Coarse-grained Model Research Articles

Extracting coarse-grained classifiers from large Convolutional Neural Networks

Coarse-grained classification and classification at different hierarchy levels are important in many engineering applications. Conventional approaches include post-inference aggregation of fine-grained predictions or multi-task learning with its disadvantages: necessity to incorporate post-prediction mechanisms, possible mistakes between unrelated categories when generic fine-grained models are used, and the need of training multi-task models with joint procedures. To overcome them, this paper proposes a novel method for extracting coarse-grained classifiers from large Convolutional Neural Networks (CNNs) trained on fine-grained tasks with no additional training. Leveraging the knowledge transfer capabilities of CNNs and acknowledging that a model proficient in a challenging task should inherently address easier, hierarchically related problems, the approach finds and aggregates available representatives of coarse-grained classes within existing fine-grained models. Unlike conventional approaches, the proposed technique aggregates the fine-grained model’s weights and not its predictions. As a result, a new coarse-grained model is obtained with the same feature extractor as the original model. The original and new models can be used to create a multi-output model without the multi-task learning. The method eliminates additional post-prediction mechanisms and limits the mistakes between unrelated categories. It can be used with three strategies to find the sets of fine-grained classes for weight aggregation. They are based on external WordNet knowledge or internal network knowledge. Two of the methods leverage the concepts of semantic and visual similarity. Experimental results with MobileNetV2, InceptionV3, ResNet50V2, EfficientNetV2B0 and ConvNeXt-Small trained on ImageNet demonstrate up to 98% accuracy in the coarse-grained classification, which is superior to the post-prediction aggregation.

Dissecting the Roles of Electrostatic Interactions in Modulating the Folding Stability and Cooperativity of Engrailed Homeodomain.

Engrailed homeodomain (EngHD), a highly charged transcription factor regulating over 200 genes, is a fast-folding protein. Recent studies have shown that the abundant charged residues in EngHD not only facilitate protein-DNA interactions but also influence the conformational disorder of its native structure. However, the mechanisms by which electrostatic interactions modulate the folding of EngHD remain unclear. Here, we employ a coarse-grained structure-based model that incorporates the salt-dependent Debye-Hückel model to investigate the (un)folding behavior of EngHD under various salt concentrations. Our findings demonstrate that increasing salt concentrations enhance both folding stability and cooperativity, while the folding barrier height remains relatively constant due to the distinct electrostatic effects on individual residues. By modulating the energetic balance between local and nonlocal interactions, we shift the folding of EngHD from a downhill process to a two-state process. Notably, we observe a nonmonotonic relationship between the strength of local interactions and residue-level coupling degree during (un)folding, likely attributed to the repulsive electrostatic interactions present in the native structure of EngHD. Additionally, we identify a critical turning point in the dependence of folding cooperativity on salt concentration, classified by the energetic balance of local and nonlocal interactions. Our results provide valuable insights into how electrostatic interactions influence the folding of EngHD, contributing to the theoretical framework for engineering highly charged proteins.

Coarse-grained molecular dynamics model to evaluate the mechanical and thermal properties of graphene/copper composites

Coarse-grained molecular dynamics model to evaluate the mechanical and thermal properties of graphene/copper composites

Unraveling GPCRs Allosteric Modulation. Cannabinoid 1 Receptor as a Case Study.

G-protein-coupled receptors (GPCRs) constitute one of the most prominent families of integral membrane receptor proteins that mediate most transmembrane signaling processes. Malfunction of these signal transduction processes is one of the underlying causes of many human pathologies (Parkinson's, Huntington's, heart diseases, etc), provoking that GPCRs are the largest family of druggable proteins. However, these receptors have been targeted traditionally by orthosteric ligands, which usually causes side effects due to the simultaneous targeting of homologous receptor subtypes. Allosteric modulation offers a promising alternative approach to circumvent this problematic and, thus, comprehending its details is a most important task. Here we use the Cannabinoid type-1 receptor (CB1R) in trying to shed light on this issue, focusing on positive allosteric modulation. This is done by using the protein-dipole Langevin-dipole (PDLD) within the linear response approximation (LRA) framework (PDLD/S-2000) along with our coarse-grained (CG) model of membrane proteins to evaluate the dissociation constants (KBs) and cooperativity factors (αs) for a diverse series of CB1R positive allosteric modulators belonging to the 2-phenylindole structural class, considering CP55940 as an agonist. The agreement with the experimental data evinces that significantly populated allosteric modulator:CB1R and allosteric modulator:CP55940:CB1R complexes have been identified and characterized successfully. Analyzing them, it has been determined that CB1R positive allosteric modulation lies in an outwards displacement of transmembrane α helix (TM) 4 extracellular end and in the regulation of the range of motion of a compound TM7 movement for binary and ternary complexes, respectively. In this respect, we achieved a better comprehension of the molecular architecture of CB1R positive allosteric site, identifying Lys1923.28 and Gly1943.30 as key residues regarding electrostatic interactions inside this cavity, and to rationalize (at both structural and molecular level) the exhibited stereoselectivity in relation to positive allosteric modulation activity by considered CB1R allosteric modulators. Additionally, putative/postulated allosteric binding sites have been screened successfully, identifying the real CB1R positive allosteric site, and most structure-activity relationship (SAR) studies of CB1R 2-phenylindole allosteric modulators have been rationalized. All these findings point out towards the predictive value of the methodology used in the current work, which can be applied to other biophysical systems of interest. The results presented in this study contribute significantly to understand GPCRs allosteric modulation and, hopefully, will encourage a more thorough exploration of the topic.

Thermodynamic Transferability in Coarse-Grained Force Fields Using Graph Neural Networks.

Coarse-graining is a molecular modeling technique in which an atomistic system is represented in a simplified fashion that retains the most significant system features that contribute to a target output while removing the degrees of freedom that are less relevant. This reduction in model complexity allows coarse-grained molecular simulations to reach increased spatial and temporal scales compared with corresponding all-atom models. A core challenge in coarse-graining is to construct a force field that represents the interactions in the new representation in a way that preserves the atomistic-level properties. Many approaches to building coarse-grained force fields have limited transferability between different thermodynamic conditions as a result of averaging over internal fluctuations at a specific thermodynamic state point. Here, we use a graph-convolutional neural network architecture, the Hierarchically Interacting Particle Neural Network with Tensor Sensitivity (HIP-NN-TS), to develop a highly automated training pipeline for coarse-grained force fields, which allows for studying the transferability of coarse-grained models based on the force-matching approach. We show that this approach yields not only highly accurate force fields but also that these force fields are more transferable through a variety of thermodynamic conditions. These results illustrate the potential of machine learning techniques, such as graph neural networks, to improve the construction of transferable coarse-grained force fields.

Implementation of the UNRES/SUGRES-1P Coarse-Grained Model of Heparin for Simulating Protein/Heparin Interactions.

Heparin is a natural highly sulfated unbranched periodic polysaccharide that plays a critical role in regulating various cellular events through interactions with its protein targets such as growth factors and cytokines. Although all-atom simulations of heparin-containing systems provide valuable insights into their structural and dynamical properties, long chains of heparin participate in many biologically relevant processes at much bigger scales and longer times than the ones which all-atom MD is able to effectively deal with. Among these processes is the establishment of chemokine gradients, amyloidogenesis, or collagen network organization. To address this limitation, coarse-grained models simplify these systems by reducing the number of degrees of freedom, allowing for the efficient exploration of structural changes within protein/heparin complexes. We introduce and validate the accuracy of a new coarse-grained physics-based model designed for studying protein/heparin interactions, which has been incorporated into the UNRES software package. The effective energy functions from UNRES and SUGRES-1P have been employed for the protein and heparin components, respectively. A good agreement between the obtained coarse-grained simulation results and experimental data confirms the suitability of the combined coarse-grained UNRES and SUGRES-1P model for in silico analysis of complex biological phenomena involving heparin, spanning time scales and molecular system sizes not attainable by conventional atomistic molecular dynamics simulations.

Coarse-Grained Modeling of the Water/Alkane Wetting and Dewetting Processes on Fluorinated Coatings.

This work provides a framework to digitally assess any droplet's static and dynamic contact angles on coatings and polymeric substrates. We are introducing a new dissipative particle dynamics coarse-grained model to attain the spatiotemporal conditions and the coexistence of different phases that such investigation dictates. Two computational techniques are additionally developed; a robust technique to calculate the static contact angle using density profiles and a perturbation method to evaluate dynamic contact angles. A parallel force to the surface force is applied to emulate the receding and advancing dynamics. We have validated our protocols for the static contact angle of water for a series of polymeric surfaces and the dynamic contact angle for three different fluorinated additives. We reproduced the correct hysteresis trends between the droplet content and the surface. The fluorinated nature of the additive's tails is the driving force of directed self-assembly and, consequently, the repelling nature of the surface. An equally important factor for designating the interaction profile of the surface is the coating's chemical structure, which is responsible for inhibiting or favoring the aqueous media interaction.

From Fine-Grain to Coarse-Grain Modeling: Estimating Kinetic Parameters of DNA Molecules.

Coarse-grain models are essential to understand the biological function of DNA molecules because the length and time scales of the sequence-dependent physical properties of DNA are often beyond the reach of experimental and all-atom computational methods. Simulating coarse-grain models of DNA, e.g. using Langevin dynamics, requires the parametrization of both potential and kinetic energy functions. Many studies have shown that the flexibility (i.e., potential energy) of a DNA molecule depends on its sequence. In contrast, little is known about the sequence-dependence of DNA mass parameters required to model its kinetic energy. In this paper, an algebraic expression is derived for the kinetic energy as a function of linear and angular velocities of each DNA base parameterized by its mass, center of mass, and rotational inertia tensor. The parameters of this function are then approximated from a set of fine-grain molecular dynamics simulations representing all combinations of the four DNA base pairs AT, TA, GC, and CG, in different sequence contexts. Compatibility conditions associated with the assumption of each base being modeled as a rigid body were verified to be good approximations. The kinetic parameters were found to be significantly different between the four G, C, A, and T bases, and to not be dependent on the sequence context. This suggests that the effective kinetic parameters of a DNA base may depend only on the base itself, not on its neighbors.

Dynamics and Collective Behavior of Chemically Propelled Janus Sphere Dimers in Complex Solvents.

The propulsion mechanisms and collective dynamics of chemically powered Janus sphere dimers at the micro- and nanoscales, confined in a quasi-two-dimensional geometry, are investigated using a coarse-grained microscopic dynamical model. These active Janus dimers consist of two identical Janus spheres, featuring a catalytic cap on one hemisphere. The chemical reaction taking place on the catalytic surface generates asymmetric concentration gradients of product molecules around the Janus sphere, leading to the self-propulsion of the dimers. Depending on the dimer configuration, they exhibit various motion behaviors such as forward propulsion, rotation, and restricted stochastic motion. Due to chemotactic effects and self-diffusiophoretic forces, ensembles of dimers spontaneously form diverse structures, such as transient clusters, stable rotational ensembles, and antiparallel aligned doublets. This study demonstrates that the configurations of Janus sphere dimers significantly influence their self-propulsion and collective behaviors, providing crucial insights for the design and control of active micro- and nanoscale systems.

Physiological cost of antibiotic resistance: Insights from a ribosome variant in bacteria.

Antibiotic-resistant ribosome variants arise spontaneously in bacterial populations; however, their impact on the overall bacterial physiology remains unclear. We studied the naturally arising antibiotic-resistant L22* ribosome variant of Bacillus subtilis and identified a Mg2+-dependent physiological cost. Coculture competition experiments show that Mg2+ limitation hinders the growth of the L22* variant more than the wild type (WT), even under antibiotic pressure. This growth disadvantage of L22* cells is not due to lower ribosome abundance but rather due to reduced intracellular Mg2+ levels. Coarse-grained elastic-network modeling of ribosome conformational dynamics suggests that L22* ribosomes associate more tightly with Mg2+ when compared to WT. We combined the structural modeling and experimental measurements in a steady-state model to predict cellular adenosine 5'-triphosphate (ATP) levels, which also depend on Mg2+. Experiments confirmed a predicted ATP drop in L22* cells under Mg2+ limitation, while WT cells were less affected. Intracellular competition for a finite Mg2+ pool can thus suppress the establishment of an antibiotic-resistant ribosome variant.

Evolution equations for open systems and collective variables: Which equation would you like to solve by molecular dynamics simulation?

In molecular dynamics simulations, the Langevin equation is frequently used to model the dynamics of collective variables and of systems coupled to baths. Often, external forces are added to the Langevin equation (e.g., when using targeted or steered molecular dynamics in biomolecular simulation). It is also popular to add derivatives of thermodynamic potentials to the Langevin equation as effective forces (e.g., when using a potential of mean force in a coarse-grained polymer model). These practices can be adventurous. In this article, we recall derivations of different versions of the Langevin equation and we discuss why care is needed if one would like to make changes to the structure of the equation.

DeepBBQ: A Deep Learning Approach to the Protein Backbone Reconstruction.

Coarse-grained models have provided researchers with greatly improved computational efficiency in modeling structures and dynamics of biomacromolecules, but, to be practically useful, they need fast and accurate conversion methods back to the all-atom representation. Reconstruction of atomic details may also be required in the case of some experimental methods, like electron microscopy, which may provide Cα-only structures. In this contribution, we present a new method for recovery of all backbone atom positions from just the Cα coordinates. Our approach, called deepBBQ, uses a deep convolutional neural network to predict a single internal coordinate per peptide plate, based on Cα trace geometric features, and then proceeds to recalculate the cartesian coordinates based on the assumption that the peptide plate atoms lie in the same plane. Extensive comparison with similar programs shows that our solution is accurate and cost-efficient. The deepBBQ program is available as part of the open-source bioinformatics toolkit Bioshell and is free for download and the documentation is available online.

Fluctuating Chromatin Facilitates Enhancer-Promoter Communication by Regulating Transcriptional Clustering Dynamics.

Enhancers regulate gene expression by forming contacts with distant promoters. Phase-separated condensates or clusters formed by transcription factors (TFs) and cofactors are thought to facilitate these enhancer-promoter (E-P) interactions. Using polymer physics, we developed distinct coarse-grained chromatin models that produce similar ensemble-averaged Hi-C maps but with "stable" and "dynamic" characteristics. Our findings, consistent with recent experiments, reveal a multistep E-P communication process. The dynamic model facilitates E-P proximity by enhancing TF clustering and subsequently promotes direct E-P interactions by destabilizing the TF clusters through chain flexibility. Our study promotes physical understanding of the molecular mechanisms governing E-P communication in transcriptional regulation.

Enhancing the Assembly Properties of Bottom-Up Coarse-Grained Phospholipids.

A plethora of key biological events occur at the cellular membrane where the large spatiotemporal scales necessitate dimensionality reduction or coarse-graining approaches over conventional all-atom molecular dynamics simulation. Constructing coarse-grained descriptions of membranes systematically from statistical mechanical principles has largely remained challenging due to the necessity of capturing amphipathic self-assembling behavior in coarse-grained models. We show that bottom-up coarse-grained lipid models can possess metastable morphological behavior and that this potential metastability has ramifications for accurate development and training. We in turn develop a training algorithm which evades metastability issues by linking model training to self-assembling behavior, and demonstrate its robustness via construction of solvent-free coarse-grained models of various phospholipid membranes, including lipid species such as phosphatidylcholines, phosphatidylserines, sphingolipids, and cholesterol. The resulting coarse-grained lipid models are orders of magnitude faster than their atomistic counterparts while retaining structural fidelity and constitute a promising direction for the development of coarse-grained models of realistic cell membranes.

Interaction of complex particles: A framework for the rapid and accurate approximation of pair potentials using neural networks

Motivated by the limitations of conventional coarse-grained molecular dynamics for simulation of large systems of nanoparticles and the challenges in efficiently representing general pair potentials for rigid bodies, we present a method for approximating general rigid body pair potentials based on a specialized type of deep neural network that maintains essential properties, such as conservation of energy and invariance to the chosen origins of the particles. The network uses a specialized geometric abstraction layer to convert the relative coordinates of the rigid bodies to input more suitable to a conventional artificial neural network, which is trained together with the specialized layer. This results in geometric representations of the particles optimized for the specific potential. The network can be trained directly on scalar values to fit a model without explicit gradient and then used to efficiently evaluate the force and torque on the particles resulting from the potential. The concept is demonstrated with an atomistic interaction model for carbon nanotubes and the resulting model is compared with a common type of coarse-grained model optimized for the same potential, with even very small networks comparing favourably and larger networks achieving up to two orders of magnitude lower cost. The sensitivity to noise in the training data is investigated and the model is found to strongly reject noise up to 12.5% given a dataset of 107 samples. The performance of a proof-of-concept implementation is demonstrated on a variety of hardware, showing the models viability for large-scale simulations. Furthermore, generalization to soft bodies and potentials for polydisperse systems are discussed. Published by the American Physical Society 2024

MARTINI Coarse-Grained Force Field for Thermoplastic Starch Nanocomposites.

Thermoplastic starch (TPS) is an excellent film-forming material, and the addition of fillers, such as tetramethylammonium-montmorillonite (TMA-MMT) clay, has significantly expanded its use in packaging applications. We first used an all-atom (AA) simulation to predict several macroscopic (Young's modulus, glass transition temperature, density) and microscopic (conformation along 1-4 and 1-6 glycosidic linkages, composite morphology) properties of TPS melt and TPS-TMA-MMT composite. The interplay of polymer-surface (weakly repulsive), plasticizer-surface (attractive), and polymer-plasticizer (weakly attractive) interactions leads to conformational and dynamics properties distinct from those in systems with either attractive or repulsive polymer-surface interactions. A subset of AA properties was used to parametrize the MARTINI-2 coarse-grained (CG) force field (FF) for the melt and composite systems. The missing bonded parameters of amylose and amylopectin and the bead types for 1-4 and 1-6 linked α-D glucose were determined using two-body excess entropy, density, and bond and angle distributions in the AA TPS melt. This new MARTINI-2 CG model was also compared with the MARTINI-3 model for the TPS melt. However, the requirement of a polarizable water model necessitates the use of MARTINI-2 FF for the composite system. This liquid-liquid partitioning-based FF shows freezing and compaction of polymer chains near the clay surface, further accentuated by lowering of dispersive interactions between pairs of high-covalent-coordination ring units of TPS polymers and the montmorillonite sheet. A rescaling of the effective dispersive component of TPS-MMT cross interactions was used to optimize the MARTINI-2 FF for the composite system with structural (chain size distribution), thermodynamic (chain conformational entropy and density), and dynamic (self-diffusion coefficient) properties obtained from long AA simulations forming the constraints for optimization. The obtained CG FF parameters provided excellent estimates for several other properties of the melt and composite systems not used in parameter estimation, thus establishing the robustness of the developed model.

Unveiling Nucleosome Dynamics: A Comparative Study Using All-Atom and Coarse-Grained Simulations Enhanced by Principal Component Analysis.

This study investigates nucleosome dynamics using both all-atom and coarse-grained (CG) molecular dynamics simulations, focusing on the SIRAH force field. Simulations are performed for two nucleosomal DNA sequences, ASP and Widom-601, over six microseconds at physiological salt concentrations. Comparative analysis of structural parameters, such as groove widths and base pair geometries, reveals good agreement between atomistic and CG models, though CG simulations exhibit broader conformational sampling and greater breathing motion of DNA ends. Principal component analysis (PCA) is applied to DNA structural parameters, revealing multiple free energy minima, especially in CG simulations. These findings highlight the potential of the SIRAH CG force field for studying large-scale nucleosome dynamics, offering insights into DNA repositioning and sequence-dependent behavior.

Integration of molecular coarse-grained model into geometric representation learning framework for protein-protein complex property prediction

Structure-based machine learning algorithms have been utilized to predict the properties of protein-protein interaction (PPI) complexes, such as binding affinity, which is critical for understanding biological mechanisms and disease treatments. While most existing algorithms represent PPI complex graph structures at the atom-scale or residue-scale, these representations can be computationally expensive or may not sufficiently integrate finer chemical-plausible interaction details for improving predictions. Here, we introduce MCGLPPI, a geometric representation learning framework that combines graph neural networks (GNNs) with MARTINI molecular coarse-grained (CG) models to predict PPI overall properties accurately and efficiently. Extensive experiments on three types of downstream PPI property prediction tasks demonstrate that at the CG-scale, MCGLPPI achieves competitive performance compared with the counterparts at the atom- and residue-scale, but with only a third of computational resource consumption. Furthermore, CG-scale pre-training on protein domain-domain interaction structures enhances its predictive capabilities for PPI tasks. MCGLPPI offers an effective and efficient solution for PPI overall property predictions, serving as a promising tool for the large-scale analysis of biomolecular interactions.

Reparameterization of the mW model to accurately predict the experimental phase diagram of methane hydrate.

Due to their high computational efficiency, the coarse-grained water models are of particular importance for practical molecular simulations of gas hydrates. In these models, the mW model is successfully used to study many thermodynamics and dynamics of methane hydrate. Yet, despite several decades of intense research, the mW model is still found to overestimate the melting temperature of methane hydrate. We here employ the minimum mean squared error estimation to revisit the key parameter of the mW model, which determines the strength of the tetrahedral angle of the water system. Relying on the free energy calculations, we first estimate the chemical potentials of water in the liquid phase for temperatures at which methane hydrate forms. We then turn to the mean squared error to describe the chemical potential deviation between the mW model and the TIP4P/ice model (the latter could reproduce the experimental phase diagram of methane hydrate). By minimizing the mean squared error, we finally have an optimized parameter for the mW model. In this part, we also discuss the pressure effect on such reparameterization procedure. Moreover, relying on the direct coexistence method, the melting temperature determined using the reparameterized mW model is found to be consistent with the experimental data. This strategy provides a means to improve the coarse-grained model to match the experimental observations for temperatures in the range of interest.

Unraveling the role of exercise in cancer suppression: insights from a mathematical model

Recent experimental studies have shown that physical exercise has the potential to suppress tumor progression. Such suppression has been reported to be mediated by the exercise-induced activation of natural killer (NK) cells through the release of IL-6, a cytokine. Aimed at shedding light on how exercise-induced NK cell activation helps in the suppression of cancer, we developed a coarse-grained mathematical model based on a system of ordinary differential equations describing the interaction between IL-6, NK-cells, and tumor cells. The model is then used to study how exercise duration and exercise intensity affect tumor suppression. Our results show that increasing exercise intensity or increasing exercise duration leads to greater and sustained tumor suppression. Furthermore, multi-bout exercise patterns hold promise for improving cancer treatment strategies by adjusting exercise intensity and frequency. Thus, the proposed mathematical model provides insights into the role of exercise in tumor suppression and can be instrumental in guiding future experimental studies, potentially leading to more effective exercise interventions.