Modeling pH-Dependent Protein Dynamics by Integrating Coarse-Grained Molecular Simulation and the Deep Neural Network Model.

Multiscale Modeling of Intra- and Inter-Molecular Communications Through Protein Structures

We present a systematic derivation of a coarse grained (CG) model for molecular dynamics (MD) simulations of a liquid crystalline (LC) compound containing an azobenzene mesogen. The model aims at a later use in a multiscale modeling approach to study liquid crystalline phase transitions that are (photo)induced by the trans/cis photoisomerization of the mesogen. One of the major challenges in the coarse graining process is the development of models that are for a given chemical system structurally consistent with for example an all-atom reference model and reproduce relevant thermodynamic properties such as the LC phase behavior around the state point of interest. The reduction of number of degrees of freedom makes the resulting coarse models by construction state point dependent; that is, they cannot easily be transferred to a range of temperatures, densities, system compositions, etc. These are significant challenges, in particular if one wants to study LC phase transitions (thermally or photoinduced). In the present paper we show how one can systematically derive a CG model for a LC molecule that is highly consistent with an atomistic description by choosing an appropriate state point for the reference simulation. The reference state point is the supercooled liquid just below the smectic-isotropic phase transition which is characterized by a high degree of local nematic order while being overall isotropic. With the resulting CG model it is possible to switch between the atomistic and the CG levels (and vice versa) in a seamless manner maintaining values of all the relevant order parameters which describe the smectic A (smA) state. This model will allow us in the future to link large length scale and long time scale CG simulations of the LC state with chemically accurate QM/MM simulations of the photoisomerization process.

Molecular dynamics simulations based on coarse-grained (CG) models are used to accelerate conformational dynamics of biomolecules and other chemical systems with reduced computational costs. CG models achieve this by discarding atomic information necessary for downstream structural analysis. Recovering the atomic detail from CG structures, i.e., backmapping, remains a fundamental challenge in multiscale modeling, especially for proteins and complex biomolecular assemblies. Recent machine learning methods have shown promise in reconstructing atomistic details, but most approaches only target simple systems at a small scale. In particular, conventional backmapping pipelines often fail to preserve stereochemistry, induce high-energy configurations, or require extensive minimization. Here we present CGBack, a backmapping framework that employs a denoising diffusion probabilistic model to reconstruct all-atom molecular structures from CG representations. CGBack consists of backmapping and refinement procedures and accurately recovers atomic coordinates across diverse protein systems from small to large scales. We show that CGBack is capable of accurately backmapping both single-chain and multichain molecular systems, including densely packed intrinsically disordered proteins in condensates. These results suggest that CGBack can be a powerful tool for multiscale molecular simulation pipelines. We anticipate that CGBack will enable more efficient workflows for protein modeling, as well as for other biomolecules across different CG models.

Chapter 16 The Proton as an Integrating Effector in Metabolic Activation

Despite the significant increase in computational power, molecular modeling of protein structure using classical all-atom approaches remains inefficient, at least for most of the protein targets in the focus of biomedical research. Perhaps the most successful strategy to overcome the inefficiency problem is multiscale modeling to merge all-atom and coarse-grained models. This chapter describes a well-established CABS coarse-grained protein model. The CABS (C-Alpha, C-Beta, and Side chains) model assumes a 2-4 united-atom representation of amino acids, knowledge-based force field (derived from the statistical regularities seen in known protein sequences and structures) and efficient Monte Carlo sampling schemes (MC dynamics, MC replica-exchange, and combinations). A particular emphasis is given to the unique design of the CABS force-field, which is largely defined using one-dimensional structural properties of proteins, including protein secondary structure. This chapter also presents CABS-based modeling methods, including multiscale tools for de novo structure prediction, modeling of protein dynamics and prediction of protein-peptide complexes. CABS-based tools are freely available at http://biocomp.chem.uw.edu.pl/tools.

In the last decade, various coarse-grained elastic network models have been developed to study the large-scale motions of proteins and protein complexes where computer simulations using detailed all-atom models are not feasible. Among these models, the Gaussian Network Model (GNM) and Anisotropic Network Model (ANM) have been widely used. Both models have strengths and limitations. GNM can predict the relative magnitudes of the fluctuations well, but due to its isotropic assumption, it can not be applied to predict the directions of the fluctuations. In contrast, ANM adds the ability to do the latter, but it loses a significant amount of precision in the prediction of the magnitudes. In this article, we develop a generalized spring tensor model (STeM) that is able to predict well both the magnitudes and the directions of the fluctuations. STeM also outperforms ANM in explaining protein conformation changes. All of these are accomplished without sacrificing the essential features that have made ANM and GNM attractive.

This article investigates an ensemble-based technique called Bayesian Model Averaging (BMA) to improve the performance of protein amino acid pKa predictions. Structure-based pKa calculations play an important role in the mechanistic interpretation of protein structure and are also used to determine a wide range of protein properties. A diverse set of methods currently exist for pKa prediction, ranging from empirical statistical models to ab initio quantum mechanical approaches. However, each of these methods are based on a set of conceptual assumptions that can effect a model's accuracy and generalizability for pKa prediction in complicated biomolecular systems. We use BMA to combine eleven diverse prediction methods that each estimate pKa values of amino acids in staphylococcal nuclease. These methods are based on work conducted for the pKa Cooperative and the pKa measurements are based on experimental work conducted by the García-Moreno lab. Our cross-validation study demonstrates that the aggregated estimate obtained from BMA outperforms all individual prediction methods with improvements ranging from 45 to 73% over other method classes. This study also compares BMA's predictive performance to other ensemble-based techniques and demonstrates that BMA can outperform these approaches with improvements ranging from 27 to 60%. This work illustrates a new possible mechanism for improving the accuracy of pKa prediction and lays the foundation for future work on aggregate models that balance computational cost with prediction accuracy.

Uptake of proteins and ampholytic solutes into polyelectrolyte brushes underlies some biological processes and also applications in sensing or biomedicine. Especially uptake on the “wrong” side of the isoelectric point (pI) remains puzzling, with charge regulation and solute patchiness proposed as possible mechanisms. Using a hierarchy of approximations – coarse-grained molecular simulations, self-consistent mean-field and a simple phenomenological model – we investigated the uptake of model ampholytic solutes into polyanionic brushes across varying pH, salt concentrations, pKa values and peptide sequences. In a narrow pH range on the wrong side of pI, charge regulation enables uptake of the ampholytes by inducing charge inversion, so that they become positively charge in the brush despite being negatively charged in the bulk. This charge inversion can be calculated from the pH difference between the brush and the bulk, related to the Donnan potential. It is strongest for ampholytes with small differences between acidic and basic pKa values and decreases with increasing salt. Our phenomenological model reproduces universal effect of charge regulation promoting ampholyte uptake into brushes, but fails to be quantitative. Mean field model is close to explicit simulations for alternating sequences but fails to describe the effect of charge patchiness, which is only captured by explicit simulations. Thus, our phenomenological framework offers a practical rule of thumb for estimating uptake from experimentally accessible parameters without sophisticated calculations. Deviations from this rule of thumb for complex ampholytes, such as proteins or peptides with patterned charge sequences, are only captured by explicit simulations.

The integral equation coarse-graining (IECG) approach is a promising high-level coarse-graining (CG) method for polymer melts, with variable resolution from soft spheres to multi CG sites, which preserves the structural and thermodynamical consistencies with the related atomistic simulations. When compared to the atomistic description, the procedure of coarse-graining results in smoother free energy surfaces, longer-ranged potentials, a decrease in the number of interaction sites for a given polymer, and more. Because these changes have competing effects on the computational efficiency of the CG model, care needs to be taken when studying the effect of coarse-graining on the computational speed-up in CG molecular dynamics simulations. For instance, treatment of long-range CG interactions requires the selection of cutoff distances that include the attractive part of the effective CG potential and force. In particular, we show how the complex nature of the range and curvature of the effective CG potential, the selection of a suitable CG timestep, the choice of the cutoff distance, the molecular dynamics algorithms, and the smoothness of the CG free energy surface affect the efficiency of IECG simulations. By direct comparison with the atomistic simulations of relatively short chain polymer melts, we find that the overall computational efficiency is highest for the highest level of CG (soft spheres), with an overall improvement of the computational efficiency being about 106-108 for various CG levels/resolutions. Therefore, the IECG method can have important applications in molecular dynamics simulations of polymeric systems. Finally, making use of the standard spatial decomposition algorithm, the parallel scalability of the IECG simulations for various levels of CG is presented. Optimal parallel scaling is observed for a reasonably large number of processors. Although this study is performed using the IECG approach, its results on the relation between the level of CG and the computational efficiency are general and apply to any properly-constructed CG model.

Performing protein fold recognition by exploiting a stack convolutional neural network with the attention mechanism

Protein conformational changes are activated processes essential for protein functions. Activation in a protein differs from activation in a small molecule in that it involves directed and systematic energy flows through preferred channels encoded in the protein structure. Understanding the nature of these energy flow channels and how energy flows through them during activation is critical for understanding protein conformational changes. We recently [W. Li and A. Ma, J. Chem. Phys. 144, 114103 (2016)] developed a rigorous statistical mechanical framework for understanding potential energy flows. Here, we complete this theoretical framework with a rigorous theory for kinetic energy flows: potential and kinetic energies interconvert when impressed forces oppose inertial forces, whereas kinetic energy transfers directly from one coordinate to another when inertial forces oppose each other. This theory is applied to analyzing a prototypic system for biomolecular conformational dynamics: the isomerization of an alanine dipeptide. Among the two essential energy flow channels for this process, dihedral ϕ confronts the activation barrier, whereas dihedral θ1 receives energy from potential energy flows. Intriguingly, θ1 helps ϕ to cross the activation barrier by transferring to ϕ via direct kinetic energy flow all the energy it received-an increase in θ̇1 caused by potential energy flow converts into an increase in ϕ̇. As a compensation, θ1 receives kinetic energy from bond angle α via a direct mechanism and bond angle β via an indirect mechanism.

Phenolic compounds can undergo auto-oxidation, especially at alkaline pH, forming reactive o -quinones that bind covalently to proteins and may affect the protein structure, solubility, and functional properties. Yet, it is still unclear how the phenolic compounds' structure and properties affect their reaction with proteins, and how they influence the resulting changes in protein structure and functionality. Therefore, the model protein β-lactoglobulin (BLG) was incubated with ten common phenolic compounds at pH 8.5 for 24 h at a phenolic-to-protein molar ratio of 5:1. RP-HPLC was used to screen for covalent modifications. Protein structural changes were investigated using MALDI-TOF-MS, OPA and Ellman's assays, ATR-FTIR, tryptophan fluorescence quenching, SDS-PAGE, and SEC. Protein functionality changes were determined by oil droplet size measurement after emulsion formation via high pressure homogenization. Only phenolic compounds with a di or-trihydroxybenzene moiety resulted in noteworthy BLG modification (>40 %), with an average of one phenolic compound bound per protein molecule, primarily on the thiol groups of the cysteine residues. Modification decreased the protein's α-helices and shifted the intramolecular β-sheets to higher wavelengths. Protein modification resulted in the formation of smaller oil droplets (from 1.38 to 2 μm) at low homogenization pressure. A positive relationship was found between the presence of a carboxyl group in the phenolic compounds, the unfolding of the protein's tertiary structure (R 2 = 0.95), and smaller oil droplet size. The insights from this study support the selection of phenolic compounds for targeted protein modifications or for avoiding undesired protein modifications. • Only phenolics with a catechol or pyrogallol moiety modify proteins at alkaline pH • At pH 8.5, phenolic compounds primarily bind at the free thiol groups of cysteines • Modification results in a decrease and shift in intramolecular β-sheets • Phenolic compounds with a carboxyl group induced protein tertiary structure changes • Protein tertiary structure changes lead to a decrease in emulsion droplet size

Coarse-grained (CG) modeling has emerged as an essential tool in computational biology, offering a simplified yet effective representation of proteins and their interactions. By reducing atomic detail, CG models enhance computational efficiency while preserving critical physical and chemical properties, enabling the study of large-scale biological phenomena. These models facilitate the exploration of complex processes-such as protein folding, conformational dynamics, molecular interactions, and supramolecular assemblies-that are often inaccessible to all-atom simulations. This chapter provides an overview of CG protein modeling, tracing its historical development from early simplified representations to advanced coarse-graining techniques. We discuss fundamental principles, including bottom-up and top-down parameterization strategies, statistical potentials, and structure-based approaches like elastic network models and Gō-like models. Key applications are explored, including insights into protein folding mechanisms, protein-protein interactions, phase separation, and protein-lipid interactions in complex cellular environments. Recent advances in CG-based drug discovery are also highlighted. The chapter concludes with a discussion on future directions for CG modeling, emphasizing hybrid approaches, artificial intelligence-driven parameterization, and enhanced force fields to improve accuracy and broaden applicability in computational biology.

Coarse-grained (CG) models of biomolecules have been widely used in protein/ribonucleic acid (RNA) three-dimensional structure prediction, docking, drug design, and molecular simulations due to their superiority in computational efficiency. Most of these applications strongly depend on the reasonable estimation of solvation free energy, which requires the accurate calculation of solvent accessible surface area (SASA). Although algorithms for SASA calculations with all-atom protein and RNA structures have been well-established, accurately estimating the SASA based on CG structures is extremely challenging. In this work, we developed a deep learning-based SASA estimator (DeepCGSA), which can provide almost perfect SASA estimation based on CG structures of protein and RNA molecules. Extensive testing analysis showed that for three types of widely used CG protein models, including the Cα-based, Cα-Cβ, and Martini models, the correlation coefficients between the predicted values and the reference values can be as high as 0.95-0.99, which perform dramatically better than available methods. In addition, the new method can be used for CG RNA structures and unfolded protein structures with much improved accuracy. We anticipate that DeepCGSA will be highly useful in the protein/RNA structure prediction, drug design, and other applications, in which accurate estimations of SASA for CG biomolecular structures are critically important.

Crowded, Cell-like Environment Induces Shape Changes In Aspherical Protein