Quantifying Artifacts in Ewald Simulations of Inhomogeneous Systems with a Net Charge

Molecular simulations of proteins: From simplified physical interactions to complex biological phenomena

Molecular dynamics simulation is the most popular computational technique for investigating the structural and dynamical behaviour of proteins, in search of the molecular basis of their function. Far from being a completely settled field of research, simulations are still evolving to best capture the essential features of the atomic interactions that govern a protein's inner motions. Modern force fields are becoming increasingly accurate in providing a physical description adequate to this purpose, and allow us to model complex biological systems under fairly realistic conditions. Furthermore, the use of accelerated sampling techniques is improving our access to the observation of progressively larger molecular structures, longer time scales, and more hidden functional events. In this review, the basic principles of molecular dynamics simulations and a number of key applications in the area of protein science are summarized, and some of the most important results are discussed. Examples include the study of the structure, dynamics and binding properties of 'difficult' targets, such as intrinsically disordered proteins and membrane receptors, and the investigation of challenging phenomena like hydration-driven processes and protein aggregation. The findings described provide an overall picture of the current state of this research field, and indicate new perspectives on the road ahead to the upcoming future of molecular simulations.

Broadly neutralizing antibodies target a haemagglutinin anchor epitope

Broadly neutralizing antibodies that target epitopes of haemagglutinin on the influenza virus have the potential to provide near universal protection against influenza virus infection1. However, viral mutants that escape broadly neutralizing antibodies have been reported2,3. The identification of broadly neutralizing antibody classes that can neutralize viral escape mutants is critical for universal influenza virus vaccine design. Here we report a distinct class of broadly neutralizing antibodies that target a discrete membrane-proximal anchor epitope of the haemagglutinin stalk domain. Anchor epitope-targeting antibodies are broadly neutralizing across H1 viruses and can cross-react with H2 and H5 viruses that are a pandemic threat. Antibodies that target this anchor epitope utilize a highly restricted repertoire, which encodes two public binding motifs that make extensive contacts with conserved residues in the fusion peptide. Moreover, anchor epitope-targeting B cells are common in the human memory B cell repertoire and were recalled in humans by an oil-in-water adjuvanted chimeric haemagglutinin vaccine4,5, which is a potential universal influenza virus vaccine. To maximize protection against seasonal and pandemic influenza viruses, vaccines should aim to boost this previously untapped source of broadly neutralizing antibodies that are widespread in the human memory B cell pool.

CDR loop interactions can determine heavy and light chain pairing preferences in bispecific antibodies

As the current biotherapeutic market is dominated by antibodies, the design of different antibody formats, like bispecific antibodies, is critical to the advancement of the field. In contrast to monovalent antibodies, which consist of two identical antigen-binding sites, bispecific antibodies can target two different epitopes by containing two different antigen-binding sites. Thus, the rise of new formats as successful therapeutics has reignited the interest in advancing and facilitating the efficient production of bispecific antibodies. Here, we investigate the influence of point mutations in the antigen-binding site, the paratope, on heavy and light chain pairing preferences by using molecular dynamics simulations. In agreement with experiments, we find that specific residues in the antibody variable domain (Fv), i.e., the complementarity-determining region (CDR) L3 and H3 loops, determine heavy and light chain pairing preferences. Excitingly, we observe substantial population shifts in CDR-H3 and CDR-L3 loop conformations in solution accompanied by a decrease in bispecific IgG yield. These conformational changes in the CDR3 loops induced by point mutations also influence all other CDR loop conformations and consequentially result in different CDR loop states in solution. However, besides their effect on the obtained CDR loop ensembles, point mutations also lead to distinct interaction patterns in the V_H-V_L interface. By comparing the interaction patterns among all investigated variants, we observe specific contacts in the interface that drive heavy and light chain pairing. Thus, these findings have broad implications in the field of antibody engineering and design because they provide a mechanistic understanding of antibody interfaces, by identifying critical factors driving the pairing preferences, and thus can help to advance the design of bispecific antibodies.

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.

Computer Simulations of Deep Eutectic Solvents: Challenges, Solutions, and Perspectives

Deep eutectic solvents (DESs) are one of the most rapidly evolving types of solvents, appearing in a broad range of applications, such as nanotechnology, electrochemistry, biomass transformation, pharmaceuticals, membrane technology, biocomposite development, modern 3D-printing, and many others. The range of their applicability continues to expand, which demands the development of new DESs with improved properties. To do so requires an understanding of the fundamental relationship between the structure and properties of DESs. Computer simulation and machine learning techniques provide a fruitful approach as they can predict and reveal physical mechanisms and readily be linked to experiments. This review is devoted to the computational research of DESs and describes technical features of DES simulations and the corresponding perspectives on various DES applications. The aim is to demonstrate the current frontiers of computational research of DESs and discuss future perspectives.

Paratope states in solution improve structure prediction and docking

Structure-based antibody design and accurate predictions of antibody-antigen interactions remain major challenges in computational biology. By using molecular dynamics simulations, we show that a single static X-ray structure is not sufficient to identify determinants of antibody-antigen recognition. Here, we investigate antibodies that undergo substantial conformational changes upon antigen binding and have been classified as difficult cases in an extensive benchmark for antibody-antigen docking. We present thermodynamics and transition kinetics of these conformational rearrangements and show that paratope states can be used to improve antibody-antigen docking. By using the unbound antibody X-ray structure as starting structure for molecular dynamics simulations, we retain a binding competent conformation substantially different to the unbound antibody X-ray structure. We also observe that the kinetically dominant antibody paratope conformations are chosen by the bound antigen conformation with the highest probability. Thus, we show that paratope states in solution can improve antibody-antigen docking and structure prediction.

Simulation of pH-Dependent Conformational Transitions in Membrane Proteins: The CLC-ec1 Cl-/H+ Antiporter

Intracellular transport of chloride by members of the CLC transporter family involves a coupled exchange between a Cl⁻ anion and a proton (H⁺), which makes the transport function dependent on ambient pH. Transport activity peaks at pH 4.5 and stalls at neutral pH. However, a structure of the WT protein at acidic pH is not available, making it difficult to assess the global conformational rearrangements that support a pH-dependent gating mechanism. To enable modeling of the CLC-ec1 dimer at acidic pH, we have applied molecular dynamics simulations (MD) featuring a new force field modification scheme—termed an Equilibrium constant pH approach (ECpH). The ECpH method utilizes linear interpolation between the force field parameters of protonated and deprotonated states of titratable residues to achieve a representation of pH-dependence in a narrow range of physiological pH values. Simulations of the CLC-ec1 dimer at neutral and acidic pH comparing ECpH-MD to canonical MD, in which the pH-dependent protonation is represented by a binary scheme, substantiates the better agreement of the conformational changes and the final model with experimental data from NMR, cross-link and AFM studies, and reveals structural elements that support the gate-opening at pH 4.5, including the key glutamates Glu_in and Glu_ex.

High-throughput molecular simulations reveal the origin of ion free energy barriers in graphene oxide membranes

Graphene oxide (GO) membranes are highly touted as materials for contemporary separation challenges including desalination, yet understanding of the interplay between their structure and salt rejection is limited. K⁺ ion permeation through hydrated GO membranes was investigated by combining structurally realistic molecular models and high-throughput molecular dynamics simulations. We show that it is essential to consider the complex GO microstructure to quantitatively reproduce experimentally-derived free energy barriers to K⁺ permeation for membranes with various interlayer distances less than 1.3 nm. This finding confirms the non-uniformity of GO nanopores and the necessity of the high-throughput approach for this class of material. The large barriers arise due to significant dehydration of K⁺ inside the membrane, which can have as few as 3 coordinated water molecules, compared to 7 in bulk solution. Thus, even if the membranes have an average pore size larger than the ion's hydrated diameter, the significant presence of pores whose size is smaller than the hydrated diameter creates bottlenecks for the permeation process.

Germline-Dependent Antibody Paratope States and Pairing Specific VH-VL Interface Dynamics

Antibodies have emerged as one of the fastest growing classes of biotherapeutic proteins. To improve the rational design of antibodies, we investigate the conformational diversity of 16 different germline combinations, which are composed of 4 different kappa light chains paired with 4 different heavy chains. In this study, we systematically show that different heavy and light chain pairings strongly influence the paratope, interdomain interaction patterns and the relative V_H-V_L interface orientations. We observe changes in conformational diversity and substantial population shifts of the complementarity determining region (CDR) loops, resulting in distinct dominant solution structures and differently favored canonical structures. Additionally, we identify conformational changes in the structural diversity of the CDR-H3 loop upon different heavy and light chain pairings, as well as upon changes in sequence and structure of the neighboring CDR loops, despite having an identical CDR-H3 loop amino acid sequence. These results can also be transferred to all CDR loops and to the relative V_H-V_L orientation, as certain paratope states favor distinct interface angle distributions. Furthermore, we directly compare the timescales of sidechain rearrangements with the well-described transition kinetics of conformational changes in the backbone of the CDR loops. We show that sidechain flexibilities are strongly affected by distinct heavy and light chain pairings and decipher germline-specific structural features co-determining stability. These findings reveal that all CDR loops are strongly correlated and that distinct heavy and light chain pairings can result in different paratope states in solution, defined by a characteristic combination of CDR loop conformations and V_H-V_L interface orientations. Thus, these results have broad implications in the field of antibody engineering, as they clearly show the importance of considering paired heavy and light chains to understand the antibody binding site, which is one of the key aspects in the design of therapeutics.

Recent Developments in Free Energy Calculations for Drug Discovery

The grand challenge in structure-based drug design is achieving accurate prediction of binding free energies. Molecular dynamics (MD) simulations enable modeling of conformational changes critical to the binding process, leading to calculation of thermodynamic quantities involved in estimation of binding affinities. With recent advancements in computing capability and predictive accuracy, MD based virtual screening has progressed from the domain of theoretical attempts to real application in drug development. Approaches including the Molecular Mechanics Poisson Boltzmann Surface Area (MM-PBSA), Linear Interaction Energy (LIE), and alchemical methods have been broadly applied to model molecular recognition for drug discovery and lead optimization. Here we review the varied methodology of these approaches, developments enhancing simulation efficiency and reliability, remaining challenges hindering predictive performance, and applications to problems in the fields of medicine and biochemistry.

N-Glycosylation Enhances Conformational Flexibility of Protein Disulfide Isomerase Revealed by Microsecond Molecular Dynamics and Markov State Modeling

Secreted proteins of eukaryotes are decorated with branched carbohydrate oligomers called glycans. This fact is only starting to be considered for in silico investigations of protein dynamics. Using all-atom molecular dynamics (MD) simulations and Markov state modeling (MSM), we unveil the influence of glycans on the conformational flexibility of the multidomain protein disulfide isomerase (PDI), which is a ubiquitous chaperone in the endoplasmic reticulum (ER). Yeast PDI (yPDI) from Saccharomyces cerevisiae is glycosylated at asparagine side chains and the knowledge of its five modified sites enables a realistic computational modeling. We compare simulations of glycosylated and unglycosylated yPDI and find that the presence of glycan-glycan and glycan-protein interactions influences the flexibility of PDI in different ways. For example, glycosylation reduces interdomain interactions, shifting the conformational ensemble toward more open, extended structures. In addition, we compare our results on yPDI with structural information of homologous proteins such as human PDI (hPDI), which is natively unglycosylated. Interestingly, hPDI lacks a surface recess that is present in yPDI. We find that glycosylation of yPDI facilitates its catalytic site to reach close to this surface recess. Hence, this might point to a possible functional relevance of glycosylation in yeast to act on substrates, while glycosylation seems redundant for the human homologous protein. We conclude that glycosylation is fundamental for protein dynamics, making it a necessity for a truthful representation of the flexibility and function in in silico studies of glycoproteins.

Individual Ion Activity Coefficients in Aqueous Electrolytes from Explicit-Water Molecular Dynamics Simulations

We compute individual ion activity coefficients (IIACs) in aqueous NaCl, KCl, NaF, and KF solutions from explicit-water molecular dynamics simulations. Free energy changes are obtained from insertion of single ions-accompanied by uniform neutralizing backgrounds-into solution by gradually turning on first Lennard-Jones interactions, followed by Coulombic interactions using Ewald electrostatics. Simulations are performed at multiple system sizes, and all results are extrapolated to the thermodynamic limit, thus eliminating any possible artifacts from the neutralizing backgrounds. Because of controversies associated with measurements of IIACs from electrochemical cells with ion-selective electrodes, the reported experimental data are not widely accepted; thus there remains a knowledge gap with respect to the contributions of individual ions to solution nonidealities. Our results are in good qualitative agreement with these reported measurements, though significantly larger in magnitude. In particular, the relative positioning for the activity coefficients of anions and cations matches the experimental ordering for all four systems. This work establishes a robust thermodynamic framework, without a need to invoke extra hypotheses, that sheds light on the behavior of individual ions and their contributions to nonidealities of aqueous electrolyte solutions.

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.

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.

Fast bilayer-micelle fusion mediated by hydrophobic dipeptides

To understand the transition from inanimate matter to life, we studied a process that directly couples simple metabolism to evolution via natural selection, demonstrated experimentally by Adamala and Szostak. In this process, dipeptides synthesized inside precursors of cells promote absorption of fatty acid micelles to vesicles, inducing their preferential growth and division at the expense of other vesicles. The process is explained on the basis of coarse-grained molecular dynamics simulations, each extending for tens of microseconds, carried out to model fusion between a micelle and a membrane, both made of fatty acids in the absence and presence of hydrophobic dipeptides. In all systems with dipeptides, but not in their absence, fusion events were observed. They involve the formation of a stalk made by hydrophobic chains from the micelle and the membrane, similar to that postulated for vesicle-vesicle fusion. The emergence of a stalk is facilitated by transient clusters of dipeptides, side chains of which form hydrophobic patches at the membrane surface. Committor probability calculations indicate that the size of a patch is a suitable reaction coordinate and allows for identifying the transition state for fusion. Free-energy barrier to fusion is greatly reduced in the presence of dipeptides to only 4-5 kcal/mol, depending on the hydrophobicity of side chains. The mechanism of mediated fusion, which is expected to apply to other small peptides and hydrophobic molecules, provides a robust means by which a nascent metabolism can confer evolutionary advantage to precursors of cells.

The fragment molecular orbital method combined with density-functional tight-binding and periodic boundary conditions

The density-functional tight-binding (DFTB) formulation of the fragment molecular orbital method is combined with periodic boundary conditions. Long-range electrostatics and dispersion are evaluated with the Ewald summation technique. The first analytic derivatives of the energy with respect to atomic coordinates and lattice parameters are formulated. The accuracy of the method is established in comparison to numerical gradients and DFTB without fragmentation. The largest elementary cell in this work has 1631 atoms. The method is applied to elucidate the polarization, charge transfer, and interactions in the solution.

Mutation of Framework Residue H71 Results in Different Antibody Paratope States in Solution

Characterizing and understanding the antibody binding interface have become a pre-requisite for rational antibody design and engineering. The antigen-binding site is formed by six hypervariable loops, known as the complementarity determining regions (CDRs) and by the relative interdomain orientation (V_H-V_L). Antibody CDR loops with a certain sequence have been thought to be limited to a single static canonical conformation determining their binding properties. However, it has been shown that antibodies exist as ensembles of multiple paratope states, which are defined by a characteristic combination of CDR loop conformations and interdomain orientations. In this study, we thermodynamically and kinetically characterize the prominent role of residue 71^H (Chothia nomenclature), which does not only codetermine the canonical conformation of the CDR-H2 loop but also results in changes in conformational diversity and population shifts of the CDR-H1 and CDR-H3 loop. As all CDR loop movements are correlated, conformational rearrangements of the heavy chain CDR loops also induce conformational changes in the CDR-L1, CDR-L2, and CDR-L3 loop. These overall conformational changes of the CDR loops also influence the interface angle distributions, consequentially leading to different paratope states in solution. Thus, the type of residue of 71^H, either an alanine or an arginine, not only influences the CDR-H2 loop ensembles, but co-determines the paratope states in solution. Characterization of the functional consequences of mutations of residue 71^H on the paratope states and interface orientations has broad implications in the field of antibody engineering.

Revisiting the interaction of heme with hemopexin

In hemolytic disorders, erythrocyte lysis results in massive release of hemoglobin and, subsequently, toxic heme. Hemopexin is the major protective factor against heme toxicity in human blood and currently considered for therapeutic use. It has been widely accepted that hemopexin binds heme with extraordinarily high affinity of <1 pM in a 1:1 ratio. However, several lines of evidence point to a higher stoichiometry and lower affinity than determined 50 years ago. Here, we re-analyzed these data. SPR and UV/Vis spectroscopy were used to monitor the interaction of heme with the human protein. The heme-binding sites of hemopexin were characterized using hemopexin-derived peptide models and competitive displacement assays. We obtained a K _D value of 0.32 ± 0.04 nM and the ratio for the interaction was determined to be 1:1 at low heme concentrations and at least 2:1 (heme:hemopexin) at high concentrations. We were able to identify two yet unknown potential heme-binding sites on hemopexin. Furthermore, molecular modelling with a newly created homology model of human hemopexin suggested a possible recruiting mechanism by which heme could consecutively bind several histidine residues on its way into the binding pocket. Our findings have direct implications for the potential administration of hemopexin in hemolytic disorders.

Antibody CDR loops as ensembles in solution vs. canonical clusters from X-ray structures

In the past decade, the relevance of antibodies as therapeutics has increased substantially. Therefore, structural and functional characterization, in particular of the complementarity-determining regions (CDRs), is crucial to the design and engineering of antibodies with unique binding properties. Various studies have focused on classifying the CDR loops into a small set of main-chain conformations to facilitate antibody design by assuming that certain sequences can only adopt a limited number of conformations. Here, we present a kinetic classification of CDR loop structures as ensembles in solution. Using molecular dynamics simulations in combination with strong experimental structural information, we observe conformational transitions between canonical clusters and additional dominant solution structures in the micro-to-millisecond timescale for all CDR loops, independent of length and sequence composition. Besides identifying all relevant conformations in solution, our results revealed that various canonical cluster medians actually belong to the same kinetic minimum. Additionally, we reconstruct the kinetics and probabilities of the conformational transitions between canonical clusters, and thereby extend the model of static canonical structures to reveal a dynamic conformational ensemble in solution as a new paradigm in the field of antibody structure design.

Abbreviations: CDR: Complementary-determining region; Fv: Antibody variable fragment; PCCA: Perron cluster analysis; tICA: Time-lagged independent component analysis; V_H: Heavy chain variable region; V_L: Light chain variable region

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.

Molecular dynamics simulations of liquid-liquid interfaces in an electric field: The water-1,2-dichloroethane interface

The polarized interface between two immiscible liquids plays a central role in many technological processes. In particular, for electroanalytical and ion extraction applications, an external electric field is typically used to selectively induce the transfer of ionic species across the interfaces. Given that it is experimentally challenging to obtain an atomistic insight into the ion transfer process and the structure of liquid-liquid interfaces, atomistic simulations have often been used to fill this knowledge gap. However, due to the long-range nature of the electrostatic interactions and the use of 3D periodic boundary conditions, the use of external electric fields in molecular dynamics simulations requires special care. Here, we show how the simulation setup affects the dielectric response of the materials and demonstrate how by a careful design of the system it is possible to obtain the correct electric field on both sides of a liquid-liquid interface when using standard 3D Ewald summation methods. In order to prove the robustness of our approach, we ran extensive molecular dynamics simulations with a rigid-ion and polarizable force field of the water/1,2-dichloroethane interface in the presence of weak external electric fields.

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.

Rheology of water in small nanotubes

The properties of water in confinement are very different from those under bulk conditions. In some cases the melting point of ice may be shifted and one may find either ice, icelike water, or a state in which freezing is completely inhibited. Understanding the dynamics and rheology of water in confined media, such as small nanotubes, is of fundamental importance to the biological properties of micro-organisms at low temperatures, to the development of new devices for preserving DNA samples, and for other biological materials and fluids, lubrication, and development of nanostructured materials. We study rheology and dynamics of water in small nanotubes using extensive equilibrium and nonequilibrium molecular dynamics simulations. The results demonstrate that in strong confinement in nanotubes at temperatures significantly below and above bulk freezing temperature water behaves as a shear-thinning fluid at shear rates smaller than the inverse of the relaxation time in the confined medium. In addition, our results indicate the presence of regions in which the local density of water varies significantly over the same range of temperature in the nanotube. These findings may also have important implications for the design of nanofluidic systems.

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.

A Computational and Modeling Study of the Reaction Mechanism of Staphylococcus aureus Monoglycosyltransferase Reveals New Insights on the GT51 Family of Enzymes

Bacterial glycosyltransferases of the GT51 family are key enzymes in bacterial cell wall synthesis. Inhibiting cell wall synthesis is a very effective approach for development of antibiotics, as this can lead to either bacteriostatic or bactericidal effects. Even though the existence of this family has been known for over 50 years, only one potent inhibitor exists, which is an analog of the lipid IV product and derived from a natural product. Drug development focused on bacterial transglycosylase has been hampered due to little being know about its structure and reaction mechanism. In this study, Staphylococcus aureus monoglycosyltransferase was investigated at an atomistic level using computational methods. Classical molecular dynamics simulations were used to reveal information about the large-scale dynamics of the enzyme-substrate complex and the importance of magnesium in structure and function of the protein, while mixed mode quantum mechanics/molecular mechanics calculations unveiled a novel hypothesis for the reaction mechanism. From these results, we present a new model for the binding mode of lipid II and the reaction mechanism of the GT51 glycosyltransferases. A metal-bound hydroxide catalyzed reaction mechanism yields an estimated free energy barrier of 16.1 ± 1.0 kcal/mol, which is in line with experimental values. The importance of divalent cations is also further discussed. These findings could significantly aid targeted drug design, particularly the efficient development of transition state analogues as potential inhibitors for the GT51 glycosyltransferases.

Local and Global Rigidification Upon Antibody Affinity Maturation

During the affinity maturation process the immune system produces antibodies with higher specificity and activity through various rounds of somatic hypermutations in response to an antigen. Elucidating the affinity maturation process is fundamental in understanding immunity and in the development of biotherapeutics. Therefore, we analyzed 10 pairs of antibody fragments differing in their specificity and in distinct stages of affinity maturation using metadynamics in combination with molecular dynamics (MD) simulations. We investigated differences in flexibility of the CDR-H3 loop and global changes in plasticity upon affinity maturation. Among all antibody pairs we observed a substantial rigidification in flexibility and plasticity reflected in a substantial decrease of conformational diversity. To visualize and characterize these findings we used Markov-states models to reconstruct the kinetics of CDR-H3 loop dynamics and for the first time provide a method to define and localize surface plasticity upon affinity maturation.

T-Cell Receptor CDR3 Loop Conformations in Solution Shift the Relative Vα-Vβ Domain Distributions

T-cell receptors are an important part in the adaptive immune system as they are responsible for detecting foreign proteins presented by the major histocompatibility complex (MHC). The affinity is predominantly determined by structure and sequence of the complementarity determining regions (CDRs), of which the CDR3 loops are responsible for peptide recognition. We present a kinetic classification of T-cell receptor CDR3 loops with different loop lengths into canonical and non-canonical solution structures. Using molecular dynamics simulations, we do not only sample available X-ray structures, but we also observe a substantially broader CDR3 loop ensemble with various distinct kinetic minima in solution. Our results strongly imply, that for given CDR3 loop sequences several canonical structures have to be considered to characterize the conformational diversity of these loops. Our suggested dominant solution structures could extend the repertoire of available canonical clusters by including kinetic minimum structures present in solution. Thus, the CDR3 loops need to be characterized as conformational ensembles in solution. Furthermore, the conformational changes of the CDR3 loops follow the paradigm of conformational selection, because the experimentally determined binding competent state is present within this ensemble of pre-existing conformations without the presence of the antigen. We also identify strong correlations between the CDR3 loops and include combined state descriptions. Additionally, we observe a strong dependency of the CDR3 loop conformations on the relative Vα-Vβ interdomain orientations, revealing that certain CDR3 loop states favor specific interface orientations.

Kinetic pathways of water exchange in the first hydration shell of magnesium

Water exchange between the coordination shells of metal cations in aqueous solutions is fundamental in understanding their role in biochemical processes. Despite the importance, the microscopic mechanism of water exchange in the first hydration shell of Mg²⁺ has not been resolved since the exchange dynamics is out of reach for conventional all-atom simulations. To overcome this challenge, transition path sampling is applied to resolve the kinetic pathways, to characterize the reaction mechanism and to provide an accurate estimate of the exchange rate. The results reveal that water exchange involves the concerted motion of two exchanging water molecules and the collective rearrangement of all water molecules in the first hydration shell. Using a recently developed atomistic model for Mg²⁺, water molecules remain in the first hydration shell for about 40 ms, a time considerably longer compared to the 0.1 ms predicted by transition state theory based on the coordinates of a single water molecule. The discrepancy between these timescales arises from the neglected degrees of freedom of the second exchanging water molecule that plays a decisive role in the reaction mechanism. The approach presented here contributes molecular insights into the dynamics of water around metal cations and provides the basis for developing accurate atomistic models or for understanding complex biological processes involving metal cations.

Mass-zero constrained molecular dynamics for electrode charges in simulations of electrochemical systems

Classical molecular dynamics simulations have recently become a standard tool for the study of electrochemical systems. State-of-the-art approaches represent the electrodes as perfect conductors, modeling their responses to the charge distribution of electrolytes via the so-called fluctuating charge model. These fluctuating charges are additional degrees of freedom that, in a Born-Oppenheimer spirit, adapt instantaneously to changes in the environment to keep each electrode at a constant potential. Here, we show that this model can be treated in the framework of constrained molecular dynamics, leading to a symplectic and time-reversible algorithm for the evolution of all the degrees of freedom of the system. The computational cost and the accuracy of the new method are similar to current alternative implementations of the model. The advantage lies in the accuracy and long term stability guaranteed by the formal properties of the algorithm and in the possibility to systematically introduce additional kinematic conditions of arbitrary number and form. We illustrate the performance of the constrained dynamics approach by enforcing the electroneutrality of the electrodes in a simple capacitor consisting of two graphite electrodes separated by a slab of liquid water.

DNA-BINDING and DNA-protecting activities of small natural organic molecules and food extracts

The review summarizes literature data on the DNA-binding, DNA-protecting and DNA-damaging activities of a range of natural human endogenous and exogenous compounds. Small natural organic molecules bind DNA in a site-specific mode, by arranging tight touch with the structure of the major and minor grooves, as well as individual bases in the local duplex DNA. Polyphenols are the best-studied exogenous compounds from this point of view. Many of them demonstrate hormetic effects, producing both beneficial and damaging effects. An attempt to establish the dependence of DNA damage or DNA protection on the concentration of the compound turned out to be successful for some polyphenols, daidzein, genistein and resveratrol, which were DNA protecting in low concentrations and DNA damaging in high concentrations. There was no evident dependence on concentration for quercetin and kaempferol. Probably, the DNA-protecting effect is associated with the affinity to DNA. Caffeine and theophylline are DNA binders; at the same time, they favor DNA repair. Although most alkaloids damage DNA, berberine can protect DNA against damage. Among the endogenous compounds, hormones belonging to the amine class, thyroid and steroid hormones appear to bind DNA and produce some DNA damage. Thus, natural compounds continue to reveal beneficial or adverse effects on genome integrity and provide a promising source of therapeutic activities.

Ion Pairing and Redissociaton in Low-Permittivity Electrolytes for Multivalent Battery Applications

Detailed speciation of electrolytes as a function of chemical system and concentration provides the foundation for understanding bulk transport as well as possible decomposition mechanisms. In particular, multivalent electrolytes have shown a strong coupling between anodic stability and solvation structure. Furthermore, solvents that are found to exhibit reasonable stability against alkaline-earth metals generally exhibit low permittivity, which typically increases the complexity of the electrolyte species. To improve our understanding of ionic population and associated transport in these important classes of electrolytes, the speciation of Mg(TFSI)₂ in monoglyme and diglyme systems is studied via a multiscale thermodynamic model using first-principles calculations for ion association and molecular dynamics simulations for dielectric properties. The results are then compared to Raman and dielectric relaxation spectroscopies, which independently confirm the modeling insights. We find that the significant presence of free ions in the low-permittivity glymes in the concentration range from 0.02 to 0.6 M is well-explained by the low-permittivity redissociation hypothesis. Here, salt speciation is largely dictated by long-range electrostatics, which includes permittivity increases due to polar contact ion pairs. The present results suggest that other low-permittivity multivalent electrolytes may also reach high conductivities as a result of redissociation.

T-Cell Receptor Variable β Domains Rigidify During Affinity Maturation

We investigated T-cell receptor variable β chains binding to the superantigen staphylococcal enterotoxin C3 (SEC 3) with structure information in different stages of affinity maturation. Metadynamics in combination with molecular dynamics simulations allow to access the micro-to-millisecond timescale and reveal a strong effect of energetically significant mutations on the flexibility of the antigen-binding site. The observed changes in dynamics of the complementarity determining region (CDR) loops, especially the CDR 2, and HV 4 loop on this specific pathway of affinity maturation are reflected in their structural diversity, thermodynamics of conformations and kinetics of structural transitions. In addition, this affinity maturation pathway follows the concept of conformational selection, because even without the presence of the antigen the binding competent state is present in this pre-existing ensemble of conformations. In all stages of this affinity maturation process we observe a link between specificity and reduced flexibility.

Self-assembly of glycerol monooleate with the antimicrobial peptide LL-37: a molecular dynamics study

Over the past decade, the rapid increase in the incidence of antibiotic-resistant bacteria has promoted research towards alternative therapeutics such as antimicrobial peptides (AMPs), but their biodegradability limits their application. Encapsulation into nanocarriers based on the self-assembly of surfactant-like lipids is emerging as a promising strategy for the improvement of AMPs' stability and their protection against degradation when in biological media. An in-depth understanding of the interactions between the structure-forming lipids and AMPs is required for the design of nanocarriers. This in silico study, demonstrates the self-assembly of the amphiphilic lipid glycerol monooleate (GMO) with the antimicrobial peptide LL-37 into nanocarriers on the molecular scale. Molecular dynamics (MD) simulations show the formation of direct micelles, with either one or two interacting LL-37, and vesicles in this two-component system in agreement with experimental results from small-angle X-ray scattering studies. The hydrophobic contacts between LL-37 and GMOs in water appear responsible for the formation of these nanoparticles. The results also suggest that the enhanced antimicrobial efficiency of LL-37 in these nanocarriers that was previously observed experimentally can be explained by the availability of its side chains with charged amino acids, an increase of the electrostatic interaction and a decrease of the peptide's conformational entropy upon interacting with GMO. The results of this study contribute to the fundamental understanding of lipid-AMP interactions and may guide the comprehensive design of lipid-based self-assembled nanocarriers for antimicrobial peptides.

Split the Charge Difference in Two! A Rule of Thumb for Adding Proper Amounts of Ions in MD Simulations

Despite the relevance of properly setting ionic concentrations in Molecular Dynamics (MD) simulations, methods or practical rules to set ionic strength are scarce and rarely documented. Based on a recently proposed thermodynamics method we provide an accurate rule of thumb to define the electrolytic content in simulation boxes. Extending the use of good practices in setting up MD systems is promptly needed to ensure reproducibility and consistency in molecular simulations.

Understanding and Controlling Food Protein Structure and Function in Foods: Perspectives from Experiments and Computer Simulations

The structure and interactions of proteins play a critical role in determining the quality attributes of many foods, beverages, and pharmaceutical products. Incorporating a multiscale understanding of the structure-function relationships of proteins can provide greater insight into, and control of, the relevant processes at play. Combining data from experimental measurements, human sensory panels, and computer simulations through machine learning allows the construction of statistical models relating nanoscale properties of proteins to the physicochemical properties, physiological outcomes, and tastes of foods. This review highlights several examples of advanced computer simulations at molecular, mesoscale, and multiscale levels that shed light on the mechanisms at play in foods, thereby facilitating their control. It includes a practical simulation toolbox for those new to in silico modeling.

Antibody humanization-the Influence of the antibody framework on the CDR-H3 loop ensemble in solution

Antibody engineering of non-human antibodies has focused on reducing immunogenicity by humanization, being a major limitation in developing monoclonal antibodies. We analyzed four series of antibody binding fragments (Fabs) and a variable fragment (Fv) with structural information in different stages of humanization to investigate the influence of the framework, point mutations and specificity on the complementarity determining region (CDR)-H3 loop dynamics. We also studied a Fv without structural information of the anti-idiotypic antibody Ab2/3H6, because it completely lost its binding affinity upon superhumanization, as an example of a failed humanization. Enhanced sampling techniques in combination with molecular dynamics simulations allow to access micro- to milli-second timescales of the CDR-H3 loop dynamics and reveal kinetic and thermodynamic changes involved in the process of humanization. In most cases, we observe a reduced conformational diversity of the CDR-H3 loop when grafted on a human framework and find a conformational shift of the dominant CDR-H3 loop conformation in solution. A shallow side minimum of the conformational CDR-H3 loop ensemble attached to the murine framework becomes the dominant conformation in solution influenced by the human framework. Additionally, we observe in the case of the failed humanization that the potentially binding competent murine CDR-H3 loop ensemble in solution shows nearly no kinetical or structural overlap with the superhumanized variant, thus explaining the loss of binding.

Conformational selection of allergen-antibody complexes-surface plasticity of paratopes and epitopes

Antibodies have the ability to bind various types of antigens and to recognize different antibody-binding sites (epitopes) of the same antigen with different binding affinities. Due to the conserved structural framework of antibodies, their specificity to antigens is mainly determined by their antigen-binding site (paratope). Therefore, characterization of epitopes in combination with describing the involved conformational changes of the paratope upon binding is crucial in understanding and predicting antibody-antigen binding. Using molecular dynamics simulations complemented with strong experimental structural information, we investigated the underlying binding mechanism and the resulting local and global surface plasticity in the binding interfaces of distinct antibody-antigen complexes. In all studied allergen-antibody complexes, we clearly observe that experimentally suggested epitopes reveal less plasticity, while non-epitope regions show high surface plasticity. Surprisingly, the paratope shows higher conformational diversity reflected in substantially higher surface plasticity, compared to the epitope. This work allows a visualization and characterization of antibody-antigen interfaces and might have strong implications for antibody-antigen docking and in the area of epitope prediction.

Approaching protein design with multisite λ dynamics: Accurate and scalable mutational folding free energies in T4 lysozyme

The estimation of changes in free energy upon mutation is central to the problem of protein design. Modern protein design methods have had remarkable success over a wide range of design targets, but are reaching their limits in ligand binding and enzyme design due to insufficient accuracy in mutational free energies. Alchemical free energy calculations have the potential to supplement modern design methods through more accurate molecular dynamics based prediction of free energy changes, but suffer from high computational cost. Multisite λ dynamics (MSλD) is a particularly efficient and scalable free energy method with potential to explore combinatorially large sequence spaces inaccessible with other free energy methods. This work aims to quantify the accuracy of MSλD and demonstrate its scalability. We apply MSλD to the classic problem of calculating folding free energies in T4 lysozyme, a system with a wealth of experimental measurements. Single site mutants considering 32 mutations show remarkable agreement with experiment with a Pearson correlation of 0.914 and mean unsigned error of 1.19 kcal/mol. Multisite mutants in systems with up to five concurrent mutations spanning 240 different sequences show comparable agreement with experiment. These results demonstrate the promise of MSλD in exploring large sequence spaces for protein design.

Transitions of CDR-L3 Loop Canonical Cluster Conformations on the Micro-to-Millisecond Timescale

Sequence and structural diversity of antibodies are concentrated on six hypervariable loops, also known as the complementarity determining regions (CDRs). Five of six antibody CDR loops presumably adopt a so-called canonical structure out of a limited number of conformations. However, here we show for four antibody CDR-L3 loops differing in length and sequence, that each loop undergoes conformational transitions between different canonical structures. By extensive sampling in combination with Markov-state models we reconstruct the kinetics and probabilities of the transitions between canonical structures. Additionally, for these four CDR-L3 loops, we identify all relevant conformations in solution. Thereby we extend the model of static canonical structures to a dynamic conformational ensemble as a new paradigm in the field of antibody structure design.

Improving the efficiency of Monte Carlo simulations of ions using expanded grand canonical ensembles

While ionic liquids have promising applications as industrial solvents, predicting their fluid phase properties and coexistence remains a challenge. Grand canonical Monte Carlo simulation is an effective method for such predictions, but equilibration is hampered by the apparent requirement to insert and delete neutral sets of ions simultaneously in order to maintain charge neutrality. For relatively high densities and low temperatures, previously developed methods have been shown to be essential in improving equilibration by gradual insertion and deletion of these neutral sets of ions. We introduce an expanded ensemble approach which may be used in conjunction with these existing methods to further improve efficiency. Individual ions are inserted or deleted in one Monte Carlo trial rather than simultaneous insertion/deletion of neutral sets. We show how charge neutrality is maintained and show rigorous quantitative agreement between the conventional and the proposed expanded ensemble approaches, but with up to an order of magnitude increase in efficiency at high densities. The expanded ensemble approach is also more straightforward to implement than simultaneous insertion/deletion of neutral sets, and its implementation is demonstrated within open source software.

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.

Grand-canonical approach to density functional theory of electrocatalytic systems: Thermodynamics of solid-liquid interfaces at constant ion and electrode potentials

Properties of solid-liquid interfaces are of immense importance for electrocatalytic and electrochemical systems, but modeling such interfaces at the atomic level presents a serious challenge and approaches beyond standard methodologies are needed. An atomistic computational scheme needs to treat at least part of the system quantum mechanically to describe adsorption and reactions, while the entire system is in thermal equilibrium. The experimentally relevant macroscopic control variables are temperature, electrode potential, and the choice of the solvent and ions, and these need to be explicitly included in the computational model as well; this calls for a thermodynamic ensemble with fixed ion and electrode potentials. In this work, a general framework within density functional theory (DFT) with fixed electron and ion chemical potentials in the grand canonical (GC) ensemble is established for modeling electrocatalytic and electrochemical interfaces. Starting from a fully quantum mechanical description of multi-component GC-DFT for nuclei and electrons, a systematic coarse-graining is employed to establish various computational schemes including (i) the combination of classical and electronic DFTs within the GC ensemble and (ii) on the simplest level a chemically and physically sound way to obtain various (modified) Poisson-Boltzmann (mPB) implicit solvent models. The detailed and rigorous derivation clearly establishes which approximations are needed for coarse-graining as well as highlights which details and interactions are omitted in vein of computational feasibility. The transparent approximations also allow removing some of the constraints and coarse-graining if needed. We implement various mPB models within a linear dielectric continuum in the GPAW code and test their capabilities to model capacitance of electrochemical interfaces as well as study different approaches for modeling partly periodic charged systems. Our rigorous and well-defined DFT coarse-graining scheme to continuum electrolytes highlights the inadequacy of current linear dielectric models for treating properties of the electrochemical interface.

Conformational sampling and polarization of Asp26 in pKa calculations of thioredoxin

Thioredoxin is a protein that has been used as model system by various computational methods to predict the pK_a of aspartate residue Asp26 which is 3.5 units higher than a solvent exposed one (eg, Asp20). Here, we use extensive atomistic molecular dynamics simulations of two different protonation states of Asp26 in combination with conformational analysis based on RMSD clustering and principle component analysis to identify representative conformations of the protein in solution. For each conformation, the Gibbs free energy of proton transfer between Asp26 and Asp20, which is fully solvated in a loop region of the protein, is calculated with the Amber99sb force field in alchemical transformations. The varying polarization of the two residues in different molecular environments and protonation states is described by Hirshfeld-I (HI) atomic charges obtained from the averaged polarized electron density. Our results show that the Gibbs free energy of proton transfer is dependent on the protein conformation, the proper sampling of the neighboring Lys57 residue orientations and on water molecules entering the hydrophobic cavity upon deprotonating Asp26. The inclusion of the polarization of both aspartate residues in the free energy cycle by HI atomic charges corrects the results from the non-polarizable force field and reproduces the experimental ΔpK_a value of Asp26.