Probing the effect of conformational constraint on phosphorylated ligand binding to an SH2 domain using polarizable force field simulations

Thermodynamic consequences of stapling side-chains on a peptide ligand using a lactam-bridge: A theoretical study on anti-angiogenic peptides targeting VEGF

Peptides are promising therapeutic agents for various biological targets due to their high efficacy and low toxicity, and the design of peptide ligands with high binding affinity to the target of interest is of utmost importance in peptide-based drug design. Introducing a conformational constraint to a flexible peptide ligand using a side-chain lactam-bridge is a convenient and efficient method to improve its binding affinity to the target. However, in general, such a small structural modification to a flexible ligand made with the intent of lowering the configurational entropic penalty for binding may have unintended consequences in different components of the binding enthalpy and entropy, including the configurational entropy component, which are still not clearly understood. Toward probing this, we examine different components of the binding enthalpy and entropy as well as the underlying structure and dynamics, for a side-chain lactam-bridged peptide inhibitor and its flexible analog forming complexes with vascular endothelial growth factor (VEGF), using all-atom molecular dynamics simulations. It is found that introducing a side-chain lactam-bridge constraint into the flexible peptide analog led to a gain in configurational entropy change but losses in solvation entropy, solute internal energy, and solvation energy changes upon binding, pinpointing the opportunities and challenges in drug design. The present study features an interplay between configurational and solvation entropy changes, as well as the one between binding enthalpy and entropy, in ligand-target binding upon imposing a conformational constraint into a flexible ligand.

Insights into Modeling Approaches in Chemistry: Assessing Ligand-Protein Binding Thermodynamics Based on Rigid-Flexible Model Molecules

In the field of chemistry, model compounds find extensive use for investigating complex objects. One prime example of such object is the protein-ligand supramolecular interaction. Prediction the enthalpic and entropic contribution to the free energy associated with this process, as well as the structural and dynamic characteristics of protein-ligand complexes poses considerable challenges. This review exemplifies modeling approaches used to study protein-ligand binding (PLB) thermodynamics by employing pairs of conformationally constrained/flexible model molecules. Strategically designing the model molecules can reduce the number of variables that influence thermodynamic parameters. This enables scientists to gain deeper insights into the enthalpy and entropy of PLB, which is relevant for medicinal chemistry and drug design. The model studies reviewed here demonstrate that rigidifying ligands may induce compensating changes in the enthalpy and entropy of binding. Some "rules of thumb" have started to emerge on how to minimize entropy-enthalpy compensation and design efficient rigidified or flexible ligands.

Perspectives on Ligand/Protein Binding Kinetics Simulations: Force Fields, Machine Learning, Sampling, and User-Friendliness

Computational techniques applied to drug discovery have gained considerable popularity for their ability to filter potentially active drugs from inactive ones, reducing the time scale and costs of preclinical investigations. The main focus of these studies has historically been the search for compounds endowed with high affinity for a specific molecular target to ensure the formation of stable and long-lasting complexes. Recent evidence has also correlated the in vivo drug efficacy with its binding kinetics, thus opening new fascinating scenarios for ligand/protein binding kinetic simulations in drug discovery. The present article examines the state of the art in the field, providing a brief summary of the most popular and advanced ligand/protein binding kinetics techniques and evaluating their current limitations and the potential solutions to reach more accurate kinetic models. Particular emphasis is put on the need for a paradigm change in the present methodologies toward ligand and protein parametrization, the force field problem, characterization of the transition states, the sampling issue, and algorithms' performance, user-friendliness, and data openness.

Computationally driven discovery of SARS-CoV-2 Mpro inhibitors: from design to experimental validation

We report a fast-track computationally driven discovery of new SARS-CoV-2 main protease (M^pro) inhibitors whose potency ranges from mM for the initial non-covalent ligands to sub-μM for the final covalent compound (IC₅₀ = 830 ± 50 nM). The project extensively relied on high-resolution all-atom molecular dynamics simulations and absolute binding free energy calculations performed using the polarizable AMOEBA force field. The study is complemented by extensive adaptive sampling simulations that are used to rationalize the different ligand binding poses through the explicit reconstruction of the ligand–protein conformation space. Machine learning predictions are also performed to predict selected compound properties. While simulations extensively use high performance computing to strongly reduce the time-to-solution, they were systematically coupled to nuclear magnetic resonance experiments to drive synthesis and for in vitro characterization of compounds. Such a study highlights the power of in silico strategies that rely on structure-based approaches for drug design and allows the protein conformational multiplicity problem to be addressed. The proposed fluorinated tetrahydroquinolines open routes for further optimization of M^pro inhibitors towards low nM affinities.

The dominant binding mode of the QUB-00006-Int-07 main protease inhibitor during absolute binding free energy simulations.

Synthesis and structural characterization of a monocarboxylic inhibitor for GRB2 SH2 domain

A monocarboxylic inhibitor was designed and synthesized to disrupt the protein-protein interaction (PPI) between GRB2 and phosphotyrosine-containing proteins. Biochemical characterizations show compound 7 binds with the Src homology 2 (SH2) domain of GRB2 and is more potent than EGFR₁₀₆₈ phosphopeptide 14-mer. X-ray crystallographic studies demonstrate compound 7 occupies the GRB2 binding site for phosphotyrosine-containing sequences and reveal key structural features for GRB2-inhibitor binding. This compound with a -1 formal charge offers a new direction for structural optimization to generate cell-permeable inhibitors for this key protein target of the aberrant Ras-MAPK signaling cascade.

Multipolar electrostatics for hairpin and pseudoknots in RNA: Improving the accuracy of force field potential energy function

Molecular dynamics (MD) simulations that rely on force field methods has been widely used to explore the structure and function of RNAs. However, the current commonly used force fields are limited by the electrostatic description offered by atomic charge, dipole and at most quadrupole moments, failing to capture the anisotropic picture of electronic features. Actually, the distribution of electrons around atomic nuclei is not spherically symmetric but is geometry dependent. A multipolar electrostatic model based on high rank multipole moments is described in this work, which allows us to combine polarizability and anisotropy of electron density. RNA secondary structure was taken as a research system, and its substructures including stem, loops (hairpin loop, bulge loop, internal loop, and multi-branch loop), and pseudoknots (H-type and K-type) were investigated, respectively, as well as the hairpin. First, the atom-atom electrostatic properties derived from one chain of a duplex RNA 2MVY in our previous work (Ref. 58) were measured by the pilot RNA systems of hairpin, hairpin loop, stem, and H-type pseudoknot, respectively. The prediction results were not satisfactory. Consequently, to obtain a general set of electrostatic parameters for RNA force fields, the convergence behavior of the atom-atom electrostatic interactions in the pilot RNA systems was explored using high rank atomic multipole moments. The pilot RNA systems were cut into four types of different-sized molecular fragments, and the single nucleotide fragment and nucleotide-paired fragment proved to be the most reasonable systems for base-unpairing regions and base-pairing regions to investigate the convergence behavior of all types of atom-atom electrostatic interactions, respectively. Transferability of the electrostatic properties drawn from the pilot RNA systems to the corresponding test systems was also investigated. Furthermore, the convergence behavior of atomic electrostatic interactions in other substructures including bulge loop, internal loop, multi-branch loop, and K-type pseudoknot was expected to be modeled via the hairpin.

Some thermodynamic effects of varying nonpolar surfaces in protein-ligand interactions

Understanding how making structural changes in small molecules affects their binding affinities for targeted proteins is central to improving strategies for rational drug design. To assess the effects of varying the nature of nonpolar groups upon binding entropies and enthalpies, we designed and prepared a set of Grb2-SH2 domain ligands, Ac-pTyr-Ac₆c-Asn-(CH₂)_n-R, in which the size and electrostatic nature of R groups at the pTyr+3 site were varied. The complexes of these ligands with the Grb2-SH2 domain were evaluated in a series of studies in which the binding thermodynamics were determined using isothermal titration calorimetry, and binding interactions were examined in crystallographic studies of two different complexes. Notably, adding nonpolar groups to the pTyr+3 site leads to higher binding affinities, but the magnitude and energetic origins of these effects vary with the nature of the R substituent. For example, enhancements to binding affinities using aliphatic R groups are driven by more favorable changes in binding entropies, whereas aryl R groups improve binding free energies through a combination of more favorable changes in binding enthalpies and entropies. However, enthalpy/entropy compensation plays a significant role in these associations and mitigates against any significant variation in binding free energies, which vary by only 0.8 kcal•mol^-1, with changes in the electrostatic nature and size of the R group. Crystallographic studies show that differences in ΔG° or ΔH° correlate with buried nonpolar surface area, but they do not correlate with the total number of polar or van der Waals contacts. The relative number of ordered water molecules and relative order in the side chains at pTyr+3 correlate with differences in -TΔS°. Overall, these studies show that burial of nonpolar surface can lead to enhanced binding affinities arising from dominating entropy- or enthalpy-driven hydrophobic effects, depending upon the electrostatic nature of the apolar R group.

Structure-thermodynamics-relationships of hepatitis C viral NS3 protease inhibitors

Thermodynamic parameters were determined for structurally-related inhibitors of HCV NS3 protease to assess how binding entropies and enthalpies vary with incremental changes at the P2 and P3 inhibitor subsites. Changing the heterocyclic substituent at P2 from a pyridyl to a 7-methoxy-2-phenyl-4-quinolyl group leads to a 710-fold increase in affinity. Annelating a benzene ring onto a pyridine ring leads to quinoline-derived inhibitors having higher affinities, but the individual enthalpy and entropy contributions are markedly different for each ligand pair. Introducing a phenyl group at C2 of the heterocyclic ring at P2 uniformly leads to higher affinity analogs with more favorable binding entropies, while adding a methoxy group at C7 of the quinoline ring at P2 provides derivatives with more favorable binding enthalpies. Significant enthalpy/entropy compensation is observed for structural changes made to inhibitors lacking a 2-phenyl substituent, whereas favorable changes in both binding enthalpies and entropies accompany structural modifications when a 2-phenyl group is present. Overall, binding energetics of inhibitors having a 2-phenyl-4-quinolyl group at P2 are dominated by entropic effects, whereas binding of the corresponding norphenyl analogs are primarily enthalpy driven. Notably, the reversal from an entropy driven association to an enthalpy driven one for this set of inhibitors also correlates with alternate binding modes. When the steric bulk of the side chain at P3 is increased from a hydrogen atom to a tert-butyl group, there is a 770-fold improvement in affinity. The 30-fold increase resulting from the first methyl group is solely the consequence of a more favorable change in entropy, whereas subsequent additions of methyl groups leads to modest increases in affinity that arise primarily from incremental improvements in binding enthalpies accompanied with smaller favorable entropic contributions.

Computational insights into the binding of IN17 inhibitors to MELK

The protein kinase MELK is an important kinase in cell signaling and has shown to be a promising anti-cancer target. Recent work has resulted in a novel small molecule scaffold targeting MELK, IN17. However, there has been little structural information or physical understanding of MELK-IN17 interactions. Using Tinker-OpenMM on GPUs, we have performed free energy simulations on MELK binding with IN17 and 11 derivatives. This series of studies provides structural insights into how substitution on IN17 leads to differences in complex structure and binding thermodynamics. In addition, this study serves as an assessment of the current capabilities of the AMOEBA forcefield, accelerated by GPU computing, to serve as a molecular-dynamics-based free energy simulation platform for lead optimization.

Polarizable Force Fields for Biomolecular Simulations: Recent Advances and Applications

Realistic modeling of biomolecular systems requires an accurate treatment of electrostatics, including electronic polarization. Due to recent advances in physical models, simulation algorithms, and computing hardware, biomolecular simulations with advanced force fields at biologically relevant timescales are becoming increasingly promising. These advancements have not only led to new biophysical insights but also afforded opportunities to advance our understanding of fundamental intermolecular forces. This article describes the recent advances and applications, as well as future directions, of polarizable force fields in biomolecular simulations.

Force Fields for Small Molecules

Molecular dynamics (MD) simulations have been widely applied to computer-aided drug design (CADD). While MD has been used in a variety of applications such as free energy perturbation and long-time simulations, the accuracy of the results from those methods depends strongly on the force field used. Force fields for small molecules are crucial, as they not only serve as building blocks for developing force fields for larger biomolecules but also act as model compounds that will be transferred to ligands used in CADD. Currently, a wide range of small molecule force fields based on additive or nonpolarizable models have been developed. While these nonpolarizable force fields can produce reasonable estimations of physical properties and have shown success in a variety of systems, there is still room for improvements due to inherent limitations in these models including the lack of an electronic polarization response. For this reason, incorporating polarization effects into the energy function underlying a force field is believed to be an important step forward, giving rise to the development of polarizable force fields. Recent simulations of biological systems have indicated that polarizable force fields are able to provide a better physical representation of intermolecular interactions and, in many cases, better agreement with experimental properties than nonpolarizable, additive force fields. Therefore, this chapter focuses on the development of small molecule force fields with emphasis on polarizable models. It begins with a brief introduction on the importance of small molecule force fields and their evolution from additive to polarizable force fields. Emphasis is placed on the additive CHARMM General Force Field and the polarizable force field based on the classical Drude oscillator. The theory for the Drude polarizable force field and results for small molecules are presented showing their improvements over the additive model. The potential importance of polarization for their application in a wide range of biological systems including CADD is then discussed.

Protein-ligand binding enthalpies from near-millisecond simulations: Analysis of a preorganization paradox

Calorimetric studies of protein-ligand binding sometimes yield thermodynamic data that are difficult to understand. Today, molecular simulations can be used to seek insight into such calorimetric puzzles, and, when simulations and experiments diverge, the results can usefully motivate further improvements in computational methods. Here, we apply near-millisecond duration simulations to estimate the relative binding enthalpies of four peptidic ligands with the Grb2 SH2 domain. The ligands fall into matched pairs, where one member of each pair has an added bond that preorganizes the ligand for binding and thus may be expected to favor binding entropically, due to a smaller loss in configurational entropy. Calorimetric studies have shown that the constrained ligands do in fact bind the SH2 domain more tightly than the flexible ones, but, paradoxically, the improvement in affinity for the constrained ligands is enthalpic, rather than entropic. The present enthalpy calculations yield the opposite trend, as they suggest that the flexible ligands bind more exothermically. Additionally, the small relative binding enthalpies are found to be balances of large differences in the energies of structural components such as ligand and the binding site residues. As a consequence, the deviations from experiment in the relative binding enthalpies represent small differences between these large numbers and hence may be particularly susceptible to error, due, for example, to approximations in the force field. We also computed first-order estimates of changes in configurational entropy on binding. These too are, arguably, paradoxical, as they tend to favor binding of the flexible ligands. The paradox is explained in part by the fact that the more rigid constrained ligands reduce the entropy of binding site residues more than their flexible analogs do, at least in the simulations. This result offers a rather general counterargument to the expectation that preorganized ligands should be associated with more favorable binding entropies, other things being equal.

Efficient minimization of multipole electrostatic potentials in torsion space

The development of models of macromolecular electrostatics capable of delivering improved fidelity to quantum mechanical calculations is an active field of research in computational chemistry. Most molecular force field development takes place in the context of models with full Cartesian coordinate degrees of freedom. Nevertheless, a number of macromolecular modeling programs use a reduced set of conformational variables limited to rotatable bonds. Efficient algorithms for minimizing the energies of macromolecular systems with torsional degrees of freedom have been developed with the assumption that all atom-atom interaction potentials are isotropic. We describe novel modifications to address the anisotropy of higher order multipole terms while retaining the efficiency of these approaches. In addition, we present a treatment for obtaining derivatives of atom-centered tensors with respect to torsional degrees of freedom. We apply these results to enable minimization of the Amoeba multipole electrostatics potential in a system with torsional degrees of freedom, and validate the correctness of the gradients by comparison to finite difference approximations. In the interest of enabling a complete model of electrostatics with implicit treatment of solvent-mediated effects, we also derive expressions for the derivative of solvent accessible surface area with respect to torsional degrees of freedom.

AMOEBA Polarizable Atomic Multipole Force Field for Nucleic Acids

The AMOEBA polarizable atomic multipole force field for nucleic acids is presented. Valence and electrostatic parameters were determined from high-level quantum mechanical data, including structures, conformational energy, and electrostatic potentials, of nucleotide model compounds. Previously derived parameters for the phosphate group and nucleobases were incorporated. A total of over 35 μs of condensed-phase molecular dynamics simulations of DNA and RNA molecules in aqueous solution and crystal lattice were performed to validate and refine the force field. The solution and/or crystal structures of DNA B-form duplexes, RNA duplexes, and hairpins were captured with an average root-mean-squared deviation from NMR structures below or around 2.0 Å. Structural details, such as base pairing and stacking, sugar puckering, backbone and χ-torsion angles, groove geometries, and crystal packing interfaces, agreed well with NMR and/or X-ray. The interconversion between A- and B-form DNAs was observed in ethanol-water mixtures at 328 K. Crystal lattices of B- and Z-form DNA and A-form RNA were examined with simulations. For the RNA tetraloop, single strand tetramers, and HIV TAR with 29 residues, the simulated conformational states, 3 J-coupling, nuclear Overhauser effect, and residual dipolar coupling data were compared with NMR results. Starting from a totally unstacked/unfolding state, the rCAAU tetranucleotide was folded into A-form-like structures during ∼1 μs molecular dynamics simulations.

A Polarizable Atomic Multipole-Based Force Field for Molecular Dynamics Simulations of Anionic Lipids

In all of the classical force fields, electrostatic interaction is simply treated and explicit electronic polarizability is neglected. The condensed-phase polarization, relative to the gas-phase charge distributions, is commonly accounted for in an average way by increasing the atomic charges, which remain fixed throughout simulations. Based on the lipid polarizable force field DMPC and following the same framework as Atomic Multipole Optimized Energetics for BiomoleculAr (AMOEBA) simulation, the present effort expands the force field to new anionic lipid models, in which the new lipids contain DMPG and POPS. The parameters are compatible with the AMOEBA force field, which includes water, ions, proteins, etc. The charge distribution of each atom is represented by the permanent atomic monopole, dipole and quadrupole moments, which are derived from the ab initio gas phase calculations. Many-body polarization including the inter- and intramolecular polarization is modeled in a consistent manner with distributed atomic polarizabilities. Molecular dynamics simulations of the two aqueous DMPG and POPS membrane bilayer systems, consisting of 72 lipids with water molecules, were then carried out to validate the force field parameters. Membrane width, area per lipid, volume per lipid, deuterium order parameters, electron density profile, electrostatic potential difference between the center of the bilayer and water are all calculated, and compared with limited experimental data.

Tinker-OpenMM: Absolute and relative alchemical free energies using AMOEBA on GPUs

The capabilities of the polarizable force fields for alchemical free energy calculations have been limited by the high computational cost and complexity of the underlying potential energy functions. In this work, we present a GPU-based general alchemical free energy simulation platform for polarizable potential AMOEBA. Tinker-OpenMM, the OpenMM implementation of the AMOEBA simulation engine has been modified to enable both absolute and relative alchemical simulations on GPUs, which leads to a ∼200-fold improvement in simulation speed over a single CPU core. We show that free energy values calculated using this platform agree with the results of Tinker simulations for the hydration of organic compounds and binding of host-guest systems within the statistical errors. In addition to absolute binding, we designed a relative alchemical approach for computing relative binding affinities of ligands to the same host, where a special path was applied to avoid numerical instability due to polarization between the different ligands that bind to the same site. This scheme is general and does not require ligands to have similar scaffolds. We show that relative hydration and binding free energy calculated using this approach match those computed from the absolute free energy approach. © 2017 Wiley Periodicals, Inc.

LNA Thymidine Monomer Enables Differentiation of the Four Single-Nucleotide Variants by Melting Temperature

High-resolution melting (HRM) analysis of DNA is a closed-tube single-nucleotide polymorphism (SNP) detection method that has shown many advantages in point-of-care diagnostics and personalized medicine. While recently developed melting probes have demonstrated significantly improved discrimination of mismatched (mutant) alleles from matched (wild-type) alleles, no effort has been made to design a simple melting probe that can reliably distinguish all four SNP alleles in a single experiment. Such a new probe could facilitate the discovery of rare genetic mutations at lower cost. Here we demonstrate that a melting probe embedded with a single locked thymidine monomer (t_L) can reliably differentiate the four SNP alleles by four distinct melting temperatures (termed the "4T_m probe"). This enhanced discriminatory power comes from the decreased melting temperature of the t_L·C mismatched hybrid as compared to that of the t·C mismatched hybrid, while the melting temperatures of the t_L-A, t_L·G and t_L·T hybrids are increased or remain unchanged as compared to those of their canonical counterparts. This phenomenon is observed not only in the HRM experiments but also in the molecular dynamics simulations.

Drude polarizable force field for aliphatic ketones and aldehydes, and their associated acyclic carbohydrates

The majority of computer simulations exploring biomolecular function employ Class I additive force fields (FF), which do not treat polarization explicitly. Accordingly, much effort has been made into developing models that go beyond the additive approximation. Development and optimization of the Drude polarizable FF has yielded parameters for selected lipids, proteins, DNA and a limited number of carbohydrates. The work presented here details parametrization of aliphatic aldehydes and ketones (viz. acetaldehyde, propionaldehyde, butaryaldehyde, isobutaryaldehyde, acetone, and butanone) as well as their associated acyclic sugars (D-allose and D-psicose). LJ parameters are optimized targeting experimental heats of vaporization and molecular volumes, while the electrostatic parameters are optimized targeting QM water interactions, dipole moments, and molecular polarizabilities. Bonded parameters are targeted to both QM and crystal survey values, with the models for ketones and aldehydes shown to be in good agreement with QM and experimental target data. The reported heats of vaporization and molecular volumes represent a compromise between the studied model compounds. Simulations of the model compounds show an increase in the magnitude and the fluctuations of the dipole moments in moving from gas phase to condensed phases, which is a phenomenon that the additive FF is intrinsically unable to reproduce. The result is a polarizable model for aliphatic ketones and aldehydes including the acyclic sugars D-allose and D-psicose, thereby extending the available biomolecules in the Drude polarizable FF.

Characterization of Promiscuous Binding of Phosphor Ligands to Breast-Cancer-Gene 1 (BRCA1) C-Terminal (BRCT): Molecular Dynamics, Free Energy, Entropy and Inhibitor Design

Inhibition of the protein-protein interaction (PPI) mediated by breast-cancer-gene 1 C-terminal (BRCT) is an attractive strategy to sensitize breast and ovarian cancers to chemotherapeutic agents that induce DNA damage. Such inhibitors could also be used for studies to understand the role of this PPI in DNA damage response. However, design of BRCT inhibitors is challenging because of the inherent flexibility associated with this domain. Several studies identified short phosphopeptides as tight BRCT binders. Here we investigated the thermodynamic properties of 18 phosphopeptides or peptide with phosphate mimic and three compounds with phosphate groups binding to BRCT to understand promiscuous molecular recognition and guide inhibitor design. We performed molecular dynamics (MD) simulations to investigate the interactions between inhibitors and BRCT and their dynamic behavior in the free and bound states. MD simulations revealed the key role of loops in altering the shape and size of the binding site to fit various ligands. The mining minima (M2) method was used for calculating binding free energy to explore the driving forces and the fine balance between configuration entropy loss and enthalpy gain. We designed a rigidified ligand, which showed unfavorable experimental binding affinity due to weakened enthalpy. This was because it lacked the ability to rearrange itself upon binding. Investigation of another phosphate group containing compound, C1, suggested that the entropy loss can be reduced by preventing significant narrowing of the energy well and introducing multiple new compound conformations in the bound states. From our computations, we designed an analog of C1 that introduced new intermolecular interactions to strengthen attractions while maintaining small entropic penalty. This study shows that flexible compounds do not always encounter larger entropy penalty, compared with other more rigid binders, and highlights a new strategy for inhibitor design.

Promiscuous proteins are commonly observed in biological systems, such as modular domains that recognize phosphopeptides during signal transduction. The use of phosphopeptides and compounds with phosphate groups as inhibitors to protein–protein interactions have attracted increasing interest for years. By using atomistic molecular dynamics simulations, we are able to perform detailed analyses of the dihedral space to explore protein fluctuation upon ligand binding to better understand promiscuous molecular recognition. Free energy calculation can further provide insights into the mechanism of binding, including both enthalpic and entropic contributions for molecular recognition, which assist in inhibitor design. Our calculation results show that pre-rigidifying a ligand is not always advantageous, suggesting the challenge in retaining optimized intermolecular interactions in pre-rigidified ligand. Instead, certain flexible ligands with multiple binding conformations can reduce entropic penalty, and therefore improves binding affinity. According to our computations, we can introduce new intermolecular interactions to flexible ligand to strengthen attractions while maintaining small entropic penalty by retaining its plasticity in the bound conformation. The study might cast light on a new general strategy for designing inhibitors targeting promiscuous modular domains and protein–protein interactions.

Molecular Simulation of Conformational Pre-Organization in Cyclic RGD Peptides

To test the ability of molecular simulations to accurately predict the solution-state conformational properties of peptidomimetics, we examined a test set of 18 cyclic RGD peptides selected from the literature, including the anticancer drug candidate cilengitide, whose favorable binding affinity to integrin has been ascribed to its pre-organization in solution. For each design, we performed all-atom replica-exchange molecular dynamics simulations over several microseconds and compared the results to extensive published NMR data. We find excellent agreement with experimental NOE distance restraints, suggesting that molecular simulation can be a useful tool for the computational design of pre-organized solution-state structure. Moreover, our analysis of conformational populations estimates that, despite the potential for increased flexibility due to backbone amide isomerizaton, N-methylation provides about 0.5 kcal/mol of reduced conformational entropy to cyclic RGD peptides. The combination of pre-organization and binding-site compatibility explains the strong binding affinity of cilengitide to integrin.

Using docking and alchemical free energy approach to determine the binding mechanism of eEF2K inhibitors and prioritizing the compound synthesis

A-484954 is a known eEF2K inhibitor with submicromolar IC₅₀ potency. However, the binding mechanism and the crystal structure of the kinase remains unknown. Here, we employ a homology eEF2K model, docking and alchemical free energy simulations to probe the binding mechanism of eEF2K, and in turn, guide the optimization of potential lead compounds. The inhibitor was docked into the ATP-binding site of a homology model first. Three different binding poses, hypothesis 1, 2, and 3, were obtained and subsequently applied to molecular dynamics (MD) based alchemical free energy simulations. The calculated relative binding free energy of the analogs of A-484954 using the binding pose of hypothesis 1 show a good correlation with the experimental IC₅₀ values, yielding an r² coefficient of 0.96 after removing an outlier (compound 5). Calculations using another two poses show little correlation with experimental data, (r² of less than 0.5 with or without removing any outliers). Based on hypothesis 1, the calculated relative free energy suggests that bigger cyclic groups, at R1 e.g., cyclobutyl and cyclopentyl promote more favorable binding than smaller groups, such as cyclopropyl and hydrogen. Moreover, this study also demonstrates the ability of the alchemical free energy approach in combination with docking and homology modeling to prioritize compound synthesis. This can be an effective means of facilitating structure-based drug design when crystal structures are not available.

Bridging Calorimetry and Simulation through Precise Calculations of Cucurbituril-Guest Binding Enthalpies

We used microsecond time scale molecular dynamics simulations to compute, at high precision, binding enthalpies for cucurbit[7]uril (CB7) with eight guests in aqueous solution. The results correlate well with experimental data from previously published isothermal titration calorimetry studies, and decomposition of the computed binding enthalpies by interaction type provides plausible mechanistic insights. Thus, dispersion interactions appear to play a key role in stabilizing these complexes, due at least in part to the fact that their packing density is greater than that of water. On the other hand, strongly favorable Coulombic interactions between the host and guests are compensated by unfavorable solvent contributions, leaving relatively modest electrostatic contributions to the binding enthalpies. The better steric fit of the aliphatic guests into the circular host appears to explain why their binding enthalpies tend to be more favorable than those of the more planar aromatic guests. The present calculations also bear on the validity of the simulation force field. Somewhat unexpectedly, the TIP3P water yields better agreement with experiment than the TIP4P-Ew water model, although the latter is known to replicate the properties of pure water more accurately. More broadly, the present results demonstrate the potential for computational calorimetry to provide atomistic explanations for thermodynamic observations.

Relative Binding Enthalpies from Molecular Dynamics Simulations Using a Direct Method

The potential for reliably predicting relative binding enthalpies, ΔΔE, from a direct method utilizing molecular dynamics is examined for a system of three phosphotyrosyl peptides binding to a protein receptor, the Src SH2 domain. The binding enthalpies were calculated from the potential energy differences between the bound and the unbound end-states of each peptide from equilibrium simulations in explicit water. The statistical uncertainties in the ensemble-mean energy values from multiple, independent simulations were obtained using a bootstrap method. Simulations were initiated with different starting coordinates as well as different velocities. Statistical uncertainties in ΔΔE are 2 to 3 kcal/mol based on calculations from 40, 10 ns trajectories for each system (three SH2–peptide complexes or unbound peptides). Uncertainties in relative component energies, comprising solute–solute, solute–solvent and solvent–solvent interactions, are considerably larger. Energy values were estimated from an unweighted ensemble averaging of multiple trajectories with the a priori assumption that all trajectories are equally likely. Distributions in energy–rmsd space indicate that the trajectories sample the same basin and the difference in mean energy values between trajectories is due to sampling of alternative local regions of this superbasin. The direct estimate of relative binding enthalpies is concluded to be a reasonable approach for well-ordered systems with ΔΔE values greater than ∼3 kcal/mol, although the approach would benefit from future work to determine properly distributed starting points that would enable efficient sampling of conformational space using multiple trajectories.

Cyclodextrin-templated porphyrin nanorings

α- and β-Cyclodextrins have been used as scaffolds for the synthesis of six- and seven-legged templates by functionalizing every primary CH₂OH with a 4-pyridyl moiety. Although these templates are flexible, they are very effective for directing the synthesis of macrocyclic porphyrin oligomers consisting of six or seven porphyrin units. The transfer of chirality from the cyclodextrin templates to their nanoring hosts is evident from NMR and circular dichroism spectroscopy. Surprisingly, the mean effective molarity for binding the flexible α-cyclodextrin-based template within the six-porphyrin nanoring (74 m) is almost as high as for the previously studied rigid hexadentate template (180 m). The discovery that flexible templates are effective in this system, and the availability of a template with a prime number of binding sites, open up many possibilities for the template-directed synthesis of larger macrocycles.

Protein-ligand interactions: probing the energetics of a putative cation-π interaction

In order to probe the energetics associated with a putative cation-π interaction, thermodynamic parameters are determined for complex formation between the Grb2 SH2 domain and tripeptide derivatives of RCO-pTyr-Ac6c-Asn wherein the R group is varied to include different alkyl, cycloalkyl, and aryl groups. Although an indole ring is reputed to have the strongest interaction with a guanidinium ion, binding free energies, ΔG°, for derivatives of RCO-pTyr-Ac6c-Asn bearing cyclohexyl and phenyl groups were slightly more favorable than their indolyl analog. Crystallographic analysis of two complexes reveals that test ligands bind in similar poses with the notable exception of the relative orientation and proximity of the phenyl and indolyl rings relative to an arginine residue of the domain. These spatial orientations are consistent with those observed in other cation-π interactions, but there is no net energetic benefit to such an interaction in this biological system. Accordingly, although cation-π interactions are well documented as important noncovalent forces in molecular recognition, the energetics of such interactions may be mitigated by other nonbonded interactions and solvation effects in protein-ligand associations.

Hydration Free Energy from Orthogonal Space Random Walk and Polarizable Force Field

The orthogonal space random walk (OSRW) method has shown enhanced sampling efficiency in free energy calculations from previous studies. In this study, the implementation of OSRW in accordance with the polarizable AMOEBA force field in TINKER molecular modeling software package is discussed and subsequently applied to the hydration free energy calculation of 20 small organic molecules, among which 15 are positively charged and five are neutral. The calculated hydration free energies of these molecules are compared with the results obtained from the Bennett acceptance ratio method using the same force field, and overall an excellent agreement is obtained. The convergence and the efficiency of the OSRW are also discussed and compared with BAR. Combining enhanced sampling techniques such as OSRW with polarizable force fields is very promising for achieving both accuracy and efficiency in general free energy calculations.

Current and emerging opportunities for molecular simulations in structure-based drug design

An overview of the current capabilities and limitations of molecular simulation of biomolecular complexes in the context of computer-aided drug design is provided. Steady improvements in computer hardware coupled with more refined representations of energetics are leading to a new appreciation of the driving forces of molecular recognition. Molecular simulations are poised to more frequently guide the interpretation of biophysical measurements of biomolecular complexes. Ligand design strategies emerge from detailed analyses of computed structural ensembles. The feasibility of routine applications to ligand optimization problems hinges upon successful extensive large scale validation studies and the development of protocols to intelligently automate computations.

Modeling organochlorine compounds and the σ-hole effect using a polarizable multipole force field

The charge distribution of halogen atoms on organochlorine compounds can be highly anisotropic and even display a so-called σ-hole, which leads to strong halogen bonds with electron donors. In this paper, we have systematically investigated a series of chloromethanes with one to four chloro substituents using a polarizable multipole-based molecular mechanics model. The atomic multipoles accurately reproduced the ab initio electrostatic potential around chloromethanes, including CCl₄, which has a prominent σ-hole on the Cl atom. The van der Waals parameters for Cl were fitted to the experimental density and heat of vaporization. The calculated hydration free energy, solvent reaction fields, and interaction energies of several homo- and heterodimer of chloromethanes are in good agreement with experimental and ab initio data. This study suggests that sophisticated electrostatic models, such as polarizable atomic multipoles, are needed for accurate description of electrostatics in organochlorine compounds and halogen bonds, although further improvement is necessary for better transferability.

Correlating structure and energetics in protein-ligand interactions: paradigms and paradoxes

Predicting protein-binding affinities of small molecules, even closely related ones, is a formidable challenge in biomolecular recognition and medicinal chemistry. A thermodynamic approach to optimizing affinity in protein-ligand interactions requires knowledge and understanding of how altering the structure of a small molecule will be manifested in protein-binding enthalpy and entropy changes; however, there is a relative paucity of such detailed information. In this review, we examine two strategies commonly used to increase ligand potency. The first of these involves introducing a cyclic constraint to preorganize a small molecule in its biologically active conformation, and the second entails adding nonpolar groups to a molecule to increase the amount of hydrophobic surface that is buried upon binding. Both of these approaches are motivated by paradigms suggesting that protein-binding entropy changes should become more favorable, but paradoxes can emerge that defy conventional wisdom.

Protein-Ligand Interactions: Thermodynamic Effects Associated with Increasing the Length of an Alkyl Chain

Thermodynamic parameters were determined for complex formation between the Grb2 SH2 domain and tripeptides of the general form Ac-pTyr-Xaa-Asn in which the Xaa residue bears a linear alkyl chain varying in length from 1-5 carbon atoms. Binding affinity increases upon adding a methylene group to the Ala derivative, but further chain extension gives no extra enhancement in potency. The thermodynamic signatures of the ethyl and n-propyl derivatives are virtually identical as are those for the n-butyl and n-pentyl analogs. Crystallographic analysis of the complexes reveals a high degree of similarity in the structure of the domain and the bound ligands with the notable exception that there is a gauche interaction in the side chains in the bound conformations of ligands having n-propyl, n-butyl, and n-pentyl groups. However, eliminating this unfavorable interaction by introducing a Z-double bond into the side chain of the n-propyl analog does not result in an increase in affinity. Increases in the amount of nonpolar surface that is buried upon ligand binding correlate with favorable changes in ΔH°, but these are usually offset by corresponding unfavorable changes in -TΔS°; there is little correlation of ΔC_p with changes in the amount of buried nonpolar surface.

Force Field for Peptides and Proteins based on the Classical Drude Oscillator

Presented is a polarizable force field based on a classical Drude oscillator framework, currently implemented in the programs CHARMM and NAMD, for modeling and molecular dynamics (MD) simulation studies of peptides and proteins. Building upon parameters for model compounds representative of the functional groups in proteins, the development of the force field focused on the optimization of the parameters for the polypeptide backbone and the connectivity between the backbone and side chains. Optimization of the backbone electrostatic parameters targeted quantum mechanical conformational energies, interactions with water, molecular dipole moments and polarizabilities and experimental condensed phase data for short polypeptides such as (Ala)₅. Additional optimization of the backbone φ, ψ conformational preferences included adjustments of the tabulated two-dimensional spline function through the CMAP term. Validation of the model included simulations of a collection of peptides and proteins. This 1^st generation polarizable model is shown to maintain the folded state of the studied systems on the 100 ns timescale in explicit solvent MD simulations. The Drude model typically yields larger RMS differences as compared to the additive CHARMM36 force field (C36) and shows additional flexibility as compared to the additive model. Comparison with NMR chemical shift data shows a small degradation of the polarizable model with respect to the additive, though the level of agreement may be considered satisfactory, while for residues shown to have significantly underestimated S² order parameters in the additive model, improvements are calculated with the polarizable model. Analysis of dipole moments associated with the peptide backbone and tryptophan side chains show the Drude model to have significantly larger values than those present in C36, with the dipole moments of the peptide backbone enhanced to a greater extent in sheets versus helices and the dipoles of individual moieties observed to undergo significant variations during the MD simulations. Although there are still some limitations, the presented model, termed Drude-2013, is anticipated to yield a molecular picture of peptide and protein structure and function that will be of increased physical validity and internal consistency in a computationally accessible fashion.

The Polarizable Atomic Multipole-based AMOEBA Force Field for Proteins

Development of the AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Simulation) force field for proteins is presented. The current version (AMOEBA-2013) utilizes permanent electrostatic multipole moments through the quadrupole at each atom, and explicitly treats polarization effects in various chemical and physical environments. The atomic multipole electrostatic parameters for each amino acid residue type are derived from high-level gas phase quantum mechanical calculations via a consistent and extensible protocol. Molecular polarizability is modeled via a Thole-style damped interactive induction model based upon distributed atomic polarizabilities. Inter- and intramolecular polarization is treated in a consistent fashion via the Thole model. The intramolecular polarization model ensures transferability of electrostatic parameters among different conformations, as demonstrated by the agreement between QM and AMOEBA electrostatic potentials, and dipole moments of dipeptides. The backbone and side chain torsional parameters were determined by comparing to gas-phase QM (RI-TRIM MP2/CBS) conformational energies of dipeptides and to statistical distributions from the Protein Data Bank. Molecular dynamics simulations are reported for short peptides in explicit water to examine their conformational properties in solution. Overall the calculated conformational free energies and J-coupling constants are consistent with PDB statistics and experimental NMR results, respectively. In addition, the experimental crystal structures of a number of proteins are well maintained during molecular dynamics (MD) simulation. While further calculations are necessary to fully validate the force field, initial results suggest the AMOEBA polarizable multipole force field is able to describe the structure and energetics of peptides and proteins, in both gas-phase and solution environments.

Prediction of protein relative enthalpic stability from molecular dynamics simulations of the folded and unfolded states

For proteins of known structure, the relative enthalpic stability with respect to wild-type, ΔΔH(U), can be estimated by direct computation of the folded and unfolded state energies. We propose a model by which the change in stability upon mutation can be predicted from all-atom molecular dynamics simulations for the folded state and a peptide-based model for the unfolded state. The unfolding enthalpies are expressed in terms of environmental and hydration-solvent reorganization contributions that readily allow a residue-specific analysis of ΔΔH(U). The method is applied to estimate the relative enthalpic stability of variants with buried charged groups in T4 lysozyme. The predicted relative stabilities are in good agreement with experimental data. Environmental factors are observed to contribute more than hydration to the overall ΔΔH(U). The residue-specific analysis finds that the effects of burying charge are both localized and long-range. The enthalpy for hydration-solvent reorganization varies considerably among different amino-acid types, but because the variant folded state structures are similar to those of the wild-type, the hydration-solvent reorganization contribution to ΔΔH(U) is localized at the mutation site, in contrast to environmental contributions. Overall, mutation of apolar and polar amino acids to charged amino acids are destabilizing, but the reasons are complex and differ from site to site.