Biomolecularmodeling and simulation: a field coming of age

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.

Perspectives on Computational Enzyme Modeling: From Mechanisms to Design and Drug Development

Understanding enzyme mechanisms is essential for unraveling the complex molecular machinery of life. In this review, we survey the field of computational enzymology, highlighting key principles governing enzyme mechanisms and discussing ongoing challenges and promising advances. Over the years, computer simulations have become indispensable in the study of enzyme mechanisms, with the integration of experimental and computational exploration now established as a holistic approach to gain deep insights into enzymatic catalysis. Numerous studies have demonstrated the power of computer simulations in characterizing reaction pathways, transition states, substrate selectivity, product distribution, and dynamic conformational changes for various enzymes. Nevertheless, significant challenges remain in investigating the mechanisms of complex multistep reactions, large-scale conformational changes, and allosteric regulation. Beyond mechanistic studies, computational enzyme modeling has emerged as an essential tool for computer-aided enzyme design and the rational discovery of covalent drugs for targeted therapies. Overall, enzyme design/engineering and covalent drug development can greatly benefit from our understanding of the detailed mechanisms of enzymes, such as protein dynamics, entropy contributions, and allostery, as revealed by computational studies. Such a convergence of different research approaches is expected to continue, creating synergies in enzyme research. This review, by outlining the ever-expanding field of enzyme research, aims to provide guidance for future research directions and facilitate new developments in this important and evolving field.

Amphiphilic peptide Mastoparan-B induces conformational changes within the AdeB efflux pump, down-regulates adeB gene expression, and restores antibiotic susceptibility in an MDR strain of Acinetobacter baumannii

Mastoparan B (MP-B) is an amphiphilic peptide with a potent antimicrobial activity against most Gram-negative bacteria. However, there is little information available on the inhibition of the Acinetobacter baumannii resistance-nodulation-cell-division (RND) efflux pump using this antimicrobial peptide. Here, we carried out a series of in-silico experiments to find the mechanisms underlying the anti-efflux activity of MP-B using a multi-drug resistant (MDR) strain of A. baumannii (AB). According to our findings, MP-B demonstrated a potent antibacterial activity against an MDR-AB (minimum inhibitory concentration [MIC] = 1 μg/mL) followed by a 20-fold reduction in the adeB gene expression in the presence of sub-MIC of this peptide. Using Groningen Machine for Chemicals Simulation (GROMACS) via PyMOL Graphical User Interface (GUI), (we observed that, the AdeB transporter had conserved helix-turn-helix regions and a tight pore rich in Phe and Ala residues. To understand how inhibition of the AdeB is achieved, we generated 20 apo-MP-B poses using the InterPep and SiteMap tools. The high-quality model was created by homology modeling and used for docking via AutoDock/Vina to identify the MP-B binding sites. We established that the most apo-MP-B formed H-bonds to the backbone of five amino acids in the Helix-5. As a result, the dihedral angles of the involved amino acids shift by 9.0-9.6 Ǻ, causing a change in the conformation of the AdeB protein. This led to helix conformation stereoisomerization and block the AdeB activity. MP-B presumably has dual mechanisms. (1) It blocks the AdeB transporter by changing its conformation. (2) MP-B influences the adeB gene expression by binding to G-protein which laterally controls efflux regulators like MarA, RamA, SoxS, and Rob proteins.

Temperature dependence of DNA elasticity: An all-atom molecular dynamics simulation study

We used all-atom molecular dynamics simulation to investigate the elastic properties of double-stranded DNA (dsDNA). We focused on the influences of temperature on the stretch, bend, and twist elasticities, as well as the twist-stretch coupling, of the dsDNA over a wide range of temperature. The results showed that the bending and twist persistence lengths, together with the stretch and twist moduli, decrease linearly with temperature. However, the twist-stretch coupling behaves in a positive correction and enhances as the temperature increases. The potential mechanisms of how temperature affects dsDNA elasticity and coupling were investigated by using the trajectories from atomistic simulation, in which thermal fluctuations in structural parameters were analyzed in detail. We analyzed the simulation results by comparing them with previous simulation and experimental data, which are in good agreement. The prediction about the temperature dependence of dsDNA elastic properties provides a deeper understanding of DNA elasticities in biological environments and potentially helps in the further development of DNA nanotechnology.

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.

Progress in Simulation Studies of Insulin Structure and Function

Insulin is a peptide hormone known for chiefly regulating glucose level in blood among several other metabolic processes. Insulin remains the most effective drug for treating diabetes mellitus. Insulin is synthesized in the pancreatic β-cells where it exists in a compact hexameric architecture although its biologically active form is monomeric. Insulin exhibits a sequence of conformational variations during the transition from the hexamer state to its biologically-active monomer state. The structural transitions and the mechanism of action of insulin have been investigated using several experimental and computational methods. This review primarily highlights the contributions of molecular dynamics (MD) simulations in elucidating the atomic-level details of conformational dynamics in insulin, where the structure of the hormone has been probed as a monomer, dimer, and hexamer. The effect of solvent, pH, temperature, and pressure have been probed at the microscopic scale. Given the focus of this review on the structure of the hormone, simulation studies involving interactions between the hormone and its receptor are only briefly highlighted, and studies on other related peptides (e.g., insulin-like growth factors) are not discussed. However, the review highlights conformational dynamics underlying the activities of reported insulin analogs and mimetics. The future prospects for computational methods in developing promising synthetic insulin analogs are also briefly highlighted.

Molecular simulations of proteins: From simplified physical interactions to complex biological phenomena

Molecular dynamics simulation is the most popular computational technique for investigating the structural and dynamical behaviour of proteins, in search of the molecular basis of their function. Far from being a completely settled field of research, simulations are still evolving to best capture the essential features of the atomic interactions that govern a protein's inner motions. Modern force fields are becoming increasingly accurate in providing a physical description adequate to this purpose, and allow us to model complex biological systems under fairly realistic conditions. Furthermore, the use of accelerated sampling techniques is improving our access to the observation of progressively larger molecular structures, longer time scales, and more hidden functional events. In this review, the basic principles of molecular dynamics simulations and a number of key applications in the area of protein science are summarized, and some of the most important results are discussed. Examples include the study of the structure, dynamics and binding properties of 'difficult' targets, such as intrinsically disordered proteins and membrane receptors, and the investigation of challenging phenomena like hydration-driven processes and protein aggregation. The findings described provide an overall picture of the current state of this research field, and indicate new perspectives on the road ahead to the upcoming future of molecular simulations.

Recent advances in design and applications of biomimetic self-assembled peptide hydrogels for hard tissue regeneration

Abstract

The development of natural biomaterials applied for hard tissue repair and regeneration is of great importance, especially in societies with a large elderly population. Self-assembled peptide hydrogels are a new generation of biomaterials that provide excellent biocompatibility, tunable mechanical stability, injectability, trigger capability, lack of immunogenic reactions, and the ability to load cells and active pharmaceutical agents for tissue regeneration. Peptide-based hydrogels are ideal templates for the deposition of hydroxyapatite crystals, which can mimic the extracellular matrix. Thus, peptide-based hydrogels enhance hard tissue repair and regeneration compared to conventional methods. This review presents three major self-assembled peptide hydrogels with potential application for bone and dental tissue regeneration, including ionic self-complementary peptides, amphiphilic (surfactant-like) peptides, and triple-helix (collagen-like) peptides. Special attention is given to the main bioactive peptides, the role and importance of self-assembled peptide hydrogels, and a brief overview on molecular simulation of self-assembled peptide hydrogels applied for bone and dental tissue engineering and regeneration.

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Biomolecular Modeling and Simulation: A Prospering Multidisciplinary Field

We reassess progress in the field of biomolecular modeling and simulation, following up on our perspective published in 2011. By reviewing metrics for the field's productivity and providing examples of success, we underscore the productive phase of the field, whose short-term expectations were overestimated and long-term effects underestimated. Such successes include prediction of structures and mechanisms; generation of new insights into biomolecular activity; and thriving collaborations between modeling and experimentation, including experiments driven by modeling. We also discuss the impact of field exercises and web games on the field's progress. Overall, we note tremendous success by the biomolecular modeling community in utilization of computer power; improvement in force fields; and development and application of new algorithms, notably machine learning and artificial intelligence. The combined advances are enhancing the accuracy andscope of modeling and simulation, establishing an exemplary discipline where experiment and theory or simulations are full partners.

Biomolecular modeling thrives in the age of technology

The biomolecular modeling field has flourished since its early days in the 1970s due to the rapid adaptation and tailoring of state-of-the-art technology. The resulting dramatic increase in size and timespan of biomolecular simulations has outpaced Moore's law. Here, we discuss the role of knowledge-based versus physics-based methods and hardware versus software advances in propelling the field forward. This rapid adaptation and outreach suggests a bright future for modeling, where theory, experimentation and simulation define three pillars needed to address future scientific and biomedical challenges.

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.

Insights of structure-based pharmacophore studies and inhibitor design against Gal3 receptor through molecular dynamics simulations

Our present work studies the structure-based pharmacophore modeling and designing inhibitor against Gal3 receptor through molecular dynamics (MD) simulations extensively. Pharmacophore models play a key role in computer-aided drug discovery like in the case of virtual screening of chemical databases, de novo drug design and lead optimization. Structure-based methods for developing pharmacophore models are important, and there have been a number of studies combining such methods with the use of MD simulations to model protein's flexibility. The two potential antagonists SNAP 37889 and SNAP 398299 were docked and simulated for 250 ns and the results are analyzed and carried for the structure-based pharmacophore studies. This helped in identification of the subtype selectivity of the binding sites of the Gal3 receptor. Our work mainly focuses on identifying these binding site residues and to design more potent inhibitors compared to the previously available inhibitors through pharmacophore models. The study provides crucial insight into the binding site residues Ala2, Asp3, Ala4, Gln5, Phe24, Gln79, Ala80, Ile82, Tyr83, Trp88, His99, Ile102, Tyr103, Met106, Tyr157, Tyr161, Pro174, Trp176, Arg181, Ala183, Leu184, Asp185, Thr188, Trp248, His251, His252, Ile255, Leu256, Phe258, Trp259, Tyr270, Arg273, Leu274 and His277, which plays a significant role in the conformational changes of the receptor and helps to understand the inhibition mechanism. Communicated by Ramaswamy H. Sarma.

Solvation Free Energy of Self-Assembled Complexes: Using Molecular Dynamics to Understand the Separation of ssDNA-Wrapped Single-Walled Carbon Nanotubes

Molecular dynamics simulations were used to characterize the self-assembly of single-stranded DNA (ssDNA) on a (6,5) single-walled carbon nanotube (SWCNT) in aqueous solution for the purpose of gaining an improved theoretical understanding of separation strategies for SWCNTs using ssDNA as a dispersant. Four separate ssDNA sequences, ((TAT)4, TTA(TAT)2ATT, C12, (GTC)2GT), at various levels of loading, were chosen for study based on published experimental work showing selective extraction of particular SWCNT species based on the ssDNA dispersant sequence. We develop a unique workflow based on free energy perturbation (FEP) and use this to determine the relative solubility of these complexes due to the adsorption of the ssDNA on the SWCNT surface, and hence, rank the favorability of separations observed during experiments. Results qualitatively agree with experiments and indicate that the nucleobase sequence of the adsorbed ssDNA greatly affects the free energy of complex solvation which ultimately drives SWCNT separation. Further, to elucidate the underlying physics governing the ssDNA-SWCNT solubility rankings, we also present calculations for four structural characteristics of ssDNA adsorption. We demonstrate that a unique type of intra-strand hydrogen bonding is the most important factor contributing to the stability of the ssDNA-SWCNT complexes and show how these adsorption characteristics are coupled with the FEP results.

Analysis of local density potentials

Low resolution coarse-grained (CG) models are widely adopted for investigating phenomena that cannot be effectively simulated with all-atom (AA) models. Since the development of the many-body dissipative particle dynamics method, CG models have increasingly supplemented conventional pair potentials with one-body potentials of the local density (LD) around each site. These LD potentials appear to significantly extend the transferability of CG models, while also enabling more accurate descriptions of thermodynamic properties, interfacial phenomena, and many-body correlations. In this work, we systematically examine the properties of LD potentials. We first derive and numerically demonstrate a nontrivial transformation of pair and LD potentials that leaves the total forces and equilibrium distribution invariant. Consequently, the pair and LD potentials determined via bottom-up methods are not unique. We then investigate the sensitivity of CG models for glycerol to the weighting function employed for defining the local density. We employ the multiscale coarse-graining (MS-CG) method to simultaneously parameterize both pair and LD potentials. When employing a short-ranged Lucy function that defines the local density from the first solvation shell, the MS-CG model accurately reproduces the pair structure, pressure-density equation of state, and liquid-vapor interfacial profile of the AA model. The accuracy of the model generally decreases as the range of the Lucy function increases further. The MS-CG model provides similar accuracy when a smoothed Heaviside function is employed to define the local density from the first solvation shell. However, the model performs less well when this function acts on either longer or shorter length scales.

Dual-potential approach for coarse-grained implicit solvent models with accurate, internally consistent energetics and predictive transferability

The dual-potential approach promises coarse-grained (CG) models that accurately reproduce both structural and energetic properties, while simultaneously providing predictive estimates for the temperature-dependence of the effective CG potentials. In this work, we examine the dual-potential approach for implicit solvent CG models that reflect large entropic effects from the eliminated solvent. Specifically, we construct implicit solvent models at various resolutions, R, by retaining a fraction 0.10 ≤ R ≤ 0.95 of the molecules from a simple fluid of Lennard-Jones spheres. We consider the dual-potential approach in both the constant volume and constant pressure ensembles across a relatively wide range of temperatures. We approximate the many-body potential of mean force for the remaining solutes with pair and volume potentials, which we determine via multiscale coarse-graining and self-consistent pressure-matching, respectively. Interestingly, with increasing temperature, the pair potentials appear increasingly attractive, while the volume potentials become increasingly repulsive. The dual-potential approach not only reproduces the atomic energetics but also quite accurately predicts this temperature-dependence. We also derive an exact relationship between the thermodynamic specific heat of an atomic model and the energetic fluctuations that are observable at the CG resolution. With this generalized fluctuation relationship, the approximate CG models quite accurately reproduce the thermodynamic specific heat of the underlying atomic model.

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.

Computational Modeling of Realistic Cell Membranes

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

Atomistic molecular dynamics simulations of the LCST conformational transition in poly(N-vinylcaprolactam) in water

Thermoresponsive poly(N-vinylcaprolactam) (PVCL) has received growing interest due to a temperature-induced phase transition, which switches its solubility in aqueous solutions. However, the lower critical solution temperature (LCST) of PVCL is greatly influenced by the molecular weight, morphology and the environment. Therefore, despite of numerous experimental studies of the thermal response of PVCL, a driving force and a molecular origin of conformation transitions in solution remain far less studied. To get a better understanding of the coil-to-globule conformation transition of PVCL in aqueous solution, we examined the structure and conformation dynamics of a single-chain PVCL₃₀ in a temperature range of 280-360 K by using atomistic molecular dynamics (MD) simulations. The united-atom GROMOS G53a6 force field was re-parameterized and fine-tuned by DFT calculations to reproduce the experimental LCST transition of PVCL. Our MD model reproduces the LCST transition of PVCL₃₀ to occur within a temperature range of 34.6-38.5°. MD simulation results suggest a significant difference between the hydration state of the carbonyl group of PVCL below and above the LCST threshold. The analysis of the number of hydrogen bonds of PVCL with water molecules demonstrates that dehydration of the polymer plays an important role and drives the temperature-induced polymer collapse. Finally, the developed MD model and FF parameters were successfully tested for large-scale systems, such as mixture PVCL₃₀ oligomer and single-chain PVCL₈₁₆ polymer, respectively.

Experimental and theoretical tools to elucidate the binding mechanisms of solid-binding peptides

The interactions between biomolecules and solid surfaces play an important role in designing new materials and applications which mimic nature. Recently, solid-binding peptides (SBPs) have emerged as potential molecular building blocks in nanobiotechnology. SBPs exhibit high selectivity and binding affinity towards a wide range of inorganic and organic materials. Although these peptides have been widely used in various applications, there is a need to understand the interaction mechanism between the peptide and its material substrate, which is challenging both experimentally and theoretically. This review describes the main characterisation techniques currently available to study SBP-surface interactions and their contribution to gain a better insight for designing new peptides for tailored binding.

Multiconfigurational Coarse-Grained Molecular Dynamics

Standard low resolution coarse-grained modeling techniques have difficulty capturing multiple configurations of protein systems. Here, we present a method for creating accurate coarse-grained (CG) models with multiple configurations using a linear combination of functions or “states”. Individual CG models are created to capture the individual states, and the approximate coupling between the two states is determined from an all-atom potential of mean force. We show that the resulting multiconfiguration coarse-graining (MCCG) method accurately captures the transition state as well as the free energy between the two states. We have tested this method on the folding of dodecaalanine, as well as the amphipathic helix of endophilin.

Recent Trends and Applications of Molecular Modeling in GPCR⁻Ligand Recognition and Structure-Based Drug Design

G protein-coupled receptors represent the largest family of human membrane proteins and are modulated by a variety of drugs and endogenous ligands. Molecular modeling techniques, especially enhanced sampling methods, have provided significant insight into the mechanism of GPCR–ligand recognition. Notably, the crucial role of the membrane in the ligand-receptor association process has earned much attention. Additionally, docking, together with more accurate free energy calculation methods, is playing an important role in the design of novel compounds targeting GPCRs. Here, we summarize the recent progress in the computational studies focusing on the above issues. In the future, with continuous improvement in both computational hardware and algorithms, molecular modeling would serve as an indispensable tool in a wider scope of the research concerning GPCR–ligand recognition as well as drug design targeting GPCRs.

MM-PBSA and per-residue decomposition energy studies on 7-Phenyl-imidazoquinolin-4(5H)-one derivatives: Identification of crucial site points at microsomal prostaglandin E synthase-1 (mPGES-1) active site

The huge therapeutic potential and the market share of painkillers are well-known. Due to the side effects associated with traditional NSAIDs and selective cyclooxygenase (COX-2) inhibitors, a new generation of painkillers is the need of the hour. In this regard, microsomal prostaglandin E synthase-1 (mPGES-1) offers great potential as an alternative drug target against inflammatory disorders. The present study is aimed at identifying the amino acids crucial in effective inhibitor binding at the mPGES-1 active site by performing molecular dynamics based studies on a series of 7-Phenyl-imidazoquinolin-4(5H)-one derivatives. Molecular dynamics (MD) simulations, MM-PBSA, per-residue energy decomposition and Dimensionality Reduction through Covariance matrix Transformation for Identification of Differences in dynamics (DIRECT-ID) analysis were performed to get insights into the structural details that can aid in novel drug design against mPGES-1. The high correlations of electrostatic and polar energy terms with biological activity highlight their importance and applicability in in silico screening studies. Further, per-residue energy decomposition studies revealed that Lys42, Arg52, Arg122, Pro124, Ser127, Val128 and Thr131 were contributing more towards inhibitor binding energy. The results clearly show that MM-PBSA can act as a filter in virtual screening experiments and can play major role in facilitating various mPGES-1 drug discovery studies.

Adventures with RNA graphs

The structure of RNA has been a natural subject for mathematical modeling, inviting many innovative computational frameworks. This single-stranded polynucleotide chain can fold upon itself in numerous ways to form hydrogen-bonded segments, imperfect with single-stranded loops. Illustrating these paired and non-paired interaction networks, known as RNA's secondary (2D) structure, using mathematical graph objects has been illuminating for RNA structure analysis. Building upon such seminal work from the 1970s and 1980s, graph models are now used to study not only RNA structure but also describe RNA's recurring modular units, sample the conformational space accessible to RNAs, predict RNA's three-dimensional folds, and apply the combined aspects to novel RNA design. In this article, we outline the development of the RNA-As-Graphs (or RAG) approach and highlight current applications to RNA structure prediction and design.

Focused conformational sampling in proteins

A detailed understanding of the conformational dynamics of biological molecules is difficult to obtain by experimental techniques due to resolution limitations in both time and space. Computer simulations avoid these in theory but are often too short to sample rare events reliably. Here we show that the progress index-guided sampling (PIGS) protocol can be used to enhance the sampling of rare events in selected parts of biomolecules without perturbing the remainder of the system. The method is very easy to use as it only requires as essential input a set of several features representing the parts of interest sufficiently. In this feature space, new states are discovered by spontaneous fluctuations alone and in unsupervised fashion. Because there are no energetic biases acting on phase space variables or projections thereof, the trajectories PIGS generates can be analyzed directly in the framework of transition networks. We demonstrate the possibility and usefulness of such focused explorations of biomolecules with two loops that are part of the binding sites of bromodomains, a family of epigenetic "reader" modules. This real-life application uncovers states that are structurally and kinetically far away from the initial crystallographic structures and are also metastable. Representative conformations are intended to be used in future high-throughput virtual screening campaigns.

Effects of Peutz-Jeghers syndrome (PJS) causing missense mutations L67P, L182P, G242V and R297S on the structural dynamics of LKB1 (Liver kinase B1) protein

The liver kinase B1 (LKB1) is encoded by LKB1 gene. Several pathogenic mutations of LKB1 causing Peutz-Jeghers syndrome and also cancers in breast, gastric, pancreas, and colon have been reported. The present study is focused to analyze the effects on the structural dynamics of LKB1 caused by the 4 pathogenic missense mutations (L67P, L182P, G242V, and R297S), which are reported to reduce the catalytic activity. In this study, the structural changes of LKB1 in apo- and in heterotrimeric complex (LKB1-STRADα-MO25α) form with wild and mutated LKB1 are investigated using all atomistic molecular dynamic simulation. The present study reveals that these four mutations initiate local structural distortions and the solvent accessibility of the surrounding regions of ATP-binding pocket such as glycine-rich loop, αB and αC loop, activation and catalytic loops. The mutations of L67P, L182P, and G242 V induce distortions of the secondary structure of β1-β3 sheets, π - π interaction (observed between Phe204 of LKB1 and Phe243 of MO25α), and increase the helical properties (both helical twist and length) of the adjacent αH-helix, respectively. The active kinase features like the conformation of catalytic and activation loops, salt bridge and, finally, the formation of stable R- and C-hydrophobic spines are also found to be perturbed by these mutations. Hence, the observed mutation-induced structural distortions fail to coordinate the essential binding nature of LKB1 with STRADα and MO25α, which eventually affects the native function of LKB1. These observations are in line with the experimentally reported reduced kinase activity of LKB1.

FAST UPDATING MULTIPOLE COULOMBIC POTENTIAL CALCULATION

We present a numerical method to efficiently and accurately re-compute the Coulomb potential of a large ensemble of charged particles after a subset of the particles undergoes a change of position. Errors are bounded even after a large number of such shifts, making it practical for use in Monte Carlo Markov chain methods in molecular dynamics, computational astrophysics, computational chemistry, and other applications. The method uses truncated multipole expansions of the potential energy functional and a tree decomposition of the computational domain to reduce the computational complexity. Computational costs scale logarithmically in the size of the problem. Scaling, accuracy, and efficiency are confirmed with numerical experiments. The new method outperforms a direct calculation for moderate problem sizes.

Understanding ligand-receptor non-covalent binding kinetics using molecular modeling

Kinetic properties may serve as critical differentiators and predictors of drug efficacy and safety, in addition to the traditionally focused binding affinity. However the quantitative structure-kinetics relationship (QSKR) for modeling and ligand design is still poorly understood. This review provides an introduction to the kinetics of drug binding from a fundamental chemistry perspective. We focus on recent developments of computational tools and their applications to non-covalent binding kinetics.

Partially Assembled Nucleosome Structures at Atomic Detail

The evidence is now overwhelming that partially assembled nucleosome states (PANS) are as important as the canonical nucleosome structure for the understanding of how accessibility to genomic DNA is regulated in cells. We use a combination of molecular dynamics simulation and atomic force microscopy to deliver, in atomic detail, structural models of three key PANS: the hexasome (H2A·H2B)·(H3·H4)₂, the tetrasome (H3·H4)₂, and the disome (H3·H4). Despite fluctuations of the conformation of the free DNA in these structures, regions of protected DNA in close contact with the histone core remain stable, thus establishing the basis for the understanding of the role of PANS in DNA accessibility regulation. On average, the length of protected DNA in each structure is roughly 18 basepairs per histone protein. Atomistically detailed PANS are used to explain experimental observations; specifically, we discuss interpretation of atomic force microscopy, Förster resonance energy transfer, and small-angle x-ray scattering data obtained under conditions when PANS are expected to exist. Further, we suggest an alternative interpretation of a recent genome-wide study of DNA protection in active chromatin of fruit fly, leading to a conclusion that the three PANS are present in actively transcribing regions in a substantial amount. The presence of PANS may not only be a consequence, but also a prerequisite for fast transcription in vivo.

Structural Determination of a DNA Oligomer for a Molecular Spin Qubit Lloyd Model of Quantum Computers

The global molecular and local spin-site structures of a DNA duplex 22-oligomer with site-directed four spin-labeling were simulated by molecular mechanics (MM) calculations combined with Q-band pulsed electron-electron double resonance (PELDOR) spectroscopy. This molecular-spin bearing DNA oligomer is designed to give a complex testing ground for the structural determination of molecular spins incorporated in the DNA duplex, which serves as a platform for 1D periodic arrays of two or three non-equivalent electron spin qubit systems, (AB)n or (ABC)n, respectively, enabling to execute quantum computing or quantum information processing (Lloyd model of electron spin versions): A, B and C designate non-equivalent addressable spin qubits for quantum operations. The non-equivalence originates in difference in the electronic g-tensor. It is not feasible to determine the optimal structures for such DNA oligomers having molecular flexibility only by the MM calculations because there are many local minima in energy for their possible molecular structures. The spin-distance information derived from the PELDOR spectroscopy helps determine the optimal structures out of the possible ones acquired by the MM calculations. Based on the MM searched structures, we suggest the optimal structures for semi-macromolecules having site-directed multi-spin qubits. We emphasize that for our four molecular spins embedded in the DNA oligomer the Fajer’s error analysis in PELDOR-based distance measurements was of essential importance.

Accuracy limit of rigid 3-point water models

Classical 3-point rigid water models are most widely used due to their computational efficiency. Recently, we introduced a new approach to constructing classical rigid water models [S. Izadi et al., J. Phys. Chem. Lett. 5, 3863 (2014)], which permits a virtually exhaustive search for globally optimal model parameters in the sub-space that is most relevant to the electrostatic properties of the water molecule in liquid phase. Here we apply the approach to develop a 3-point Optimal Point Charge (OPC3) water model. OPC3 is significantly more accurate than the commonly used water models of same class (TIP3P and SPCE) in reproducing a comprehensive set of liquid bulk properties, over a wide range of temperatures. Beyond bulk properties, we show that OPC3 predicts the intrinsic charge hydration asymmetry (CHA) of water - a characteristic dependence of hydration free energy on the sign of the solute charge - in very close agreement with experiment. Two other recent 3-point rigid water models, TIP3PFB and H2ODC, each developed by its own, completely different optimization method, approach the global accuracy optimum represented by OPC3 in both the parameter space and accuracy of bulk properties. Thus, we argue that an accuracy limit of practical 3-point rigid non-polarizable models has effectively been reached; remaining accuracy issues are discussed.

All-atom/coarse-grained hybrid predictions of distribution coefficients in SAMPL5

We present blind predictions submitted to the SAMPL5 challenge on calculating distribution coefficients. The predictions were based on estimating the solvation free energies in water and cyclohexane of the 53 compounds in the challenge. These free energies were computed using alchemical free energy simulations based on a hybrid all-atom/coarse-grained model. The compounds were treated with the general Amber force field, whereas the solvent molecules were treated with the Elba coarse-grained model. Considering the simplicity of the solvent model and that we approximate the distribution coefficient with the partition coefficient of the neutral species, the predictions are of good accuracy. The correlation coefficient, R is 0.64, 82 % of the predictions have the correct sign and the mean absolute deviation is 1.8 log units. This is on a par with or better than the other simulation-based predictions in the challenge. We present an analysis of the deviations to experiments and compare the predictions to another submission that used all-atom solvent.

Insertion of oxidized nucleotide triggers rapid DNA polymerase opening

A novel mechanism is unveiled to explain why a pro-mutagenic nucleotide lesion (oxidized guanine, 8-oxoG) causes the mammalian DNA repair polymerase-β (pol-β) to rapidly transition to an inactive open conformation. The mechanism involves unexpected features revealed recently in time-lapse crystallography. Specifically, a delicate water network associated with a lesion-stabilizing auxilliary product ion Mg(p) triggers a cascade of events that leads to poor active site geometry and the rupture of crucial molecular interactions between key residues in both the anti(8-oxoG:C) and syn(8-oxoG:A) systems. Once the base pairs in these lesioned systems are broken, dislocation of both Asp192 (a metal coordinating ligand) and the oxoG phosphate group (PO₄) interfere with the hydrogen bonding between Asp192 and Arg258, whose rotation toward Asp192 is crucial to the closed-to-open enzyme transition. Energetically, the lesioned open states are similar in energy to those of the corresponding closed complexes after chemistry, in marked contrast to the unlesioned pol-β anti(G:C) system, whose open state is energetically higher than the closed state. The delicate surveillance system offers a fundamental protective mechanism in the cell that triggers DNA repair events which help deter insertion of oxidized lesions.

Molecular dynamics characterization of the conformational landscape of small peptides: A series of hands-on collaborative practical sessions for undergraduate students

Molecular modelling and simulations are nowadays an integral part of research in areas ranging from physics to chemistry to structural biology, as well as pharmaceutical drug design. This popularity is due to the development of high-performance hardware and of accurate and efficient molecular mechanics algorithms by the scientific community. These improvements are also benefitting scientific education. Molecular simulations, their underlying theory, and their applications are particularly difficult to grasp for undergraduate students. Having hands-on experience with the methods contributes to a better understanding and solidification of the concepts taught during the lectures. To this end, we have created a computer practical class, which has been running for the past five years, composed of several sessions where students characterize the conformational landscape of small peptides using molecular dynamics simulations in order to gain insights on their binding to protein receptors. In this report, we detail the ingredients and recipe necessary to establish and carry out this practical, as well as some of the questions posed to the students and their expected results. Further, we cite some examples of the students' written reports, provide statistics, and share their feedbacks on the structure and execution of the sessions. These sessions were implemented alongside a theoretical molecular modelling course but have also been used successfully as a standalone tutorial during specialized workshops. The availability of the material on our web page also facilitates this integration and dissemination and lends strength to the thesis of open-source science and education.

Comparing pharmacophore models derived from crystal structures and from molecular dynamics simulations

ABSTRACT

Pharmacophore modeling is a widely used technique in computer-aided drug discovery. Structure-based pharmacophore models of a ligand in complex with a protein have proven to be useful for supporting in silico hit discovery, hit to lead expansion, and lead optimization. As a structure-based approach it depends on the correct interpretation of ligand-protein interactions. There are legitimate concerns about the fidelity of the bound ligand and about non-physiological contacts with parts of the crystal and the solvent effects that influence the protein structure. A possible way to refine the structure of a protein-ligand system is to use the final structure of a given MD simulation. In this study we compare pharmacophore models built using the initial protein-ligand structure obtained from the protein data bank (PDB) with pharmacophore models built with the final structure of a molecular dynamics simulation. We show that the pharmacophore models differ in feature number and feature type and that the pharmacophore models built from the last structure of a MD simulation shows in some cases better ability to distinguish between active and decoy ligand structures.

GRAPHICAL ABSTRACT

Speed of conformational change: comparing explicit and implicit solvent molecular dynamics simulations

Adequate sampling of conformation space remains challenging in atomistic simulations, especially if the solvent is treated explicitly. Implicit-solvent simulations can speed up conformational sampling significantly. We compare the speed of conformational sampling between two commonly used methods of each class: the explicit-solvent particle mesh Ewald (PME) with TIP3P water model and a popular generalized Born (GB) implicit-solvent model, as implemented in the AMBER package. We systematically investigate small (dihedral angle flips in a protein), large (nucleosome tail collapse and DNA unwrapping), and mixed (folding of a miniprotein) conformational changes, with nominal simulation times ranging from nanoseconds to microseconds depending on system size. The speedups in conformational sampling for GB relative to PME simulations, are highly system- and problem-dependent. Where the simulation temperatures for PME and GB are the same, the corresponding speedups are approximately onefold (small conformational changes), between ∼1- and ∼100-fold (large changes), and approximately sevenfold (mixed case). The effects of temperature on speedup and free-energy landscapes, which may differ substantially between the solvent models, are discussed in detail for the case of miniprotein folding. In addition to speeding up conformational sampling, due to algorithmic differences, the implicit solvent model can be computationally faster for small systems or slower for large systems, depending on the number of solute and solvent atoms. For the conformational changes considered here, the combined speedups are approximately twofold, ∼1- to 60-fold, and ∼50-fold, respectively, in the low solvent viscosity regime afforded by the implicit solvent. For all the systems studied, 1) conformational sampling speedup increases as Langevin collision frequency (effective viscosity) decreases; and 2) conformational sampling speedup is mainly due to reduction in solvent viscosity rather than possible differences in free-energy landscapes between the solvent models.

SimRNA: a coarse-grained method for RNA folding simulations and 3D structure prediction

RNA molecules play fundamental roles in cellular processes. Their function and interactions with other biomolecules are dependent on the ability to form complex three-dimensional (3D) structures. However, experimental determination of RNA 3D structures is laborious and challenging, and therefore, the majority of known RNAs remain structurally uncharacterized. Here, we present SimRNA: a new method for computational RNA 3D structure prediction, which uses a coarse-grained representation, relies on the Monte Carlo method for sampling the conformational space, and employs a statistical potential to approximate the energy and identify conformations that correspond to biologically relevant structures. SimRNA can fold RNA molecules using only sequence information, and, on established test sequences, it recapitulates secondary structure with high accuracy, including correct prediction of pseudoknots. For modeling of complex 3D structures, it can use additional restraints, derived from experimental or computational analyses, including information about secondary structure and/or long-range contacts. SimRNA also can be used to analyze conformational landscapes and identify potential alternative structures.

The chromatin fiber: multiscale problems and approaches

The structure of chromatin, affected by many factors from DNA linker lengths to posttranslational modifications, is crucial to the regulation of eukaryotic cells. Combined experimental and computational methods have led to new insights into its structural and dynamical features, from interactions due to the flexible core histone tails or linker histones to the physical mechanism driving the formation of chromosomal domains. Here we present a perspective of recent advances in chromatin modeling techniques at the atomic, mesoscopic, and chromosomal scales with a view toward developing multiscale computational strategies to integrate such findings. Innovative modeling methods that connect molecular to chromosomal scales are crucial for interpreting experiments and eventually deciphering the complex dynamic organization and function of chromatin in the cell.

Boundary condition effects on the dynamic and electric properties of hydration layers

Water solvation has a central role in several biochemical processes ranging from protein folding to biomolecular recognition and enzyme catalysis. Because of its importance, the structure and dynamics of hydration layers around biological macromolecules have been the targets of a great number of experimental and computational studies. In the present contribution, we have investigated the effects of periodic boundary conditions (PBCs), as used in conjunction with molecular dynamics (MD) simulations, on the dynamic and electric properties of water layers. In particular, we have systematically performed MD simulations of neat water and biomolecules in aqueous solutions by imposing a different external dielectric constant, a generally overlooked parameter in PBC simulations. The effect of the system size has also been addressed. Overall, our results consistently indicate that the dipole moment properties of water layers, and specifically the dipole moment fluctuations and the reorientational correlation functions, can be sensitive to the choice of the external boundary conditions, whereas other molecular properties, such as the self-diffusion coefficient and the reorientational relaxation times, are not affected. We think that our investigation may help to assess appropriate simulation conditions for modeling the aqueous environment of relevant biochemical systems and processes.