Quantifying Protein-Protein Interactions in Molecular Simulations

Coarse-Grained Model of Disordered RNA for Simulations of Biomolecular Condensates

Protein-RNA condensates are involved in a range of cellular activities. Coarse-grained molecular models of intrinsically disordered proteins have been developed to shed light on and predict single-chain properties and phase separation. An RNA model compatible with such models for disordered proteins would enable the study of complex biomolecular mixtures involving RNA. Here, we present a sequence-independent coarse-grained, two-beads-per-nucleotide model of disordered, flexible RNA based on a hydropathy scale. We parametrize the model, which we term CALVADOS-RNA, using a combination of bottom-up and top-down approaches to reproduce local RNA geometry and intramolecular interactions based on atomistic simulations and in vitro experiments. The model semiquantitatively captures several aspects of RNA-RNA and RNA-protein interactions. We examined RNA-RNA interactions by comparing calculated and experimental virial coefficients and nonspecific RNA-protein interaction by studying the reentrant phase behavior of protein-RNA mixtures. We demonstrate the utility of the model by simulating the formation of mixed condensates consisting of the disordered region of MED1 and RNA chains and the selective partitioning of disordered regions from transcription factors into these and compare the results to experiments. Despite the simplicity of our model, we show that it captures several key aspects of protein-RNA interactions and may therefore be used as a baseline model to study several aspects of the biophysics and biology of protein-RNA condensates.

Estimation of Ligand Binding Free Energy Using Multi-eGO

The computational study of ligand binding to a target protein provides mechanistic insight into the molecular determinants of this process and can improve the success rate of in silico drug design. All-atom molecular dynamics (MD) simulations can be used to evaluate the binding free energy, typically by thermodynamic integration, and to probe binding mechanisms, including the description of protein conformational dynamics. The advantages of MD come at a high computational cost, which limits its use. Such cost could be reduced by using coarse-grained models, but their use is generally associated with an undesirable loss of resolution and accuracy. To address the trade-off between speed and accuracy of MD simulations, we describe the use of the recently introduced multi-eGO atomic model for the estimation of binding free energies. We illustrate this approach in the case of the binding of benzene to lysozyme by both thermodynamic integration and metadynamics, showing multiple binding/unbinding pathways of benzene. We then provide equally accurate results for the binding free energy of dasatinib and PP1 to Src kinase by thermodynamic integration. Finally, we show how we can describe the binding of the small molecule 10074-G5 to Aβ42 by single molecule simulations and by explicit titration of the ligand as a function of concentration. These results demonstrate that multi-eGO has the potential to significantly reduce the cost of accurate binding free energy calculations and can be used to develop and benchmark in silico ligand binding techniques.

Binding of Inhibitors to Nuclear Localization Signal Peptide from Venezuelan Equine Encephalitis Virus Capsid Protein Explored with All-Atom Replica Exchange Molecular Dynamics

Several small molecule inhibitors have been designed to block binding of the Venezuelan equine encephalitis virus (VEEV) nuclear localization signal (NLS) sequence to the importin-α nuclear transport protein. To probe the inhibition mechanism on a molecular level, we used all-atom explicit water replica exchange molecular dynamics to study the binding of two inhibitors, I1 and I2, to the coreNLS peptide, representing the core fragment of the VEEV NLS sequence. Our objective was to evaluate the possibility of masking wherein binding of these inhibitors to the coreNLS occurs prior to its binding to importin-α. We found that the free energy of I1 and I2 binding to the coreNLS is less favorable than that to importin-α. This outcome argues against preemptive inhibitor binding to the coreNLS prior to importin-α. Instead, both inhibitors are expected to compete with the coreNLS peptide for binding to importin-α. The two factors responsible for the low affinities of the inhibitors to the coreNLS peptide are (i) the low cooperativity of binding to the peptide and (ii) the strong hydrophobic effect associated with binding to importin-α. Our results further show that upon binding to the coreNLS peptide, the inhibitors form multiple diverse binding poses. The coreNLS peptide coincubated with I1 and I2 adopts several conformational states, including open and collapsed, which underscores the fluidity of the coreNLS conformational ensemble as a target for inhibitors. Taken together with our prior investigations, this study sheds light on the molecular mechanism by which I1 and I2 ligands inhibit binding of the VEEV capsid protein to importin-α.

Molecular insights into the interaction between a disordered protein and a folded RNA

Intrinsically disordered protein regions (IDRs) are well-established as contributors to intermolecular interactions and the formation of biomolecular condensates. In particular, RNA-binding proteins (RBPs) often harbor IDRs in addition to folded RNA-binding domains that contribute to RBP function. To understand the dynamic interactions of an IDR-RNA complex, we characterized the RNA-binding features of a small (68 residues), positively charged IDR-containing protein, SERF. At high concentrations, SERF and RNA undergo charge-driven associative phase separation to form a protein- and RNA-rich dense phase. A key advantage of this model system is that this threshold for demixing is sufficiently high that we could use solution-state biophysical methods to interrogate the stoichiometric complexes of SERF with RNA in the one-phase regime. Herein, we describe our comprehensive characterization of SERF alone and in complex with a small fragment of the HIV-1 TAR RNA (TAR) with complementary biophysical methods and molecular simulations. We find that this binding event is not accompanied by the acquisition of structure by either molecule; however, we see evidence for a modest global compaction of the SERF ensemble when bound to RNA. This behavior likely reflects attenuated charge repulsion within SERF via binding to the polyanionic RNA and provides a rationale for the higher-order assembly of SERF in the context of RNA. We envision that the SERF-RNA system will lower the barrier to accessing the details that support IDR-RNA interactions and likewise deepen our understanding of the role of IDR-RNA contacts in complex formation and liquid-liquid phase separation.

Structure-Based Protein Assembly Simulations Including Various Binding Sites and Conformations

Many biological functions are mediated by large complexes formed by multiple proteins and other cellular macromolecules. Recent progress in experimental structure determination, as well as in integrative modeling and protein structure prediction using deep learning approaches, has resulted in a rapid increase in the number of solved multiprotein assemblies. However, the assembly process of large complexes from their components is much less well-studied. We introduce a rapid computational structure-based (SB) model, GoCa, that allows to follow the assembly process of large multiprotein complexes based on a known native structure. Beyond existing SB Go̅-type models, it distinguishes between intra- and intersubunit interactions, allowing us to include coupled folding and binding. It accounts automatically for the permutation of identical subunits in a complex and allows the definition of multiple minima (native) structures in the case of proteins that undergo global transitions during assembly. The model is successfully tested on several multiprotein complexes. The source code of the GoCa program including a tutorial is publicly available on Github: https://github.com/ZachariasLab/GoCa. We also provide a web source that allows users to quickly generate the necessary input files for a GoCa simulation: https://goca.t38webservices.nat.tum.de.

Computational Approaches to Predict Protein-Protein Interactions in Crowded Cellular Environments

Investigating protein-protein interactions is crucial for understanding cellular biological processes because proteins often function within molecular complexes rather than in isolation. While experimental and computational methods have provided valuable insights into these interactions, they often overlook a critical factor: the crowded cellular environment. This environment significantly impacts protein behavior, including structural stability, diffusion, and ultimately the nature of binding. In this review, we discuss theoretical and computational approaches that allow the modeling of biological systems to guide and complement experiments and can thus significantly advance the investigation, and possibly the predictions, of protein-protein interactions in the crowded environment of cell cytoplasm. We explore topics such as statistical mechanics for lattice simulations, hydrodynamic interactions, diffusion processes in high-viscosity environments, and several methods based on molecular dynamics simulations. By synergistically leveraging methods from biophysics and computational biology, we review the state of the art of computational methods to study the impact of molecular crowding on protein-protein interactions and discuss its potential revolutionizing effects on the characterization of the human interactome.

DeePNAP: A Deep Learning Method to Predict Protein-Nucleic Acid Binding Affinity from Their Sequences

Predicting the protein-nucleic acid (PNA) binding affinity solely from their sequences is of paramount importance for the experimental design and analysis of PNA interactions (PNAIs). A large number of currently developed models for binding affinity prediction are limited to specific PNAIs while also relying on the sequence and structural information of the PNA complexes for both training and testing, and also as inputs. As the PNA complex structures available are scarce, this significantly limits the diversity and generalizability due to the small training data set. Additionally, a majority of the tools predict a single parameter, such as binding affinity or free energy changes upon mutations, rendering a model less versatile for usage. Hence, we propose DeePNAP, a machine learning-based model built from a vast and heterogeneous data set with 14,401 entries (from both eukaryotes and prokaryotes) from the ProNAB database, consisting of wild-type and mutant PNA complex binding parameters. Our model precisely predicts the binding affinity and free energy changes due to the mutation(s) of PNAIs exclusively from their sequences. While other similar tools extract features from both sequence and structure information, DeePNAP employs sequence-based features to yield high correlation coefficients between the predicted and experimental values with low root mean squared errors for PNA complexes in predicting KD and ΔΔG, implying the generalizability of DeePNAP. Additionally, we have also developed a web interface hosting DeePNAP that can serve as a powerful tool to rapidly predict binding affinities for a myriad of PNAIs with high precision toward developing a deeper understanding of their implications in various biological systems. Web interface: http://14.139.174.41:8080/.

Binding and dimerization of PGLa peptides in anionic lipid bilayer studied by replica exchange molecular dynamics

The 21-residue PGLa peptide is well known for antimicrobial activity attributed to its ability to compromize bacterial membranes. Using all-atom explicit solvent replica exchange molecular dynamics with solute tempering, we studied PGLa binding to a model anionic DMPC/DMPG bilayer at the high peptide:lipid ratio that promotes PGLa dimerization (a two peptides per leaflet system). As a reference we used our previous simulations at the low peptide:lipid ratio (a one peptide per leaflet system). We found that the increase in the peptide:lipid ratio suppresses PGLa helical propensity, tilts the bound peptide toward the bilayer hydrophobic core, and forces it deeper into the bilayer. Surprisingly, at the high peptide:lipid ratio PGLa binding induces weaker bilayer thinning, but deeper water permeation. We explain these effects by the cross-correlations between lipid shells surrounding PGLa that leads to a much diminished efflux of DMPC lipids from the peptide proximity at the high peptide:lipid ratio. Consistent with the experimental data the propensity for PGLa dimerization was found to be weak resulting in coexistence of monomers and dimers with distinctive properties. PGLa dimers assemble via apolar criss-cross interface and become partially expelled from the bilayer residing at the bilayer-water boundary. We rationalize their properties by the dimer tendency to preserve favorable electrostatic interactions between lysine and phosphate lipid groups as well as to avoid electrostatic repulsion between lysines in the low dielectric environment of the bilayer core. PGLa homedimer interface is predicted to be distinct from that involved in PGLa-magainin heterodimers.

Breakdown of Langmuir Adsorption Isotherm in Small Closed Systems

For more than a century, monolayer adsorptions in which adsorbate molecules and adsorbing sites behave ideally have been successfully described by Langmuir's adsorption isotherm. For example, the amount of adsorbed material, as a function of concentration of the material which is not adsorbed, obeys Langmuir's equation. In this paper, we argue that this relation is valid only for macroscopic systems. However, when particle numbers of adsorbate molecules and/or adsorbing sites are small, Langmuir's model fails to describe the chemical equilibrium of the system. This is because the kinetics of forming, or the probability of observing, occupied sites arises from two-body interactions, and as such, ought to include cross-correlations between particle numbers of the adsorbate and adsorbing sites. The effect of these correlations, as reflected by deviations in predicting composition when correlations are ignored, increases with decreasing particle numbers and becomes substantial when only few adsorbate molecules, or adsorbing sites, are present in the system. In addition, any change that augments the fraction of occupied sites at equilibrium (e.g., smaller volume, lower temperature, or stronger adsorption energy) further increases the discrepancy between observed properties of small systems and those predicted by Langmuir's theory. In contrast, for large systems, these cross-correlations become negligible, and therefore when expressing properties involving two-body processes, it is possible to consider independently the concentration of each component. By applying statistical mechanics concepts, we derive a general expression of the equilibrium constant for adsorption. It is also demonstrated that in ensembles in which total numbers of particles are fixed, the magnitudes of fluctuations in particle numbers alone can predict the average chemical composition of the system. Moreover, an alternative adsorption equation, predicting the average fraction of occupied sites from the value of the equilibrium constant, is proposed. All derived relations were tested against results obtained by Monte Carlo simulations.

Hexagonal Lattices of HIV Capsid Proteins Explored by Simulations Based on a Thermodynamically Consistent Model

HIV capsid proteins (CAs) may self-assemble into a variety of shapes under in vivo and in vitro conditions. Here, we employed simulations based on a residue-level coarse-grained (CG) model with full conformational flexibility to investigate hexagonal lattices, which are the underlying structural pattern for CA aggregations. Facilitated by enhanced sampling simulations to rigorously calculate CA dimerization and polymerization affinities, we calibrated our model to reproduce the experimentally measured affinities. Using the calibrated model, we performed unbiased simulations on several large systems consisting of 1512 CA subunits, allowing reversible binding and unbinding of the CAs in a thermodynamically consistent manner. In one simulation, a preassembled hexagonal CA sheet developed spontaneous curvatures reminiscent of those observed in experiments, and the edges of the sheet exhibited local curvatures larger than those of the interior. In other simulations starting with randomly distributed CAs at different concentrations, existing CA assemblies grew by binding free capsomeres to the edges and by merging with other assemblies. At high CA concentrations, rapid establishment of predominant aggregates was followed by much slower adjustments toward more regular hexagonal lattices, with increasing numbers of intact CA hexamers and pentamers being formed. Our approach of adapting a general CG model to specific systems by using experimental binding data represents a practical and effective strategy for simulating and elucidating intricate protein aggregations.

Fascin - F-actin interaction studied by molecular dynamics simulation and protein network analysis

Actin bundles are an important component of cellular cytoskeleton and participate in the movement of cells. The formation of actin bundles requires the participation of many actin binding proteins (ABPs). Fascin is a member of ABPs, which plays a key role in bundling filamentous actin (F-actin) to bundles. However, the detailed interactions between fascin and F-actin are unclear. In this study, we construct an atomic-level structure of fascin - F-actin complex based on a rather poor cryo-EM data with resolution of 20 nm. We first optimized the geometries of the complex by molecular dynamics (MD) simulation and analyzed the binding site and pose of fascin which bundles two F-actin chains. Next, binding free energy of fascin was calculated by MM/GBSA method. Finally, protein structure network analysis (PSNs) was performed to analyze the key residues for fascin binding. Our results show that residues of K22, E27, E29, K41, K43, R110, R149, K358, R408 and K471 on fascin are important for its bundling, which are in good agreement with the experimental data. On the other hand, the consistent results indicate that the atomic-level model of fascin - F-actin complex is reliable. In short, this model can be used to understand the detailed interactions between fascin and F-actin, and to develop novel potential drugs targeting fascin.Communicated by Ramaswamy H. Sarma.

DNA Nanomachine-Driven Heterogeneous Quadratic Amplification for Sensitive and Programmable miRNA Profiling

Inspired by the molecular crowding effect in biological systems, a novel heterogeneous quadratic amplification molecular circuit (HEQAC) was developed for sensitive bimodal miRNA profiling (HEQAC-BMP) by combining an MNAzyme-based DNA nanomachine with an entropy-driven catalytic hairpin assembly (E-CHA) autocatalytic circuit. Utilizing ferromagnetic nanomaterials as the substrate for DNA nanomachines, a biomimetic heterogeneous interface was established; thus, a localized molecular crowding system was created that can elevate the local reaction concentration and accelerate the molecular recognition process for a significant threshold signal. Simultaneously, the threshold signal undergoes further amplification by E-CHA and is transformed into a chemical signal, enabling a colorimetric-fluorescence bimodal signal readout. The HEQAC-BMP enables miRNA detection from 10 aM to 10 nM with detection limits of 3.7 aM (colorimetry) and 4.8 aM (fluorometry), respectively. Moreover, the design principle and strategy of HEQAC-BMP can be customized to address other critical viruses or diseases with life-threatening and socioeconomic impacts, enhancing healthcare outcomes for individuals.

Enhanced sampling in explicit solvent by deep learning module in FSATOOL

FSATOOL is an integrated molecular simulation and data analysis program. Its old molecular dynamics engine only supports simulations in vacuum or implicit solvent. In this work, we implement the well-known smooth particle mesh Ewald method for simulations in explicit solvent. The new developed engine is runnable on both CPU and GPU. All the existed analysis modules in the program are compatible with the new engine. Moreover, we also build a complete deep learning module in FSATOOL. Based on the module, we further implement two useful trajectory analysis methods: state-free reversible VAMPnets and time-lagged autoencoder. They are good at searching the collective variables related to the conformational transitions of biomolecules. In FSATOOL, these collective variables can be further used to construct a bias potential for the enhanced sampling purpose. We introduce the implementation details of the methods and present their actual performances in FSATOOL by a few enhanced sampling simulations.

Binding of Venezuelan Equine Encephalitis Virus Inhibitors to Importin-α Receptors Explored with All-Atom Replica Exchange Molecular Dynamics

Although Venezuelan equine encephalitis virus (VEEV) is a life-threatening pathogen with a capacity for epidemic outbreaks, there are no FDA-approved VEEV antivirals for humans. VEEV cytotoxicity is partially attributed to the formation of a tetrameric complex between the VEEV capsid protein, the nuclear import proteins importin-α and importin-β, and the nuclear export protein CRM1, which together block trafficking through the nuclear pore complex. Experimental studies have identified small molecules from the CL6662 scaffold as potential inhibitors of the viral nuclear localization signal (NLS) sequence binding to importin-α. However, little is known about the molecular mechanism of CL6662 inhibition. To address this issue, we employed all-atom replica exchange molecular dynamics simulations to probe, in atomistic detail, the binding mechanism of CL6662 ligands to importin-α. Three ligands, including G281-1485 and two congeners with varying hydrophobicities, were considered. We investigated the distribution of ligand binding poses, their locations, and ligand specificities measured by the strength of binding interactions. We found that G281-1485 binds nonspecifically without forming well-defined binding poses throughout the NLS binding site. Binding of the less hydrophobic congener becomes strongly on-target with respect to the NLS binding site but remains nonspecific. However, a more hydrophobic congener is a strongly specific binder and the only ligand out of three to form a well-defined binding pose, while partially overlapping with the NLS binding site. On the basis of free energy estimates, we argue that all three ligands weakly compete with the viral NLS sequence for binding to importin-α in an apparent compromise to preserve host NLS binding. We further show that all-atom replica exchange binding simulations are a viable tool for studying ligands binding nonspecifically without forming well-defined binding poses.

Analysis of protein-protein interface with incorporating low-frequency molecular interactions in molecular dynamics simulation

Protein-protein interactions are vital for various biological processes such as immune reaction, signal transduction, and viral infection. Molecular Dynamics (MD) simulation is a powerful tool for analyzing non-covalent interactions between two protein molecules. In general, MD simulation studies on the protein-protein interface have focused on the analysis of major and frequent molecular interactions. In this study, we demonstrate that minor interactions with low-frequency need to be incorporated to analyze the molecular interactions in the protein-protein interface more efficiently using the complex of SARS-CoV2-RBD and ACE2 receptor as a model system. It was observed that the dominance of interactions in the MD-simulated structures didn't directly correlate with the interactions in the experimentally determined structure. The interactions from the experimentally determined structure could be reproduced better in the ensemble of MD simulated structures by including the less frequent interactions compared to the norm of choosing only highly frequent interactions. Residue Interaction Networks (RINs) analysis also showed that the critical residues in the protein-protein interface could be more efficiently identified by incorporating low-frequency interactions in MD simulation. It is expected that the approach proposed in this study can be a new way of studying protein-protein interaction through MD simulation.

IRAA: A statistical tool for investigating a protein-protein interaction interface from multiple structures

Understanding protein-protein interactions (PPIs) is fundamental to infer how different molecular systems work. A major component to model molecular recognition is the buried surface area (BSA), that is, the area that becomes inaccessible to solvent upon complex formation. To date, many attempts tried to connect BSA to molecular recognition principles, and in particular, to the underlying binding affinity. However, the most popular approach to calculate BSA is to use a single (or in some cases few) bound structures, consequently neglecting a wealth of structural information of the interacting proteins derived from ensembles corresponding to their unbound and bound states. Moreover, the most popular method inherently assumes the component proteins to bind as rigid entities. To address the above shortcomings, we developed a Monte Carlo method-based Interface Residue Assessment Algorithm (IRAA), to calculate a combined distribution of BSA for a given complex. Further, we apply our algorithm to human ACE2 and SARS-CoV-2 Spike protein complex, a system of prime importance. Results show a much broader distribution of BSA compared to that obtained from only the bound structure or structures and extended residue members of the interface with implications to the underlying biomolecular recognition. We derive that specific interface residues of ACE2 and of S-protein are consistently highly flexible, whereas other residues systematically show minor conformational variations. In effect, IRAA facilitates the use of all available structural data for any biomolecular complex of interest, extracting quantitative parameters with statistical significance, thereby providing a deeper biophysical understanding of the molecular system under investigation.

Computer aided drug design in the development of proteolysis targeting chimeras

Proteolysis targeting chimeras represent a class of drug molecules with a number of attractive properties, most notably a potential to work for targets that, so far, have been in-accessible for conventional small molecule inhibitors. Due to their different mechanism of action, and physico-chemical properties, many of the methods that have been designed and applied for computer aided design of traditional small molecule drugs are not applicable for proteolysis targeting chimeras. Here we review recent developments in this field focusing on three aspects: de-novo linker-design, estimation of absorption for beyond-rule-of-5 compounds, and the generation and ranking of ternary complex structures. In spite of this field still being young, we find that a good number of models and algorithms are available, with the potential to assist the design of such compounds in-silico, and accelerate applied pharmaceutical research.

Capillary-Assisted Molecular Pendulum Bioanalysis

The development of robust biosensing strategies that can be easily implemented in everyday life remains a challenge for the future of modern biosensor research. While several reagentless approaches have attempted to address this challenge, they often achieve user-friendliness through sacrificing sensitivity or universality. While acceptable for certain applications, these trade-offs hinder the widespread adoption of reagentless biosensing technologies. Here, we report a novel approach to reagentless biosensing that achieves high sensitivity, rapid detection, and universality using the SARS-CoV-2 virus as a model target. Universality is achieved by using nanoscale molecular pendulums, which enables reagentless electrochemical biosensing through a variable antibody recognition element. Enhanced sensitivity and rapid detection are accomplished by incorporating the coffee-ring phenomenon into the sensing scheme, allowing for target preconcentration on a ring-shaped electrode. Using this approach, we obtained limits of detection of 1 fg/mL and 20 copies/mL for the SARS-CoV-2 nucleoproteins and viral particles, respectively. In addition, clinical sample analysis showed excellent agreement with Ct values from PCR-positive SARS-CoV-2 patients.

Computational models for studying physical instabilities in high concentration biotherapeutic formulations

Computational prediction of the behavior of concentrated protein solutions is particularly advantageous in early development stages of biotherapeutics when material availability is limited and a large set of formulation conditions needs to be explored. This review provides an overview of the different computational paradigms that have been successfully used in modeling undesirable physical behaviors of protein solutions with a particular emphasis on high-concentration drug formulations. This includes models ranging from all-atom simulations, coarse-grained representations to macro-scale mathematical descriptions used to study physical instability phenomena of protein solutions such as aggregation, elevated viscosity, and phase separation. These models are compared and summarized in the context of the physical processes and their underlying assumptions and limitations. A detailed analysis is also given for identifying protein interaction processes that are explicitly or implicitly considered in the different modeling approaches and particularly their relations to various formulation parameters. Lastly, many of the shortcomings of existing computational models are discussed, providing perspectives and possible directions toward an efficient computational framework for designing effective protein formulations.

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.

Multiscale simulations of protein and membrane systems

Classical multiscale simulations are perfectly suited to investigate biological soft matter systems. Owing to the bridging between microscopically realistic and lower-resolution models or the integration of a hierarchy of subsystems, one gets access to biologically relevant system sizes and timescales. In recent years, increasingly complex systems and processes have come into focus such as multidomain proteins, phase separation processes in biopolymer solutions, multicomponent biomembranes, or multiprotein complexes up to entire viruses. The review shows factors that have contributed to this progress - from improved models to machine-learning-based analysis and scale-bridging methods.

Accurate model of liquid-liquid phase behavior of intrinsically disordered proteins from optimization of single-chain properties

Many intrinsically disordered proteins (IDPs) may undergo liquid-liquid phase separation (LLPS) and participate in the formation of membraneless organelles in the cell, thereby contributing to the regulation and compartmentalization of intracellular biochemical reactions. The phase behavior of IDPs is sequence dependent, and its investigation through molecular simulations requires protein models that combine computational efficiency with an accurate description of intramolecular and intermolecular interactions. We developed a general coarse-grained model of IDPs, with residue-level detail, based on an extensive set of experimental data on single-chain properties. Ensemble-averaged experimental observables are predicted from molecular simulations, and a data-driven parameter-learning procedure is used to identify the residue-specific model parameters that minimize the discrepancy between predictions and experiments. The model accurately reproduces the experimentally observed conformational propensities of a set of IDPs. Through two-body as well as large-scale molecular simulations, we show that the optimization of the intramolecular interactions results in improved predictions of protein self-association and LLPS.

Accurate model of liquid-liquid phase behavior of intrinsically disordered proteins from optimization of single-chain properties

Many intrinsically disordered proteins (IDPs) may undergo liquid-liquid phase separation (LLPS) and participate in the formation of membraneless organelles in the cell, thereby contributing to the regulation and compartmentalization of intracellular biochemical reactions. The phase behavior of IDPs is sequence dependent, and its investigation through molecular simulations requires protein models that combine computational efficiency with an accurate description of intramolecular and intermolecular interactions. We developed a general coarse-grained model of IDPs, with residue-level detail, based on an extensive set of experimental data on single-chain properties. Ensemble-averaged experimental observables are predicted from molecular simulations, and a data-driven parameter-learning procedure is used to identify the residue-specific model parameters that minimize the discrepancy between predictions and experiments. The model accurately reproduces the experimentally observed conformational propensities of a set of IDPs. Through two-body as well as large-scale molecular simulations, we show that the optimization of the intramolecular interactions results in improved predictions of protein self-association and LLPS.

Building intuition for binding free energy calculations: Bound state definition, restraints, and symmetry

The theory behind computation of absolute binding free energies using explicit-solvent molecular simulations is well-established, yet somewhat complex, with counter-intuitive aspects. This leads to frequent frustration, common misconceptions, and sometimes erroneous numerical treatment. To improve this, we present the main practically relevant segments of the theory with constant reference to physical intuition. We pinpoint the role of the implicit or explicit definition of the bound state (or the binding site) to make a robust link between an experimental measurement and a computational result. We clarify the role of symmetry and discuss cases where symmetry number corrections have been misinterpreted. In particular, we argue that symmetry corrections as classically presented are a source of confusion and could be advantageously replaced by restraint free energy contributions. We establish that contrary to a common intuition, partial or missing sampling of some modes of symmetric bound states does not affect the calculated decoupling free energies. Finally, we review these questions and pitfalls in the context of a few common practical situations: binding to a symmetric receptor (equivalent binding sites), binding of a symmetric ligand (equivalent poses), and formation of a symmetric complex, in the case of homodimerization.

A coarse-grained xDLVO model for colloidal protein-protein interactions

Colloidal protein-protein interactions (PPIs) of attractive and repulsive nature modulate the solubility of proteins, their aggregation, precipitation and crystallization. Such interactions are very important for many biotechnological processes, but are complex and hard to control, therefore, difficult to be understood in terms of measurements alone. In diluted protein solutions, PPIs can be estimated from the osmotic second virial coefficient, B22, which has been calculated using different methods and levels of theory. The most popular approach is based on the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory and its extended versions, i.e. xDLVO. Despite much efforts, these models are not fully quantitative and must be fitted to experiments, which limits their predictive value. Here, we report an extended xDLVO-CG model, which extends existing models by a coarse-grained representation of proteins and the inclusion of an additional ion-protein dispersion interaction term. We demonstrate for four proteins, i.e. lysozyme (LYZ), subtilisin (Subs), bovine serum albumin (BSA) and immunoglobulin (IgG1), that semi-quantitative agreement with experimental values without the need to fit to experimental B22 values. While most likely not the final step in the nearly hundred years of research in PPIs, xDLVO-CG is a step towards predictive PPIs calculations that are transferable to different proteins.

Physical modeling of multivalent interactions in the nuclear pore complex

In the nuclear pore complex, intrinsically disordered proteins (FG Nups), along with their interactions with more globular proteins called nuclear transport receptors (NTRs), are vital to the selectivity of transport into and out of the cell nucleus. Although such interactions can be modeled at different levels of coarse graining, in vitro experimental data have been quantitatively described by minimal models that describe FG Nups as cohesive homogeneous polymers and NTRs as uniformly cohesive spheres, in which the heterogeneous effects have been smeared out. By definition, these minimal models do not account for the explicit heterogeneities in FG Nup sequences, essentially a string of cohesive and noncohesive polymer units, and at the NTR surface. Here, we develop computational and analytical models that do take into account such heterogeneity in a minimal fashion and compare them with experimental data on single-molecule interactions between FG Nups and NTRs. Overall, we find that the heterogeneous nature of FG Nups and NTRs does play a role in determining equilibrium binding properties but is of much greater significance when it comes to unbinding and binding kinetics. Using our models, we predict how binding equilibria and kinetics depend on the distribution of cohesive blocks in the FG Nup sequences and of the binding pockets at the NTR surface, with multivalency playing a key role. Finally, we observe that single-molecule binding kinetics has a rather minor influence on the diffusion of NTRs in polymer melts consisting of FG-Nup-like sequences.

Calculation of therapeutic antibody viscosity with coarse-grained models, hydrodynamic calculations and machine learning-based parameters

High viscosity presents a challenge for manufacturing and drug delivery of therapeutic antibodies. The viscosity is determined by protein-protein interactions among many antibodies. Molecular simulation is a promising method to study protein-protein interactions; however, all-atom models do not allow the simulation of multiple molecules, which is necessary to compute viscosity directly. Coarse-grained models, on the other hand can do this. In this work, a 12-bead coarse-grained model based on Swan and coworkers (J. Phys. Chem. B 2018, 122, 2867-2880) was applied to study antibody interactions. Two adjustable parameters related to the short-range interactions on the variable and constant regions were determined by fitting experimental data of 20 IgG1 monoclonal antibodies at 150 mg/mL. The root-mean-square deviation improved from 1 to 0.68, and the correlation coefficient improved from 0.63 to 0.87 compared to that of a previous model that assumed the short-range interactions were the same for all the beads. Our model is also able to calculate the viscosity over a wide range of concentrations without additional parameters. A tabulated viscosity based on our model is provided to facilitate antibody screening in early-stage design.

Thermodynamics and Free Energy Landscape of BAR-Domain Dimerization from Molecular Simulations

Proteins with BAR domains function to bind to and remodel biological membranes, where the dimerization of BAR domains is a key step in this function. These domains can dimerize in solution or after localizing to the membrane surface. Here, we characterize the binding thermodynamics of homodimerization between the LSP1 BAR domain proteins in solution, using molecular dynamics (MD) simulations. By combining the MARTINI coarse-grained protein models with enhanced sampling through metadynamics, we construct a two-dimensional free energy surface quantifying the bound versus unbound ensembles as a function of two distance variables. With this methodology, our simulations can simultaneously characterize the structures and relative stabilities of a range of sampled dimers, portraying a heterogeneous and extraordinarily stable bound ensemble, where the proper crystal structure dimer is the most stable in a 100 mM NaCl solution. Nonspecific dimers that are sampled involve contacts that are consistent with experimental structures of higher-order oligomers formed by the LSP1 BAR domain. Because the BAR dimers and oligomers can assemble on membranes, we characterize the relative alignment of the known membrane binding patches, finding that only the specific dimer is aligned to form strong interactions with the membrane. Hence, we would predict a strong selection of the specific dimer in binding to or assembling when on the membrane. Establishing the pairwise stabilities of homodimer contacts is difficult experimentally when the proteins form stable oligomers, but through the method used here, we can isolate these contacts, providing a foundation to study the same interactions on the membrane.

Simulation of FUS Protein Condensates with an Adapted Coarse-Grained Model

Disordered proteins and nucleic acids can condense into droplets that resemble the membraneless organelles observed in living cells. MD simulations offer a unique tool to characterize the molecular interactions governing the formation of these biomolecular condensates, their physicochemical properties, and the factors controlling their composition and size. However, biopolymer condensation depends sensitively on the balance between different energetic and entropic contributions. Here, we develop a general strategy to fine-tune the potential energy function for molecular dynamics simulations of biopolymer phase separation. We rebalance protein-protein interactions against solvation and entropic contributions to match the excess free energy of transferring proteins between dilute solution and condensate. We illustrate this formalism by simulating liquid droplet formation of the FUS low-complexity domain (LCD) with a rebalanced MARTINI model. By scaling the strength of the nonbonded interactions in the coarse-grained MARTINI potential energy function, we map out a phase diagram in the plane of protein concentration and interaction strength. Above a critical scaling factor of αc ≈ 0.6, FUS-LCD condensation is observed, where α = 1 and 0 correspond to full and repulsive interactions in the MARTINI model. For a scaling factor α = 0.65, we recover experimental densities of the dilute and dense phases, and thus the excess protein transfer free energy into the droplet and the saturation concentration where FUS-LCD condenses. In the region of phase separation, we simulate FUS-LCD droplets of four different sizes in stable equilibrium with the dilute phase and slabs of condensed FUS-LCD for tens of microseconds, and over one millisecond in aggregate. We determine surface tensions in the range of 0.01-0.4 mN/m from the fluctuations of the droplet shape and from the capillary-wave-like broadening of the interface between the two phases. From the dynamics of the protein end-to-end distance, we estimate shear viscosities from 0.001 to 0.02 Pa s for the FUS-LCD droplets with scaling factors α in the range of 0.625-0.75, where we observe liquid droplets. Significant hydration of the interior of the droplets keeps the proteins mobile and the droplets fluid.