Coarse-grain modelling of protein-protein interactions

"Assessing impact of hinge flexibility on predicted second osmotic virial coefficients"

Monoclonal antibodies (MAbs) are a key modality for treating a range of diseases because of their unique biophysical properties, such as high binding affinity and high specificity. However, MAb solutions can have unpredictable behavior that is detrimental to the drug product including aggregation and self-association, and high viscosity at elevated protein concentrations. Coarse-grained (CG) molecular simulations provide an opportunity to probe antibody behavior and self-interactions early in development without large experimental or computational burden. Recent work used a 1-bead-per-charge with 1-bead-per-domain (1bC/D) to model a combination of screened electrostatic, steric, and short-ranged non-electrostatic interactions to accurately predict experimental protein self-interactions for MAbs but neglected the influence of MAb hinge flexibility. This work includes the effects of flexibility of the hinge region while maintaining the 1bC/D resolution and computational efficiency. The flexibility is modeled by intramolecular rotations and flexing of antibody fragments about the central hinge to capture literature results for the distribution of internal structures for a single MAb. The difference between flexible and rigid models are analyzed for two body interactions for a reasonably large data set (n = 63) of different MAbs at typical commercial solution conditions. The net behavior showed small differences for the flexible vs. rigid model for most MAbs, within the range of experimental results, with a small number of exceptions. While the overall MAb-MAb self-interactions were not largely dependent on intramolecular degrees of freedom of the hinge region, there were some predicted differences in particular amino acid pairwise interactions from flexible to rigid models, which may indicate the additional computational burden of including hinge flexibility would be useful for future work focused on protein design and extensions to high protein concentration drug development where there are multi-protein spatial correlations.

Machine Learning Derived Collective Variables for the Study of Protein Homodimerization in Membrane

The accurate calculation of equilibrium constants for protein-protein association is of fundamental importance to quantitative biology and remains an outstanding challenge for computational biophysics. Traditionally, equilibrium constants have been computed from one-dimensional free energy surfaces derived from sampling along a single collective variable. Importantly, recent advances in enhanced sampling methodology have facilitated the characterization of multidimensional free energy landscapes, often exposing multiple thermodynamically important minima missed by more restrictive sampling methods. A key to the effectiveness of this multidimensional sampling approach is the identification of collective variables that effectively define the configurational space of dissociated and associated states. Here we present the application of two machine learning methods for the unbiased determination of collective variables for enhanced sampling and analysis of protein-protein association. Our results both validate prior work, based on intuition derived collective variables, and demonstrate the effectiveness of the machine learning methods for the identification of collective variables for association reactions in complex biomolecular systems.

Evaluation of Essential Dynamics and Fixed-Length Coarse Graining for Multidomain Proteins

For multiscale modeling of biomolecules, reliable coarse-grained (CG) models can offer great potential to simulate larger temporal and spatial scales than traditional all-atom (AA) models. In this study, we explore the essential dynamics coarse graining (EDCG) and fixed-length coarse graining (FLCG) approaches for constructing highly coarse-grained models for multidomain proteins (MDPs), with 1 to 10 amino acid residues per CG site. In the studies of 13 MDPs, our data indicate that both EDCG and FLCG can preserve the protein dynamics of MDPs. FLCG, which restricts an equal number of residues in each CG site, represents an excellent approximation to EDCG and a straightforward approach for coarse-graining MDPs. Furthermore, FLCG is tested with a class B G-protein-coupled receptor protein, and the agreement with prior experiments suggests its general application to various MDPs in different environments or conditions. Finally, we demonstrate another application of FLCG through progressive backmapping, showcasing the ability to recover from lower-resolution CG models (6 residues/CG site) to higher-resolution ones (1 residue/CG site). These promising outcomes underscore the broad applicability of FLCG to construct highly or ultra-coarse-grained models of complex biomolecules for multiscale simulations.

Simulations of Functional Motions of Super Large Biomolecules with a Mixed-Resolution Model

Many large protein machines function through an interplay between large-scale movements and intricate conformational changes. Understanding functional motions of these proteins through simulations becomes challenging for both all-atom and coarse-grained (CG) modeling techniques because neither approach alone can readily capture the full details of these motions. In this study, we develop a multiscale model by employing the popular MARTINI CG model to represent a heterogeneous environment and structurally stable proteins and using the united-atom (UA) model PACE to describe proteins undergoing subtle conformational changes. PACE was previously developed to be compatible with the MARTINI solvent and membrane. Here, we couple the protein descriptions of the two models by directly mixing UA and CG interaction parameters to greatly simplify parameter determination. Through extensive validations with diverse protein systems in solution or membrane, we demonstrate that only additional parameter rescaling is needed to enable the resulting model to recover the stability of native structures of proteins under mixed representation. Moreover, we identify the optimal scaling factors that can be applied to various protein systems, rendering the model potentially transferable. To further demonstrate its applicability for realistic systems, we apply the model to a mechanosensitive ion channel Piezo1 that has peripheral arms for sensing membrane tension and a central pore for ion conductance. The model can reproduce the coupling between Piezo1's large-scale arm movement and subtle pore opening in response to membrane stress while consuming much less computational costs than all-atom models. Therefore, our model shows promise for studying functional motions of large protein machines.

Molecular Dynamics Simulations in Protein-Protein Docking

Concerted interactions between all the cell components form the basis of biological processes. Protein-protein interactions (PPIs) constitute a tremendous part of this interaction network. Deeper insight into PPIs can help us better understand numerous diseases and lead to the development of new diagnostic and therapeutic strategies. PPI interfaces, until recently, were considered undruggable. However, it is now believed that the interfaces contain "hot spots," which could be targeted by small molecules. Such a strategy would require high-quality structural data of PPIs, which are difficult to obtain experimentally. Therefore, in silico modeling can complement or be an alternative to in vitro approaches. There are several computational methods for analyzing the structural data of the binding partners and modeling of the protein-protein dimer/oligomer structure. The major problem with in silico structure prediction of protein assemblies is obtaining sufficient sampling of protein dynamics. One of the methods that can take protein flexibility and the effects of the environment into account is Molecular Dynamics (MD). While sampling of the whole protein-protein association process with plain MD would be computationally expensive, there are several strategies to harness the method to PPI studies while maintaining reasonable use of resources. This chapter reviews known applications of MD in the PPI investigation workflows.

Pragmatic Coarse-Graining of Proteins: Models and Applications

The molecular details involved in the folding, dynamics, organization, and interaction of proteins with other molecules are often difficult to assess by experimental techniques. Consequently, computational models play an ever-increasing role in the field. However, biological processes involving large-scale protein assemblies or long time scale dynamics are still computationally expensive to study in atomistic detail. For these applications, employing coarse-grained (CG) modeling approaches has become a key strategy. In this Review, we provide an overview of what we call pragmatic CG protein models, which are strategies combining, at least in part, a physics-based implementation and a top-down experimental approach to their parametrization. In particular, we focus on CG models in which most protein residues are represented by at least two beads, allowing these models to retain some degree of chemical specificity. A description of the main modern pragmatic protein CG models is provided, including a review of the most recent applications and an outlook on future perspectives in the field.

Application of molecular dynamic simulations in modeling the excited state behavior of confined molecules

Relative to isotropic organic solvent medium, the structure and conformation of a reactant molecule in an organized and confining medium are often different. In addition, because of the rigidity of the immediate environment, the reacting molecule have a little freedom to undergo large changes even upon gaining energy or modifications in the electronic structure. These alterations give rise to differences in the photochemistry of a molecular and supramolecular species. In this study, one such example is presented. α-Alkyl dibenzylketones upon excitation in isotropic solvents give products via Norrish type I and type II reactions that are independent of the chain length of the alkyl substituent. On the other hand, when these molecules are enclosed within an organic capsule of volume ~ 550 Å3, they give products that are strikingly dependent on the length of the α-alkyl substitution. These previously reported experimental observations are rationalized based on the structures generated by molecular modeling (docking and molecular dynamics (MD) simulations). It is shown that MD simulations that are utilized extensively in biologically important macromolecules can also be useful to understand the excited state behavior of reactive molecules that are part of supramolecular assemblies. These simulations can provide structural information of the reactant molecule and the surroundings complementing that with the one obtained from 1 and 2D NMR experiments. MD simulated structures of seven α-alkyl dibenzylketones encapsulated within the octa acid capsule provide a clear understanding of their unique behavior in this restricted medium. Because of the rigidity of the medium, these structures although generated in the ground state can rationalize the photochemical behavior of the molecules in the excited state.

Computational insight into stability-enhanced systems of anthocyanin with protein/peptide

Anthocyanins, which belong to the flavonoid group, are commonly found in the organs of plants native to South and Central America. However, these pigments are unstable under conditions of varying pH, heat, etc., which limits their potential applications. One method for preserving the stability of anthocyanins is through encapsulation using proteins or peptides. Nevertheless, the complex and diverse structure of these molecules, as well as the limitation of experimental technologies, have hindered a comprehensive understanding of the encapsulation processes and the mechanisms by which stability is enhanced. To address these challenges, computational methods, such as molecular docking and molecular dynamics simulation have been used to study the binding affinity and dynamics of interactions between proteins/peptides and anthocyanins. This review summarizes the mechanisms of interaction between these systems, based on computational approaches, and highlights the role of proteins and peptides in the stability enhancement of anthocyanins. It also discusses the current limitations of these methods and suggests possible solutions.

Intrinsic Disorder in α-Synuclein Regulates the Exocytotic Fusion Pore Transition

Today, it is widely accepted that intrinsic disorder is strongly related to the cell cycle, during mitosis, differentiation, and apoptosis. Of particular interest are hybrid proteins possessing both structured and unstructured domains that are critical in human health and disease, such as α-synuclein. In this work, we describe how α-synuclein interacts with the nascent fusion pore as it evolves toward expansion. We unveil the key role played by its intrinsically disordered region as a thermodynamic regulator of the nucleation-expansion energy barrier. By analyzing a truncated variant of α-synuclein that lacks the disordered region, we find that the landscape of protein interactions with PIP₂ and POPS lipids is highly altered, ultimately increasing the energy cost for the fusion pore to transit from nucleation to expansion. We conclude that the intrinsically disordered region in full-length α-synuclein recognizes and allocates pivotal protein:lipid interactions during membrane remodeling in the first stages of the fusion pore.

Machine Learning-Driven Multiscale Modeling: Bridging the Scales with a Next-Generation Simulation Infrastructure

Interdependence across time and length scales is common in biology, where atomic interactions can impact larger-scale phenomenon. Such dependence is especially true for a well-known cancer signaling pathway, where the membrane-bound RAS protein binds an effector protein called RAF. To capture the driving forces that bring RAS and RAF (represented as two domains, RBD and CRD) together on the plasma membrane, simulations with the ability to calculate atomic detail while having long time and large length- scales are needed. The Multiscale Machine-Learned Modeling Infrastructure (MuMMI) is able to resolve RAS/RAF protein-membrane interactions that identify specific lipid-protein fingerprints that enhance protein orientations viable for effector binding. MuMMI is a fully automated, ensemble-based multiscale approach connecting three resolution scales: (1) the coarsest scale is a continuum model able to simulate milliseconds of time for a 1 μm2 membrane, (2) the middle scale is a coarse-grained (CG) Martini bead model to explore protein-lipid interactions, and (3) the finest scale is an all-atom (AA) model capturing specific interactions between lipids and proteins. MuMMI dynamically couples adjacent scales in a pairwise manner using machine learning (ML). The dynamic coupling allows for better sampling of the refined scale from the adjacent coarse scale (forward) and on-the-fly feedback to improve the fidelity of the coarser scale from the adjacent refined scale (backward). MuMMI operates efficiently at any scale, from a few compute nodes to the largest supercomputers in the world, and is generalizable to simulate different systems. As computing resources continue to increase and multiscale methods continue to advance, fully automated multiscale simulations (like MuMMI) will be commonly used to address complex science questions.

Performance efficient macromolecular mechanics via sub-nanometer shape based coarse graining

Dimensionality reduction via coarse grain modeling is a valuable tool in biomolecular research. For large assemblies, ultra coarse models are often knowledge-based, relying on a priori information to parameterize models thus hindering general predictive capability. Here, we present substantial advances to the shape based coarse graining (SBCG) method, which we refer to as SBCG2. SBCG2 utilizes a revitalized formulation of the topology representing network which makes high-granularity modeling possible, preserving atomistic details that maintain assembly characteristics. Further, we present a method of granularity selection based on charge density Fourier Shell Correlation and have additionally developed a refinement method to optimize, adjust and validate high-granularity models. We demonstrate our approach with the conical HIV-1 capsid and heteromultimeric cofilin-2 bound actin filaments. Our approach is available in the Visual Molecular Dynamics (VMD) software suite, and employs a CHARMM-compatible Hamiltonian that enables high-performance simulation in the GPU-resident NAMD3 molecular dynamics engine.

Exploring the Phospholipid Transport Mechanism of ATP8A1-CDC50

P4-ATPase translocates lipids from the exoplasmic to the cytosolic plasma membrane leaflet to maintain lipid asymmetry distribution in eukaryotic cells. P4-ATPase is associated with severe neurodegenerative and metabolic diseases such as neurological and motor disorders. Thus, it is important to understand its transport mechanism. However, even with progress in X-ray diffraction and cryo-electron microscopy techniques, it is difficult to obtain the dynamic information of the phospholipid transport process in detail. There are still some problems required to be resolved: (1) when does the lipid transport happen? (2) How do the key residues on the transmembrane helices contribute to the free energy of important states? In this work, we explore the phospholipid transport mechanism using a coarse-grained model and binding free energy calculations. We obtained the free energy landscape by coupling the protein conformational changes and the phospholipid transport event, taking ATP8A1-CDC50 (the typical subtype of P4-ATPase) as the research object. According to the results, we found that the phospholipid would bind to the ATP8A1-CDC50 at the early stage when ATP8A1-CDC50 changes from E2P to E2Pi-PL state. We also found that the electrostatic effects play crucial roles in the phospholipid transport process. The information obtained from this work could help us in designing novel drugs for P-type flippase disorders.

Temporally Coherent Backmapping of Molecular Trajectories From Coarse-Grained to Atomistic Resolution

Coarse-graining offers a means to extend the achievable time and length scales of molecular dynamics simulations beyond what is practically possible in the atomistic regime. Sampling molecular configurations of interest can be done efficiently using coarse-grained simulations, from which meaningful physicochemical information can be inferred if the corresponding all-atom configurations are reconstructed. However, this procedure of backmapping to reintroduce the lost atomistic detail into coarse-grain structures has proven a challenging task due to the many feasible atomistic configurations that can be associated with one coarse-grain structure. Existing backmapping methods are strictly frame-based, relying on either heuristics to replace coarse-grain particles with atomic fragments and subsequent relaxation or parametrized models to propose atomic coordinates separately and independently for each coarse-grain structure. These approaches neglect information from previous trajectory frames that is critical to ensuring temporal coherence of the backmapped trajectory, while also offering information potentially helpful to producing higher-fidelity atomic reconstructions. In this work, we present a deep learning-enabled data-driven approach for temporally coherent backmapping that explicitly incorporates information from preceding trajectory structures. Our method trains a conditional variational autoencoder to nondeterministically reconstruct atomistic detail conditioned on both the target coarse-grain configuration and the previously reconstructed atomistic configuration. We demonstrate our backmapping approach on two exemplar biomolecular systems: alanine dipeptide and the miniprotein chignolin. We show that our backmapped trajectories accurately recover the structural, thermodynamic, and kinetic properties of the atomistic trajectory data.

Frame-guided assembly from a theoretical perspective

The molecular self-assembly of various structures such as micelles and vesicles has been the subject of comprehensive studies. Recently, a new approach to design these structures, the frame-guided assembly, has been developed to progress towards fabrics of predefined shape and size, following an initially provided frame of guiding elements. Here we study frame-guided assembly into a two-dimensional membrane via computer simulations, based on a single-bead coarse grained surfactant model in continuous space. In agreement with the experiment the assembly process already starts for surfactant concentrations below the critical micelle concentration. Furthermore, upon increasing temperature the formation process gets more delocalized. Additionally, the assembly process of the resulting membrane plane is modelled by a lattice gas model. It displays a similar phenomenology but additionally allows the derivation of analytical mean-field predictions. In this way a fundamental understanding of frame-guided assembly can be gained.

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.

Paired Simulations and Experimental Investigations into the Calcium-Dependent Conformation of Albumin

Serum albumin is the most abundant protein in blood plasma, and it is involved in multiple biological processes. Serum albumin has recently been adapted for improving biomaterial integration with bone tissue, and studies have shown the importance of this protein in bone repair and regeneration. However, the mechanism of action is not yet clear. In stark contrast, other studies have demonstrated that albumin blocks cell adhesion to surfaces, which is seen as a limitation to its bone healing role. These apparent contradictions suggest that the conformation of albumin facilitates its bioactivity, leading to enhanced bone repair. Serum albumin is known to play a major role in maintaining the calcium ion concentration in blood plasma. Due to the prevalence of calcium at bone repair and regeneration sites, it has been hypothesized that calcium binding to serum albumin triggers a conformational change, leading to bioactivity. In the current study, molecular modeling approaches including molecular docking, atomic molecular dynamics (MD) simulation, and coarse-grained MD simulation were used to test this hypothesis by investigating the conformational changes induced in bovine serum albumin by interaction with calcium ions. The computational results were qualitatively validated with experimental Fourier-transform infrared spectroscopy analysis. We find that free calcium ions in solution transiently bind with the three major loops in albumin, triggering a conformational change where N-terminal and C-terminal domains separate from each other in a partial unfolding process. The separation distance between these domains was found to correlate with the calcium ion concentration. The experimental data support the simulation results showing that albumin has enhanced conformational heterogeneity upon exposure to intermediate levels of calcium, without any significant secondary structure changes.

Transport Behavior of Commercial Anticancer Drug Protein-Bound Paclitaxel (Paclicad) in a Micron-Sized Channel

Protein-bound paclitaxel has been developed clinically as one of the most successful chemotherapy drugs for the treatment of a wide variety of cancers. However, these medications, due to their nanoscale properties, may often induce capillary blocking while migrating through minute blood vessels. Considering the detrimental impact of this restriction, we investigated the transport of protein-bound paclitaxel, Paclicad, in a 7 μm microchannel mimicking the identical mechanical confinement of the blood capillaries. The drug was reported to migrate through a constricted microchannel without obstruction at a solution flow rate of 20-50 μL/h. The onset of an agglomeration site was observed at higher flow rates of 70-90 μL/h, while complete capillary obstruction was observed at 100 μL/h. The mobility of the particles was also calculated, and the results suggested that the presence of varying cross-sections affects the mobility of the drug particles. The trajectory of the particle migration was observed to be less tortuous at the higher flow rate, but the tortuous nature appeared to increase with the presence of agglomeration sites in the flow field. The experimental results were also compared with the computational model of the drug particle. The drug particle was modeled both as Newtonian and as an FENE-P viscoelastic drop. The drop interface tracking was done by the VOF method using the open source software Basilisk. The particle displacement was better estimated by both the FENE-P and Newtonian model at a flow rate of 30 μL/h, while deviation was observed at a flow rate of 50 μL/h. The FENE-P model was observed to show higher deformation than the Newtonian model at both flow rates. The experimental results provided better insight into the agglomeration tendency of Paclicad, migrating through a constricted microchannel at higher flow rates. The numerical model could be further employed to understand the more complex intravenous transport of drugs.

A generic force field for simulating native protein structures using dissipative particle dynamics

A coarse-grained force field for molecular dynamics simulations of the native structures of proteins in a dissipative particle dynamics (DPD) framework is developed. The parameters for bonded interactions are derived by mapping the bonds and angles for 20 amino acids onto target distributions obtained from fully atomistic simulations in explicit solvent. A dual-basin potential is introduced for stabilizing backbone angles, to cover a wide spectrum of protein secondary structures. The backbone dihedral potential enables folding of the protein from an unfolded initial state to the folded native structure. The proposed force field is validated by evaluating the structural properties of several model peptides and proteins including the SARS-CoV-2 fusion peptide, consisting of α-helices, β-sheets, loops and turns. Detailed comparisons with fully atomistic simulations are carried out to assess the ability of the proposed force field to stabilize the different secondary structures present in proteins. The compact conformations of the native states were evident from the radius of gyration and the high intensity peaks of the root mean square deviation histograms, which were found to be within 0.4 nm. The Ramachandran-like energy landscape on the phase space of backbone angles (θ) and dihedrals (ϕ) effectively captured the conformational phase space of α-helices at ∼(ϕ = 50°,θ = 90°) and β-strands at ∼(ϕ = ±180°,θ = 90-120°). Furthermore, the residue-residue native contacts were also well reproduced by the proposed DPD model. The applicability of the model to multidomain complexes was assessed using lysozyme and a large α-helical bacterial pore-forming toxin, cytolysin A. Our study illustrates that the proposed force field is generic, and can potentially be extended for efficient in silico investigations of membrane bound polypeptides and proteins using DPD simulations.

Protein-polymer mixtures in the colloid limit: Aggregation, sedimentation, and crystallization

While proteins have been treated as particles with a spherically symmetric interaction, of course in reality, the situation is rather more complex. A simple step toward higher complexity is to treat the proteins as non-spherical particles and that is the approach we pursue here. We investigate the phase behavior of the enhanced green fluorescent protein (eGFP) under the addition of a non-adsorbing polymer, polyethylene glycol. From small angle x-ray scattering, we infer that the eGFP undergoes dimerization and we treat the dimers as spherocylinders with aspect ratio L/D - 1 = 1.05. Despite the complex nature of the proteins, we find that the phase behavior is similar to that of hard spherocylinders with an ideal polymer depletant, exhibiting aggregation and, in a small region of the phase diagram, crystallization. By comparing our measurements of the onset of aggregation with predictions for hard colloids and ideal polymers [S. V. Savenko and M. Dijkstra, J. Chem. Phys. 124, 234902 (2006) and Lo Verso et al., Phys. Rev. E 73, 061407 (2006)], we find good agreement, which suggests that the behavior of the eGFP is consistent with that of hard spherocylinders and ideal polymers.

Conservative Potentials for a Lattice-Mapped Coarse-Grained Scheme

The conservative potential, arising from a coarse-grain (CG) mapping scheme for nonbonded atomistic particles, is studied. This is a bottom-up approach from first-principles that maps atomistic particles to fluid element-like subcells whose centers lie on a regular, cubic lattice. Unlike standard CG mapping schemes, the current one uses dynamic labeling which on-the-fly changes the CG labels of the particles. The subcells can also be different sizes and shapes, in principle. Equilibrium atomistic molecular dynamics trajectories for different Lennard-Jones fluids are calculated and converted to CG ones, from which CG probability distribution functions are calculated. Correlation studies show position and mass CG variables are uncoupled in a given subcell, as are different vector components of position. Furthermore, the strongest coupling occurs with neighboring cells in specific directions, and the resulting distribution is well described by a multivariate Gaussian. This implies the CG potential has a generalized quadratic form, whose derivative can be determined analytically. A microscopic rationalization is provided for the signs and relative magnitudes of different correlation coefficients, and in some cases, a connection is made with bulk properties of the fluid. We argue the generalized quadratic form should be robust to changes in the particulars of the CG scheme, as well as the nature of the atomistic intermolecular potential. Only a few potential parameters need to be calculated from the underlying atomistic system. This is significant because it indicates the transferability of this form to other, more complex systems. This transferability will be tested in future work, where mapping schemes with fuzzy boundaries will be considered.

Protein-Protein Docking with Large-Scale Backbone Flexibility Using Coarse-Grained Monte-Carlo Simulations

Most of the protein-protein docking methods treat proteins as almost rigid objects. Only the side-chains flexibility is usually taken into account. The few approaches enabling docking with a flexible backbone typically work in two steps, in which the search for protein-protein orientations and structure flexibility are simulated separately. In this work, we propose a new straightforward approach for docking sampling. It consists of a single simulation step during which a protein undergoes large-scale backbone rearrangements, rotations, and translations. Simultaneously, the other protein exhibits small backbone fluctuations. Such extensive sampling was possible using the CABS coarse-grained protein model and Replica Exchange Monte Carlo dynamics at a reasonable computational cost. In our proof-of-concept simulations of 62 protein-protein complexes, we obtained acceptable quality models for a significant number of cases.

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.

Perspectives on High-Throughput Ligand/Protein Docking With Martini MD Simulations

Molecular docking is central to rational drug design. Current docking techniques suffer, however, from limitations in protein flexibility and solvation models and by the use of simplified scoring functions. All-atom molecular dynamics simulations, on the other hand, feature a realistic representation of protein flexibility and solvent, but require knowledge of the binding site. Recently we showed that coarse-grained molecular dynamics simulations, based on the most recent version of the Martini force field, can be used to predict protein/ligand binding sites and pathways, without requiring any a priori information, and offer a level of accuracy approaching all-atom simulations. Given the excellent computational efficiency of Martini, this opens the way to high-throughput drug screening based on dynamic docking pipelines. In this opinion article, we sketch the roadmap to achieve this goal.

A critical perspective on Markov state model treatments of protein-protein association using coarse-grained simulations

Atomic-level information is essential to explain the specific interactions governing protein–protein recognition in terms of structure and dynamics. Of particular interest is a characterization of the time-dependent kinetic aspects of protein–protein association and dissociation. A powerful framework to characterize the dynamics of complex molecular systems is provided by Markov State Models (MSMs). The central idea is to construct a reduced stochastic model of the full system by defining a set of conformational featured microstates and determining the matrix of transition probabilities between them. While a MSM framework can sometimes be very effective, different combinations of input featurization and simulation methods can significantly affect the robustness and the quality of the information generated from MSMs in the context of protein association. Here, a systematic examination of a variety of MSMs methodologies is undertaken to clarify these issues. To circumvent the uncertainties caused by sampling issues, we use a simplified coarse-grained model of the barnase–barstar protein complex. A sensitivity analysis is proposed to identify the microstates of an MSM that contribute most to the error in conjunction with the transition-based reweighting analysis method for a more efficient and accurate MSM construction.

Optimizing Gō-MARTINI Coarse-Grained Model for F-BAR Protein on Lipid Membrane

Coarse-grained (CG) molecular dynamics (MD) simulations allow us to access much larger length and time scales than atomistic MD simulations, providing an attractive alternative to the conventional simulations. Based on the well-known MARTINI CG force field, the recently developed Gō-MARTINI model for proteins describes large-amplitude structural dynamics, which has not been possible with the commonly used elastic network model. Using the Gō-MARTINI model, we conduct MD simulations of the F-BAR Pacsin1 protein on lipid membrane. We observe that structural changes of the non-globular protein are largely dependent on the definition of the native contacts in the Gō model. To address this issue, we introduced a simple cutoff scheme and tuned the cutoff distance of the native contacts and the interaction strength of the Lennard-Jones potentials in the Gō-MARTINI model. With the optimized Gō-MARTINI model, we show that it reproduces structural fluctuations of the Pacsin1 dimer from atomistic simulations. We also show that two Pacsin1 dimers properly assemble through lateral interaction on the lipid membrane. Our work presents a first step towards describing membrane remodeling processes in the Gō-MARTINI CG framework by simulating a crucial step of protein assembly on the membrane.

Computational modelling of flavivirus dynamics: The ins and outs

Enveloped viruses such as the flaviviruses represent a significant burden to human health around the world, with hundreds of millions of people each year affected by dengue alone. In an effort to improve our understanding of the molecular basis for the infective mechanisms of these viruses, extensive computational modelling approaches have been applied to elucidate their conformational dynamics. Multiscale protocols have been developed to simulate flavivirus envelopes in close accordance with biophysical data, in particular derived from cryo-electron microscopy, enabling high-resolution refinement of their structures and elucidation of the conformational changes associated with adaptation both to host environments and to immunological factors such as antibodies. Likewise, integrative modelling efforts combining data from biophysical experiments and from genome sequencing with chemical modification are providing unparalleled insights into the architecture of the previously unresolved nucleocapsid complex. Collectively, this work provides the basis for the future rational design of new antiviral therapeutics and vaccine development strategies targeting enveloped viruses.

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

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

Pseudo-Improper-Dihedral Model for Intrinsically Disordered Proteins

We present a new coarse-grained C_α-based protein model with a nonradial multibody pseudo-improper-dihedral potential that is transferable, time-independent, and suitable for molecular dynamics. It captures the nature of backbone and side-chain interactions between amino acid residues by adapting a simple improper dihedral term for a one-bead-per-residue model. It is parameterized for intrinsically disordered proteins and applicable to simulations of such proteins and their assemblies on millisecond time scales.

Machine Learning Driven Analysis of Large Scale Simulations Reveals Conformational Characteristics of Ubiquitin Chains

Understanding the conformational characteristics of protein complexes in solution is crucial for a deeper insight in their biological function. Molecular dynamics simulations performed on high performance computing plants and with modern simulation techniques can be used to obtain large data sets that contain conformational and thermodynamic information about biomolecular systems. While this can in principle give a detailed picture of protein-protein interactions in solution and therefore complement experimental data, it also raises the challenge of processing exceedingly large high-dimensional data sets with several million samples. Here we present a novel method for the characterization of protein-protein interactions, which combines a neural network based dimensionality reduction technique to obtain a two-dimensional representation of the conformational space with a density based clustering algorithm for state detection and a metric which assesses the (dis)similarity between different conformational spaces. This method is highly scalable and therefore makes the analysis of massive data sets computationally tractable. We demonstrate the power of this approach to large scale data analysis by characterizing highly dynamic conformational phase spaces of differently linked ubiquitin (Ub) oligomers from coarse-grained simulations. We are able to extract a protein-protein interaction model for two unlinked Ub proteins which is then used to determine how the Ub-Ub interaction pattern is altered in Ub oligomers by the introduction of a covalent linkage. We find that the Ub chain conformational ensemble depends highly on the linkage type and for some cases also on the Ub chain length. By this, we obtain insight into the conformational characteristics of different Ub chains and how this may contribute to linkage type and chain length specific recognition.

Computational Modeling of Claudin Structure and Function

Tight junctions form a barrier to control passive transport of ions and small molecules across epithelia and endothelia. In addition to forming a barrier, some of claudins control transport properties of tight junctions by forming charge- and size-selective ion channels. It has been suggested claudin monomers can form or incorporate into tight junction strands to form channels. Resolving the crystallographic structure of several claudins in recent years has provided an opportunity to examine structural basis of claudins in tight junctions. Computational and theoretical modeling relying on atomic description of the pore have contributed significantly to our understanding of claudin pores and paracellular transport. In this paper, we review recent computational and mathematical modeling of claudin barrier function. We focus on dynamic modeling of global epithelial barrier function as a function of claudin pores and molecular dynamics studies of claudins leading to a functional model of claudin channels.

Statistical field theory of ion–molecular solutions

Schematic representation of the multipolar molecule surrounded by salt ions in a dielectric solvent medium.

Dimerization energetics of the G-protein coupled bile acid receptor TGR5 from all-atom simulations

We describe the first extensive energetic evaluation of GPCR dimerization on the atomistic level by means of potential of mean force (PMF) computations and implicit solvent/implicit membrane end-point free energy calculations (MM-PBSA approach). Free energies of association computed from the PMFs show that the formation of both the 1/8 and 4/5 interface is energetically favorable for TGR5, the first GPCR known to be activated by hydrophobic bile acids and neurosteroids. Furthermore, formation of the 1/8 interface is favored over that of the 4/5 interface. Both results are in line with our previous FRET experiments in live cells. Differences in lipid-protein interactions are identified to contribute to the observed differences in free energies of association. A per-residue decomposition of the MM-PBSA effective binding energy reveals hot spot residues specific for both interfaces that form clusters. This knowledge may be used to guide the design of dimerization inhibitors or perform mutational studies to explore physiological consequences of distorted TGR5 association. Finally, we characterized the role of Y111, located in the conserved (D/E)RY motif, as a facilitator of TGR5 interactions. The types of computations performed here should be transferable to other transmembrane proteins that form dimers or higher oligomers as long as good structural models of the dimeric or oligomeric states are available. Such computations may help to overcome current restrictions due to an imperfect energetic representation of protein association at the coarse-grained level. © 2019 Wiley Periodicals, Inc.

Efficient flexible backbone protein-protein docking for challenging targets

Motivation

Binding-induced conformational changes challenge current computational docking algorithms by exponentially increasing the conformational space to be explored. To restrict this search to relevant space, some computational docking algorithms exploit the inherent flexibility of the protein monomers to simulate conformational selection from pre-generated ensembles. As the ensemble size expands with increased flexibility, these methods struggle with efficiency and high false positive rates.

Results

Here, we develop and benchmark RosettaDock 4.0, which efficiently samples large conformational ensembles of flexible proteins and docks them using a novel, six-dimensional, coarse-grained score function. A strong discriminative ability allows an eight-fold higher enrichment of near-native candidate structures in the coarse-grained phase compared to RosettaDock 3.2. It adaptively samples 100 conformations each of the ligand and the receptor backbone while increasing computational time by only 20-80%. In local docking of a benchmark set of 88 proteins of varying degrees of flexibility, the expected success rate (defined as cases with ≥50% chance of achieving 3 near-native structures in the 5 top-ranked ones) for blind predictions after resampling is 77% for rigid complexes, 49% for moderately flexible complexes and 31% for highly flexible complexes. These success rates on flexible complexes are a substantial step forward from all existing methods. Additionally, for highly flexible proteins, we demonstrate that when a suitable conformer generation method exists, the method successfully docks the complex.

Availability and implementation

As a part of the Rosetta software suite, RosettaDock 4.0 is available at https://www.rosettacommons.org to all non-commercial users for free and to commercial users for a fee.

Supplementary information

Supplementary data are available at Bioinformatics online.

Curvature induction and sensing of the F-BAR protein Pacsin1 on lipid membranes via molecular dynamics simulations

F-Bin/Amphiphysin/Rvs (F-BAR) domain proteins play essential roles in biological processes that involve membrane remodelling, such as endocytosis and exocytosis. It has been shown that such proteins transform the lipid membrane into tubes. Notably, Pacsin1 from the Pacsin/Syndapin subfamily has the ability to transform the membrane into various morphologies: striated tubes, featureless wide and thin tubes, and pearling vesicles. The molecular mechanism of this interesting ability remains elusive. In this study, we performed all-atom (AA) and coarse-grained (CG) molecular dynamics simulations to investigate the curvature induction and sensing mechanisms of Pacsin1 on a membrane. From AA simulations, we show that Pacsin1 has internal structural flexibility. In CG simulations with parameters tuned from the AA simulations, spontaneous assembly of two Pacsin1 dimers through lateral interaction is observed. Based on the complex structure, we show that the regularly assembled Pacsin1 dimers bend a tensionless membrane. We also show that a single Pacsin1 dimer senses the membrane curvature, binding to a buckled membrane with a preferred curvature. These results provide molecular insights into polymorphic membrane remodelling.

Adversarial-residual-coarse-graining: Applying machine learning theory to systematic molecular coarse-graining

We utilize connections between molecular coarse-graining (CG) approaches and implicit generative models in machine learning to describe a new framework for systematic molecular CG. Focus is placed on the formalism encompassing generative adversarial networks. The resulting method enables a variety of model parameterization strategies, some of which show similarity to previous CG methods. We demonstrate that the resulting framework can rigorously parameterize CG models containing CG sites with no prescribed connection to the reference atomistic system (termed virtual sites); however, this advantage is offset by the lack of a closed-form expression for the CG Hamiltonian at the resolution obtained after integration over the virtual CG sites. Computational examples are provided for cases in which these methods ideally return identical parameters as relative entropy minimization CG but where traditional relative entropy minimization CG optimization equations are not applicable.

Molecular Dynamics Simulation of Pure n-Alkanes and Their Mixtures at Elevated Temperatures Using Atomistic and Coarse-Grained Force Fields

The properties of higher n-alkanes and their mixtures is a topic of significant interest for the oil and chemical industry. However, the experimental data at high temperatures are scarce. The present study focuses on simulating n-dodecane, n-octacosane, their binary mixture at a n-dodecane mole fraction of 0.3, and a model mixture of the commercially available hydrocarbon wax SX-70 to evaluate the performance of several force fields on the reproduction of properties such as liquid densities, surface tension, and viscosities. Molecular dynamics simulations over a broad temperature range from 323.15 to 573.15 K were employed in examining a broad set of atomistic molecular models assessed for the reproduction of experimental data. The well-established united atom TraPPE (TraPPE-UA) was compared against the all atom optimized potentials for liquid simulations (OPLS) reparametrization for long n-alkanes, L-OPLS, as well as Lipid14 and MARTINI force fields. All models qualitatively reproduce the temperature dependence of the aforementioned properties, but TraPPE-UA was found to reproduce liquid densities most accurately and consistently over the entire temperature range. TraPPE-UA and MARTINI were very successful in reproducing surface tensions, and L-OPLS was found to be the most accurate in reproducing the measured viscosities as compared to the other models. Our simulations show that these widely used force fields originating from the world of biomolecular simulations are suitable candidates in the study of n-alkane properties, both in the pure and mixture states.

Untangling Direct and Domain-Mediated Interactions Between Nicotinic Acetylcholine Receptors in DHA-Rich Membranes

At the neuromuscular junction (NMJ), the nicotinic acetylcholine receptor (nAChR) self-associates to give rise to rapid muscle movement. While lipid domains have maintained nAChR aggregates in vitro, their specific roles in nAChR clustering are currently unknown. In the present study, we carried out coarse-grained molecular dynamics simulations (CG-MD) of 1-4 nAChR molecules in two membrane environments: one mixture containing domain-forming, homoacidic lipids, and a second mixture consisting of heteroacidic lipids. Spontaneous dimerization of nAChRs was up to ten times more likely in domain-forming membranes; however, the effect was not significant in four-protein systems, suggesting that lipid domains are less critical to nAChR oligomerization when protein concentration is higher. With regard to lipid preferences, nAChRs consistently partitioned into liquid-disordered domains occupied by the omega-3 ([Formula: see text]-3) fatty acid, docosahexaenoic acid (DHA); enrichment of DHA boundary lipids increased with protein concentration, particularly in homoacidic membranes. This result suggests dimer formation blocks access of saturated chains and cholesterol, but not polyunsaturated chains, to boundary lipid sites.

Rational modulator design by exploitation of protein-protein complex structures

The horizon of drug discovery is currently expanding to target and modulate protein-protein interactions (PPIs) in globular proteins and intrinsically disordered proteins that are involved in various diseases. To either interrupt or stabilize PPIs, the 3D structure of target protein-protein (or protein-peptide) complexes can be exploited to rationally design PPI modulators (inhibitors or stabilizers) through structure-based molecular design. In this review, we present an overview of experimental and computational methods that can be used to determine 3D structures of protein-protein complexes. Several approaches including rational and in silico methods that can be applied to design peptides, peptidomimetics and small compounds by utilization of determined 3D protein-protein/peptide complexes are summarized and illustrated.

Computational Modeling of Realistic Cell Membranes

Cell membranes contain a large variety of lipid types and are crowded with proteins, endowing them with the plasticity needed to fulfill their key roles in cell functioning. The compositional complexity of cellular membranes gives rise to a heterogeneous lateral organization, which is still poorly understood. Computational models, in particular molecular dynamics simulations and related techniques, have provided important insight into the organizational principles of cell membranes over the past decades. Now, we are witnessing a transition from simulations of simpler membrane models to multicomponent systems, culminating in realistic models of an increasing variety of cell types and organelles. Here, we review the state of the art in the field of realistic membrane simulations and discuss the current limitations and challenges ahead.

Characterization of Lipid-Protein Interactions and Lipid-Mediated Modulation of Membrane Protein Function through Molecular Simulation

The cellular membrane constitutes one of the most fundamental compartments of a living cell, where key processes such as selective transport of material and exchange of information between the cell and its environment are mediated by proteins that are closely associated with the membrane. The heterogeneity of lipid composition of biological membranes and the effect of lipid molecules on the structure, dynamics, and function of membrane proteins are now widely recognized. Characterization of these functionally important lipid-protein interactions with experimental techniques is however still prohibitively challenging. Molecular dynamics (MD) simulations offer a powerful complementary approach with sufficient temporal and spatial resolutions to gain atomic-level structural information and energetics on lipid-protein interactions. In this review, we aim to provide a broad survey of MD simulations focusing on exploring lipid-protein interactions and characterizing lipid-modulated protein structure and dynamics that have been successful in providing novel insight into the mechanism of membrane protein function.

A Peptide-Nanoparticle System with Improved Efficacy against Multidrug Resistant Bacteria

The recent rise of multidrug resistant microbial strains requires development of new and novel therapeutic alternatives. In this study, we present a novel antibacterial system that comprises of modified naturally abundant antimicrobial peptides in conjugation with silver nanoparticles. Further, we propose a simple route to incorporate a cysteine residue either at the N- or C-terminal of the parent peptide. Tagging a cysteine residue at the terminals not only enhances the binding propensity of the resultant peptide with the silver nanoparticle, but also increases its antimicrobial property against several pathogenic bacterial strains including K. pneumoniae. The minimum inhibitory concentration (MIC) values of the cysteine tagged nanoconjugates were obtained in the range of 5-15 μM compared to 50 μM for peptides devoid of the cysteines. The origin and mechanism of such improved activity of the conjugates were investigated using NMR spectroscopy and molecular dynamics (MD) simulations. The application of ¹³C-isotope labelled media to track the metabolic lifecycle of E. coli cells provided further insights into the system. MD simulations showed that pore formation in membrane bilayer is mediated through a hydrophobic collapse mechanism. The design strategy described herein opens up new-avenues for using biocompatible nanomedicines as a potential alternative to conventional antibiotics.

Transmembrane domain dimerization induces cholesterol rafts in curved lipid bilayers

Are the dimerization of transmembrane (TM) domains and the reorganization of the lipid bilayer two independent events?

Lipid composition and salt concentration as regulatory factors of the anion selectivity of VDAC studied by coarse-grained molecular dynamics simulations

The voltage-dependent anion channel (VDAC) is a mitochondrial outer membrane protein whose fundamental function is to facilitate and regulate the flow of metabolites between the cytosol and the mitochondrial intermembrane space. Using coarse-grained molecular dynamics simulations, we investigated the dependence of VDAC selectivity towards small inorganic anions on two factors: the ionic strength and the lipid composition. In agreement with experimental data we found that VDAC becomes less anion selective with increasing salt concentration due to the screening of a few basic residues that point into the pore lumen. The molecular dynamics simulations provide insight into the regulation mechanism of VDAC selectivity by the composition in the lipid membrane and suggest that the ion distribution is differently modulated by POPE compared to the POPC bilayer. This occurs through the more persistent interactions of acidic residues located at both rims of the β-barrel with head groups of POPE which in turn impact the electrostatic potential and thereby the selectivity of the pore. This mechanism occurs not only in POPE single component membranes but also in a mixed POPE/POPC bilayer by an enrichment of POPE over POPC lipids on the surface of VDAC. Thus we show here that computationally-inexpensive coarse-grained simulations are able to capture, in a semi-quantitative way, essential features of VDAC anion selectivity and could pave the way toward a molecular level understanding of metabolite transport in natural membranes.

Biophysical characterization and molecular simulation of electrostatically driven self-association of a single-chain antibody

Colloidal protein-protein interactions (PPI) are often expected to impact key behaviors of proteins in solution, such as aggregation rates and mechanisms, aggregate structure, protein solubility, and solution viscosity. PPI of an anti-fluorescein single chain antibody variable fragment (scFv) were characterized experimentally at low to intermediate ionic strength using a combination of static light scattering and sedimentation equilibrium ultracentrifugation. Surprisingly, the results indicated that interactions were strongly net-attractive and electrostatics promoted self-association. Only repulsive interactions were expected based on prior work and calculations based a homology model of a related scFv crystal structure. However, the crystal structure lacks the charged, net-neutral linker sequence. PyRosetta was used to generate a set of scFv structures with different linker conformations, and coarse-grained Monte Carlo simulations were used to evaluate the effect of different linker configurations via second osmotic virial coefficient (B22 ) simulations. The results show that the configuration of the linker has a significant effect on the calculated B22 values, and can result in strong electrostatic attractions between oppositely charged residues on the protein surface. This is particularly relevant for development of non-natural antibody products, where charged linkers and other loop regions may be prevalent. The results also provide a preliminary computational framework to evaluate the effect of unstructured linkers on experimental protein-protein interaction parameters such as B22 .