Comment on 'Valid molecular dynamics simulations of human hemoglobin require a surprisingly large box size'

A single mutation in dairy cow-associated H5N1 viruses increases receptor binding breadth

Clade 2.3.4.4b H5N1 is causing an unprecedented outbreak in dairy cows in the United States. To understand if recent H5N1 viruses are changing their receptor use, we screened recombinant hemagglutinin (HA) from historical and recent 2.3.4.4b H5N1 viruses for binding to distinct glycans bearing terminal sialic acids using a glycan microarray. We find that H5 from A/Texas/37/2024, an isolate from the dairy cow outbreak, has increased binding breadth to core glycans bearing terminal α2,3 sialic acids, the avian receptor, compared to historical and recent 2.3.4.4b H5N1 viruses. We do not observe any binding to α2,6 sialic acids, the receptor used by human seasonal influenza viruses. Using molecular dynamics and a cryo-EM structure of A/Texas/37/2024 H5, we show A/Texas/37/2024 H5 is more flexible within the receptor-binding site compared to a 2.3.4.4b H5 from 2022. We identify a single mutation outside of the receptor binding site, T199I, is responsible for increased binding breadth, as it increases receptor binding site flexibility. Together, these data show recent H5N1 viruses are evolving increased receptor binding breadth which could impact the host range and cell types infected with H5N1.

CDR L3 Loop Rearrangement Switches Multispecific SPE-7 IgE Antibody From Hapten to Protein Binding

The monoclonal IgE antibody SPE-7 was originally raised against a 2,4-dinitrophenyl (DNP) target. Through its ability to adopt multiple conformations, the antibody is capable of binding to a diverse range of small haptens and large proteins. The present study examines a dataset of experimentally determined crystal structures of the SPE-7 antibody to gain insight into the mechanisms that contribute to its multispecificity. With the emergence of more and more therapeutic antibodies against a huge repertoire of different targets, our research could be of great interest for future drug development. We are able to discriminate between the different paratope-binding states in the conformational ensembles obtained by enhanced sampling molecular dynamics simulations, and to calculate their transition timescales and state probabilities. Furthermore, we describe the key residues responsible for discriminating between the different binding capacities and identify a tryptophan in a central position of the CDR L3 loop as the residue of greatest interest. The overall dynamics of the paratope appear to be mainly influenced by the CDR L3 and CDR L1 loops.

Defining the cross-reactivity between peanut allergens Ara h 2 and Ara h 6 using monoclonal antibodies

In peanut allergy, Arachis hypogaea 2 (Ara h 2) and Arachis hypogaea 6 (Ara h 6) are two clinically relevant peanut allergens with known structural and sequence homology and demonstrated cross-reactivity. We have previously utilized X-ray crystallography and epitope binning to define the epitopes on Ara h 2. We aimed to quantitatively characterize the cross-reactivity between Ara h 2 and Ara h 6 on a molecular level using human monoclonal antibodies (mAbs) and structural characterization of allergenic epitopes. We utilized mAbs cloned from Ara h 2 positive single B cells isolated from peanut-allergic, oral immunotherapy-treated patients to quantitatively analyze cross-reactivity between recombinant Ara h 2 (rAra h 2) and Ara h 6 (rAra h 6) proteins using biolayer interferometry and indirect inhibitory ELISA. Molecular dynamics simulations assessed time-dependent motions and interactions in the antibody-antigen complexes. Three epitopes-conformational epitopes 1.1 and 3, and the sequential epitope KRELRNL/KRELMNL-are conserved between Ara h 2 and Ara h 6, while two more conformational and three sequential epitopes are not. Overall, mAb affinity was significantly lower to rAra h 6 than it was to rAra h 2. This difference in affinity was primarily due to increased dissociation of the antibodies from rAra h 6, a phenomenon explained by the higher conformational flexibility of the Ara h 6-antibody complexes in comparison to Ara h 2-antibody complexes. Our results further elucidate the cross-reactivity of peanut 2S albumins on a molecular level and support the clinical immunodominance of Ara h 2.

The Role of Force Fields and Water Models in Protein Folding and Unfolding Dynamics

Protein folding is a fascinating, not fully understood phenomenon in biology. Molecular dynamics (MD) simulations are an invaluable tool to study conformational changes in atomistic detail, including folding and unfolding processes of proteins. However, the accuracy of the conformational ensembles derived from MD simulations inevitably relies on the quality of the underlying force field in combination with the respective water model. Here, we investigate protein folding, unfolding, and misfolding of fast-folding proteins by examining different force fields with their recommended water models, i.e., ff14SB with the TIP3P model and ff19SB with the OPC model. To this end, we generated long conventional MD simulations highlighting the perks and pitfalls of these setups. Using Markov state models, we defined kinetically independent conformational substates and emphasized their distinct characteristics, as well as their corresponding state probabilities. Surprisingly, we found substantial differences in thermodynamics and kinetics of protein folding, depending on the combination of the protein force field and water model, originating primarily from the different water models. These results emphasize the importance of carefully choosing the force field and the respective water model as they determine the accuracy of the observed dynamics of folding events. Thus, the findings support the hypothesis that the water model is at least equally important as the force field and hence needs to be considered in future studies investigating protein dynamics and folding in all areas of biophysics.

Guidelines for Free-Energy Calculations Involving Charge Changes

The Coulomb interactions in molecular simulations are inherently approximated due to the finite size of the molecular box sizes amenable to current-day compute power. Several methods exist for treating long-range electrostatic interactions, yet these approaches are subject to various finite-size-related artifacts. Lattice-sum methods are frequently used to approximate long-range interactions; however, these approaches also suffer from artifacts which become particularly pronounced for free-energy calculations that involve charge changes. The artifacts, however, also affect the sampling when plain simulations are performed, leading to a biased ensemble. Here, we investigate two previously described model systems to determine if artifacts continue to play a role when overall neutral boxes are considered, in the context of both free-energy calculations and sampling. We find that ensuring that no net-charge changes take place, while maintaining a neutral simulation box, may be sufficient provided that the simulation boxes are large enough. Addition of salt to the solution (when appropriate) can further alleviate the remaining artifacts in the sampling or the calculated free-energy differences. We provide practical guidelines to avoid finite-size artifacts.

Phage display assisted discovery of a pH-dependent anti-α-cobratoxin antibody from a natural variable domain library

Recycling IgG antibodies bind to their target antigen at physiological pH in the blood stream and release them upon endocytosis when pH levels drop, allowing the IgG antibodies to be recycled into circulation via FcRn-mediated cellular pathways, while the antigens undergo lysosomal degradation. This enables recycling antibodies to achieve comparable therapeutic effect at lower doses than their non-recycling counterparts. The development of such antibodies is typically achieved by histidine doping of their variable regions or by performing in vitro antibody selection campaigns utilizing histidine doped libraries. Both are strategies that may introduce sequence liabilities. Here, we present a methodology that employs a naïve antibody phage display library, consisting of natural variable domains, to discover antibodies that bind α-cobratoxin from the venom of Naja kaouthia in a pH-dependent manner. As a result, an antibody was discovered that exhibits a 7-fold higher off-rate at pH 5.5 than pH 7.4 in bio-layer interferometry experiments. Interestingly, no histidine residues were found in its variable domains, and in addition, the antibody showed pH-dependent binding to a histidine-devoid antigen mutant. As such, the results demonstrate that pH-dependent antigen-antibody binding may not always be driven by histidine residues. By employing molecular dynamics simulations, different protonation states of titratable residues were found, which potentially could be responsible for the observed pH-dependent antigen binding properties of the antibody. Finally, given the typically high diversity of naïve antibody libraries, the methodology presented here can likely be applied to discover recycling antibodies against different targets ab initio without the need for histidine doping.

Structural Investigation of DHICA Eumelanin Using Density Functional Theory and Classical Molecular Dynamics Simulations

Eumelanin is an important pigment, for example, in skin, hair, eyes, and the inner ear. It is a highly heterogeneous polymer with 5,6-dihydroxyindole-2-carboxylic acid (DHICA) and 5,6-dihydroxyindole (DHI) building blocks, of which DHICA is reported as the more abundant in natural eumelanin. The DHICA-eumelanin protomolecule consists of three building blocks, indole-2-carboxylic acid-5,6-quinone (ICAQ), DHICA and pyrrole-2,3,5-tricarboxylic acid (PTCA). Here, we focus on the self-assembly of DHICA-eumelanin using multi-microsecond molecular dynamics (MD) simulations at various concentrations in aqueous solutions. The molecule was first parameterized using density functional theory (DFT) calculations. Three types of systems were studied: (1) uncharged DHICA-eumelanin, (2) charged DHICA-eumelanin corresponding to physiological pH, and (3) a binary mixture of both of the above protomolecules. In the case of uncharged DHICA-eumelanin, spontaneous aggregation occurred and water molecules were present inside the aggregates. In the systems corresponding to physiological pH, all the carboxyl groups are negatively charged and the DHICA-eumelanin model has a net charge of -4. The effect of K+ ions as counterions was investigated. The results show high probability of binding to the deprotonated oxygens of the carboxylate anions in the PTCA moiety. Furthermore, the K+ counterions increased the solubility of DHICA-eumelanin in its charged form. A possible explanation is that the charged protomolecules favor binding to the K+ ions rather than aggregating and binding to other protomolecules. The binary mixtures show aggregation of uncharged DHICA-eumelanins; unlike the charged systems with no aggregation, a few charged DHICA-eumelanins are present on the surface of the uncharged aggregation, binding to the K+ ions.

Implementation of Telescoping Boxes in Adaptive Steered Molecular Dynamics

Long-time dynamical processes, such as those involving protein unfolding and ligand interactions, can be accelerated and realized through steered molecular dynamics (SMD). The challenge has been the extraction of information from such simulations that generalize for complex nonequilibrium processes. The use of Jarzynski's equality opened the possibility of determining the free energy along the steered coordinate, but sampling over the nonequilibrium trajectories is slow to converge. Adaptive steered molecular dynamics (ASMD) and other related techniques have been introduced to overcome this challenge through the use of stages. Here, we take advantage of these stages to address the numerical cost that arises from the required use of very large solvent boxes. We introduce telescoping box schemes within adaptive steered molecular dynamics (ASMD) in which we adjust the solvent box between stages and thereby vary (and optimize) the required number of solvent molecules. We have benchmarked the method on a relatively long α-helical peptide, Ala₃₀, with respect to the potential of mean force and hydrogen bonds. We show that the use of telescoping boxes introduces little numerical error while significantly reducing the computational cost.

Nanobody Paratope Ensembles in Solution Characterized by MD Simulations and NMR

Variable domains of camelid antibodies (so-called nanobodies or VHH) are the smallest antibody fragments that retain complete functionality and therapeutic potential. Understanding of the nanobody-binding interface has become a pre-requisite for rational antibody design and engineering. The nanobody-binding interface consists of up to three hypervariable loops, known as the CDR loops. Here, we structurally and dynamically characterize the conformational diversity of an anti-GFP-binding nanobody by using molecular dynamics simulations in combination with experimentally derived data from nuclear magnetic resonance (NMR) spectroscopy. The NMR data contain both structural and dynamic information resolved at various timescales, which allows an assessment of the quality of protein MD simulations. Thus, in this study, we compared the ensembles for the anti-GFP-binding nanobody obtained from MD simulations with results from NMR. We find excellent agreement of the NOE-derived distance maps obtained from NMR and MD simulations and observe similar conformational spaces for the simulations with and without NOE time-averaged restraints. We also compare the measured and calculated order parameters and find generally good agreement for the motions observed in the ps-ns timescale, in particular for the CDR3 loop. Understanding of the CDR3 loop dynamics is especially critical for nanobodies, as this loop is typically critical for antigen recognition.

Free Energy and Stacking of Eumelanin Nanoaggregates

Eumelanin, a member of the melanin family, is a black-brown insoluble pigment. It possesses a broad range of properties such as antioxidation, free radical scavenging, photoprotection, and charge carrier transportation. Surprisingly, the exact molecular structure of eumelanin remains undefined. It is, however, generally considered to consist of two main building blocks, 5,6-dihydroxyindole (DHI) and 5,6- dihydroxyindole carboxylic acid (DHICA). We focus on DHI and report, for the first time, a computational investigation of the structural properties of DHI-eumelanin aggregates in aqueous solutions. First, multimicrosecond molecular dynamics (MD) simulations at different concentrations were performed to investigate the aggregation and ordering of tetrameric DHI-eumelanin protomolecules. This was followed by umbrella sampling (US) and density functional theory (DFT) calculations to study the physical mechanisms of stacking. Aggregation occurs through formation of nanoscale stacks and was observed in all systems. Further analyses showed that aggregation and coarsening of the domains is due to a decrease in hydrogen bonds between the eumelanins and water; while domains exist, there is no long-range order. The results show noncovalent stacks with the interlayer distance between eumelanin protomolecules being less than 3.5 Å. This is in good agreement with transmission electron microscopy data. Both free energy calculations and DFT revealed strong stacking interactions. The electrostatic potential map provides an explanation and a rationale for the slightly sheared relative orientations and, consequently, for the curved shapes of the nanoscale domains.

Comparing Antibody Interfaces to Inform Rational Design of New Antibody Formats

As the current biotherapeutic market is dominated by antibodies, the design of different antibody formats, like bispecific antibodies and other new formats, represent a key component in advancing antibody therapy. When designing new formats, a targeted modulation of pairing preferences is key. Several existing approaches are successful, but expanding the repertoire of design possibilities would be desirable. Cognate immunoglobulin G antibodies depend on homodimerization of the fragment crystallizable regions of two identical heavy chains. By modifying the dimeric interface of the third constant domain (CH3-CH3), with different mutations on each domain, the engineered Fc fragments form rather heterodimers than homodimers. The first constant domain (CH1-CL) shares a very similar fold and interdomain orientation with the CH3-CH3 dimer. Thus, numerous well-established design efforts for CH3-CH3 interfaces, have also been applied to CH1-CL dimers to reduce the number of mispairings in the Fabs. Given the high structural similarity of the CH3-CH3 and CH1-CL domains we want to identify additional opportunities in comparing the differences and overlapping interaction profiles. Our vision is to facilitate a toolkit that allows for the interchangeable usage of different design tools from crosslinking the knowledge between these two interface types. As a starting point, here, we use classical molecular dynamics simulations to identify differences of the CH3-CH3 and CH1-CL interfaces and already find unexpected features of these interfaces shedding new light on possible design variations. Apart from identifying clear differences between the similar CH3-CH3 and CH1-CL dimers, we structurally characterize the effects of point-mutations in the CH3-CH3 interface on the respective dynamics and interface interaction patterns. Thus, this study has broad implications in the field of antibody engineering as it provides a structural and mechanistical understanding of antibody interfaces and thereby presents a crucial aspect for the design of bispecific antibodies.

Dynamics of camel and human hemoglobin revealed by molecular simulations

Hemoglobin is one of the most widely studied proteins genetically, biochemically, and structurally. It is an oxygen carrying tetrameric protein that imparts the characteristic red color to blood. Each chain of hemoglobin harbors a heme group embedded in a hydrophobic pocket. Several studies have investigated structural variations present in mammalian hemoglobin and their functional implications. However, camel hemoglobin has not been thoroughly explored, especially from a structural perspective. Importantly, very little is known about how the heme group interacts with hemoglobin under varying conditions of osmolarity and temperature. Several experimental studies have indicated that the tense (T) state is more stable than the relaxed (R) state of hemoglobin under normal physiological conditions. Despite the fact that R state is less stable than the T state, no extensive structural dynamics studies have been performed to investigate global quaternary transitions of R state hemoglobin under normal physiological conditions. To evaluate this, several 500 ns all-atom molecular dynamics simulations were performed to get a deeper understanding of how camel hemoglobin behaves under stress, which it is normally exposed to, when compared to human hemoglobin. Notably, camel hemoglobin was more stable under physiological stress when compared to human hemoglobin. Additionally, when compared to camel hemoglobin, cofactor-binding regions of hemoglobin also exhibited more fluctuations in human hemoglobin under the conditions studied. Several differences were observed between the residues of camel and human hemoglobin that interacted with heme. Importantly, distal residues His58 of α hemoglobin and His63 of β hemoglobin formed more sustained interactions, especially at higher temperatures, in camel hemoglobin. These residues are important for oxygen binding to hemoglobin. Thus, this work provides insights into how camel and human hemoglobin differ in their interactions under stress.

The functional role of the hemoglobin-water interface

The interface between hemoglobin (Hb) and its environment, in particular water, is of great physiological relevance. Here, results from in vitro, in vivo, and computational experiments (molecular dynamics simulations) are summarized and put into perspective. One of the main findings from the computations is that the stability of the deoxy, ligand-free T-state (T₀) can be stabilized relative to the deoxy R-state (R₀) only in sufficiently large simulation boxes for the hydrophobic effect to manifest itself. This effect directly influences protein stability and is operative also under physiological conditions. Furthermore, molecular simulations provide a dynamical interpretation of the Perutz model for Hb function. Results from experiments using higher protein concentrations and realistic cellular environments are also discussed. One of the next great challenges for computational studies, which as we show is likely to be taken up in the near future, is to provide a molecular-level understanding of the dynamics of proteins in such crowded environments.

Molecular Dynamics of Hemoglobin Reveals Structural Alterations and Explains the Interactions Driving Sickle Cell Fibrillation

In sickle cell anemia, deoxyhemoglobin deforms RBCs by forming fibrils inside that disintegrate on oxygenation. We studied 100 ns long all-atom molecular dynamics (MD) for sickle and normal hemoglobin fibril models to understand this process, complemented by multiple 1 μs MD for a single tetramer of sickle and normal hemoglobin in deoxy and oxy states. We find that the presence of hydrophobic residues without a bulky side chain at β-6 in hemoglobin is the reason for the stability of the fibrils. Moreover, the free energy landscapes from MD of hemoglobin starting in the tensed (T) state capture the putative transition from T to relaxed (R) state, associated with oxygen binding. The three conformational wells in the landscapes are characterized by the quaternary changes where one αβ dimer rotates with respect to the other. The conformational changes from the oxygenation of sickle hemoglobin hinder the intermolecular contacts necessary for fibril formation.

Ensembles Are Required to Handle Aleatoric and Parametric Uncertainty in Molecular Dynamics Simulation

Classical molecular dynamics is a computer simulation technique that is in widespread use across many areas of science, from physics and chemistry to materials, biology, and medicine. The method continues to attract criticism due its oft-reported lack of reproducibility which is in part due to a failure to submit it to reliable uncertainty quantification (UQ). Here we show that the uncertainty arises from a combination of (i) the input parameters and (ii) the intrinsic stochasticity of the method controlled by the random seeds. To illustrate the situation, we make a systematic UQ analysis of a widely used molecular dynamics code (NAMD), applied to estimate binding free energy of a ligand-bound to a protein. In particular, we replace the usually fixed input parameters with random variables, systematically distributed about their mean values, and study the resulting distribution of the simulation output. We also perform a sensitivity analysis, which reveals that, out of a total of 175 parameters, just six dominate the variance in the code output. Furthermore, we show that binding energy calculations dampen the input uncertainty, in the sense that the variation around the mean output free energy is less than the variation around the mean of the assumed input distributions, if the output is ensemble-averaged over the random seeds. Without such ensemble averaging, the predicted free energy is five times more uncertain. The distribution of the predicted properties is thus strongly dependent upon the random seed. Owing to this substantial uncertainty, robust statistical measures of uncertainty in molecular dynamics simulation require the use of ensembles in all contexts.

Pore mutation N617D in the skeletal muscle DHPR blocks Ca2+ influx due to atypical high-affinity Ca2+ binding

Skeletal muscle excitation-contraction (EC) coupling roots in Ca²⁺-influx-independent inter-channel signaling between the sarcolemmal dihydropyridine receptor (DHPR) and the ryanodine receptor (RyR1) in the sarcoplasmic reticulum. Although DHPR Ca²⁺ influx is irrelevant for EC coupling, its putative role in other muscle-physiological and developmental pathways was recently examined using two distinct genetically engineered mouse models carrying Ca²⁺ non-conducting DHPRs: DHPR(N617D) (Dayal et al., 2017) and DHPR(E1014K) (Lee et al., 2015). Surprisingly, despite complete block of DHPR Ca²⁺-conductance, histological, biochemical, and physiological results obtained from these two models were contradictory. Here, we characterize the permeability and selectivity properties and henceforth the mechanism of Ca²⁺ non-conductance of DHPR(N617). Our results reveal that only mutant DHPR(N617D) with atypical high-affinity Ca²⁺ pore-binding is tight for physiologically relevant monovalent cations like Na⁺ and K⁺. Consequently, we propose a molecular model of cooperativity between two ion selectivity rings formed by negatively charged residues in the DHPR pore region.

Uncertainty quantification in classical molecular dynamics

Molecular dynamics simulation is now a widespread approach for understanding complex systems on the atomistic scale. It finds applications from physics and chemistry to engineering, life and medical science. In the last decade, the approach has begun to advance from being a computer-based means of rationalizing experimental observations to producing apparently credible predictions for a number of real-world applications within industrial sectors such as advanced materials and drug discovery. However, key aspects concerning the reproducibility of the method have not kept pace with the speed of its uptake in the scientific community. Here, we present a discussion of uncertainty quantification for molecular dynamics simulation designed to endow the method with better error estimates that will enable it to be used to report actionable results. The approach adopted is a standard one in the field of uncertainty quantification, namely using ensemble methods, in which a sufficiently large number of replicas are run concurrently, from which reliable statistics can be extracted. Indeed, because molecular dynamics is intrinsically chaotic, the need to use ensemble methods is fundamental and holds regardless of the duration of the simulations performed. We discuss the approach and illustrate it in a range of applications from materials science to ligand-protein binding free energy estimation. This article is part of the theme issue 'Reliability and reproducibility in computational science: implementing verification, validation and uncertainty quantification in silico'.

Accurate absolute free energies for ligand-protein binding based on non-equilibrium approaches

The accurate calculation of the binding free energy for arbitrary ligand-protein pairs is a considerable challenge in computer-aided drug discovery. Recently, it has been demonstrated that current state-of-the-art molecular dynamics (MD) based methods are capable of making highly accurate predictions. Conventional MD-based approaches rely on the first principles of statistical mechanics and assume equilibrium sampling of the phase space. In the current work we demonstrate that accurate absolute binding free energies (ABFE) can also be obtained via theoretically rigorous non-equilibrium approaches. Our investigation of ligands binding to bromodomains and T4 lysozyme reveals that both equilibrium and non-equilibrium approaches converge to the same results. The non-equilibrium approach achieves the same level of accuracy and convergence as an equilibrium free energy perturbation (FEP) method enhanced by Hamiltonian replica exchange. We also compare uni- and bi-directional non-equilibrium approaches and demonstrate that considering the work distributions from both forward and reverse directions provides substantial accuracy gains. In summary, non-equilibrium ABFE calculations are shown to yield reliable and well-converged estimates of protein-ligand binding affinity.

Biomolecular Modeling and Simulation: A Prospering Multidisciplinary Field

We reassess progress in the field of biomolecular modeling and simulation, following up on our perspective published in 2011. By reviewing metrics for the field's productivity and providing examples of success, we underscore the productive phase of the field, whose short-term expectations were overestimated and long-term effects underestimated. Such successes include prediction of structures and mechanisms; generation of new insights into biomolecular activity; and thriving collaborations between modeling and experimentation, including experiments driven by modeling. We also discuss the impact of field exercises and web games on the field's progress. Overall, we note tremendous success by the biomolecular modeling community in utilization of computer power; improvement in force fields; and development and application of new algorithms, notably machine learning and artificial intelligence. The combined advances are enhancing the accuracy andscope of modeling and simulation, establishing an exemplary discipline where experiment and theory or simulations are full partners.

Shark Antibody Variable Domains Rigidify Upon Affinity Maturation-Understanding the Potential of Shark Immunoglobulins as Therapeutics

Sharks and other cartilaginous fish are the phylogenetically oldest living organisms that have antibodies as part of their adaptive immune system. As part of their humoral adaptive immune response, they produce an immunoglobulin, the so-called immunoglobulin new antigen receptor (IgNAR), a heavy-chain only antibody. The variable domain of an IgNAR, also known as V NAR , binds the antigen as an independent soluble domain. In this study, we structurally and dynamically characterized the affinity maturation mechanism of the germline and somatically matured (PBLA8) V NAR to better understand their function and their applicability as therapeutics. We observed a substantial rigidification upon affinity maturation, which is accompanied by a higher number of contacts, thereby contributing to the decrease in flexibility. Considering the static x-ray structures, the observed rigidification is not obvious, as especially the mutated residues undergo conformational changes during the simulation, resulting in an even stronger network of stabilizing interactions. Additionally, the simulations of the V NAR in complex with the hen egg-white lysozyme show that the V NAR antibodies evidently follow the concept of conformational selection, as the binding-competent state already preexisted even without the presence of the antigen. To have a more detailed description of antibody-antigen recognition, we also present here the binding/unbinding mechanism between the hen egg-white lysozyme and both the germline and matured V NAR s. Upon maturation, we observed a substantial increase in the resulting dissociation-free energy barrier. Furthermore, we were able to kinetically and thermodynamically describe the binding process and did not only identify a two-step binding mechanism, but we also found a strong population shift upon affinity maturation toward the native binding pose.

Rapid, accurate, precise and reproducible ligand-protein binding free energy prediction

A central quantity of interest in molecular biology and medicine is the free energy of binding of a molecule to a target biomacromolecule. Until recently, the accurate prediction of binding affinity had been widely regarded as out of reach of theoretical methods owing to the lack of reproducibility of the available methods, not to mention their complexity, computational cost and time-consuming procedures. The lack of reproducibility stems primarily from the chaotic nature of classical molecular dynamics (MD) and the associated extreme sensitivity of trajectories to their initial conditions. Here, we review computational approaches for both relative and absolute binding free energy calculations, and illustrate their application to a diverse set of ligands bound to a range of proteins with immediate relevance in a number of medical domains. We focus on ensemble-based methods which are essential in order to compute statistically robust results, including two we have recently developed, namely thermodynamic integration with enhanced sampling and enhanced sampling of MD with an approximation of continuum solvent. Together, these form a set of rapid, accurate, precise and reproducible free energy methods. They can be used in real-world problems such as hit-to-lead and lead optimization stages in drug discovery, and in personalized medicine. These applications show that individual binding affinities equipped with uncertainty quantification may be computed in a few hours on a massive scale given access to suitable high-end computing resources and workflow automation. A high level of accuracy can be achieved using these approaches.

Surprisingly Fast Interface and Elbow Angle Dynamics of Antigen-Binding Fragments

Fab consist of a heavy and light chain and can be subdivided into a variable (V H and V L ) and a constant region (C H 1 and C L ). The variable region contains the complementarity-determining region (CDR), which is formed by six hypervariable loops, shaping the antigen binding site, the paratope. Apart from the CDR loops, both the elbow angle and the relative interdomain orientations of the V H -V L and the C H 1-C L domains influence the shape of the paratope. Thus, characterization of the interface and elbow angle dynamics is essential to antigen specificity. We studied nine antigen-binding fragments (Fab) to investigate the influence of affinity maturation, antibody humanization, and different light-chain types on the interface and elbow angle dynamics. While the CDR loops reveal conformational transitions in the micro-to-millisecond timescale, both the interface and elbow angle dynamics occur on the low nanosecond timescale. Upon affinity maturation, we observe a substantial rigidification of the V H and V L interdomain and elbow-angle flexibility, reflected in a narrower and more distinct distribution. Antibody humanization describes the process of grafting non-human CDR loops onto a representative human framework. As the antibody framework changes upon humanization, we investigated if both the interface and the elbow angle distributions are changed or shifted. The results clearly showed a substantial shift in the relative V H -V L distributions upon antibody humanization, indicating that different frameworks favor distinct interface orientations. Additionally, the interface and elbow angle dynamics of five antibody fragments with different light-chain types are included, because of their strong differences in elbow angles. For these five examples, we clearly see a high variability and flexibility in both interface and elbow angle dynamics, highlighting the fact that Fab interface orientations and elbow angles interconvert between each other in the low nanosecond timescale. Understanding how the relative interdomain orientations and the elbow angle influence antigen specificity, affinity, and stability has broad implications in the field of antibody modeling and engineering.

Antibodies exhibit multiple paratope states influencing VH-VL domain orientations

In the last decades, antibodies have emerged as one of the most important and successful classes of biopharmaceuticals. The highest variability and diversity of an antibody is concentrated on six hypervariable loops, also known as complementarity determining regions (CDRs) shaping the antigen-binding site, the paratope. Whereas it was assumed that certain sequences can only adopt a limited set of backbone conformations, in this study we present a kinetic classification of several paratope states in solution. Using molecular dynamics simulations in combination with experimental structural information we capture the involved conformational transitions between different canonical clusters and additional dominant solution structures occurring in the micro-to-millisecond timescale. Furthermore, we observe a strong correlation of CDR loop movements. Another important aspect when characterizing different paratope states is the relative VH/VL orientation and the influence of the distinct CDR loop states on the VH/VL interface. Conformational rearrangements of the CDR loops do not only have an effect on the relative VH/VL orientations, but also influence in some cases the elbow-angle dynamics and shift the respective distributions. Thus, our results show that antibodies exist as several interconverting paratope states, each contributing to the antibody's properties.

On the importance of statistics in molecular simulations for thermodynamics, kinetics and simulation box size

Computational simulations, akin to wetlab experimentation, are subject to statistical fluctuations. Assessing the magnitude of these fluctuations, that is, assigning uncertainties to the computed results, is of critical importance to drawing statistically reliable conclusions. Here, we use a simulation box size as an independent variable, to demonstrate how crucial it is to gather sufficient amounts of data before drawing any conclusions about the potential thermodynamic and kinetic effects. In various systems, ranging from solvation free energies to protein conformational transition rates, we showcase how the proposed simulation box size effect disappears with increased sampling. This indicates that, if at all, the simulation box size only minimally affects both the thermodynamics and kinetics of the type of biomolecular systems presented in this work.

Water Dynamics Around Proteins: T- and R-States of Hemoglobin and Melittin

The water dynamics, as characterized by the local hydrophobicity (LH), is investigated for tetrameric hemoglobin (Hb) and dimeric melittin. For the T₀ to R₀ transition in Hb, it is found that LH provides additional molecular-level insight into the Perutz mechanism, i.e., the breaking and formation of salt bridges at the α₁/β₂ and α₂/β₁ interface is accompanied by changes in LH. For Hb in cubic water boxes with 90 and 120 Å edge length it is observed that following a decrease in LH as a consequence of reduced water density or change of water orientation at the protein/water interface the α/β interfaces are destabilized; this is a hallmark of the Perutz stereochemical model for the T to R transition in Hb. The present work thus provides a dynamical view of the classical structural model relevant to the molecular foundations of Hb function. For dimeric melittin, earlier results by Cheng and Rossky [ Nature 1998, 392, 696-699] are confirmed and interpreted on the basis of LH from simulations in which the protein structure is frozen. For the flexible melittin dimer, the changes in the local hydration can be as much as 30% greater than for the rigid dimer, reflecting the fact that protein and water dynamics are coupled.

A remark on the efficiency of the double-system/single-box nonequilibrium approach in the SAMPL6 SAMPLing challenge

The alchemical nonequilibrium switching technique was one of several methods in the top tier of performance in the recent SAMPL6 SAMPLing challenge in both accuracy and efficiency. In this paper, in the context of nonequilibrium alchemical switching, we compare the efficiency of the double-system/single-box (DSSB) approach (used in the SAMPL6 challenges) to the standard single-system/double-box method (SSDB). Exploiting the Crooks theorem in a simple but effective test case, we analytically show that the DSSB approach is almost twice as efficient as SSDB for slow near-equilibrium switching but it gives basically no gain over the conventional SSDB approach when the variance of the work distribution exceeds few [Formula: see text], with the potential of producing artifacts and entanglements if not judiciously implemented.

Response to comment on 'Valid molecular dynamics simulations of human hemoglobin require a surprisingly large box size'

We recently reported that molecular dynamics simulations for hemoglobin require a surprisingly large box size to stabilize the T(0) state relative to R(0), as observed in experiments (El Hage et al., 2018). Gapsys and de Groot have commented on this work but do not provide convincing evidence that the conclusions of El Hage et al., 2018 are incorrect. Here we respond to these concerns, argue that our original conclusions remain valid, and raise our own concerns about some of the results reported in the comment by Gapsys and de Groot that require clarification.

CDR-H3 loop ensemble in solution - conformational selection upon antibody binding

We analyzed pairs of protein-binding, peptide-binding and hapten-binding antibodies crystallized as complex and in the absence of the antigen with and without conformational differences upon binding in the complementarity-determining region (CDR)-H3 loop. Here, we introduce a molecular dynamics-based approach to capture a diverse conformational ensemble of the CDR-H3 loop in solution. The results clearly indicate that the inherently flexible CDR-H3 loop indeed needs to be characterized as a conformational ensemble. The conformational changes of the CDR-H3 loop in all antibodies investigated follow the paradigm of conformation selection, because we observe the experimentally determined binding competent conformation without the presence of the antigen within the ensemble of pre-existing conformational states in solution before binding. We also demonstrate for several examples that the conformation observed in the antibody crystal structure without antigen present is actually selected to bind the carboxyterminal tail region of the antigen-binding fragment (Fab). Thus, special care must be taken when characterizing antibody CDR-H3 loops by Fab X-ray structures, and the possibility that pre-existing conformations are present should always be considered.