New Computational Approach for External Entropy in Protein-Protein Binding

Atomic-level thermodynamics analysis of the binding free energy of SARS-CoV-2 neutralizing antibodies

Understanding how protein-protein binding affinity is determined from molecular interactions at the interface is essential in developing protein therapeutics such as antibodies, but this has not yet been fully achieved. Among the major difficulties are the facts that it is generally difficult to decompose thermodynamic quantities into contributions from individual molecular interactions and that the solvent effect-dehydration penalty-must also be taken into consideration for every contact formation at the binding interface. Here, we present an atomic-level thermodynamics analysis that overcomes these difficulties and illustrate its utility through application to SARS-CoV-2 neutralizing antibodies. Our analysis is based on the direct interaction energy computed from simulated antibody-protein complex structures and on the decomposition of solvation free energy change upon complex formation. We find that the formation of a single contact such as a hydrogen bond at the interface barely contributes to binding free energy due to the dehydration penalty. On the other hand, the simultaneous formation of multiple contacts between two interface residues favorably contributes to binding affinity. This is because the dehydration penalty is significantly alleviated: the total penalty for multiple contacts is smaller than a sum of what would be expected for individual dehydrations of those contacts. Our results thus provide a new perspective for designing protein therapeutics of improved binding affinity.

A dynamical view of protein-protein complexes: Studies by molecular dynamics simulations

Protein-protein interactions are at the basis of many protein functions, and the knowledge of 3D structures of protein-protein complexes provides structural, mechanical and dynamical pieces of information essential to understand these functions. Protein-protein interfaces can be seen as stable, organized regions where residues from different partners form non-covalent interactions that are responsible for interaction specificity and strength. They are commonly described as a peripheral region, whose role is to protect the core region that concentrates the most contributing interactions, from the solvent. To get insights into the dynamics of protein-protein complexes, we carried out all-atom molecular dynamics simulations in explicit solvent on eight different protein-protein complexes of different functional class and interface size by taking into account the bound and unbound forms. On the one hand, we characterized structural changes upon binding of the proteins, and on the other hand we extensively analyzed the interfaces and the structural waters involved in the binding. Based on our analysis, in 6 cases out of 8, the interfaces rearranged during the simulation time, in stable and long-lived substates with alternative residue-residue contacts. These rearrangements are not restricted to side-chain fluctuations in the periphery but also affect the core interface. Finally, the analysis of the waters at the interface and involved in the binding pointed out the importance to take into account their role in the estimation of the interaction strength.

Computational Screening of a Functional Cyclodextrin Derivative for Suppressing a Side Effect of Doxorubicin

The binding affinity of the beta-cyclodextrin (β-CyD) derivatives with Doxorubicin (Dox) is evaluated by means of the 3D-RISM/KH theory combined with the molecular dynamics simulation in order to screen the compounds for suppressing a side-effect of the cancer drug. A protocol revised for the external and conformational entropies of the host-guest system is employed to calculate the binding free energy. It is found that the direct interactions of CyD with Dox and the desolvation free-energies of the both compounds largely cancel out to leave moderate contributions to the affinity, which are comparable to those from the entropies. The results shed light on the entropy terms for determining the binding affinity, although the external-entropy terms are essentially constant over all the compounds examined and do not affect the screening. The theoretical result is compared with the experimental data of the association constant for a CyD derivative which was predicted to be the best compound by the preliminary calculation without the entropy terms.

Nuclear Quantum Effects from the Analysis of Smoothed Trajectories: Pilot Study for Water

Nuclear quantum effects have significant contributions to thermodynamic quantities and structural properties; furthermore, very expensive methods are necessary for their accurate computation. In most calculations, these effects, for instance, zero-point energies, are simply neglected or only taken into account within the quantum harmonic oscillator approximation. Herein, we present a new method, Generalized Smoothed Trajectory Analysis, to determine nuclear quantum effects from molecular dynamics simulations. The broad applicability is demonstrated with the examples of a harmonic oscillator and different states of water. Ab initio molecular dynamics simulations have been performed for ideal gas up to the temperature of 5000 K. Classical molecular dynamics have been carried out for hexagonal ice, liquid water, and vapor at atmospheric pressure. With respect to the experimental heat capacity, our method outperforms previous calculations in the literature in a wide temperature range at lower computational cost than other alternatives. Dynamic and structural nuclear quantum effects of water are also discussed.

Effect of linker on the binding free energy of stapled p53/HDM2 complex

Inactivation of the tumor suppressor p53 resulting from the binding with a negative regulator HDM2 is among the predominant defects in human cancers. p53-mimicking peptides whose conformational and proteolytic stability is enhanced by an all-hydrocarbon staple are being recognized as promising anticancer agents for disrupting the p53–HDM2 binding and reactivating p53. Herein, we conduct a computational modeling and thermodynamic characterization of stapled p53/HDM2 complex via molecular docking, simulations, and binding free energy analysis. The binding thermodynamics analysis is done based on the end-point calculation of the effective binding energy—a sum of the direct peptide–protein interaction energy and the dehydration penalty—and on its decomposition into contributions from specific groups constituting the complex. This allows us to investigate how individual amino acids in the stapled p53 and HDM2 contribute to the binding affinity. We find that not only the epitope residues (F19, W23 and L26), but also the hydrocarbon linker of the stapled p53 impart significant contributions. Our computational approach will be useful in designing new stapled peptides in which the staple location is also optimized to improve the binding affinity.

Folding Free Energy Landscape of Ordered and Intrinsically Disordered Proteins

Folding funnel is the essential concept of the free energy landscape for ordered proteins. How does this concept apply to intrinsically disordered proteins (IDPs)? Here, we address this fundamental question through the explicit characterization of the free energy landscapes of the representative α-helical (HP-35) and β-sheet (WW domain) proteins and of an IDP (pKID) that folds upon binding to its partner (KIX). We demonstrate that HP-35 and WW domain indeed exhibit the steep folding funnel: the landscape slope for these proteins is ca. −50 kcal/mol, meaning that the free energy decreases by ~5 kcal/mol upon the formation of 10% native contacts. On the other hand, the landscape of pKID is funneled but considerably shallower (slope of −24 kcal/mol), which explains why pKID is disordered in free environments. Upon binding to KIX, the landscape of pKID now becomes significantly steep (slope of −54 kcal/mol), which enables otherwise disordered pKID to fold. We also show that it is the pKID–KIX intermolecular interactions originating from hydrophobic residues that mainly confer the steep folding funnel. The present work not only provides the quantitative characterization of the protein folding free energy landscape, but also establishes the usefulness of the folding funnel concept to IDPs.

Entropic Stabilization of Cas4 Protein SSO0001 Predicted with Popcoen

Popcoen is a method for configurational entropy estimation of proteins based on machine-learning. Entropy is predicted with an artificial neural network which was trained on simulation trajectories of a large set of representative proteins. Popcoen is extremely fast compared to other approaches based on the sampling of a multitude of microstates. Consequently, Popcoen can be incorporated into a large class of protein software which currently neglects configurational entropy for performance reasons. Here, we apply Popcoen to various conformations of the Cas4 protein SSO0001 of Sulfolobus solfataricus, a protein that assembles to a decamer of known toroidal shape. We provide numerical evidence that the native state (NAT) of a SSO0001 monomer has a similar structure to the protomers of the oligomer, where NAT of the monomer is stabilized mainly entropically. Due to its large amount of configurational entropy, NAT has lower free energy than alternative conformations of very low enthalpy and solvation free-energy. Hence, SSO0001 serves as an example case where neglecting configurational entropy leads to incorrect conclusion. Our results imply that no refolding of the subunits is required during oligomerization which suggests that configurational entropy is employed by nature to largely enhance the rate of assembly.

Dynamics of Hydration Water Plays a Key Role in Determining the Binding Thermodynamics of Protein Complexes

Interfacial waters are considered to play a crucial role in protein–protein interactions, but in what sense and why are they important? Here, using molecular dynamics simulations and statistical thermodynamic analyses, we demonstrate distinctive dynamic characteristics of the interfacial water and investigate their implications for the binding thermodynamics. We identify the presence of extraordinarily slow (~1,000 times slower than in bulk water) hydrogen-bond rearrangements in interfacial water. We rationalize the slow rearrangements by introducing the “trapping” free energies, characterizing how strongly individual hydration waters are captured by the biomolecular surface, whose magnitude is then traced back to the number of water–protein hydrogen bonds and the strong electrostatic field produced at the binding interface. We also discuss the impact of the slow interfacial waters on the binding thermodynamics. We find that, as expected from their slow dynamics, the conventional approach to the water-mediated interaction, which assumes rapid equilibration of the waters’ degrees of freedom, is inadequate. We show instead that an explicit treatment of the extremely slow interfacial waters is critical. Our results shed new light on the role of water in protein–protein interactions, highlighting the need to consider its dynamics to improve our understanding of biomolecular bindings.

Elucidating the energetic contributions to the binding free energy

New exact equations are derived for the terms contributing to the binding free energy (ΔG⁰) of a ligand-receptor pair using our recently introduced formalism which we here call perturbation-divergence formalism (PDF). Specifically, ΔG⁰ equals the sum of the average of the perturbation (pertaining to new interactions) and additional dissipative terms. The average of the perturbation includes the sum of the average receptor-ligand interactions and the average of the change of solvation energies upon association. The Kullback-Leibler (KL) divergence quantifies the energetically dissipative terms, which are due to the configurational changes and, using the chain rule of KL divergence, can be decomposed into (i) dissipation due to limiting the external liberation (translation and rotation) of the ligand relative to the receptor and (ii) dissipation due to conformational (internal) changes inside the receptor and the ligand. We also identify all exactly canceling energetic terms which do not contribute to ΔG⁰. Furthermore, the PDF provides a new approach towards dimensionality reduction in the representation of the association process and towards relating the dynamic (high dimensional) with the thermodynamic (one-dimensional) changes.

Computer Simulations of Intrinsically Disordered Proteins

The investigation of intrinsically disordered proteins (IDPs) is a new frontier in structural and molecular biology that requires a new paradigm to connect structural disorder to function. Molecular dynamics simulations and statistical thermodynamics potentially offer ideal tools for atomic-level characterizations and thermodynamic descriptions of this fascinating class of proteins that will complement experimental studies. However, IDPs display sensitivity to inaccuracies in the underlying molecular mechanics force fields. Thus, achieving an accurate structural characterization of IDPs via simulations is a challenge. It is also daunting to perform a configuration-space integration over heterogeneous structural ensembles sampled by IDPs to extract, in particular, protein configurational entropy. In this review, we summarize recent efforts devoted to the development of force fields and the critical evaluations of their performance when applied to IDPs. We also survey recent advances in computational methods for protein configurational entropy that aim to provide a thermodynamic link between structural disorder and protein activity.