Protein-Folding Dynamics: Overview of Molecular Simulation Techniques

Quantum synergy in peptide folding: A comparative study of CVaR-variational quantum eigensolver and molecular dynamics simulation

One of the technological fields that is developing the fastest is quantum computing in biology. One of the main problems is protein folding, which calls for precise, effective algorithms with fast computing times. Mapping the least energy conformation state of proteins with disordered areas requires enormous computing resources. The current study uses quantum algorithms, such as the Variational Quantum Eigensolver (VQE), to estimate the lowest energy value of 50 peptides, each consisting of seven amino acids. To determine the ground state energy value, Variational Quantum Optimisation (VQE) is first utilised to generate the energy values along with Conditional Value at Risk (CVaR) as an aggregation function is applied over 100 iterations of 500,000 shots each. This is contrasted with 50 millisecond molecular dynamics-based simulations to determine the energy levels and folding pattern. In comparison to MD-based simulations, the results point to CvaR-VQE producing more effective folding outcomes with respect to sampling and global optimization. Protein folding can be solved to get deep insights into biological processes and drug formulation with improving quantum technology and algorithms.

Advanced computational approaches to understand protein aggregation

Protein aggregation is a widespread phenomenon implicated in debilitating diseases like Alzheimer's, Parkinson's, and cataracts, presenting complex hurdles for the field of molecular biology. In this review, we explore the evolving realm of computational methods and bioinformatics tools that have revolutionized our comprehension of protein aggregation. Beginning with a discussion of the multifaceted challenges associated with understanding this process and emphasizing the critical need for precise predictive tools, we highlight how computational techniques have become indispensable for understanding protein aggregation. We focus on molecular simulations, notably molecular dynamics (MD) simulations, spanning from atomistic to coarse-grained levels, which have emerged as pivotal tools in unraveling the complex dynamics governing protein aggregation in diseases such as cataracts, Alzheimer's, and Parkinson's. MD simulations provide microscopic insights into protein interactions and the subtleties of aggregation pathways, with advanced techniques like replica exchange molecular dynamics, Metadynamics (MetaD), and umbrella sampling enhancing our understanding by probing intricate energy landscapes and transition states. We delve into specific applications of MD simulations, elucidating the chaperone mechanism underlying cataract formation using Markov state modeling and the intricate pathways and interactions driving the toxic aggregate formation in Alzheimer's and Parkinson's disease. Transitioning we highlight how computational techniques, including bioinformatics, sequence analysis, structural data, machine learning algorithms, and artificial intelligence have become indispensable for predicting protein aggregation propensity and locating aggregation-prone regions within protein sequences. Throughout our exploration, we underscore the symbiotic relationship between computational approaches and empirical data, which has paved the way for potential therapeutic strategies against protein aggregation-related diseases. In conclusion, this review offers a comprehensive overview of advanced computational methodologies and bioinformatics tools that have catalyzed breakthroughs in unraveling the molecular basis of protein aggregation, with significant implications for clinical interventions, standing at the intersection of computational biology and experimental research.

Generative Retrieval-Augmented Ontologic Graph and Multiagent Strategies for Interpretive Large Language Model-Based Materials Design

Transformer neural networks show promising capabilities, in particular for uses in materials analysis, design, and manufacturing, including their capacity to work effectively with human language, symbols, code, and numerical data. Here, we explore the use of large language models (LLMs) as a tool that can support engineering analysis of materials, applied to retrieving key information about subject areas, developing research hypotheses, discovery of mechanistic relationships across disparate areas of knowledge, and writing and executing simulation codes for active knowledge generation based on physical ground truths. Moreover, when used as sets of AI agents with specific features, capabilities, and instructions, LLMs can provide powerful problem-solution strategies for applications in analysis and design problems. Our experiments focus on using a fine-tuned model, MechGPT, developed based on training data in the mechanics of materials domain. We first affirm how fine-tuning endows LLMs with a reasonable understanding of subject area knowledge. However, when queried outside the context of learned matter, LLMs can have difficulty recalling correct information and may hallucinate. We show how this can be addressed using retrieval-augmented Ontological Knowledge Graph strategies. The graph-based strategy helps us not only to discern how the model understands what concepts are important but also how they are related, which significantly improves generative performance and also naturally allows for injection of new and augmented data sources into generative AI algorithms. We find that the additional feature of relatedness provides advantages over regular retrieval augmentation approaches and not only improves LLM performance but also provides mechanistic insights for exploration of a material design process. Illustrated for a use case of relating distinct areas of knowledge, here, music and proteins, such strategies can also provide an interpretable graph structure with rich information at the node, edge, and subgraph level that provides specific insights into mechanisms and relationships. We discuss other approaches to improve generative qualities, including nonlinear sampling strategies and agent-based modeling that offer enhancements over single-shot generations, whereby LLMs are used to both generate content and assess content against an objective target. Examples provided include complex question answering, code generation, and execution in the context of automated force-field development from actively learned density functional theory (DFT) modeling and data analysis.

Hierarchical Framework for Predicting Entropies in Bottom-Up Coarse-Grained Models

The thermodynamic entropy of coarse-grained (CG) models stands as one of the most important properties for quantifying the missing information during the CG process and for establishing transferable (or extendible) CG interactions. However, performing additional CG simulations on top of model construction often leads to significant additional computational overhead. In this work, we propose a simple hierarchical framework for predicting the thermodynamic entropies of various molecular CG systems. Our approach employs a decomposition of the CG interactions, enabling the estimation of the CG partition function and thermodynamic properties a priori. Starting from the ideal gas description, we leverage classical perturbation theory to systematically incorporate simple yet essential interactions, ranging from the hard sphere model to the generalized van der Waals model. Additionally, we propose an alternative approach based on multiparticle correlation functions, allowing for systematic improvements through higher-order correlations. Numerical applications to molecular liquids validate the high fidelity of our approach, and our computational protocols demonstrate that a reduced model with simple energetics can reasonably estimate the thermodynamic entropy of CG models without performing any CG simulations. Overall, our findings present a systematic framework for estimating not only the entropy but also other thermodynamic properties of CG models, relying solely on information from the reference system.

Accuracy Assessment of Atomistic Neural Network Potentials: The Impact of Cutoff Radius and Message Passing

Atomistic neural network potentials have achieved great success in accelerating atomistic simulations in complicated systems in recent years. They are typically based on the atomic decomposition of total properties, truncating the interatomic correlations to a local environment within a given cutoff radius. A more recently developed message passing (MP) neural network framework can, in principle, incorporate nonlocal effects through iteratively correlating some atoms outside the cutoff sphere with atoms inside, a process referred to as MP. However, how the model accuracy depends on the cutoff radius and the MP process has rarely been discussed. In this work, we investigate this dependence using a recursively embedded atom neural network method that possesses both local and MP features, in two representative systems: liquid H2O and solid Al2O3. We focus on how these settings influence predictions for structural and vibrational properties, namely, radial distribution functions (RDFs) and vibrational density of states (VDOSs). We find that while MP lowers test errors of energy and forces in general, it may not improve the prediction for RDFs and/or VDOSs if direct interatomic correlations in the local environment are insufficiently described. A cutoff radius exceeding the first neighbor shell is necessary, beyond which involving MP quickly enhances the model accuracy until convergence. This is a potentially more efficient way to increase the model accuracy than directly increasing the cutoff radius, especially with more memory savings in the GPU implementation. Our findings also suggest that using the mean test error as the measure of the model accuracy alone is inadequate.

Activating mutations drive human MEK1 kinase using a gear-shifting mechanism

There is an unmet need to classify cancer-promoting kinase mutations in a mechanistically cognizant way. The challenge is to understand how mutations stabilize different kinase configurations to alter function, and how this influences pathogenic potential of the kinase and its responses to therapeutic inhibitors. This goal is made more challenging by the complexity of the mutational landscape of diseases, and is further compounded by the conformational plasticity of each variant where multiple conformations coexist. We focus here on the human MEK1 kinase, a vital component of the RAS/MAPK pathway in which mutations cause cancers and developmental disorders called RASopathies. We sought to explore how these mutations alter the human MEK1 kinase at atomic resolution by utilizing enhanced sampling simulations and free energy calculations. We computationally mapped the different conformational stabilities of individual mutated systems by delineating the free energy landscapes, and showed how this relates directly to experimentally quantified developmental transformation potentials of the mutations. We conclude that mutations leverage variations in the hydrogen bonding network associated with the conformational plasticity to progressively stabilize the active-like conformational state of the kinase while destabilizing the inactive-like state. The mutations alter residue-level internal molecular correlations by differentially prioritizing different conformational states, delineating the various modes of MEK1 activation reminiscent of a gear-shifting mechanism. We define the molecular basis of conversion of this kinase from its inactive to its active state, connecting structure, dynamics, and function by delineating the energy landscape and conformational plasticity, thus augmenting our understanding of MEK1 regulation.

Gaussian representation of coarse-grained interactions of liquids: Theory, parametrization, and transferability

Coarse-grained (CG) interactions determined via bottom-up methodologies can faithfully reproduce the structural correlations observed in fine-grained (atomistic resolution) systems, yet they can suffer from limited extensibility due to complex many-body correlations. As part of an ongoing effort to understand and improve the applicability of bottom-up CG models, we propose an alternative approach to address both accuracy and transferability. Our main idea draws from classical perturbation theory to partition the hard sphere repulsive term from effective CG interactions. We then introduce Gaussian basis functions corresponding to the system's characteristic length by linking these Gaussian sub-interactions to the local particle densities at each coordination shell. The remaining perturbative long-range interaction can be treated as a collective solvation interaction, which we show exhibits a Gaussian form derived from integral equation theories. By applying this numerical parametrization protocol to CG liquid systems, our microscopic theory elucidates the emergence of Gaussian interactions in common phenomenological CG models. To facilitate transferability for these reduced descriptions, we further infer equations of state to determine the sub-interaction parameter as a function of the system variables. The reduced models exhibit excellent transferability across the thermodynamic state points. Furthermore, we propose a new strategy to design the cross-interactions between distinct CG sites in liquid mixtures. This involves combining each Gaussian in the proper radial domain, yielding accurate CG potentials of mean force and structural correlations for multi-component systems. Overall, our findings establish a solid foundation for constructing transferable bottom-up CG models of liquids with enhanced extensibility.

Structural impairment of p53 C-terminal due to the effect of phosphorylation and acetylation: a study on the interdependence of PTM

The C-terminal of tumor suppressor protein p53 is intrinsically disordered while unbound. This particular segment often shows structural plasticity when bound to other binding partners. The disordered component undergoes a disordered to ordered transition upon recognition. Post-translational modifications (PTMs), namely phosphorylation and acetylation, significantly alter the structural motifs of the segment. Among the various types of PTMs, phosphorylation, and acetylation of p53 at both N- and C- terminals lead to stabilization and activation. It has been noted experimentally that phosphorylation often regulates (enhances or reduces) the acetylation at specific sites. The phosphorylation of Thr377 and Ser378 reduces the acetylation of Lys373 and Lys382. Mutations of Thr377 and Ser378 to neutral Ala enhance and phospho mimic Asp reduce the acetylation of Lys373 and Lys382. Simulations of several single-point and pair-wise mutated systems have been generated to compare how the presence or absence of phosphorylation favors or disfavors the acetylation by thermodynamic and conformational analysis. We are using implicit solvent replica exchange molecular dynamics simulations to get 200 ns well-converged conformational ensembles of each system. Different sets of systems having both single and double PTMs are simulated. The results admit the appreciable change in the secondary structural level upon specific PTM. Also, the residual structure of the unbound p53 with single-point PTM varies significantly with pair-wise modifications. These observations further shed light on the relationship between the interdependencies of the specific PTM sites and the secondary structural levels.Communicated by Ramaswamy H. Sarma.

Protein and Peptide-Based Nanotechnology for Enhancing Stability, Bioactivity, and Delivery of Anthocyanins

Anthocyanin, a unique natural polyphenol, is abundant in plants and widely utilized in biomedicine, cosmetics, and the food industry due to its excellent antioxidant, anticancer, antiaging, antimicrobial, and anti-inflammatory properties. However, the degradation of anthocyanin in an extreme environment, such as alkali pH, high temperatures, and metal ions, limits its physiochemical stabilities and bioavailabilities. Encapsulation and combining anthocyanin with biomaterials could efficiently stabilize anthocyanin for protection. Promisingly, natural or artificially designed proteins and peptides with favorable stabilities, excellent biocapacity, and wide sources are potential candidates to stabilize anthocyanin. This review focuses on recent progress, strategies, and perspectives on protein and peptide for anthocyanin functionalization and delivery, i.e., formulation technologies, physicochemical stability enhancement, cellular uptake, bioavailabilities, and biological activities development. Interestingly, due to the simplicity and diversity of peptide structure, the interaction mechanisms between peptide and anthocyanin could be illustrated. This work sheds light on the mechanism of protein/peptide-anthocyanin nanoparticle construction and expands on potential applications of anthocyanin in nutrition and biomedicine.

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.

Topological Analysis of Molecular Dynamics Simulations using the Euler Characteristic

Molecular dynamics (MD) simulations are used in diverse scientific and engineering fields such as drug discovery, materials design, separations, biological systems, and reaction engineering. These simulations generate highly complex data sets that capture the 3D spatial positions, dynamics, and interactions of thousands of molecules. Analyzing MD data sets is key for understanding and predicting emergent phenomena and in identifying key drivers and tuning design knobs of such phenomena. In this work, we show that the Euler characteristic (EC) provides an effective topological descriptor that facilitates MD analysis. The EC is a versatile, low-dimensional, and easy-to-interpret descriptor that can be used to reduce, analyze, and quantify complex data objects that are represented as graphs/networks, manifolds/functions, and point clouds. Specifically, we show that the EC is an informative descriptor that can be used for machine learning and data analysis tasks such as classification, visualization, and regression. We demonstrate the benefits of the proposed approach through case studies that aim to understand and predict the hydrophobicity of self-assembled monolayers and the reactivity of complex solvent environments.

Statistical Mechanical Design Principles for Coarse-Grained Interactions across Different Conformational Free Energy Surfaces

Systematic bottom-up coarse-graining (CG) of molecular systems provides a means to explore different coupled length and time scales while treating the molecular-scale physics at a reduced level. However, the configuration dependence of CG interactions often results in CG models with limited applicability for exploring the parametrized configurations. We propose a statistical mechanical theory to design CG interactions across different configurations and conditions. In order to span wide ranges of conformational space, distinct classical CG free energy surfaces for characteristic configurations are identified using molecular collective variables. The coupling interaction between different CG free energy surfaces can then be systematically determined by analogy to quantum mechanical approaches describing coupled states. The present theory can accurately capture the underlying many-body potentials of mean force in the CG variables for various order parameters applied to liquids, interfaces, and in principle proteins, uncovering the complex nature underlying the coupling interaction and imparting a new protocol for the design of predictive multiscale models.

Optimization of parallel implementation of UNRES package for coarse-grained simulations to treat large proteins

We report major algorithmic improvements of the UNRES package for physics-based coarse-grained simulations of proteins. These include (i) introduction of interaction lists to optimize computations, (ii) transforming the inertia matrix to a pentadiagonal form to reduce computing and memory requirements, (iii) removing explicit angles and dihedral angles from energy expressions and recoding the most time-consuming energy/force terms to minimize the number of operations and to improve numerical stability, (iv) using OpenMP to parallelize those sections of the code for which distributed-memory parallelization involves unfavorable computing/communication time ratio, and (v) careful memory management to minimize simultaneous access of distant memory sections. The new code enables us to run molecular dynamics simulations of protein systems with size exceeding 100,000 amino-acid residues, reaching over 1 ns/day (1 μs/day in all-atom timescale) with 24 cores for proteins of this size. Parallel performance of the code and comparison of its performance with that of AMBER, GROMACS and MARTINI 3 is presented.

Understanding dynamics in coarse-grained models. II. Coarse-grained diffusion modeled using hard sphere theory

The first paper of this series [J. Chem. Phys. 158, 034103 (2023)] demonstrated that excess entropy scaling holds for both fine-grained and corresponding coarse-grained (CG) systems. Despite its universality, a more exact determination of the scaling relationship was not possible due to the semi-empirical nature. In this second paper, an analytical excess entropy scaling relation is derived for bottom-up CG systems. At the single-site CG resolution, effective hard sphere systems are constructed that yield near-identical dynamical properties as the target CG systems by taking advantage of how hard sphere dynamics and excess entropy can be analytically expressed in terms of the liquid packing fraction. Inspired by classical equilibrium perturbation theories and recent advances in constructing hard sphere models for predicting activated dynamics of supercooled liquids, we propose a new approach for understanding the diffusion of molecular liquids in the normal regime using hard sphere reference fluids. The proposed "fluctuation matching" is designed to have the same amplitude of long wavelength density fluctuations (dimensionless compressibility) as the CG system. Utilizing the Enskog theory to derive an expression for hard sphere diffusion coefficients, a bridge between the CG dynamics and excess entropy is then established. The CG diffusion coefficient can be roughly estimated using various equations of the state, and an accurate prediction of accelerated CG dynamics at different temperatures is also possible in advance of running any CG simulation. By introducing another layer of coarsening, these findings provide a more rigorous method to assess excess entropy scaling and understand the accelerated CG dynamics of molecular fluids.

Understanding dynamics in coarse-grained models. I. Universal excess entropy scaling relationship

Coarse-grained (CG) models facilitate an efficient exploration of complex systems by reducing the unnecessary degrees of freedom of the fine-grained (FG) system while recapitulating major structural correlations. Unlike structural properties, assessing dynamic properties in CG modeling is often unfeasible due to the accelerated dynamics of the CG models, which allows for more efficient structural sampling. Therefore, the ultimate goal of the present series of articles is to establish a better correspondence between the FG and CG dynamics. To assess and compare dynamical properties in the FG and the corresponding CG models, we utilize the excess entropy scaling relationship. For Paper I of this series, we provide evidence that the FG and the corresponding CG counterpart follow the same universal scaling relationship. By carefully reviewing and examining the literature, we develop a new theory to calculate excess entropies for the FG and CG systems while accounting for entropy representability. We demonstrate that the excess entropy scaling idea can be readily applied to liquid water and methanol systems at both the FG and CG resolutions. For both liquids, we reveal that the scaling exponents remain unchanged from the coarse-graining process, indicating that the scaling behavior is universal for the same underlying molecular systems. Combining this finding with the concept of mapping entropy in CG models, we show that the missing entropy plays an important role in accelerating the CG dynamics.

3D Conformational Generative Models for Biological Structures Using Graph Information-Embedded Relative Coordinates

Developing molecular generative models for directly generating 3D conformation has recently become a hot research area. Here, an autoencoder based generative model was proposed for molecular conformation generation. A unique feature of our method is that the graph information embedded relative coordinate (GIE-RC), satisfying translation and rotation invariance, was proposed as a novel way for encoding molecular three-dimensional structure. Compared with commonly used Cartesian coordinate and internal coordinate, GIE-RC is less sensitive on errors when decoding latent variables to 3D coordinates. By using this method, a complex 3D generation task can be turned into a graph node feature generation problem. Examples were shown that the GIE-RC based autoencoder model can be used for both ligand and peptide conformation generation. Additionally, this model was used as an efficient conformation sampling method to augment conformation data needed in the construction of neural network-based force field.

Snapshots of urea-induced early structural changes and unfolding of an ankyrin repeat protein at atomic resolution

Protein folding and unfolding is a complex process, underscored by the many proteotoxic diseases associated with misfolded proteins. Mapping pathways from a native structure to an unfolded protein or vice versa, identifying the intermediates, and defining the role of sequence and structure en route remain outstanding problems in the field. It is even more challenging to capture the events at atomistic resolution. X-ray diffraction has so far been used to understand how urea interacts with and unfolds two stable globular proteins. Here, we present the case study on PSMD10Gankyrin , a prototype for a moderately stable, non-globular repeat protein, long and rigid, with its termini located at either end.   We define structural changes in the time dimension using low urea concentrations to arrive at the following conclusions. (a) Unfolding is rapidly initiated at the C-terminus, slowly at the N-terminus, and proceeds inwards from both ends. (b) C-terminus undergoes an α to 310 helix transition, representing the structure of a potential early unfolding intermediate before disorder sets in. (c) Distinct and progressive changes in the electrostatic landscape of PSMD10Gankyrin were observed, indicative of conformational changes in the seemingly inflexible motif involved in protein-protein interaction. We believe this unique study will open up the field for better and bolder queries and increase the choice of model proteins for a better understanding of the challenging problems of protein folding, protein interactions, protein degradation, and diseases associated with misfolding.

Insight into the Initial Stages of the Folding Process in Onconase Revealed by UNRES

The unfolded state of proteins presents many challenges to elucidate the structural basis for biological function. This state is characterized by a large degree of structural heterogeneity which makes it difficult to generate structural models. However, recent experiments into the initial folding events of the 104-residue ribonuclease homologue onconase (ONC) were able to identify the regions in the protein that participate in the initial folding of this protein. Therefore, to gain additional structural insight into the unfolded state of proteins, this study utilized molecular dynamics simulations using the UNited-RESidue (UNRES) force field to evaluate whether there is a good agreement between the experimentally determined initial structures and the structures identified by computer simulations along a folding pathway. Indeed, these UNRES simulations accurately identified the two regions experimentally observed to form the initial native structure along the folding pathway of ONC. In addition, these regions are determined to be chain folding initiation sites (CFIS) according to methods developed previously. Subsequent self-organization maps (SOM) analysis has revealed key structural states involved in these early folding events.

A New Transfer Free Energy Based Implicit Solvation Model for the Description of Disordered and Folded Proteins

Most biological events occur on time scales that are difficult to access using conventional all-atom molecular dynamics simulations in explicit solvent. Implicit solvent techniques offer a promising solution to this problem, alleviating the computational cost associated with the simulation of large systems and accelerating the sampling compared to explicit solvent models. The substitution of water molecules by a mean field, however, introduces simplifications that may penalize accuracy and impede the prediction of certain physical properties. We demonstrate that existing implicit solvent models developed using a transfer free energy approach, while satisfactory at reproducing the folding behavior of globular proteins, fare less well in characterizing the conformational properties of intrinsically disordered proteins. We develop a new implicit solvent model that maximizes the degree of accuracy for both disordered and folded proteins. We show, by comparing the simulation outputs to experimental data, that in combination with the a99SB-disp force field, the implicit solvent model can describe both disordered (aβ40, PaaA2, and drkN SH3) and folded ((AAQAA)₃, CLN025, Trp-cage, and GTT) peptides. Our implicit solvent model permits a computationally efficient investigation of proteins containing both ordered and disordered regions, as well as the study of the transition between ordered and disordered protein states.

High Energy Channeling and Malleable Transition States: Molecular Dynamics Simulations and Free Energy Landscapes for the Thermal Unfolding of Protein U1A and 13 Mutants

The spliceosome protein U1A is a prototype case of the RNA recognition motif (RRM) ubiquitous in biological systems. The in vitro kinetics of the chemical denaturation of U1A indicate that the unfolding of U1A is a two-state process but takes place via high energy channeling and a malleable transition state, an interesting variation of typical two-state behavior. Molecular dynamics (MD) simulations have been applied extensively to the study of two-state unfolding and folding of proteins and provide an opportunity to obtain a theoretical account of the experimental results and a molecular model for the transition state ensemble. We describe herein all-atom MD studies including explicit solvent of up to 100 ns on the thermal unfolding (UF) of U1A and 13 mutants. Multiple MD UF trajectories are carried out to ensure accuracy and reproducibility. A vector representation of the MD unfolding process in RMSD space is obtained and used to calculate a free energy landscape for U1A unfolding. A corresponding MD simulation and free energy landscape for the protein CI2, well known to follow a simple two state folding/unfolding model, is provided as a control. The results indicate that the unfolding pathway on the MD calculated free energy landscape of U1A shows a markedly extended transition state compared with that of CI2. The MD results support the interpretation of the observed chevron plots for U1A in terms of a high energy, channel-like transition state. Analysis of the MDUF structures shows that the transition state ensemble involves microstates with most of the RRM secondary structure intact but expanded by ~14% with respect to the radius of gyration. Comparison with results on a prototype system indicates that the transition state involves an ensemble of molten globule structures and extends over the region of ~1-35 ns in the trajectories. Additional MDUF simulations were carried out for 13 U1A mutants, and the calculated φ-values show close accord with observed results and serve to validate our methodology.

Molecular Simulation Study and Analytical Model for Oil–Water Two-Phase Fluid Transport in Shale Inorganic Nanopores

Shale reservoirs contain omnipresent nanopores. The fluid transport phenomena on the nanoscale are significantly different from that on the macroscale. The understandings of fluid transport behavior, especially multiphase flow, are still ambiguous on the nanoscale and the traditional hydrodynamic models are insufficient to describe the fluid flow in shale. In this work, we firstly use a molecular dynamics simulation to study the oil–water two-phase flow in shale inorganic quartz nanopores and investigated the unique interfacial phenomena and their influences on fluid transport in a confined nanospace. The results of the molecular simulation revealed that the water-oil-water layered structure was formed in quartz nanopores. There is no-slip boundary condition between water and quartz surface. The density dip and the extremely low apparent viscosity of the oil–water interface region were observed. The liquid–liquid slip effect happened at the oil–water interface. Based on the nano-effects obtained by the molecular simulation, two mathematical models were proposed to describe the nanoscale oil–water two-phase flow, considering both the solid–liquid and liquid–liquid interfacial phenomena, and the performances of two mathematical models were validated. This study shed light on the flow behaviors of oil and water on the nanoscale, and provides the theoretical basis for scale-upgrading, from the nanoscale to the macroscale.

REANN: A PyTorch-based end-to-end multi-functional deep neural network package for molecular, reactive, and periodic systems

In this work, we present a general purpose deep neural network package for representing energies, forces, dipole moments, and polarizabilities of atomistic systems. This so-called recursively embedded atom neural network model takes advantages of both the physically inspired atomic descriptor based neural networks and the message-passing based neural networks. Implemented in the PyTorch framework, the training process is parallelized on both the central processing unit and the graphics processing unit with high efficiency and low memory in which all hyperparameters can be optimized automatically. We demonstrate the state-of-the-art accuracy, high efficiency, scalability, and universality of this package by learning not only energies (with or without forces) but also dipole moment vectors and polarizability tensors in various molecular, reactive, and periodic systems. An interface between a trained model and LAMMPs is provided for large scale molecular dynamics simulations. We hope that this open-source toolbox will allow for future method development and applications of machine learned potential energy surfaces and quantum-chemical properties of molecules, reactions, and materials.

MLIMC: Machine Learning-Based Implicit-Solvent Monte Carlo

Monte Carlo (MC) methods are important computational tools for molecular structure optimizations and predictions. When solvent effects are explicitly considered, MC methods become very expensive due to the large degree of freedom associated with the water molecules and mobile ions. Alternatively implicit-solvent MC can largely reduce the computational cost by applying a mean field approximation to solvent effects and meanwhile maintains the atomic detail of the target molecule. The two most popular implicit-solvent models are the Poisson-Boltzmann (PB) model and the Generalized Born (GB) model in a way such that the GB model is an approximation to the PB model but is much faster in simulation time. In this work, we develop a machine learning-based implicit-solvent Monte Carlo (MLIMC) method by combining the advantages of both implicit solvent models in accuracy and efficiency. Specifically, the MLIMC method uses a fast and accurate PB-based machine learning (PBML) scheme to compute the electrostatic solvation free energy at each step. We validate our MLIMC method by using a benzene-water system and a protein-water system. We show that the proposed MLIMC method has great advantages in speed and accuracy for molecular structure optimization and prediction.

Boosting the conformational sampling by combining replica exchange with solute tempering and well-sliced metadynamics

Methods that combine collective variable (CV) based enhanced sampling and global tempering approaches are used in speeding-up the conformational sampling and free energy calculation of large and soft systems with a plethora of energy minima. In this paper, a new method of this kind is proposed in which the well-sliced metadynamics approach (WSMTD) is united with replica exchange with solute tempering (REST2) method. WSMTD employs a divide-and-conquer strategy wherein high-dimensional slices of a free energy surface are independently sampled and combined. The method enables one to accomplish a controlled exploration of the CV-space with a restraining bias as in umbrella sampling, and enhance-sampling of one or more orthogonal CVs using a metadynamics like bias. The new hybrid method proposed here enables boosting the sampling of more slow degrees of freedom in WSMTD simulations, without the need to specify associated CVs, through a replica exchange scheme within the framework of REST2. The high-dimensional slices of the probability distributions of CVs computed from the united WSMTD and REST2 simulations are subsequently combined using the weighted histogram analysis method to obtain the free energy surface. We show that the new method proposed here is accurate, improves the conformational sampling, and achieves quick convergence in free energy estimates. We demonstrate this by computing the conformational free energy landscapes of solvated alanine tripeptide and Trp-cage mini protein in explicit water.

CORE-MD II: A fast, adaptive, and accurate enhanced sampling method

In this paper, we present a fast and adaptive correlation guided enhanced sampling method (CORE-MD II). The CORE-MD II technique relies, in part, on partitioning of the entire pathway into short trajectories that we refer to as instances. The sampling within each instance is accelerated by adaptive path-dependent metadynamics simulations. The second part of this approach involves kinetic Monte Carlo (kMC) sampling between the different states that have been accessed during each instance. Through the combination of the partition of the total simulation into short non-equilibrium simulations and the kMC sampling, the CORE-MD II method is capable of sampling protein folding without any a priori definitions of reaction pathways and additional parameters. In the validation simulations, we applied the CORE-MD II on the dialanine peptide and the folding of two peptides: TrpCage and TrpZip2. In a comparison with long time equilibrium Molecular Dynamics (MD), 1 µs replica exchange MD (REMD), and CORE-MD I simulations, we find that the level of convergence of the CORE-MD II method is improved by a factor of 8.8, while the CORE-MD II method reaches acceleration factors of ∼120. In the CORE-MD II simulation of TrpZip2, we observe the formation of the native state in contrast to the REMD and the CORE-MD I simulations. The method is broadly applicable for MD simulations and is not restricted to simulations of protein folding or even biomolecules but also applicable to simulations of protein aggregation, protein signaling, or even materials science simulations.

Theory and Practice of Coarse-Grained Molecular Dynamics of Biologically Important Systems

Molecular dynamics with coarse-grained models is nowadays extensively used to simulate biomolecular systems at large time and size scales, compared to those accessible to all-atom molecular dynamics. In this review article, we describe the physical basis of coarse-grained molecular dynamics, the coarse-grained force fields, the equations of motion and the respective numerical integration algorithms, and selected practical applications of coarse-grained molecular dynamics. We demonstrate that the motion of coarse-grained sites is governed by the potential of mean force and the friction and stochastic forces, resulting from integrating out the secondary degrees of freedom. Consequently, Langevin dynamics is a natural means of describing the motion of a system at the coarse-grained level and the potential of mean force is the physical basis of the coarse-grained force fields. Moreover, the choice of coarse-grained variables and the fact that coarse-grained sites often do not have spherical symmetry implies a non-diagonal inertia tensor. We describe selected coarse-grained models used in molecular dynamics simulations, including the most popular MARTINI model developed by Marrink's group and the UNICORN model of biological macromolecules developed in our laboratory. We conclude by discussing examples of the application of coarse-grained molecular dynamics to study biologically important processes.

Combined Use of Structure Analysis, Studies of Molecular Association in Solution, and Molecular Modelling to Understand the Different Propensities of Dihydroxybenzoic Acids to Form Solid Phases

The arrangement of hydroxyl groups in the benzene ring has a significant effect on the propensity of dihydroxybenzoic acids (diOHBAs) to form different solid phases when crystallized from solution. All six diOHBAs were categorized into distinctive groups according to the solid phases obtained when crystallized from selected solvents. A combined study using crystal structure and molecule electrostatic potential surface analysis, as well as an exploration of molecular association in solution using spectroscopic methods and molecular dynamics simulations were used to determine the possible mechanism of how the location of the phenolic hydroxyl groups affect the diversity of solid phases formed by the diOHBAs. The crystal structure analysis showed that classical carboxylic acid homodimers and ring-like hydrogen bond motifs consisting of six diOHBA molecules are prominently present in almost all analyzed crystal structures. Both experimental spectroscopic investigations and molecular dynamics simulations indicated that the extent of intramolecular bonding between carboxyl and hydroxyl groups in solution has the most significant impact on the solid phases formed by the diOHBAs. Additionally, the extent of hydrogen bonding with solvent molecules and the mean lifetime of solute-solvent associates formed by diOHBAs and 2-propanol were also investigated.

An efficient alpha helix model and simulation framework for stationary electrostatic interaction force estimation

The alpha-helix coiled-coils within talin's rod domain have mechanical and signalling functions through their unfolding and refolding dynamics. A better understanding of talin unfolding events and the forces that are involved should allow better prediction of talin signalling. To overcome the current limitations of force measuring in molecular dynamics simulations, a new simulation framework was developed which operated directly within the force domain. Along with a corresponding alpha-helix modelling method, the simulation framework was developed drawing on robotic kinematics to specifically target force interactions. Coordinate frames were used efficiently to compartmentalise the simulation structures and static analysis was applied to determine the propagation of forces and torques through the protein structure. The results of the electrostatic approximation using Coulomb's law shows a simulated force interaction within the physiological relevant range of 5-40 pN for the rod sub-domains of talin. This covers the range of forces talin operates in and is 2-3 orders of magnitude closer to experimentally measured values than the compared all-atom and coarse-grained molecular dynamics. This targeted, force-based simulation is, therefore, able to produce more realistic forces values than previous simulation methods.

The concept of protein folding/unfolding and its impacts on human health

Proteins have evolved in specific 3D structures and play different functions in cells and determine various reactions and pathways. The newly synthesized amino acid chains once depart ribosome must crumple into three-dimensional structures so can be biologically active. This process of protein that makes a functional molecule is called protein folding. The protein folding is both a biological and a physicochemical process that depends on the sequence of it. In fact, this process occurs more complicated and in some cases and in exposure to some molecules like glucose (glycation), mistaken folding leads to amyloid structures and fatal disorders called conformational diseases. Such conditions are detected by the quality control system of the cell and these abnormal proteins undergo renovation or degradation. This scenario takes place by the chaperones, chaperonins, and Ubiquitin-proteasome complex. Understanding of protein folding mechanisms from different views including experimental and computational approaches has revealed some intermediate ensembles such as molten globule and has been subjected to biophysical and molecular biology attempts to know more about prevalent conformational diseases.

A new one-site coarse-grained model for water: Bottom-up many-body projected water (BUMPer). I. General theory and model

Water is undoubtedly one of the most important molecules for a variety of chemical and physical systems, and constructing precise yet effective coarse-grained (CG) water models has been a high priority for computer simulations. To recapitulate important local correlations in the CG water model, explicit higher-order interactions are often included. However, the advantages of coarse-graining may then be offset by the larger computational cost in the model parameterization and simulation execution. To leverage both the computational efficiency of the CG simulation and the inclusion of higher-order interactions, we propose a new statistical mechanical theory that effectively projects many-body interactions onto pairwise basis sets. The many-body projection theory presented in this work shares similar physics from liquid state theory, providing an efficient approach to account for higher-order interactions within the reduced model. We apply this theory to project the widely used Stillinger-Weber three-body interaction onto a pairwise (two-body) interaction for water. Based on the projected interaction with the correct long-range behavior, we denote the new CG water model as the Bottom-Up Many-Body Projected Water (BUMPer) model, where the resultant CG interaction corresponds to a prior model, the iteratively force-matched model. Unlike other pairwise CG models, BUMPer provides high-fidelity recapitulation of pair correlation functions and three-body distributions, as well as N-body correlation functions. BUMPer extensively improves upon the existing bottom-up CG water models by extending the accuracy and applicability of such models while maintaining a reduced computational cost.

A new one-site coarse-grained model for water: Bottom-up many-body projected water (BUMPer). II. Temperature transferability and structural properties at low temperature

A number of studies have constructed coarse-grained (CG) models of water to understand its anomalous properties. Most of these properties emerge at low temperatures, and an accurate CG model needs to be applicable to these low-temperature ranges. However, direct use of CG models parameterized from other temperatures, e.g., room temperature, encounters a problem known as transferability, as the CG potential essentially follows the form of the many-body CG free energy function. Therefore, temperature-dependent changes to CG interactions must be accounted for. The collective behavior of water at low temperature is generally a many-body process, which often motivates the use of expensive many-body terms in the CG interactions. To surmount the aforementioned problems, we apply the Bottom-Up Many-Body Projected Water (BUMPer) CG model constructed from Paper I to study the low-temperature behavior of water. We report for the first time that the embedded three-body interaction enables BUMPer, despite its pairwise form, to capture the growth of ice at the ice/water interface with corroborating many-body correlations during the crystal growth. Furthermore, we propose temperature transferable BUMPer models that are indirectly constructed from the free energy decomposition scheme. Changes in CG interactions and corresponding structures are faithfully recapitulated by this framework. We further extend BUMPer to examine its ability to predict the structure, density, and diffusion anomalies by employing an alternative analysis based on structural correlations and pairwise potential forms to predict such anomalies. The presented analysis highlights the existence of these anomalies in the low-temperature regime and overcomes potential transferability problems.

Amyloid-Like Peptide Aggregates

Self-assembly of proteins and peptides into the amyloid fold is a widespread phenomenon in the natural world. The structural hallmark of self-assembly into amyloid fibrillar assemblies is the cross-beta motif, which conveys distinct morphological and mechanical properties. The amyloid fibril formation has contrasting results depending on the organism, in the sense that it can bestow an organism with the advantages of mechanical strength and improved functionality or, on the contrary, could give rise to pathological states. In this chapter we review the existing information on amyloid-like peptide aggregates, which could either be derived from protein sequences, but also could be rationally or de novo designed in order to self-assemble into amyloid fibrils under physiological conditions. Moreover, the development of self-assembled fibrillar biomaterials that are tailored for the desired properties towards applications in biomedical or environmental areas is extensively analyzed. We also review computational studies predicting the amyloid propensity of the natural amino acid sequences and the structure of amyloids, as well as designing novel functional amyloid materials.

Application of a Distance-Dependent Sigmoidal Dielectric Constant to the REMC/SAAP3D Simulations of Chignolin, Trp-Cage, and the G10q Mutant

The replica-exchange Monte Carlo method based on the single amino acid potential (SAAP) force field, i.e., REMC/SAAP3D, was recently developed by our group for the molecular simulation of short peptides. In this study, the method has been improved by applying a distance-dependent dielectric (DDD) constant and extended to the peptides containing D-amino acid (AA) residues. For chignolin (10 AAs), a sigmoidal DDD model reasonably allocated the native-like β-hairpin structure with all-atom root mean square deviation (RMSD) = 2.0 Å as a global energy minimum. The optimal DDD condition was subsequently applied for Trp-cage (20 AAs) and its G10q mutant. The native-like α-rich folded structures with main-chain RMSD = 3.7 and 3.8 Å were obtained as global energy minima for Trp-cage and G10q, respectively. The results suggested that the REMC/SAAP3D method with the sigmoidal DDD model is useful for structural prediction for the short peptides comprised of up to 20 AAs. In addition, the relative contributions of SAAP to the total energy (%SAAP) were evaluated by energetic component analysis. The ratios of %SAAP were about 40 and 20% for chignolin and Trp-cage (or G10q), respectively. It was proposed that SAAP is more important for the secondary structure formation than for the assembly to a higher-order folded structure, in which the attractive van der Waals interaction may play a more important role.

Capacities and efficient computation of first-passage probabilities

A reversible diffusion process is initialized at position x_{0} and run until it first hits any of several targets. What is the probability that it terminates at a particular target? We propose a computationally efficient approach for estimating this probability, focused on those situations in which it takes a long time to hit any target. In these cases, direct simulation of the hitting probabilities becomes prohibitively expensive. On the other hand, if the timescales are sufficiently long, then the system will essentially "forget" its initial condition before it encounters a target. In these cases the hitting probabilities can be accurately approximated using only local simulations around each target, obviating the need for direct simulations. In empirical tests, we find that these local estimates can be computed in the same time it would take to compute a single direct simulation, but that they achieve an accuracy that would require thousands of direct simulation runs.

Variance of Atomic Coordinates as a Dynamical Metric to Distinguish Proteins and Protein-Protein Interactions in Molecular Dynamics Simulations

Protein dynamics is a manifestation of the complex trajectories of these biomolecules on a multidimensional rugged potential energy surface (PES) driven by thermal energy. At present, computational methods such as atomistic molecular dynamics (MD) simulations can describe thermal protein conformational changes in fully solvated environments over millisecond timescales. Despite these advances, a quantitative assessment of protein dynamics remains a complicated topic, intricately linked to issues such as sampling convergence and the identification of appropriate reaction coordinates/structural features to describe protein conformational states and motions. Here, we present the cumulative variance of atomic coordinate fluctuations (CVCF) along trajectories as an intuitive PES sensitive metric to assess both the extent of sampling and protein dynamics captured in MD simulations. We first examine the sampling problem in model one- (1D) and two-dimensional (2D) PES to demonstrate that the CVCF when traced as a function of the sampling variable (time in MD simulations) can identify local and global equilibria. Further, even far from global equilibrium, a situation representative of standard MD trajectories of proteins, the CVCF can distinguish different PES and therefore resolve the resultant protein dynamics. We demonstrate the utility of our CVCF analysis by applying it to distinguish the dynamics of structurally homologous proteins from the ubiquitin family (ubiquitin, SUMO1, SUMO2) and ubiquitin protein-protein interactions. Our CVCF analysis reveals that differential side-chain dynamics from the structured part of the protein (the conserved β-grasp fold) present distinct protein PES to distinguish ubiquitin from SUMO isoforms. Upon binding to two functionally distinct protein partners (UBCH5A and UEV), intrinsic ubiquitin dynamics changes to reflect the binding context even though the two proteins have similar binding modes, which lead to negligible (sub-angstrom scale) structural changes.

Fast and flexible coarse-grained prediction of protein folding routes using ensemble modeling and evolutionary sequence variation

MOTIVATION

Protein folding is a dynamic process through which polypeptide chains reach their native 3D structures. Although the importance of this mechanism is widely acknowledged, very few high-throughput computational methods have been developed to study it.

RESULTS

In this paper, we report a computational platform named P3Fold that combines statistical and evolutionary information for predicting and analyzing protein folding routes. P3Fold uses coarse-grained modeling and efficient combinatorial schemes to predict residue contacts and evaluate the folding routes of a protein sequence within minutes or hours. To facilitate access to this technology, we devise graphical representations and implement an interactive web interface that allows end-users to leverage P3Fold predictions. Finally, we use P3Fold to conduct large and short scale experiments on the human proteome that reveal the broad conservation and variations of structural intermediates within protein families.

AVAILABILITY AND IMPLEMENTATION

A Web server of P3Fold is freely available at http://csb.cs.mcgill.ca/P3Fold.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Self-organized emergence of folded protein-like network structures from geometric constraints

The intricate three-dimensional geometries of protein tertiary structures underlie protein function and emerge through a folding process from one-dimensional chains of amino acids. The exact spatial sequence and configuration of amino acids, the biochemical environment and the temporal sequence of distinct interactions yield a complex folding process that cannot yet be easily tracked for all proteins. To gain qualitative insights into the fundamental mechanisms behind the folding dynamics and generic features of the folded structure, we propose a simple model of structure formation that takes into account only fundamental geometric constraints and otherwise assumes randomly paired connections. We find that despite its simplicity, the model results in a network ensemble consistent with key overall features of the ensemble of Protein Residue Networks we obtained from more than 1000 biological protein geometries as available through the Protein Data Base. Specifically, the distribution of the number of interaction neighbors a unit (amino acid) has, the scaling of the structure’s spatial extent with chain length, the eigenvalue spectrum and the scaling of the smallest relaxation time with chain length are all consistent between model and real proteins. These results indicate that geometric constraints alone may already account for a number of generic features of protein tertiary structures.

Molecular dynamics study of ACBP denaturation in alkyl sulfates demonstrates possible pathways of unfolding through fused surfactant clusters

Anionic surfactants denature proteins at low millimolar concentrations, yet little is known about the underlying molecular mechanisms. Here, we undertake 1-μs-long atomistic molecular dynamics simulations of the denaturation of acyl coenzyme A binding protein (ACBP) and compare our results with previously published and new experimental data. Since increasing surfactant chain length is known to lead to more rapid denaturation, we studied denaturation using both the medium-length alkyl chain surfactant sodium dodecyl sulfate (SDS) and the long alkyl chain surfactant sodium hexadecyl sulfate (SHS). In silico denaturation on the microsecond timescale was not achieved using preformed surfactant micelles but required ACBP to be exposed to monomeric surfactant molecules. Micellar self-assembly occurred together with protein denaturation. To validate our analyses, we calculated small-angle X-ray scattering spectra of snapshots from the simulations. These agreed well with experimental equilibrium spectra recorded on ACBP-SDS mixtures with similar compositions. Protein denaturation occurs through the binding of partial micelles to multiple preferred binding sites followed by the accretion of surfactant monomers until these partial micelles merge to form a mature micelle and the protein chain is left disordered on the surface of the micelle. While the two surfactants attack in a similar fashion, SHS’s longer alkyl chain leads to a more efficient denaturation through the formation of larger clusters that attack ACBP, a more rapid drop in native contacts, a greater expansion in size, as well as a more thorough rearrangement of hydrogen bonds and disruption of helices.

Structural Prediction and Inverse Design by a Strongly Correlated Neural Network

Macromolecules contain molecular units as the coding information for their correlated structures in physical dimensions. The relationship between these two features is governed by the interaction energies of the involved molecular units and their encoded sequences. We present a neural network algorithm that treats molecular units themselves as neural networks, which has the flexibility to allow each unit to respond to its own environment and to influence others in the system. Through a deep neural network and a self-consistent procedure, molecular units in the network establish a strong correlation to produce the desirable features in the physical world. The proposed framework is applied to the HP model. Both the forward problem of predicting folded structures from given sequences and the inverse problem of predicting required sequences for a given structure are examined.

ART-RRT: As-Rigid-As-Possible search for protein conformational transition paths

The possible functions of a protein are strongly related to its structural rearrangements in the presence of other molecules or environmental changes. Hence, the evaluation of transition paths of proteins, which encodes conformational changes between stable states, is important since it may reveal the underlying mechanisms of the biochemical processes related to these motions. During the last few decades, different geometry-based methods have been proposed to predict such transition paths. However, in the cases where the solution requires complex motions, these methods, which typically constrain only locally the molecular structures, could produce physically irrelevant solutions involving self-intersection. Recently, we have proposed ART-RRT, an efficient method for finding ligand-unbinding pathways. It relies on the exploration of energy valleys in low-dimensional spaces, taking advantage of some mechanisms inspired from computer graphics to ensure the consistency of molecular structures. This article extends ART-RRT to the problem of finding probable conformational transition between two stable states for proteins. It relies on a bidirectional exploration rooted on the two end states and introduces an original strategy to attempt connections between the explored regions. The resulting method is able to produce at low computational cost biologically realistic paths free from self-intersection. These paths can serve as valuable input to other advanced methods for the study of proteins. A better understanding of conformational changes of proteins is important since it may reveal the underlying mechanisms of the biochemical processes related to such motions. Recently, the ART-RRT method has been introduced for finding ligand-unbinding pathways. This article presents an adaptation of the method for finding probable conformational transition between two stable states of a protein. The method is not only computationally cost-effective but also able to produce biologically realistic paths which are free from self-intersection.

Understanding Missing Entropy in Coarse-Grained Systems: Addressing Issues of Representability and Transferability

Coarse-grained (CG) models facilitate efficient simulation of complex systems by integrating out the atomic, or fine-grained (FG), degrees of freedom. Systematically derived CG models from FG simulations often attempt to approximate the CG potential of mean force (PMF), an inherently multidimensional and many-body quantity, using additive pairwise contributions. However, they currently lack fundamental principles that enable their extensible use across different thermodynamic state points, i.e., transferability. In this work, we investigate the explicit energy-entropy decomposition of the CG PMF as a means to construct transferable CG models. In particular, despite its high-dimensional nature, we find for liquid systems that the entropic component to the CG PMF can similarly be represented using additive pairwise contributions, which we show is highly coupled to the CG configurational entropy. This approach formally connects the missing entropy that is lost due to the CG representation, i.e., translational, rotational, and vibrational modes associated with the missing degrees of freedom, to the CG entropy. By design, the present framework imparts transferable CG interactions across different temperatures due to the explicit definition of an additive entropic contribution. Furthermore, we demonstrate that transferability across composition state points, such as between bulk liquids and their mixtures, is also achieved by designing combining rules to approximate cross-interactions from bulk CG PMFs. Using the predicted CG model for liquid mixtures, structural correlations of the fitted CG model were found to corroborate a high-fidelity combining rule. Our findings elucidate the physical nature and compact representation of CG entropy and suggest a new approach for overcoming the transferability problem. We expect that this approach will further extend the current view of CG modeling into predictive multiscale modeling.

Can the geometry of all-atom protein trajectories be reconstructed from the knowledge of Cα time evolution? A study of peptide plane O and side chain Cβ atoms

We inquire to what extent can the geometry of protein peptide plane and side chain atoms be reconstructed from the knowledge of Cα time evolution. Due to the lack of experimental data, we analyze all atom molecular dynamics trajectories from the Anton supercomputer, and for clarity, we limit our attention to the peptide plane O atoms and side chain Cβ atoms. We reconstruct their positions using four different approaches. Three of these are the publicly available reconstruction programs Pulchra, Remo, and Scwrl4. The fourth, Statistical Method, builds entirely on the statistical analysis of Protein Data Bank structures. All four methods place the O and Cβ atoms accurately along the Anton trajectories; the Statistical Method gives results that are closest to the Anton data. The results suggest that when a protein moves under physiological conditions, its all atom structures can be reconstructed with high accuracy from the knowledge of the Cα atom positions. This can help to better understand and improve all atom force fields, and advance reconstruction and refinement methods for reduced protein structures. The results provide impetus for the development of effective coarse grained force fields in terms of reduced coordinates.