Fast Calculation of Protein-Protein Binding Free Energies Using Umbrella Sampling with a Coarse-Grained Model

Perspective on Integrative Simulations of Bioenergetic Domains

Bioenergetic processes in cells, such as photosynthesis or respiration, integrate many time and length scales, which makes the simulation of energy conversion with a mere single level of theory impossible. Just like the myriad of experimental techniques required to examine each level of organization, an array of overlapping computational techniques is necessary to model energy conversion. Here, a perspective is presented on recent efforts for modeling bioenergetic phenomena with a focus on molecular dynamics simulations and its variants as a primary method. An overview of the various classical, quantum mechanical, enhanced sampling, coarse-grained, Brownian dynamics, and Monte Carlo methods is presented. Example applications discussed include multiscale simulations of membrane-wide electron transport, rate kinetics of ATP turnover from electrochemical gradients, and finally, integrative modeling of the chromatophore, a photosynthetic pseudo-organelle.

Standard Binding Free-Energy Calculations: How Far Are We from Automation?

Recent success stories suggest that in silico protein-ligand binding free-energy calculations are approaching chemical accuracy. However, their widespread application remains limited by the extensive human intervention required, posing challenges for the neophyte. As such, it is critical to develop automated workflows for estimating protein-ligand binding affinities with minimum personal involvement. Key human efforts include setting up and tuning enhanced-sampling or alchemical-transformation algorithms as a preamble to computational binding free-energy estimations. Additionally, preparing input files, bookkeeping, and postprocessing represent nontrivial tasks. In this Perspective, we discuss recent progress in automating standard binding free-energy calculations, featuring the development of adaptive or parameter-free algorithms, standardization of binding free-energy calculation workflows, and the implementation of user-friendly software. We also assess the current state of automated standard binding free-energy calculations and evaluate the limitations of existing methods. Last, we outline the requirements for future algorithms and workflows to facilitate automated free-energy calculations for diverse protein-ligand complexes.

An exploration of the binding prediction of anatoxin-a and atropine to acetylcholinesterase enzyme using multi-level computer simulations

Acetylcholinesterase (AChE) is crucial for the breakdown of acetylcholine to acetate and choline, while the inhibition of AChE by anatoxin-a (ATX-a) results in severe health complications. This study explores the structural characteristics of ATX-a and its interactions with AChE, comparing to the reference molecule atropine for binding mechanisms. Molecular docking simulations reveal strong binding affinity of both ATX-a and atropine to AChE, interacting effectively with specific amino acids in the binding site as potential inhibitors. Quantitative assessment using the MM-PBSA method demonstrates a significantly negative binding free energy of -81.659 kJ mol-1for ATX-a, indicating robust binding, while atropine exhibits a stronger binding affinity with a free energy of -127.565 kJ mol-1. Umbrella sampling calculates the ΔGbindvalues to evaluate binding free energies, showing a favorable ΔGbindof -36.432 kJ mol-1for ATX-a and a slightly lower value of -30.12 kJ mol-1for atropine. This study reveals the dual functionality of ATX-a, acting as both a nicotinic acetylcholine receptor agonist and an AChE inhibitor. Remarkably, stable complexes form between ATX-a and atropine with AChE at its active site, exhibiting remarkable binding free energies. These findings provide valuable insights into the potential use of ATX-a and atropine as promising candidates for modulating AChE activity.

An in silico approach to determine inter-subunit affinities in human septin complexes

The septins are a conserved family of filament-forming guanine nucleotide binding proteins, often named the fourth component of the cytoskeleton. Correctly assembled septin structures are required for essential intracellular processes such as cytokinesis, vesicular transport, polarity establishment, and cellular adhesion. Structurally, septins belong to the P-Loop NTPases but they do not mediate signals to effectors through GTP binding and hydrolysis. GTP binding and hydrolysis are believed to contribute to septin complex integrity, but biochemical approaches addressing this topic are hampered by the stability of septin complexes after recombinant expression and the lack of nucleotide-depleted complexes. To overcome this limitation, we used a molecular dynamics-based approach to determine inter-subunit binding free energies in available human septin dimer structures and in their apo forms, which we generated in silico. The nucleotide in the GTPase active subunits SEPT2 and SEPT7, but not in SEPT6, was identified as a stabilizing element in the G interface. Removal of GDP from SEPT2 and SEPT7 results in flipping of a conserved Arg residue and disruption of an extensive hydrogen bond network in the septin unique element, concomitant with a decreased inter-subunit affinity. Based on these findings we propose a singular "lock-hydrolysis" mechanism stabilizing human septin filaments.

Fast, Accurate, and System-Specific Variable-Resolution Modeling of Proteins

In recent years, a few multiple-resolution modeling strategies have been proposed, in which functionally relevant parts of a biomolecule are described with atomistic resolution, with the remainder of the system being concurrently treated using a coarse-grained model. In most cases, the parametrization of the latter requires lengthy reference all-atom simulations and/or the usage of off-shelf coarse-grained force fields, whose interactions have to be refined to fit the specific system under examination. Here, we overcome these limitations through a novel multiresolution modeling scheme for proteins, dubbed coarse-grained anisotropic network model for variable resolution simulations, or CANVAS. This scheme enables a user-defined modulation of the resolution level throughout the system structure; a fast parametrization of the potential without the necessity of reference simulations; and the straightforward usage of the model on the most commonly used molecular dynamics platforms. The method is presented and validated with two case studies, the enzyme adenylate kinase and the therapeutic antibody pembrolizumab, by comparing the results obtained with the CANVAS model against fully atomistic simulations. The modeling software, implemented in Python, is made freely available for the community on a collaborative github repository.

Towards an optimal monoclonal antibody with higher binding affinity to the receptor-binding domain of SARS-CoV-2 spike proteins from different variants

A highly efficient and robust multiple scales in silico protocol, consisting of atomistic Molecular Dynamics (MD), coarse-grain (CG) MD, and constant-pH CG Monte Carlo (MC), has been developed and used to study the binding affinities of selected antigen-binding fragments of the monoclonal antibody (mAbs) CR3022 and several of its here optimized versions against 11 SARS-CoV-2 variants including the wild type. Totally 235,000 mAbs structures were initially generated using the RosettaAntibodyDesign software, resulting in top 10 scored CR3022-like-RBD complexes with critical mutations and compared to the native one, all having the potential to block virus-host cell interaction. Of these 10 finalists, two candidates were further identified in the CG simulations to be the best against all SARS-CoV-2 variants. Surprisingly, all 10 candidates and the native CR3022 exhibited a higher affinity for the Omicron variant despite its highest number of mutations. The multiscale protocol gives us a powerful rational tool to design efficient mAbs. The electrostatic interactions play a crucial role and appear to be controlling the affinity and complex building. Studied mAbs carrying a more negative total net charge show a higher affinity. Structural determinants could be identified in atomistic simulations and their roles are discussed in detail to further hint at a strategy for designing the best RBD binder. Although the SARS-CoV-2 was specifically targeted in this work, our approach is generally suitable for many diseases and viral and bacterial pathogens, leukemia, cancer, multiple sclerosis, rheumatoid, arthritis, lupus, and more.

In Silico Maturation of a Nanomolar Antibody against the Human CXCR2

The steady increase in computational power in the last 50 years is opening unprecedented opportunities in biology, as computer simulations of biological systems have become more accessible and can reproduce experimental results more accurately. Here, we wanted to test the ability of computer simulations to replace experiments in the limited but practically useful scope of improving the biochemical characteristics of the abN48 antibody, a nanomolar antagonist of the CXC chemokine receptor 2 (CXCR2) that was initially selected from a combinatorial antibody library. Our results showed a good correlation between the computed binding energies of the antibody to the peptide target and the experimental binding affinities. Moreover, we showed that it is possible to design new antibody sequences in silico with a higher affinity to the desired target using a Monte Carlo Metropolis algorithm. The newly designed sequences had an affinity comparable to the best ones obtained using in vitro affinity maturation and could be obtained within a similar timeframe. The methodology proposed here could represent a valid alternative for improving antibodies in cases in which experiments are too expensive or technically tricky and could open an opportunity for designing antibodies for targets that have been elusive so far.

Wetting Properties of Clathrate Hydrates in the Presence of Polycyclic Aromatic Compounds: Evidence of Ion-Specific Effects

Polycyclic aromatic hydrocarbons (PAHs) have attracted remarkable multidisciplinary attention due to their intriguing π-π stacking configurations, showing enormous opportunity for their use in a variety of advanced applications. To secure progress, detailed knowledge on PAHs' interfacial properties is required. Employing molecular dynamics, we probe the wetting properties of brine droplets (KCl, NaCl, and CaCl₂) on sII methane-ethane hydrate surfaces immersed in various oil solvents. Our simulations show synergistic effects due to the presence of PAHs compounded by ion-specific effects. Our analysis reveals phenomenological correlations between the wetting properties and a combination of the binding free-energy difference and entropy changes upon oil solvation for PAHs at oil/brine and oil/hydrate interfaces. The detailed thermodynamic analysis conducted upon the interactions between PAHs and various interfaces identifies molecular-level mechanisms responsible for wettability alterations, which could be applicable for advancing applications in optics, microfluidics, biotechnology, medicine, as well as hydrate management.

Hazardous Shortcuts in Standard Binding Free Energy Calculations

Calculating the standard binding free energies of protein-protein and protein-ligand complexes from atomistic molecular dynamics simulations in explicit solvent is a problem of central importance in computational biophysics. A rigorous strategy for carrying out such calculations is the so-called "geometrical route". In this method, two molecular objects are progressively separated from one another in the presence of orientational and conformational restraints serving to control the change in configurational entropy that accompanies the dissociation process, thereby allowing the computations to converge within simulations of affordable length. Although the geometrical route provides a rigorous theoretical framework, a tantalizing computational shortcut consists of simply leaving out such orientational and conformational degrees of freedom during the separation process. Here the accuracy and convergence of the two approaches are critically compared in the case of two protein-ligand complexes (Abl kinase-SH3:p41 and MDM2-p53:NVP-CGM097) and three protein-protein complexes (pig insulin dimer, SARS-CoV-2 spike RBD:ACE2, and CheA kinase-P2:CheY). The results of the simulations that strictly follow the geometrical route match the experimental standard binding free energies within chemical accuracy. In contrast, simulations bereft of geometrical restraints converge more poorly, yielding inconsistent results that are at variance with the experimental measurements. Furthermore, the orientational and positional time correlation functions of the protein in the unrestrained simulations decay over several microseconds, a time scale that is far longer than the typical simulation times of the geometrical route, which explains why those simulations fail to sample the relevant degrees of freedom during the separation process of the complexes.

Antibody-nanobody combination increases their neutralizing activity against SARS-CoV-2 and nanobody H11-H4 is effective against Alpha, Kappa and Delta variants

The global spread of COVID-19 is devastating health systems and economies worldwide. While the use of vaccines has yielded encouraging results, the emergence of new variants of SARS-CoV-2 shows that combating COVID-19 remains a big challenge. One of the most promising treatments is the use of not only antibodies, but also nanobodies. Recent experimental studies revealed that the combination of antibody and nanobody can significantly improve their neutralizing ability through binding to the SARS-CoV-2 spike protein, but the molecular mechanisms underlying this observation remain largely unknown. In this work, we investigated the binding affinity of the CR3022 antibody and H11-H4 nanobody to the SARS-CoV-2 receptor binding domain (RBD) using molecular modeling. Both all-atom steered molecular dynamics simulations and coarse-grained umbrella sampling showed that, consistent with the experiment, CR3022 associates with RBD more strongly than H11-H4. We predict that the combination of CR3022 and H11-H4 considerably increases their binding affinity to the spike protein. The electrostatic interaction was found to control the association strength of CR3022, but the van der Waals interaction dominates in the case of H11-H4. However, our study for a larger set of nanobodies and antibodies showed that the relative role of these interactions depends on the specific complex. Importantly, we showed Beta, Gamma, Lambda, and Mu variants reduce the H11-H4 activity while Alpha, Kappa and Delta variants increase its neutralizing ability, which is in line with experiment reporting that the nanobody elicited from the llama is very promising for fighting against the Delta variant.

Response of Terahertz Protein Vibrations to Ligand Binding: Calmodulin-Peptide Complexes as a Case Study

Terahertz vibrations are sensitive reporters of the structure and interactions of proteins. Ligand binding alters the nature and distribution of these collective vibrations. The ligand-induced changes in the terahertz protein vibrations contribute to the binding entropy and to the overall thermodynamic stability of the resultant protein-ligand complexes. Here, we have examined the response of the low-frequency (below 6 terahertz) collective vibrations of the calcium-loaded calmodulin (CaM) to binding to five different ligands, both in the presence and absence of water, using normal-mode analysis and molecular dynamics simulations. A comparison of the vibrational spectra of hydrated and dry systems reveals that protein-solvent interactions stiffen the terahertz protein vibrations and that these solvent-coupled collective vibrations contribute significantly to the hydration-sensitive variation in the vibrational entropy of CaM. In the absence of water, the low-frequency vibrations of CaM are stiffened by ligand binding. On the contrary, the number and the cumulative vibrational entropy of low-frequency vibrational modes (ω < 200 cm^-1) of the hydrated CaM are increased noticeably after binding to the peptides, indicating binding-induced softening of collective vibrations of the protein. Although the calculated and experimental binding affinities of the chosen complexes correlated reasonably well, no systematic correlation was observed between the protein vibrational entropy and the binding affinity. The results underscored the importance of the interplay of protein-ligand and solvent interactions in modulating the low-frequency vibrations of proteins.

Communication pathways bridge local and global conformations in an IgG4 antibody

The affinity of an antibody for its antigen is primarily determined by the specific sequence and structural arrangement of the complementarity-determining regions (CDRs). Recent evidence, however, points toward a nontrivial relation between the CDR and distal sites: variations in the binding strengths have been observed upon mutating residues separated from the paratope by several nanometers, thus suggesting the existence of a communication network within antibodies, whose extension and relevance might be deeper than insofar expected. In this work, we test this hypothesis by means of molecular dynamics (MD) simulations of the IgG4 monoclonal antibody pembrolizumab, an approved drug that targets the programmed cell death protein 1 (PD-1). The molecule is simulated in both the apo and holo states, totalling 4 μs of MD trajectory. The analysis of these simulations shows that the bound antibody explores a restricted range of conformations with respect to the apo one, and that the global conformation of the molecule correlates with that of the CDR. These results support the hypothesis that pembrolizumab featues a multi-scale hierarchy of intertwined global and local conformational changes. The analysis pipeline developed in this work is general, and it can help shed further light on the mechanistic aspects of antibody function.

Recent developments in multiscale free energy simulations

Physics-based free energy simulations enable the rigorous calculation of properties, such as conformational equilibria, solvation or binding free energies. While historically most applications have occurred at the atomistic level of resolution, a range of advances in the past years make it possible now to reliably cross the temporal, spatial and theory scales for the modeling of complex systems or the efficient prediction of results at the accuracy level of expensive quantum-mechanical calculations. In this mini-review, we discuss recent methodological advances as well as opportunities opened up by the introduction of machine learning approaches, which tackle the diverse challenges across the different scales, improve the accuracy and feasibility, and push the boundaries of multiscale free energy simulations.

Deep geometric representations for modeling effects of mutations on protein-protein binding affinity

Modeling the impact of amino acid mutations on protein-protein interaction plays a crucial role in protein engineering and drug design. In this study, we develop GeoPPI, a novel structure-based deep-learning framework to predict the change of binding affinity upon mutations. Based on the three-dimensional structure of a protein, GeoPPI first learns a geometric representation that encodes topology features of the protein structure via a self-supervised learning scheme. These representations are then used as features for training gradient-boosting trees to predict the changes of protein-protein binding affinity upon mutations. We find that GeoPPI is able to learn meaningful features that characterize interactions between atoms in protein structures. In addition, through extensive experiments, we show that GeoPPI achieves new state-of-the-art performance in predicting the binding affinity changes upon both single- and multi-point mutations on six benchmark datasets. Moreover, we show that GeoPPI can accurately estimate the difference of binding affinities between a few recently identified SARS-CoV-2 antibodies and the receptor-binding domain (RBD) of the S protein. These results demonstrate the potential of GeoPPI as a powerful and useful computational tool in protein design and engineering. Our code and datasets are available at: https://github.com/Liuxg16/GeoPPI.

Estimating the binding affinities of protein-protein interactions (PPIs) is crucial to understand protein function and design new functional proteins. Since the experimental measurement in wet-labs is labor-intensive and time-consuming, fast and accurate in silico approaches have received much attention. Although considerable efforts have been made in this direction, predicting the effects of mutations on the protein-protein binding affinity is still a challenging research problem. In this work, we introduce GeoPPI, a novel computational approach that uses deep geometric representations of protein complexes to predict the effects of mutations on the binding affinity. The geometric representations are first learned via a self-supervised learning scheme and then integrated with gradient-boosting trees to accomplish the prediction. We find that the learned representations encode meaningful patterns underlying the interactions between atoms in protein structures. Also, extensive tests on major benchmark datasets show that GeoPPI has made an important improvement over the existing methods in predicting the effects of mutations on the binding affinity.

Physical constraints and functional plasticity of cellulases

Enzyme reactions, both in Nature and technical applications, commonly occur at the interface of immiscible phases. Nevertheless, stringent descriptions of interfacial enzyme catalysis remain sparse, and this is partly due to a shortage of coherent experimental data to guide and assess such work. In this work, we produced and kinetically characterized 83 cellulases, which revealed a conspicuous linear free energy relationship (LFER) between the substrate binding strength and the activation barrier. The scaling occurred despite the investigated enzymes being structurally and mechanistically diverse. We suggest that the scaling reflects basic physical restrictions of the hydrolytic process and that evolutionary selection has condensed cellulase phenotypes near the line. One consequence of the LFER is that the activity of a cellulase can be estimated from its substrate binding strength, irrespectively of structural and mechanistic details, and this appears promising for in silico selection and design within this industrially important group of enzymes.

From System Modeling to System Analysis: The Impact of Resolution Level and Resolution Distribution in the Computer-Aided Investigation of Biomolecules

The ever increasing computer power, together with the improved accuracy of atomistic force fields, enables researchers to investigate biological systems at the molecular level with remarkable detail. However, the relevant length and time scales of many processes of interest are still hardly within reach even for state-of-the-art hardware, thus leaving important questions often unanswered. The computer-aided investigation of many biological physics problems thus largely benefits from the usage of coarse-grained models, that is, simplified representations of a molecule at a level of resolution that is lower than atomistic. A plethora of coarse-grained models have been developed, which differ most notably in their granularity; this latter aspect determines one of the crucial open issues in the field, i.e. the identification of an optimal degree of coarsening, which enables the greatest simplification at the expenses of the smallest information loss. In this review, we present the problem of coarse-grained modeling in biophysics from the viewpoint of system representation and information content. In particular, we discuss two distinct yet complementary aspects of protein modeling: on the one hand, the relationship between the resolution of a model and its capacity of accurately reproducing the properties of interest; on the other hand, the possibility of employing a lower resolution description of a detailed model to extract simple, useful, and intelligible information from the latter.

Implementing and Assessing an Alchemical Method for Calculating Protein-Protein Binding Free Energy

Protein-protein binding is fundamental to most biological processes. It is important to be able to use computation to accurately estimate the change in protein-protein binding free energy due to mutations in order to answer biological questions that would be experimentally challenging, laborious, or time-consuming. Although nonrigorous free-energy methods are faster, rigorous alchemical molecular dynamics-based methods are considerably more accurate and are becoming more feasible with the advancement of computer hardware and molecular simulation software. Even with sufficient computational resources, there are still major challenges to using alchemical free-energy methods for protein-protein complexes, such as generating hybrid structures and topologies, maintaining a neutral net charge of the system when there is a charge-changing mutation, and setting up the simulation. In the current study, we have used the pmx package to generate hybrid structures and topologies, and a double-system/single-box approach to maintain the net charge of the system. To test the approach, we predicted relative binding affinities for two protein-protein complexes using a nonequilibrium alchemical method based on the Crooks fluctuation theorem and compared the results with experimental values. The method correctly identified stabilizing from destabilizing mutations for a small protein-protein complex, and a larger, more challenging antibody complex. Strong correlations were obtained between predicted and experimental relative binding affinities for both protein-protein systems.

Unusual RNA binding of FUS RRM studied by molecular dynamics simulation and enhanced sampling method

Amyotrophic lateral sclerosis (ALS) and frontotemporal lobe degeneration (FTLD) are two inter-related intractable diseases of motor neuron degeneration. Fused in sarcoma (FUS) is found in cytoplasmic accumulation of ALS and FTLD patients, which readily link the protein with the diseases. The RNA recognition motif (RRM) of FUS has the canonical α-β folds along with an unusual lysine-rich loop (KK-loop) between α1 and β2. This KK-loop is highly conserved among FET family proteins. Another contrasting feature of FUS RRM is the absence of critical binding residues, which are otherwise highly conserved in canonical RRMs. These residues in FUS RRM are Thr286, Glu336, Thr338, and Ser367, which are substitutions of lysine, phenylalanine, phenylalanine, and lysine, respectively, in other RRMs. Considering the importance of FUS in RNA regulation and metabolism, and its implication in ALS and FTLD, it is important to elucidate the underlying molecular mechanism of RNA recognition. In this study, we have performed molecular dynamics simulation with enhanced sampling to understand the conformational dynamics of noncanonical FUS RRM and its binding with RNA. We studied two sets of mutations: one with alanine mutation of KK-loop and another with KK-loop mutations along with critical binding residues mutated back to their canonical form. We find that concerted movement of KK-loop and loop between β2 and β3 facilitates the folding of the partner RNA, indicating an induced-fit mechanism of RNA binding. Flexibility of the RRM is highly restricted upon mutating the lysine residues of the KK-loop, resulting in weaker binding with the RNA. Our results also suggest that absence of the canonical residues in FUS RRM along with the KK-loop is equally important in regulating its binding dynamics. This study provides a significant structural insight into the binding of FUS RRM with its cognate RNA, which may further help in designing potential drugs targeting noncanonical RNA recognition.

Assessment of software methods for estimating protein-protein relative binding affinities

A growing number of computational tools have been developed to accurately and rapidly predict the impact of amino acid mutations on protein-protein relative binding affinities. Such tools have many applications, for example, designing new drugs and studying evolutionary mechanisms. In the search for accuracy, many of these methods employ expensive yet rigorous molecular dynamics simulations. By contrast, non-rigorous methods use less exhaustive statistical mechanics, allowing for more efficient calculations. However, it is unclear if such methods retain enough accuracy to replace rigorous methods in binding affinity calculations. This trade-off between accuracy and computational expense makes it difficult to determine the best method for a particular system or study. Here, eight non-rigorous computational methods were assessed using eight antibody-antigen and eight non-antibody-antigen complexes for their ability to accurately predict relative binding affinities (ΔΔG) for 654 single mutations. In addition to assessing accuracy, we analyzed the CPU cost and performance for each method using a variety of physico-chemical structural features. This allowed us to posit scenarios in which each method may be best utilized. Most methods performed worse when applied to antibody-antigen complexes compared to non-antibody-antigen complexes. Rosetta-based JayZ and EasyE methods classified mutations as destabilizing (ΔΔG < -0.5 kcal/mol) with high (83-98%) accuracy and a relatively low computational cost for non-antibody-antigen complexes. Some of the most accurate results for antibody-antigen systems came from combining molecular dynamics with FoldX with a correlation coefficient (r) of 0.46, but this was also the most computationally expensive method. Overall, our results suggest these methods can be used to quickly and accurately predict stabilizing versus destabilizing mutations but are less accurate at predicting actual binding affinities. This study highlights the need for continued development of reliable, accessible, and reproducible methods for predicting binding affinities in antibody-antigen proteins and provides a recipe for using current methods.

Predicting the viability of beta-lactamase: How folding and binding free energies correlate with beta-lactamase fitness

One of the long-standing holy grails of molecular evolution has been the ability to predict an organism’s fitness directly from its genotype. With such predictive abilities in hand, researchers would be able to more accurately forecast how organisms will evolve and how proteins with novel functions could be engineered, leading to revolutionary advances in medicine and biotechnology. In this work, we assemble the largest reported set of experimental TEM-1 β-lactamase folding free energies and use this data in conjunction with previously acquired fitness data and computational free energy predictions to determine how much of the fitness of β-lactamase can be directly predicted by thermodynamic folding and binding free energies. We focus upon β-lactamase because of its long history as a model enzyme and its central role in antibiotic resistance. Based upon a set of 21 β-lactamase single and double mutants expressly designed to influence protein folding, we first demonstrate that modeling software designed to compute folding free energies such as FoldX and PyRosetta can meaningfully, although not perfectly, predict the experimental folding free energies of single mutants. Interestingly, while these techniques also yield sensible double mutant free energies, we show that they do so for the wrong physical reasons. We then go on to assess how well both experimental and computational folding free energies explain single mutant fitness. We find that folding free energies account for, at most, 24% of the variance in β-lactamase fitness values according to linear models and, somewhat surprisingly, complementing folding free energies with computationally-predicted binding free energies of residues near the active site only increases the folding-only figure by a few percent. This strongly suggests that the majority of β-lactamase’s fitness is controlled by factors other than free energies. Overall, our results shed a bright light on to what extent the community is justified in using thermodynamic measures to infer protein fitness as well as how applicable modern computational techniques for predicting free energies will be to the large data sets of multiply-mutated proteins forthcoming.

Monte Carlo simulation and thermodynamic integration applied to protein charge transfer

We introduce a combination of Monte Carlo simulation and thermodynamic integration methods to address a model problem in free energy computations, electron transfer in proteins. The feasibility of this approach is tested using the ferredoxin protein from Clostridium acidurici. The results are compared to numerical solutions of the Poisson-Boltzmann equation and data from recent molecular dynamics simulations on charge transfer in a protein complex, the NrfHA nitrite reductase of Desulfovibrio vulgaris. Despite the conceptual and computational simplicity of the Monte Carlo approach, the data agree well with those obtained by other methods. A link to experiments is established via the cytochrome subunit of the bacterial photosynthetic reaction center of Rhodopseudomonas viridis.

The four-helix bundle in cholinesterase dimers: Structural and energetic determinants of stability

The crystal structures of truncated forms of cholinesterases provide good models for assessing the role of non-covalent interactions in dimer assembly in the absence of cross-linking disulfide bonds. These structures identify the four-helix bundle that serves as the interface for formation of acetylcholinesterase and butyrylcholinesterase dimers. Here we performed a theoretical comparison of the structural and energetic factors governing dimerization. This included identification of inter-subunit and intra-subunit hydrogen bonds and hydrophobic interactions, evaluation of solvent-accessible surfaces, and estimation of electrostatic contributions to dimerization. To reveal the contribution to dimerization of individual amino acids within the contact area, free energy perturbation alanine screening was performed. Markov state modelling shows that the loop between the α13 and α14 helices in BChE is unstable, and occupies 4 macro-states. The order of magnitude of mean first passage times between these macrostates is ~10^-8 s. Replica exchange molecular dynamics umbrella sampling calculations revealed that the free energy of human BChE dimerization is -15.5 kcal/mol, while that for human AChE is -26.4 kcal/mol. Thus, the C-terminally truncated human butyrylcholinesterase dimer is substantially less stable than that of human acetylcholinesterase. An animated Interactive 3D Complement (I3DC) is available in Proteopedia at http://proteopedia.org/w/Journal:CHEMBIOINT:1.

From quantum to subcellular scales: multi-scale simulation approaches and the SIRAH force field

Modern molecular and cellular biology profits from astonishing resolution structural methods, currently even reaching the whole cell level. This is encompassed by the development of computational methods providing a deep view into the structure and dynamics of molecular processes happening at very different scales in time and space. Linking such scales is of paramount importance when aiming at far-reaching biological questions. Computational methods at the interface between classical and coarse-grained resolutions are gaining momentum with several research groups dedicating important efforts to their development and tuning. An overview of such methods is addressed herein, with special emphasis on the SIRAH force field for coarse-grained and multi-scale simulations. Moreover, we provide proof of concept calculations on the implementation of a multi-scale simulation scheme including quantum calculations on a classical fine-grained/coarse-grained representation of double-stranded DNA. This opens the possibility to include the effect of large conformational fluctuations in chromatin segments on, for instance, the reactivity of particular base pairs within the same simulation framework.

Experimentally guided computational antibody affinity maturation with de novo docking, modelling and rational design

Antibodies are an important class of therapeutics that have significant clinical impact for the treatment of severe diseases. Computational tools to support antibody drug discovery have been developing at an increasing rate over the last decade and typically rely upon a predetermined co-crystal structure of the antibody bound to the antigen for structural predictions. Here, we show an example of successful in silico affinity maturation of a hybridoma derived antibody, AB1, using just a homology model of the antibody fragment variable region and a protein-protein docking model of the AB1 antibody bound to the antigen, murine CCL20 (muCCL20). In silico affinity maturation, together with alanine scanning, has allowed us to fine-tune the protein-protein docking model to subsequently enable the identification of two single-point mutations that increase the affinity of AB1 for muCCL20. To our knowledge, this is one of the first examples of the use of homology modelling and protein docking for affinity maturation and represents an approach that can be widely deployed.

Refining evERdock: Improved selection of good protein-protein complex models achieved by MD optimization and use of multiple conformations

A method for evaluating binding free energy differences of protein-protein complex structures generated by protein docking was recently developed by some of us. The method, termed evERdock, combined short (2 ns) molecular dynamics (MD) simulations in explicit water and solution theory in the energy representation (ER) and succeeded in selecting the near-native complex structures from a set of decoys. In the current work, we performed longer (up to 100 ns) MD simulations before employing ER analysis in order to further refine the structures of the decoy set with improved binding free energies. Moreover, we estimated the binding free energies for each complex structure based on an average value from five individual MD snapshots. After MD simulations, all decoys exhibit a decrease in binding free energy, suggesting that proper equilibration in explicit solvent resulted in more favourably bound complexes. During the MD simulations, non-native structures tend to become unstable and in some cases dissociate, while near-native structures maintain a stable interface. The energies after the MD simulations show an improved correlation between similarity criteria (such as interface root-mean-square distance) to the native (crystal) structure and the binding free energy. In addition, calculated binding free energies show sensitivity to the number of contacts, which was demonstrated to reflect the relative stability of structures at earlier stages of the MD simulation. We therefore conclude that the additional equilibration step along with the use of multiple conformations can make the evERdock scheme more versatile under low computational cost.

Balancing Force Field Protein-Lipid Interactions To Capture Transmembrane Helix-Helix Association

Atomistic simulations have recently been shown to be sufficiently accurate to reversibly fold globular proteins and have provided insights into folding mechanisms. Gaining similar understanding from simulations of membrane protein folding and association would be of great medical interest. All-atom simulations of the folding and assembly of transmembrane protein domains are much more challenging, not least due to very slow diffusion within the lipid bilayer membrane. Here, we focus on a simple and well-characterized prototype of membrane protein folding and assembly, namely the dimerization of glycophorin A, a homodimer of single transmembrane helices. We have determined the free energy landscape for association of the dimer using the CHARMM36 force field. We find that the native structure is a metastable state, but not stable as expected from experimental estimates of the dissociation constant and numerous experimental structures obtained under a variety of conditions. We explore two straightforward approaches to address this problem and demonstrate that they result in stable dimers with dissociation constants consistent with experimental data.