is presented as vertical bars.

As a third measure to assess the quality of FEP/REST replica exchange, we computed the overlap of Boltzmann weights $O_{ij}$.^43–45 The overlap matrix is $O=W^{T}W/N$, where $W$ is the matrix of Boltzmann weights collected for each structure and reevaluated at all conditions and $N$ is the number of structures sampled at a given condition. Then, $O_{ij}$ is the fraction of the partition function for condition $i$ that uses the states collected at condition $j$. Previously it was determined that the overlaps as low as 0.03 between neighboring ${\lambda }_r$ values are the minimum requirement for reliable free energy estimates.⁴³ Using the program pymbar,⁴¹ we computed the overlap matrices for our FEP/REST simulations and show these distributions in Fig. 4. Importantly, the minimum neighboring overlap exceeds 0.03 consistent with the reliable estimates of free energy. Taken together, the three measures presented in Figs. 2–4 suggest efficient replica mixing that is a prerequisite for equilibrium FEP/REST sampling. Thus, we surmise that our simulations follow the FEP/REST formalism.

Figure 4:

Overlap matrices $O_{ij}$ for (a) bound I0→I1, (b) bound I0→I2, (c) unbound I0→I1, and (d) unbound I0→I2 FEP/REST simulations. The numbers refer to the fraction overlaps in Boltzmann weights, i.e., the contribution of states produced at condition $j\left({\lambda }_j,T_j\right)$ to the partition function at $i\left({\lambda }_i,T_i\right)$.

Next, we focus on the question of FEP/REST convergence. In Fig. 5a,b, we plot $\Delta \Delta G$ (Eq. 1) as a function of the sampling time per replica and trajectory $\tau$. The approach to respective baselines suggests that the resulting $\Delta \Delta G$ do not require longer simulations for accurate evaluation. For instance, for I0→I1, $\Delta \Delta G$ computed using the $\tau =2\mathrm{n}\mathrm{s}$ sampling (−0.2 ± 0.2 kcal/mol) does not significantly differ from the one computed from the 10-fold longer sampling of $\tau =20\mathrm{n}\mathrm{s}$ (−0.3 ± 0.1 kcal/mol). Similar result follows from I0→I2 simulations, for which $\Delta \Delta G=0.4\pm 0.4\mathrm{k}\mathrm{c}\mathrm{a}\mathrm{l}/\mathrm{m}\mathrm{o}\mathrm{l}$ if $\tau =2\mathrm{n}\mathrm{s}$, whereas $\Delta \Delta G=0.2\pm 0.2\mathrm{k}\mathrm{c}\mathrm{a}\mathrm{l}/\mathrm{m}\mathrm{o}\mathrm{l}$ computed for $\tau =20\mathrm{n}\mathrm{s}$ is still within the error of $\tau =2\mathrm{n}\mathrm{s}$ estimate. However, additional sampling does reduce the error $\sigma \left(\tau \right)$ in $\Delta \Delta G$. This error dependence on the simulation time $\tau$ is further explored in Fig. 5c, which demonstrates that $\sigma \left(\tau \right)$ initially rapidly decreases, but stabilizes after $\tau =4\mathrm{n}\mathrm{s}$ for I0→I1 or after $\tau =16\mathrm{n}\mathrm{s}$ for I0→I2.

Figure 5:

The relative binding free energy $\Delta \Delta G$ associated with (a) I0→I1 and (b) I0→I2 transformations as a function of FEP/REST sampling time $\tau$ per replica and trajectory. Vertical bars indicate the standard error of the mean computed using each trajectory as an independent sample. (c) Sampling error $\sigma \left(\tau \right)$ of $\Delta \Delta G$ vs the sampling time $\tau$. Blue and orange lines correspond to the I0→I1 and I0→I2 transformations, respectively.

We also computed the sampling error $\sigma \left(n\right)$ as a function of the number of trajectories $n$ (Fig. 6). Because there are multiple possibilities of combining trajectories when $n>1$ or $n<N$, we considered the sampling error $\sigma \left(n\right)$ averaged over all possible trajectory combinations. Fig. 6 shows that for both transformations $\sigma \left(n\right)$ monotonically decrease with $n$. One aspect of bound FEP/REST simulations requires attention. In their course, a ligand, which is initially bound, may unbind from the minNLS amino acids due to REST heating, thermal fluctuations, or weak affinity. Indeed, we checked the binding along the trajectories and found that at $\tau =20\mathrm{n}\mathrm{s}$ the average binding probability $P_b$ at 310 K has dropped from 1.0 to ≈0.80 (Fig. S1). As stated in Methods, $\Delta G_{\mathit{\text{bound}}}$ is computed using exclusively the ensemble of ligands in the 18Å sphere. Since $\Delta \Delta G$ in Fig. 5a,b remains approximately constant, particularly at $\tau >16\mathrm{n}\mathrm{s}$, the relative binding free energy is not sensitive to the inclusion of states unbound from minNLS amino acids in both alchemical transformations. This conclusion is elaborated in SI and Table S1.

Figure 6:

Average sampling error $\sigma \left(n\right)$ in $\Delta \Delta G$ as a function of the number of trajectories $n$. The data in blue and orange correspond to I0→I1 and I0→I2 transformation, respectively. All trajectories permutations were considered to compute $\sigma \left(n\right)$. The standard errors from permutations are shown as vertical bars.

It is important to summarize the results presented in Figs. 5 and 6. First, Fig. 5 suggests that for both transformations the relative binding free energy $\Delta \Delta G$ reaches the baseline at $\tau >16\mathrm{n}\mathrm{s}$ thus demonstrating convergence. Moreover, weak dependence of $\Delta \Delta G$ on $\tau$ argues that no equilibration interval is needed in FEP/REST sampling for the simple ligands considered here. Interestingly, the REST simulations coupled with thermodynamic integration by Bhati et al. reached similar conclusion for the inhibitors bound to fibroblast growth factor receptor 3.⁴⁶ Second, after initial decline the error $\sigma \left(\tau \right)$ stabilizes in Fig. 5c contrary to the expected decrease in $\sigma \left(\tau \right)$ with $\tau$. This behavior can be indicative of ligand trapping in local free energy minima. However, one needs to keep in mind alternative explanation that as FEP/REST bound simulations progress they eventually start to sample beyond specific bound states. Longer FEP/REST simulations will not only be inefficient due to a decline in bound poses sampling but may collect skewed thermodynamic ensembles for a ligand. These problems are exacerbated by ligands with weak binding affinity, and adding REST to FEP, although motivated to avoid local minima trapping, inevitably promotes unbinding and contributes to the sampling issues.⁴⁶ It must be noted however that the dependence of the error $\sigma \left(\tau \right)$ on simulation time is system-dependent as revealed by Fig. 5c. In fact, if the ligand exhibits a high binding affinity to a protein target, increase in simulation time is a viable strategy.^13,47 Third, Fig. 6 shows that the error $\sigma \left(n\right)$ in the relative binding free energy steadily decreases with the number of FEP/REST trajectories $n$. Given inherent limitations imposed by FEP/REST on simulation length, increasing the number of FEP/REST trajectories is then a preferred way to reduce error. Similar conclusions have been reached when utilizing the fractional replication method to divide simulation data into multiple samples, where the increase in the number of samples is shown to reduce the error.⁴⁵ These findings overall mirror those learned from molecular dynamics studies in general, where an increase in the number of trajectories rather than their extension is expected to improve confidence in simulation results.^46,48–50 Finally, in SI we show that the specific definition of an independent sample has a minor impact on $\sigma \left(n\right)$ (see Fig. S2). Since FEP/REST simulations are technically challenging, the metrics described above should be routinely implemented in FEP/REST studies to provide evidence for simulation performance.

Analysis of binding energetics

I0→I1

We first investigated the alchemical transformation I0→I1 converting G281–1485 (I0) into G281–1564 (I1). As shown in Table 1, the relative binding free energy $\Delta \Delta G=-0.3\pm 0.1\mathrm{k}\mathrm{c}\mathrm{a}\mathrm{l}/\mathrm{m}\mathrm{o}\mathrm{l}$, indicating that the binding of I1 to $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$ is slightly more favorable than of I0. Decomposition of $\Delta \Delta G$ into enthalpic and entropic terms yields $\Delta \Delta H=1.6\pm 2.1\mathrm{k}\mathrm{c}\mathrm{a}\mathrm{l}/\mathrm{m}\mathrm{o}\mathrm{l}$ and $T\Delta \Delta S=1.9\pm 2.0\mathrm{k}\mathrm{c}\mathrm{a}\mathrm{l}/\mathrm{m}\mathrm{o}\mathrm{l}$, respectively. Therefore, the favorable free energy change is attributed to a relative increase in binding entropy fully compensating the enthalpic loss.

Table 1:

Energetics of alchemical transformations

System	Term	Bounda	Unbounda	Δa,b
I0→I1	$\Delta H_{\mathit{\text{bond}}}$	0.1 ± 0.9	−0.8 ± 0.0	0.9 ± 0.9
	$\Delta H_{\mathit{\text{elec}}}$	9.2 ± 1.5	6.7 ± 1.4	2.5 ± 2.1
	$\Delta H_{\mathit{\text{vdw}}}$	2.0 ± 0.5	3.7 ± 0.2	−1.7 ± 0.6
	$\Delta H$	11.2 ± 1.5	9.6 ± 1.4	1.6 ± 2.1
	$T\Delta S$	3.9 ± 1.5	2.0 ± 1.4	1.9 ± 2.0
	$\Delta G$	7.4 ± 0.1	7.7 ± 0.0	−0.3 ± 0.1
I0→I2	$\Delta H_{\mathit{\text{bond}}}$	0.3 ± 0.9	0.7 ± 0.1	−0.4 ± 0.9
	$\Delta H_{\mathit{\text{elec}}}$	32.1 ± 1.8	33.5 ± 1.5	−1.4 ± 2.4
	$\Delta H_{\mathit{\text{vdw}}}$	1.3 ± 1.3	2.5 ± 0.3	−1.2 ± 1.3
	$\Delta H$	33.7 ± 1.6	36.6 ± 1.3	−3.0 ± 2.0
	$T\Delta S$	−2.3 ± 1.5	0.9 ± 1.3	−3.2 ± 2.0
	$\Delta G$	36.0 ± 0.1	35.8 ± 0.1	0.2 ± 0.2

^aBound and unbound terms represent the free energies of mutation in kcal/mol and are rounded resulting in occasional discrepancy of up to 0.1 kcal/mol between the table values;

^bdifference between bound and unbound states.

Detailed analysis of Table 1 reveals three observations. First, the overall change in the contribution of bonded interactions to binding $\Delta \Delta H_{\mathit{\text{bond}}}$ is unfavorable. Breaking $\Delta H_{\mathit{\text{bond}}}$ into covalent, angle, and dihedral terms indicates that, in the bound state the free energy changes for covalent bonds (−0.6 ± 0.2 kcal/mol) and angles (−1.0 ± 0.7 kcal/mol) are favorable, whereas the dihedral free energy change (1.6 ± 0.7 kcal/mol) compensates them. For the unbound system, the free energy change due to covalent bonds (−0.5 ± 0.0 kcal/mol) and angles (−0.9 ± 0.0 kcal/mol) are favorable, but the dihedral term (0.6 ± 0.0 kcal/mol) is disfavored. These computations indicate that the enthalpic changes for covalent bonds and angles are state independent, while dihedral angle degrees of freedom are responsible for the overall unfavorable $\Delta \Delta H_{\mathit{\text{bond}}}$ upon I0→I1. Second, the van der Waals term $\Delta \Delta H_{vdw}$ is negative and thus favorable, because the loss $\Delta H_{\mathit{\text{vdw}}}$ in the unbound state is almost two-fold higher than in the bound state. Thus, the deletion of carbons in I0 eliminates fewer van der Waals interactions in the bound state than in the unbound suggesting a collapsed I0 unbound state. On the contrary, electrostatic term $\Delta \Delta H_{\mathit{\text{elec}}}>0$ is unfavorable, because the deletion of carbons disrupts more electrostatic interactions in the bound state than in the unbound. The relative loss of electrostatic interactions consistent with the increased polarity of I1 overrides the relative gain in van der Waals interactions leading to unfavorable enthalpic binding contribution upon I0→I1 $(\Delta \Delta H>0)$. Third, the bound entropic term $T\Delta S$ is almost two-fold larger than in the unbound state, suggesting that I0→I1 causes larger entropic gains in the bound rather than unbound states. Taken together, relative gain in electrostatic interactions in the unbound state and strain in dihedral degrees of freedom cause a loss in enthalpic binding, but it is overtaken by the relative entropic gains in the I1 bound state. Thus, stronger binding affinity of I1 compared to I0 is entropically driven.

It is instructive to compare the I0→I1 energetics revealed by alchemical FEP/REST simulations and by our previous REST simulations probing direct binding of I0 and I1 to $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$.²⁶ From REST simulations we found that $\Delta \Delta G=-0.3\pm 0.2\mathrm{k}\mathrm{c}\mathrm{a}\mathrm{l}/\mathrm{m}\mathrm{o}\mathrm{l}$, which is in a perfect agreement with FEP/REST data in Table 1. It is more challenging to reconcile the differences in I0 and I1 binding interactions with the enthalpic and entropic contributions to I0→I1. Our previous simulations have shown that I1 forms more hydrogen bonds with $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$ than I0. Since according to Table 1 the contribution of electrostatic interactions to binding upon I0→I1 is diminished, this alchemical transformation effectively strengthens ligand hydration. Also, previous REST simulations revealed a minor change in the fluctuations of ligand bound positions measured by root-mean squared fluctuations. Table 1 however implicates the entropic factor as the primary source of stronger binding of I1. It follows then that the relative gains in $T\Delta S$ in the bound state are due to changes in water distributions around I1 and/or side chain conformations. Thus, comparison with the previous REST data²⁶ allows us to clarify the origins of enthalpic and entropic changes in Table 1.

I0→I2

Next, we investigated the alchemical transformation I0→I2, which converts G281–1485 (I0) into I2 by substituting a nitrogen for a carbon (Fig. 1a). Table 1 shows that the relative change in binding free energy $\Delta \Delta G$ is 0.2 ± 0.2 kcal/mol indicating a minor loss in binding affinity. When $\Delta \Delta G$ is decomposed, its enthalpic component $\Delta \Delta H=-3.0\pm 2.0\text{kcal}/\text{mol}$, whereas its entropic term $T\Delta \Delta S=-3.2\pm 2.0\text{kcal}/\text{mol}$. More detailed analysis revealed that all enthalpic contributions,$\Delta \Delta H_{\mathit{\text{bond}}}$, $\Delta \Delta H_{\mathit{\text{elec}}}$, and $\Delta \Delta H_{\mathit{\text{vdw}}}$ (−0.4, −1.4, and −1.2 kcal/mol) are negative and favorable. Indeed, the favorable relative change $\Delta \Delta H_{\mathit{\text{bond}}}<0$ is apparently determined by the relative decrease in the bond angle (−0.2 ± 0.1 kcal/mol) and dihedral (−0.3 ± 0.7 kcal/mol) enthalpies, suggesting that the ligand experiences less strain in the bound state. More importantly, Table 1 shows that I0 nitrogen group makes more favorable electrostatic and van der Waals interactions in the unbound state with water rather than in the bound state. Consequently, replacement of nitrogen with carbon strengthens enthalpic contribution to binding, but it is still overridden by the strong entropic loss in the bound state resulting in overall decrease in I2 binding affinity.

As for the I0→I1 transformation, we compare the I0→I2 energetics probed by FEP/REST against the previous simulations of I0 and I2 binding to $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$.²⁶ Our REST simulations found $\Delta \Delta G$ to be −0.2 ± 0.3 kcal/mol, whereas our current FEP/REST data suggest 0.2 ± 0.2 kcal/mol. Within the error range, both methods predict roughly similar minor changes in the binding affinity upon the I0→I2 transformation. The most distinctive feature of I2 compared to I0 is the formation of well-defined binding pose comprising almost 30% of all I2 bound structures, whereas the largest I0 bound cluster has the populations of merely 7%.²⁶ Consequently, I2 exhibits significantly smaller RMSF than I0 due to I2 localization in the hydrophobic pocket. Strikingly, those findings are in excellent agreement with the FEP/REST analysis of I0→I2 entropic contribution. Indeed, in contrast to all other entropic changes reported in Table 1 for I1 or I2, only the entropy of bound I2 decreases compared to I0. Thus, our previous REST simulations rationalize the cause of I2 entropic loss in the bound state.²⁶

Comparing I0→I1 and I0→I2

Several conclusions follow from the comparison of the binding energetics occurring upon I0→I1 and I0→I2 transformations. First, electrostatic interactions play diverging roles in the transformations indirectly strengthening their contribution either in the unbound state for I1 or in the bound state for I2. These changes are expected given that I0→I1 and I0→I2 either increase or decrease the polarity of the ligand, respectively. Second, both transformations lead to relative gains in van der Waals interactions in the bound state, but since electrostatic interactions prevail, they determine the overall enthalpic contributions in Table 1. Consequently, enthalpic changes favor I2 binding but disfavor I1. Third, I0→I1 and I0→I2 transformations cause opposite entropic changes. If the former increases the bound state entropy more than in the unbound state, the latter actually decreases the bound state entropy. Then, the entropic factor has a diverging and ultimately controlling impact on the ligand affinity promoting I1 binding, but disfavoring I2 binding. It should be also noted that, although the ligands exhibit distributed binding, the FEP/REST sampling error in $\Delta \Delta G$ is as low as $\lesssim 0.2\text{kcal}/\text{mol}$, but it may increase for more complex ligands. In our opinion, FEP/REST provides a unique opportunity to quantify these energetic changes.

Bound conformational ensemble

Because FEP/REST simulations sample both “wild-type” (I0) and “mutant” (I1 or I2) inhibitors, we propose that their binding ensembles can be studied using FEP/REST. Typically FEP simulations are not utilized for conformational analysis. Therefore, it is useful to establish if binding conformational ensembles sampled by FEP/REST and our previous REST binding simulations²⁶ are consistent.

I0→I1 transformation

According to Eq. (2), when $\lambda =0$ the Hamiltonian only includes the terms related to I0 whereas I1 is annihilated. Under this condition, the probability of I0 binding $P_b=0.91\pm 0.03$ (Fig. 7). As $\lambda \to 0.5$, which corresponds to alchemical coexistence of partly-annihilated I0 and partly-ignited I1 and to the peak in REST temperature, the binding probability drops to $P_b\approx 0.4$. When $\lambda =1$ and the Hamiltonian only includes I1 terms, while I0 is annihilated, the I1 binding probability reaches $P_b=0.85\pm 0.04$. Therefore, in both end states the respective ligands remain overwhelmingly bound to $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$, permitting us to evaluate their binding ensembles.

Figure 7:

The probability $P_b\left(r\right)$ of inhibitor binding to $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$ minNLS residues at FEP/REST conditions $\lambda$. The data in blue and orange correspond to the I0→I1 and I0→I2 transformations, respectively. At $\lambda <0.5P_b\left(\lambda \right)$ measures the binding of I0, while at $\lambda >0.5P_b\left(\lambda \right)$ reports the binding of I1 or I2.

To characterize the binding site of an inhibitor, we computed the probabilities of forming contacts between an inhibitor and $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$ amino acids $i$ within the binding sphere, $P_c\left(i\right)$ (see Model and Methods). Then, we selected the $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$ amino acids with the top ten $P_c\left(i\right)$ values listed in Table 2 and referred to them as top ten binding amino acids. (Their convergence for I0 binding is analyzed in SI Table S2.) It follows from Table 2 that, although in a different order, these amino acids are identical for I0 and I1. Furthermore, the four top amino acids, Ser79, Asn76, Trp114, and Pro40, have identical rankings for I0 and I1. For both ligands, seven out of ten are the amino acids from the minNLS binding site⁴⁰ indicating a putative propensity for I0 and I1 to interfere with VEEV NLS binding.

Table 2:

Top ten binding $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$ amino acids^a,b

Rank	I0a	I1	I2
1	Ser79 (0.72)	Ser79 (0.71)	Ser79 (0.74)
2	Asn76 (0.62)	Asn76 (0.61)	Asn76 (0.72)
3	Trp114 (0.58)	Trp114 (0.53)	Ile42 (0.60)
4	Pro40 (0.49)	Pro40 (0.46)	Gly80 (0.57)
5	Ile42 (0.48)	Gly80 (0.44)	Pro40 (0.56)
6	Gly80 (0.47)	Ile42 (0.44)	Leu34 (0.51)
7	Trp72 (0.46)	Leu34 (0.43)	Trp114 (0.48)
8	Leu34 (0.44)	Trp161 (0.39)	Ser35 (0.41)
9	Trp161 (0.43)	Trp72 (0.39)	Trp72 (0.37)
10	Ser35 (0.36)	Ser35 (0.35)	Glu37 (0.37)

^aAmino acids belonging to minNLS binding site are in standard font, whereas non-minNLS amino acids are in bold.

^bBinding probabilities $P_c$ defined in the text are in parentheses.

^cI0 data are averaged over I0→I1 and I0→I2 simulations.

We now compare the binding of I0 and I1 sampled by FEP/REST and our previous REST simulations.²⁶ In that study a table analogous to Table 2 was reported. Their comparison shows that eight out of top ten binding amino acids for I0 are identical in FEP/REST and REST simulations with the top two being the same and appearing in the same order with very similar $P_c\left(i\right)$. For I1 there are nine identical amino acids among the top ten binding with the top three being the same and having very similar $P_c\left(i\right)$. In our previous study we measured the inhibitor binding specificity by the fraction of top binding amino acids $f_s$ with $P_c\left(i\right)>0.5$. Inhibitor targeting of the minNLS binding site was quantified by the fraction of minNLS amino acids among the top binding, $f_t$. With these definitions applied to FEP/REST data, both I0 and I1 are non-specific binders (for both $f_s=0.3$) and strongly on-target $\left(f_t=0.7\right)$. REST simulations reported the same specificities and similar on-target ratings ($f_t=0.5$ for I0 and 0.8 for I1).

I0→I2

As shown in Fig. 7, at $\lambda =1$, the probability of I2 binding to impα $P_b=0.89\pm 0.03$, which is consistent with those observed for I0 (0.91) and I1 (0.85) confirming that FEP/REST simulations can be used to extract the I2 binding ensemble. Table 2 demonstrates that nine out of top ten binding amino acids are identical between I2 and I0 or I1. Furthermore, although in general the binding amino acids have different rankings, the top two, Ser79 and Asn76, are the same across all three ligands. For I2 six out of ten are the minNLS amino acids⁴⁰ suggesting that I2 may interfere with VEEV NLS binding, albeit to a weaker extent than I0 or I1.

Following the analysis for I0 and I1, we compare the binding of I2 reported by FEP/REST and our previous REST simulations.²⁶ Comparison of top ten binding amino acids indicates that there are seven common between the two simulations and top two amino acids appear in the same order with similar $P_c\left(i\right)$. It follows from FEP/REST simulations that I2 is a specific binder with $f_s=0.6$ and on-target with $f_t=0.6$. REST simulations reported the stronger specificity of $f_s=0.9$ and weaker on-target rating $f_t=0.4$. Thus, the specificity and on-target ratings of I2 determined by REST/FEP and REST simulations somewhat differ.

In summary, by comparing FEP/REST and REST binding data we arrive at the following three conclusions. First, the top ten binding amino acids are in good (from 70 to 90%) agreement between the two simulations with two or three amino acids at the top being identical. Therefore, fundamentally different simulations nevertheless probe similar binding sites for the three inhibitors. Second, there is an excellent agreement with respect to binding specificity for I0 and I1 and slightly worse but still qualitatively consistent for I2. This observation indicates that the two simulations produce similar binding propensities for the three ligands classifying I0 and I1 as non-specific and I2 as specific. Third, a weaker agreement is seen with respect to on-target ratings, although both simulations identify I2 as the least on-target inhibitor out of three. Thus, taking the results together we surmise that FEP/REST simulations can be used not only to probe binding free energy differences but to sample ligand bound conformational ensembles.

Conclusions

We have performed FEP/REST simulations probing the two alchemical transformations of the VEEV NLS inhibitors, I0→I1 and I0→I2, which respectively increase or decrease the polarity of the parent molecule I0. The novel feature of these FEP/REST simulations is their application to the ligands binding to $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$ without defined binding poses. Therefore, our objective was three-fold - (i) to verify FEP/REST technical performance and convergence, (ii) to estimate changes in binding free energy $\Delta \Delta G$, and (iii) to determine the utility of FEP/REST simulations for conformational binding analysis. Addressing these objectives we found the following. First, our FEP/REST simulations properly follow FEP/REST formalism and produce converged $\Delta \Delta G$ estimates. Importantly, due to ligand inherent unbinding a better FEP/REST strategy lies in performing multiple independent trajectories rather than extending their length. Second, I0→I1 and I0→I2 transformations result in minor changes in inhibitor binding free energy, slightly strengthening the affinity of I1 and weakening that of I2. Electrostatic interactions play diverging roles in the two transformations, but because they prevail over van der Waals interactions, electrostatic interactions determine the overall enthalpic changes upon I0→I1 and I0→I2. More importantly, the two transformations cause opposite entropic changes. I0→I1 increases the bound state entropy relative to the unbound state, whereas I0→I2 strongly decreases it. Then, the entropic factor also has a diverging impact on the ligands promoting I1 but disfavoring I2 binding. Ultimately, the entropy change governs the binding affinity change. The validity of FEP/REST free energy estimates was confirmed by a careful comparison with our previous REST simulations directly probing binding of three ligands to $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$. Thus, FEP/REST can accurately estimate the minor affinity differences for the ligands exhibiting distributed binding. Third, FEP/REST simulations can sample ligand binding ensembles.

In conclusion, our findings established FEP/REST as a viable tool for ensemble-based drug design relevant for the ligands binding without defined poses. There are indications that such ligands represent an important category. One such example pertains to binding of drug molecules to the voluminous proximal and distal binding pockets in bacterial AcrB multidrug exporter.⁵¹ Specifically, doxorubicin has been proposed to oscillate between multiple binding poses in the proximal pocket. Independently, theoretical modeling of binding ensemble using Markov chain Monte Carlo method estimated the number of binding poses for four ligands in the binding chamber of AcrB.⁵² While minocycline was found to bind via single pose, toluene was predicted to adopt a distributed binding ensemble with the number of poses ~100 times more than of minocycline. In our opinion, the binding of these drugs to AcrB is conceptually similar to the binding of I0-I2 to $\mathrm{i}\mathrm{m}\mathrm{p}\alpha$. Finally, a recent study analyzed the electron densities in high-resolution PDB protein-ligand complexes.¹⁶ Either a poor fit of the electron density to the ligand pose or multiple ligand poses were found in 35% and 21% of structures, respectively. Note that the first case can also be explained by distributed ligand poses. Consequently, we hope that our work will provide the blueprint for applying FEP/REST simulations for energetic and conformational investigations of this class of ligands in the future.

Data and software availability:

NAMD is available at https://www.ks.uiuc.edu/Research/namd/. VMD is available at https://www.ks.uiuc.edu/Research/vmd/. Initial structures, topology files, and NAMD configuration files are available at https://github.com/KlimovLab/FEP-REST_VEEV_Inhibitors. Codes used for data analysis are available from the authors upon request.