Using the Maximum Entropy Principle to Combine Simulations and Solution Experiments

Comprehensive Comparison and Critical Assessment of RNA-Specific Force Fields

Molecular dynamics simulations play a pivotal role in elucidating the dynamic behaviors of RNA structures, offering a valuable complement to traditional methods such as nuclear magnetic resonance or X-ray. Despite this, the current precision of RNA force fields lags behind that of protein force fields. In this work, we systematically compared the performance of four RNA force fields (ff99bsc0χOL3, AMBERDES, ff99OL3_CMAP1, AMBERMaxEnt) across diverse RNA structures. Our findings highlight significant challenges in maintaining stability, particularly with regard to cross-strand and cross-loop hydrogen bonds. Furthermore, we observed the limitations in accurately describing the conformations of nonhelical structural motif, terminal nucleotides, and also base pairing and base stacking interactions by the tested RNA force fields. The identified deficiencies in existing RNA force fields provide valuable insights for subsequent force field development. Concurrently, these findings offer recommendations for selecting appropriate force fields in RNA simulations.

Boosting Ensemble Refinement with Transferable Force-Field Corrections: Synergistic Optimization for Molecular Simulations

A novel method combining the force-field fitting approach and ensemble refinement by the maximum entropy principle is presented. Its formulation allows us to continuously interpolate between these two methods, which can thus be interpreted as two limiting cases. A cross-validation procedure enables us to correctly assess the relative weight of both of them, distinguishing scenarios in which the combined approach is meaningful from those in which either ensemble refinement or force-field fitting separately prevails. The efficacy of their combination is examined for a realistic case study of RNA oligomers. Within the new scheme, molecular dynamics simulations are integrated with experimental data provided by nuclear magnetic resonance measures. We show that force-field corrections are in general superior when applied to the appropriate force-field terms but are automatically discarded by the method when applied to inappropriate force-field terms.

Bonds and bytes: The odyssey of structural biology

Characterizing structural and dynamic properties of proteins and large macromolecular assemblies is crucial to understand the molecular mechanisms underlying biological functions. In the field of structural biology, no single method comprehensively reveals the behavior of biological systems across various spatiotemporal scales. Instead, we have a versatile toolkit of techniques, each contributing a piece to the overall puzzle. Integrative structural biology combines different techniques to create accurate and precise multi-scale models that expand our understanding of complex biological systems. This review outlines recent advancements in computational and experimental methods in structural biology, with special focus on recent Artificial Intelligence techniques, emphasizes integrative approaches that combine different types of data for precise spatiotemporal modeling, and provides an outlook into future directions of this field.

Cryo-electron Microscopy and Molecular Modeling Methods to Characterize the Dynamics of Tau Bound to Microtubules

The electron microscopy metainference integrative structural biology method enables the combination of cryo-electron microscopy electron density maps with molecular modeling techniques such as molecular dynamics to unveil the atomistic biomolecular structural ensemble and the error in the map data in an efficient manner. Here we illustrate the electron microscopy metainference protocol and analysis used to elucidate the atomistic structural ensemble of the microtubule-associated protein tau bound to microtubules by using state-of-the-art molecular mechanic force field and the electron density map.

Large-scale data-driven and physics-based models offer insights into the relationships among the structures, dynamics, and functions of chromosomes

The organized three-dimensional chromosome architecture in the cell nucleus provides scaffolding for precise regulation of gene expression. When the cell changes its identity in the cell-fate decision-making process, extensive rearrangements of chromosome structures occur accompanied by large-scale adaptations of gene expression, underscoring the importance of chromosome dynamics in shaping genome function. Over the last two decades, rapid development of experimental methods has provided unprecedented data to characterize the hierarchical structures and dynamic properties of chromosomes. In parallel, these enormous data offer valuable opportunities for developing quantitative computational models. Here, we review a variety of large-scale polymer models developed to investigate the structures and dynamics of chromosomes. Different from the underlying modeling strategies, these approaches can be classified into data-driven ('top-down') and physics-based ('bottom-up') categories. We discuss their contributions to offering valuable insights into the relationships among the structures, dynamics, and functions of chromosomes and propose the perspective of developing data integration approaches from different experimental technologies and multidisciplinary theoretical/simulation methods combined with different modeling strategies.

Quantifying the large-scale chromosome structural dynamics during the mitosis-to-G1 phase transition of cell cycle

Cell cycle is known to be regulated by the underlying gene network. Chromosomes, which serve as the scaffold for gene expressions, undergo significant structural reorganizations during mitosis. Understanding the mechanism of the cell cycle from the chromosome structural perspective remains a grand challenge. In this study, we applied an integrated theoretical approach to investigate large-scale chromosome structural dynamics during the mitosis-to-G1 phase transition. We observed that the chromosome structural expansion and adaptation of the structural asphericity do not occur synchronously and attributed this behaviour to the unique unloading sequence of the two types of condensins. Furthermore, we observed that the coherent motions between the chromosomal loci are primarily enhanced within the topologically associating domains (TADs) as cells progress to the G1 phase, suggesting that TADs can be considered as both structural and dynamical units for organizing the three-dimensional chromosome. Our analysis also reveals that the quantified pathways of chromosome structural reorganization during the mitosis-to-G1 phase transition exhibit high stochasticity at the single-cell level and show nonlinear behaviours in changing TADs and contacts formed at the long-range regions. Our findings offer valuable insights into large-scale chromosome structural dynamics after mitosis.

Determination of the Structure and Dynamics of the Fuzzy Coat of an Amyloid Fibril of IAPP Using Cryo-Electron Microscopy

In recent years, major advances in cryo-electron microscopy (cryo-EM) have enabled the routine determination of complex biomolecular structures at atomistic resolution. An open challenge for this approach, however, concerns large systems that exhibit continuous dynamics. To address this problem, we developed the metadynamic electron microscopy metainference (MEMMI) method, which incorporates metadynamics, an enhanced conformational sampling approach, into the metainference method of integrative structural biology. MEMMI enables the simultaneous determination of the structure and dynamics of large heterogeneous systems by combining cryo-EM density maps with prior information through molecular dynamics, while at the same time modeling the different sources of error. To illustrate the method, we apply it to elucidate the dynamics of an amyloid fibril of the islet amyloid polypeptide (IAPP). The resulting conformational ensemble provides an accurate description of the structural variability of the disordered region of the amyloid fibril, known as fuzzy coat. The conformational ensemble also reveals that in nearly half of the structural core of this amyloid fibril, the side chains exhibit liquid-like dynamics despite the presence of the highly ordered network backbone of hydrogen bonds characteristic of the cross-β structure of amyloid fibrils.

Insights into the cell fate decision-making processes from chromosome structural reorganizations

The cell fate decision-making process, which provides the capability of a cell transition to a new cell type, involves the reorganizations of 3D genome structures. Currently, the high temporal resolution picture of how the chromosome structural rearrangements occur and further influence the gene activities during the cell-state transition is still challenging to acquire. Here, we study the chromosome structural reorganizations during the cell-state transitions among the pluripotent embryonic stem cell, the terminally differentiated normal cell, and the cancer cell using a nonequilibrium landscape-switching model implemented in the molecular dynamics simulation. We quantify the chromosome (de)compaction pathways during the cell-state transitions and find that the two pathways having the same destinations can merge prior to reaching the final states. The chromosomes at the merging states have similar structural geometries but can differ in long-range compartment segregation and spatial distribution of the chromosomal loci and genes, leading to cell-type-specific transition mechanisms. We identify the irreversible pathways of chromosome structural rearrangements during the forward and reverse transitions connecting the same pair of cell states, underscoring the critical roles of nonequilibrium dynamics in the cell-state transitions. Our results contribute to the understanding of the cell fate decision-making processes from the chromosome structural perspective.

Reweighting methods for elucidation of conformation ensembles of proteins

Proteins are inherently dynamic macromolecules that exist in equilibrium among multiple conformational states, and motions of protein backbone and side chains are fundamental to biological function. The ability to characterize the conformational landscape is particularly important for intrinsically disordered proteins, multidomain proteins, and weakly bound complexes, where single-structure representations are inadequate. As the focus of structural biology shifts from relatively rigid macromolecules toward larger and more complex systems and molecular assemblies, there is a need for structural approaches that can paint a more realistic picture of such conformationally heterogeneous systems. Here, we review reweighting methods for elucidation of structural ensembles based on experimental data, with the focus on applications to multidomain proteins.

Structure and ensemble refinement against SAXS data: Combining MD simulations with Bayesian inference or with the maximum entropy principle

Small-angle X-ray scattering (SAXS) is a powerful method for tracking conformational transitions of proteins or soft-matter complexes in solution. However, the interpretation of the experimental data is challenged by the low spatial resolution and the low information content of the data, which lead to a high risk of overinterpreting the data. Here, we illustrate how SAXS data can be integrated into all-atom molecular dynamics (MD) simulation to derive atomic structures or heterogeneous ensembles that are compatible with the data. Besides providing atomistic insight, the MD simulation adds physicochemical information, as encoded in the MD force fields, which greatly reduces the risk of overinterpretation. We present an introduction into the theory of SAXS-driven MD simulations as implemented in GROMACS-SWAXS, a modified version of the GROMACS simulation software. We discuss SAXS-driven parallel-replica ensemble refinement with commitment to the maximum entropy principle as well as a Bayesian formulation of SAXS-driven structure refinement. Practical considerations for running and interpreting the simulations are presented. The methods are freely available via GitLab at https://gitlab.com/cbjh/gromacs-swaxs.

Biomotors, viral assembly, and RNA nanobiotechnology: Current achievements and future directions

The International Society of RNA Nanotechnology and Nanomedicine (ISRNN) serves to further the development of a wide variety of functional nucleic acids and other related nanotechnology platforms. To aid in the dissemination of the most recent advancements, a biennial discussion focused on biomotors, viral assembly, and RNA nanobiotechnology has been established where international experts in interdisciplinary fields such as structural biology, biophysical chemistry, nanotechnology, cell and cancer biology, and pharmacology share their latest accomplishments and future perspectives. The results summarized here highlight advancements in our understanding of viral biology and the structure-function relationship of frame-shifting elements in genomic viral RNA, improvements in the predictions of SHAPE analysis of 3D RNA structures, and the understanding of dynamic RNA structures through a variety of experimental and computational means. Additionally, recent advances in the drug delivery, vaccine design, nanopore technologies, biomotor and biomachine development, DNA packaging, RNA nanotechnology, and drug delivery are included in this critical review. We emphasize some of the novel accomplishments, major discussion topics, and present current challenges and perspectives of these emerging fields.

Small molecules targeting the disordered transactivation domain of the androgen receptor induce the formation of collapsed helical states

Intrinsically disordered proteins, which do not adopt well-defined structures under physiological conditions, are implicated in many human diseases. Small molecules that target the disordered transactivation domain of the androgen receptor have entered human trials for the treatment of castration-resistant prostate cancer (CRPC), but no structural or mechanistic rationale exists to explain their inhibition mechanisms or relative potencies. Here, we utilize all-atom molecular dynamics computer simulations to elucidate atomically detailed binding mechanisms of the compounds EPI-002 and EPI-7170 to the androgen receptor. Our simulations reveal that both compounds bind at the interface of two transiently helical regions and induce the formation of partially folded collapsed helical states. We find that EPI-7170 binds androgen receptor more tightly than EPI-002 and we identify a network of intermolecular interactions that drives higher affinity binding. Our results suggest strategies for developing more potent androgen receptor inhibitors and general strategies for disordered protein drug design.

Quantifying Chromosome Structural Reorganizations during Differentiation, Reprogramming, and Transdifferentiation

We developed a nonequilibrium model to study chromosome structural reorganizations within a simplified cell developmental system. From the chromosome structural perspective, we predicted that the neural progenitor cell is on the neural developmental path and very close to the transdifferentiation path from the fibroblast to the neuron cell. We identified an early bifurcation of stem cell differentiation processes and the cell-of-origin-specific reprogramming pathways. Our theoretical results are in good agreement with available experimental evidence, promoting future applications of our approach.

Heterogeneous interactions and polymer entropy decide organization and dynamics of chromatin domains

Chromatin is known to be organized into multiple domains of varying sizes and compaction. While these domains are often imagined as static structures, they are highly dynamic and show cell-to-cell variability. Since processes such as gene regulation and DNA replication occur in the context of these domains, it is important to understand their organization, fluctuation, and dynamics. To simulate chromatin domains, one requires knowledge of interaction strengths among chromatin segments. Here, we derive interaction-strength parameters from experimentally known contact maps and use them to predict chromatin organization and dynamics. Taking two domains on the human chromosome as examples, we investigate its three-dimensional organization, size/shape fluctuations, and dynamics of different segments within a domain, accounting for hydrodynamic effects. Considering different cell types, we quantify changes in interaction strengths and chromatin shape fluctuations in different epigenetic states. Perturbing the interaction strengths systematically, we further investigate how epigenetic-like changes can alter the spatio-temporal nature of the domains. Our results show that heterogeneous weak interactions are crucial in determining the organization of the domains. Computing effective stiffness and relaxation times, we investigate how perturbations in interactions affect the solid- and liquid-like nature of chromatin domains. Quantifying dynamics of chromatin segments within a domain, we show how the competition between polymer entropy and interaction energy influence the timescales of loop formation and maintenance of stable loops.

Uncovering the statistical physics of 3D chromosomal organization using data-driven modeling

In recent years, much effort has been devoted to understanding the three-dimensional (3D) organization of the genome and how genomic structure mediates nuclear function. The development of experimental techniques that combine DNA proximity ligation with high-throughput sequencing, such as Hi-C, have substantially improved our knowledge about chromatin organization. Numerous experimental advancements, not only utilizing DNA proximity ligation but also high-resolution genome imaging (DNA tracing), have required theoretical modeling to determine the structural ensembles consistent with such data. These 3D polymer models of the genome provide an understanding of the physical mechanisms governing genome architecture. Here, we present an overview of the recent advances in modeling the ensemble of 3D chromosomal structures by employing the maximum entropy approach combined with polymer physics. Particularly, we discuss the minimal chromatin model (MiChroM) along with the "maximum entropy genomic annotations from biomarkers associated with structural ensembles" (MEGABASE) model, which have been remarkably successful in the accurate modeling of chromosomes consistent with both Hi-C and DNA-tracing data.

Inferring spatial source of disease outbreaks using maximum entropy

Mathematical modeling of disease outbreaks can infer the future trajectory of an epidemic, allowing for making more informed policy decisions. Another task is inferring the origin of a disease, which is relatively difficult with current mathematical models. Such frameworks, across varying levels of complexity, are typically sensitive to input data on epidemic parameters, case counts, and mortality rates, which are generally noisy and incomplete. To alleviate these limitations, we propose a maximum entropy framework that fits epidemiological models, provides calibrated infection origin probabilities, and is robust to noise due to a prior belief model. Maximum entropy is agnostic to the parameters or model structure used and allows for flexible use when faced with sparse data conditions and incomplete knowledge in the dynamical phase of disease-spread, providing for more reliable modeling at early stages of outbreaks. We evaluate the performance of our model by predicting future disease trajectories based on simulated epidemiological data in synthetic graph networks and the real mobility network of New York State. In addition, unlike existing approaches, we demonstrate that the method can be used to infer the origin of the outbreak with accurate confidence. Indeed, despite the prevalent belief on the feasibility of contact-tracing being limited to the initial stages of an outbreak, we report the possibility of reconstructing early disease dynamics, including the epidemic seed, at advanced stages.

Automatic Learning of Hydrogen-Bond Fixes in the AMBER RNA Force Field

The capability of current force fields to reproduce RNA structural dynamics is limited. Several methods have been developed to take advantage of experimental data in order to enforce agreement with experiments. Here, we extend an existing framework which allows arbitrarily chosen force-field correction terms to be fitted by quantification of the discrepancy between observables back-calculated from simulation and corresponding experiments. We apply a robust regularization protocol to avoid overfitting and additionally introduce and compare a number of different regularization strategies, namely, L1, L2, Kish size, relative Kish size, and relative entropy penalties. The training set includes a GACC tetramer as well as more challenging systems, namely, gcGAGAgc and gcUUCGgc RNA tetraloops. Specific intramolecular hydrogen bonds in the AMBER RNA force field are corrected with automatically determined parameters that we call gHBfix_opt. A validation involving a separate simulation of a system present in the training set (gcUUCGgc) and new systems not seen during training (CAAU and UUUU tetramers) displays improvements regarding the native population of the tetraloop as well as good agreement with NMR experiments for tetramers when using the new parameters. Then, we simulate folded RNAs (a kink–turn and L1 stalk rRNA) including hydrogen bond types not sufficiently present in the training set. This allows a final modification of the parameter set which is named gHBfix21 and is suggested to be applicable to a wider range of RNA systems.

Maximum Entropy Technique and Regularization Functional for Determining the Pharmacokinetic Parameters in DCE-MRI

This paper aims to solve the arterial input function (AIF) determination in dynamic contrast-enhanced MRI (DCE-MRI), an important linear ill-posed inverse problem, using the maximum entropy technique (MET) and regularization functionals. In addition, estimating the pharmacokinetic parameters from a DCE-MR image investigations is an urgent need to obtain the precise information about the AIF-the concentration of the contrast agent on the left ventricular blood pool measured over time. For this reason, the main idea is to show how to find a unique solution of linear system of equations generally in the form of [Formula: see text] named an ill-conditioned linear system of equations after discretization of the integral equations, which appear in different tomographic image restoration and reconstruction issues. Here, a new algorithm is described to estimate an appropriate probability distribution function for AIF according to the MET and regularization functionals for the contrast agent concentration when applying Bayesian estimation approach to estimate two different pharmacokinetic parameters. Moreover, by using the proposed approach when analyzing simulated and real datasets of the breast tumors according to pharmacokinetic factors, it indicates that using Bayesian inference-that infer the uncertainties of the computed solutions, and specific knowledge of the noise and errors-combined with the regularization functional of the maximum entropy problem, improved the convergence behavior and led to more consistent morphological and functional statistics and results. Finally, in comparison to the proposed exponential distribution based on MET and Newton's method, or Weibull distribution via the MET and teaching-learning-based optimization (MET/TLBO) in the previous studies, the family of Gamma and Erlang distributions estimated by the new algorithm are more appropriate and robust AIFs.

Simulation-based inference with approximately correct parameters via maximum entropy

Inferring the input parameters of simulators from observations is a crucial challenge with applications from epidemiology to molecular dynamics. Here we show a simple approach in the regime of sparse data and approximately correct models, which is common when trying to use an existing model to infer latent variables with observed data. This approach is based on the principle of maximum entropy (MaxEnt) and provably makes the smallest change in the latent joint distribution to fit new data. This method requires no likelihood or model derivatives and its fit is insensitive to prior strength, removing the need to balance observed data fit with prior belief. The method requires the ansatz that data is fit in expectation, which is true in some settings and may be reasonable in all settings with few data points. The method is based on sample reweighting, so its asymptotic run time is independent of prior distribution dimension. We demonstrate this MaxEnt approach and compare with other likelihood-free inference methods across three systems: a point particle moving in a gravitational field, a compartmental model of epidemic spread and molecular dynamics simulation of a protein.

Collective Variables for Free Energy Surface Tailoring: Understanding and Modifying Functionality in Systems Dominated by Rare Events

We introduce a method for elucidating and modifying the functionality of systems dominated by rare events that relies on the semiautomated tuning of their underlying free energy surface. The proposed approach seeks to construct collective variables (CVs) that encode the essential information regarding the rare events of the system of interest. The appropriate CVs are identified using harmonic linear discriminant analysis (HLDA), a machine-learning-based method that is trained solely on data collected from short ordinary simulations in the relevant metastable states of the system. Utilizing the interpretable form of the resulting CVs, the critical interaction potentials that determine the system's rare transitions are identified and purposely modified to tailor the free energy surface in a manner that alters functionality as desired. The applicability of the method is illustrated in the context of three different systems, thereby demonstrating that thermodynamic and kinetic properties can be tractably modified with little to no prior knowledge or intuition.

Dynamics and Pathways of Chromosome Structural Organizations during Cell Transdifferentiation

Direct conversion of one differentiated cell type into another is defined as cell transdifferentiation. In avoidance of forming pluripotency, cell transdifferentiation can reduce the potential risk of tumorigenicity, thus offering significant advantages over cell reprogramming in clinical applications. Until now, the mechanism of cell transdifferentiation is still largely unknown. It has been well recognized that cell transdifferentiation is determined by the underlying gene expression regulation, which relies on the accurate adaptation of the chromosome structure. To dissect the transdifferentiation at the molecular level, we develop a nonequilibrium landscape-switching model to investigate the chromosome structural dynamics during the state transitions between the human fibroblast and neuron cells. We uncover the high irreversibility of the transdifferentiation at the local chromosome structural ranges, where the topologically associating domains form. In contrast, the pathways in the two opposite directions of the transdifferentiation projected onto the chromosome compartment profiles are highly overlapped, indicating that the reversibility vanishes at the long-range chromosome structures. By calculating the contact strengths in the chromosome at the states along the paths, we observe strengthening contacts in compartment A concomitant with weakening contacts in compartment B at the early stages of the transdifferentiation. This further leads to adapting contacts toward the ones at the embryonic stem cell. In light of the intimate structure-function relationship at the chromosomal level, we suggest an increase of "stemness" during the transdifferentiation. In addition, we find that the neuron progenitor cell (NPC), a cell developmental state, is located on the transdifferentiation pathways projected onto the long-range chromosome contacts. The findings are consistent with the previous single-cell RNA sequencing experiment, where the NPC-like cell states were observed during the direct conversion of the fibroblast to neuron cells. Thus, we offer a promising microscopic and physical approach to study the cell transdifferentiation mechanism from the chromosome structural perspective.

Modified Maximum Entropy Method and Estimating the AIF via DCE-MRI Data Analysis

Background: For the kinetic models used in contrast-based medical imaging, the assignment of the arterial input function named AIF is essential for the estimation of the physiological parameters of the tissue via solving an optimization problem. Objective: In the current study, we estimate the AIF relayed on the modified maximum entropy method. The effectiveness of several numerical methods to determine kinetic parameters and the AIF is evaluated—in situations where enough information about the AIF is not available. The purpose of this study is to identify an appropriate method for estimating this function. Materials and Methods: The modified algorithm is a mixture of the maximum entropy approach with an optimization method, named the teaching-learning method. In here, we applied this algorithm in a Bayesian framework to estimate the kinetic parameters when specifying the unique form of the AIF by the maximum entropy method. We assessed the proficiency of the proposed method for assigning the kinetic parameters in the dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI), when determining AIF with some other parameter-estimation methods and a standard fixed AIF method. A previously analyzed dataset consisting of contrast agent concentrations in tissue and plasma was used. Results and Conclusions: We compared the accuracy of the results for the estimated parameters obtained from the MMEM with those of the empirical method, maximum likelihood method, moment matching (“method of moments”), the least-square method, the modified maximum likelihood approach, and our previous work. Since the current algorithm does not have the problem of starting point in the parameter estimation phase, it could find the best and nearest model to the empirical model of data, and therefore, the results indicated the Weibull distribution as an appropriate and robust AIF and also illustrated the power and effectiveness of the proposed method to estimate the kinetic parameters.

Refining conformational ensembles of flexible proteins against small-angle x-ray scattering data

Intrinsically disordered proteins and flexible regions in multidomain proteins display substantial conformational heterogeneity. Characterizing the conformational ensembles of these proteins in solution typically requires combining one or more biophysical techniques with computational modeling or simulations. Experimental data can either be used to assess the accuracy of a computational model or to refine the computational model to get a better agreement with the experimental data. In both cases, one generally needs a so-called forward model (i.e., an algorithm to calculate experimental observables from individual conformations or ensembles). In many cases, this involves one or more parameters that need to be set, and it is not always trivial to determine the optimal values or to understand the impact on the choice of parameters. For example, in the case of small-angle x-ray scattering (SAXS) experiments, many forward models include parameters that describe the contribution of the hydration layer and displaced solvent to the background-subtracted experimental data. Often, one also needs to fit a scale factor and a constant background for the SAXS data but across the entire ensemble. Here, we present a protocol to dissect the effect of the free parameters on the calculated SAXS intensities and to identify a reliable set of values. We have implemented this procedure in our Bayesian/maximum entropy framework for ensemble refinement and demonstrate the results on four intrinsically disordered proteins and a protein with three domains connected by flexible linkers. Our results show that the resulting ensembles can depend on the parameters used for solvent effects and suggest that these should be chosen carefully. We also find a set of parameters that work robustly across all proteins.

Deciphering the molecular mechanism of the cancer formation by chromosome structural dynamics

Cancer reflects the dysregulation of the underlying gene network, which is strongly related to the 3D genome organization. Numerous efforts have been spent on experimental characterizations of the structural alterations in cancer genomes. However, there is still a lack of genomic structural-level understanding of the temporal dynamics for cancer initiation and progression. Here, we use a landscape-switching model to investigate the chromosome structural transition during the cancerization and reversion processes. We find that the chromosome undergoes a non-monotonic structural shape-changing pathway with initial expansion followed by compaction during both of these processes. Furthermore, our analysis reveals that the chromosome with a more expanding structure than those at both the normal and cancer cell during cancerization exhibits a sparse contact pattern, which shows significant structural similarity to the one at the embryonic stem cell in many aspects, including the trend of contact probability declining with the genomic distance, the global structural shape geometry and the spatial distribution of loci on the chromosome. In light of the intimate structure-function relationship at the chromosomal level, we further describe the cell state transition processes by the chromosome structural changes, suggesting an elevated cell stemness during the formation of the cancer cells. We show that cell cancerization and reversion are highly irreversible processes in terms of the chromosome structural transition pathways, spatial repositioning of chromosomal loci and hysteresis loop of contact evolution analysis. Our model draws a molecular-scale picture of cell cancerization from the chromosome structural perspective. The process contains initial reprogramming towards the stem cell followed by the differentiation towards the cancer cell, accompanied by an initial increase and subsequent decrease of the cell stemness.

Reweighting of molecular simulations with explicit-solvent SAXS restraints elucidates ion-dependent RNA ensembles

Small-angle X-ray scattering (SAXS) experiments are increasingly used to probe RNA structure. A number of forward models that relate measured SAXS intensities and structural features, and that are suitable to model either explicit-solvent effects or solute dynamics, have been proposed in the past years. Here, we introduce an approach that integrates atomistic molecular dynamics simulations and SAXS experiments to reconstruct RNA structural ensembles while simultaneously accounting for both RNA conformational dynamics and explicit-solvent effects. Our protocol exploits SAXS pure-solute forward models and enhanced sampling methods to sample an heterogenous ensemble of structures, with no information towards the experiments provided on-the-fly. The generated structural ensemble is then reweighted through the maximum entropy principle so as to match reference SAXS experimental data at multiple ionic conditions. Importantly, accurate explicit-solvent forward models are used at this reweighting stage. We apply this framework to the GTPase-associated center, a relevant RNA molecule involved in protein translation, in order to elucidate its ion-dependent conformational ensembles. We show that (a) both solvent and dynamics are crucial to reproduce experimental SAXS data and (b) the resulting dynamical ensembles contain an ion-dependent fraction of extended structures.

Fitting Side-Chain NMR Relaxation Data Using Molecular Simulations

Proteins display a wealth of dynamical motions that can be probed using both experiments and simulations. We present an approach to integrate side-chain NMR relaxation measurements with molecular dynamics simulations to study the structure and dynamics of these motions. The approach, which we term ABSURDer (average block selection using relaxation data with entropy restraints), can be used to find a set of trajectories that are in agreement with relaxation measurements. We apply the method to deuterium relaxation measurements in T4 lysozyme and show how it can be used to integrate the accuracy of the NMR measurements with the molecular models of protein dynamics afforded by the simulations. We show how fitting of dynamic quantities leads to improved agreement with static properties and highlight areas needed for further improvements of the approach.

Recognition of N6-Methyladenosine by the YTHDC1 YTH Domain Studied by Molecular Dynamics and NMR Spectroscopy: The Role of Hydration

The YTH domain of YTHDC1 belongs to a class of protein "readers", recognizing the N6-methyladenosine (m⁶A) chemical modification in mRNA. Static ensemble-averaged structures revealed details of N6-methyl recognition via a conserved aromatic cage. Here, we performed molecular dynamics (MD) simulations along with nuclear magnetic resonance (NMR) and isothermal titration calorimetry (ITC) to examine how dynamics and solvent interactions contribute to the m⁶A recognition and negative selectivity toward an unmethylated substrate. The structured water molecules surrounding the bound RNA and the methylated substrate's ability to exclude bulk water molecules contribute to the YTH domain's preference for m⁶A. Intrusions of bulk water deep into the binding pocket disrupt binding of unmethylated adenosine. The YTHDC1's preference for the 5'-Gm⁶A-3' motif is partially facilitated by a network of water-mediated interactions between the 2-amino group of the guanosine and residues in the m⁶A binding pocket. The 5'-Im⁶A-3' (where I is inosine) motif can be recognized too, but disruption of the water network lowers affinity. The D479A mutant also disrupts the water network and destabilizes m⁶A binding. Our interdisciplinary study of the YTHDC1 protein-RNA complex reveals an unusual physical mechanism by which solvent interactions contribute toward m⁶A recognition.

Multiscale modeling of genome organization with maximum entropy optimization

Three-dimensional (3D) organization of the human genome plays an essential role in all DNA-templated processes, including gene transcription, gene regulation, and DNA replication. Computational modeling can be an effective way of building high-resolution genome structures and improving our understanding of these molecular processes. However, it faces significant challenges as the human genome consists of over 6 × 109 base pairs, a system size that exceeds the capacity of traditional modeling approaches. In this perspective, we review the progress that has been made in modeling the human genome. Coarse-grained models parameterized to reproduce experimental data via the maximum entropy optimization algorithm serve as effective means to study genome organization at various length scales. They have provided insight into the principles of whole-genome organization and enabled de novo predictions of chromosome structures from epigenetic modifications. Applications of these models at a near-atomistic resolution further revealed physicochemical interactions that drive the phase separation of disordered proteins and dictate chromatin stability in situ. We conclude with an outlook on the opportunities and challenges in studying chromosome dynamics.

Conformational Ensembles of Noncoding Elements in the SARS-CoV-2 Genome from Molecular Dynamics Simulations

The 5' untranslated region (UTR) of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) genome is a conserved, functional and structured genomic region consisting of several RNA stem-loop elements. While the secondary structure of such elements has been determined experimentally, their three-dimensional structures are not known yet. Here, we predict structure and dynamics of five RNA stem loops in the 5'-UTR of SARS-CoV-2 by extensive atomistic molecular dynamics simulations, more than 0.5 ms of aggregate simulation time, in combination with enhanced sampling techniques. We compare simulations with available experimental data, describe the resulting conformational ensembles, and identify the presence of specific structural rearrangements in apical and internal loops that may be functionally relevant. Our atomic-detailed structural predictions reveal a rich dynamics in these RNA molecules, could help the experimental characterization of these systems, and provide putative three-dimensional models for structure-based drug design studies.

Molecularly Informed Field Theories from Bottom-up Coarse-Graining

Polymer formulations possessing mesostructures or phase coexistence are challenging to simulate using atomistic particle-explicit approaches due to the disparate time and length scales, while the predictive capability of field-based simulations is hampered by the need to specify interactions at a coarser scale (e.g., χ-parameters). To overcome the weaknesses of both, we introduce a bottom-up coarse-graining methodology that leverages all-atom molecular dynamics to molecularly inform coarser field-theoretic models. Specifically, we use relative-entropy coarse-graining to parametrize particle models that are directly and analytically transformable into statistical field theories. We demonstrate the predictive capability of this approach by reproducing experimental aqueous poly(ethylene oxide) (PEO) cloud-point curves with no parameters fit to experimental data. This synergistic approach to multiscale polymer simulations opens the door to de novo exploration of phase behavior across a wide variety of polymer solutions and melt formulations.

Consistent Force Field Captures Homologue-Resolved HP1 Phase Separation

Many proteins have been shown to function via liquid-liquid phase separation. Computational modeling could offer much needed structural details of protein condensates and reveal the set of molecular interactions that dictate their stability. However, the presence of both ordered and disordered domains in these proteins places a high demand on the model accuracy. Here, we present an algorithm to derive a coarse-grained force field, MOFF, which can model both ordered and disordered proteins with consistent accuracy. It combines maximum entropy biasing, least-squares fitting, and basic principles of energy landscape theory to ensure that MOFF recreates experimental radii of gyration while predicting the folded structures for globular proteins with lower energy. The theta temperature determined from MOFF separates ordered and disordered proteins at 300 K and exhibits a strikingly linear relationship with amino acid sequence composition. We further applied MOFF to study the phase behavior of HP1, an essential protein for post-translational modification and spatial organization of chromatin. The force field successfully resolved the structural difference of two HP1 homologues despite their high sequence similarity. We carried out large-scale simulations with hundreds of proteins to determine the critical temperature of phase separation and uncover multivalent interactions that stabilize higher-order assemblies. In all, our work makes significant methodological strides to connect theories of ordered and disordered proteins and provides a powerful tool for studying liquid-liquid phase separation with near-atomistic details.

Refinement of α-Synuclein Ensembles Against SAXS Data: Comparison of Force Fields and Methods

The inherent flexibility of intrinsically disordered proteins (IDPs) makes it difficult to interpret experimental data using structural models. On the other hand, molecular dynamics simulations of IDPs often suffer from force-field inaccuracies, and long simulation times or enhanced sampling methods are needed to obtain converged ensembles. Here, we apply metainference and Bayesian/Maximum Entropy reweighting approaches to integrate prior knowledge of the system with experimental data, while also dealing with various sources of errors and the inherent conformational heterogeneity of IDPs. We have measured new SAXS data on the protein α-synuclein, and integrate this with simulations performed using different force fields. We find that if the force field gives rise to ensembles that are much more compact than what is implied by the SAXS data it is difficult to recover a reasonable ensemble. On the other hand, we show that when the simulated ensemble is reasonable, we can obtain an ensemble that is consistent with the SAXS data, but also with NMR diffusion and paramagnetic relaxation enhancement data.

How to assess the structural dynamics of transcription factors by integrating sparse NMR and EPR constraints with molecular dynamics simulations

We review recent advances in modeling structural ensembles of transcription factors from nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) spectroscopic data, integrated with molecular dynamics (MD) simulations. We focus on approaches that confirm computed conformational ensembles by sparse constraints obtained from magnetic resonance. This combination enables the deduction of functional and structural protein models even if nuclear Overhauser effects (NOEs) are too scarce for conventional structure determination. We highlight recent insights into the folding-upon-DNA binding transitions of intrinsically disordered transcription factors that could be assessed using such integrative approaches.

RNA Ensembles from Solvent Accessibility Data: Application to the SAM-I Riboswitch Aptamer Domain

Riboswitches are regulatory ribonucleic acid (RNA) elements that act as ligand-dependent conformational switches that recognize their cognate ligand via a binding pocket located in their aptamer domain. In the apo form, the aptamer domain is dynamic, requiring an ensemble representation of its structure. Here, as a proof-of-concept, we used solvent accessibility information to construct a pair of dynamical ensembles of the aptamer domain of the well-studied S-adenosylmethionine (SAM) class-I riboswitch in the absence (-SAM) and presence (+SAM) of SAM. To achieve this, we first generated a large conformational library and then reweighted conformers in the library using solvent-accessible surface area (SASA) data derived from recently reported light-activated structural examination of RNA (LASER) reactivities measured in the -SAM and +SAM states of the riboswitch. The differences in the resulting -SAM and +SAM ensembles are consistent with a SAM-dependent reshaping of the free-energy landscape of the aptamer domain. Within our -SAM ensemble, we identified a "transient" state that is missing a critical long-range contact, leading us to speculate that it may be representative of a folding intermediate. Further structural analysis also revealed that the transient state harbors a hidden binding pocket that is distinct from the SAM-binding pocket and is predicted by docking calculations to selectively bind small-molecule ligands. The SASA-based method we applied to the SAM-I riboswitch aptamer domain is general and could be used to construct dynamical ensembles for other riboswitch aptamer domains and, more broadly, other classes of structured RNAs.

A method of incorporating rate constants as kinetic constraints in molecular dynamics simulations

From the point of view of statistical mechanics, a full characterization of a molecular system requires an accurate determination of its possible states, their populations, and the respective interconversion rates. Toward this goal, well-established methods increase the accuracy of molecular dynamics simulations by incorporating experimental information about states using structural restraints and about populations using thermodynamics restraints. However, it is still unclear how to include experimental knowledge about interconversion rates. Here, we introduce a method of imposing known rate constants as constraints in molecular dynamics simulations, which is based on a combination of the maximum-entropy and maximum-caliber principles. Starting from an existing ensemble of trajectories, obtained from either molecular dynamics or enhanced trajectory sampling, this method provides a minimally perturbed path distribution consistent with the kinetic constraints, as well as modified free energy and committor landscapes. We illustrate the application of the method to a series of model systems, including all-atom molecular simulations of protein folding. Our results show that by combining experimental rate constants and molecular dynamics simulations, this approach enables the determination of transition states, reaction mechanisms, and free energies. We anticipate that this method will extend the applicability of molecular simulations to kinetic studies in structural biology and that it will assist the development of force fields to reproduce kinetic and thermodynamic observables. Furthermore, this approach is generally applicable to a wide range of systems in biology, physics, chemistry, and material science.

Using Cross-Correlated Spin Relaxation to Characterize Backbone Dihedral Angle Distributions of Flexible Protein Segments

Crucial to the function of proteins is their existence as conformational ensembles sampling numerous and structurally diverse substates. Despite this widely accepted notion there is still a high demand for meaningful and reliable approaches to characterize protein ensembles in solution. As it is usually conducted in solution, NMR spectroscopy offers unique possibilities to address this challenge. Particularly, cross-correlated relaxation (CCR) effects have long been established to encode both protein structure and dynamics in a compelling manner. However, this wealth of information often limits their use in practice as structure and dynamics might prove difficult to disentangle. Using a modern Maximum Entropy (MaxEnt) reweighting approach to interpret CCR rates of Ubiquitin, we demonstrate that these uncertainties do not necessarily impair resolving CCR-encoded structural information. Instead, a suitable balance between complementary CCR experiments and prior information is found to be the most crucial factor in mapping backbone dihedral angle distributions. Experimental and systematic deviations such as oversimplified dynamics appear to be of minor importance. Using Ubiquitin as an example, we demonstrate that CCR rates are capable of characterizing rigid and flexible residues alike, indicating their unharnessed potential in studying disordered proteins.

Combining Experimental Data and Computational Methods for the Non-Computer Specialist

Experimental methods are indispensable for the study of the function of biological macromolecules, not just as static structures, but as dynamic systems that change conformation, bind partners, perform reactions, and respond to different stimulus. However, providing a detailed structural interpretation of the results is often a very challenging task. While experimental and computational methods are often considered as two different and separate approaches, the power and utility of combining both is undeniable. The integration of the experimental data with computational techniques can assist and enrich the interpretation, providing new detailed molecular understanding of the systems. Here, we briefly describe the basic principles of how experimental data can be combined with computational methods to obtain insights into the molecular mechanism and expand the interpretation through the generation of detailed models.

DFFR: A New Method for High-Throughput Recalibration of Automatic Force-Fields for Drugs

We present drug force-field recalibration (DFFR), a new method for refining of automatic force-fields used to represent small drugs in docking and molecular dynamics simulations. The method is based on fine-tuning of torsional terms to obtain ensembles that reproduce observables derived from reference data. DFFR is fast and flexible and can be easily automatized for a high-throughput regime, making it useful in drug-design projects. We tested the performance of the method in a few model systems and also in a variety of druglike molecules using reference data derived from: (i) density functional theory coupled to a self-consistent reaction field (DFT/SCRF) calculations on highly populated conformers and (ii) enhanced sampling quantum mechanical/molecular mechanics (QM/MM) where the drug is reproduced at the QM level, while the solvent is represented by classical force-fields. Extension of the method to include other sources of reference data is discussed.

Microscopic Chromosomal Structural and Dynamical Origin of Cell Differentiation and Reprogramming

As an essential and fundamental process of life, cell development involves large-scale reorganization of the 3D genome architecture, which forms the basis of gene regulation. Here, a landscape-switching model is developed to explore the microscopic chromosomal structural origin of embryonic stem cell (ESC) differentiation and somatic cell reprogramming. It is shown that chromosome structure exhibits significant compartment-switching in the unit of topologically associating domain. It is found that the chromosome during differentiation undergoes monotonic compaction with spatial repositioning of active and inactive chromosomal loci toward the chromosome surface and interior, respectively. In contrast, an overexpanded chromosome, which exhibits universal localization of loci at the chromosomal surface with erasing the structural characteristics formed in the somatic cells, is observed during reprogramming. An early distinct differentiation pathway from the ESC to the terminally differentiated cell, giving rise to early bifurcation on the Waddington landscape for the ESC differentiation is suggested. The theoretical model herein including the non-equilibrium effects, draws a picture of the highly irreversible cell differentiation and reprogramming processes, in line with the experiments. The predictions provide a physical understanding of cell differentiation and reprogramming from the chromosomal structural and dynamical perspective and can be tested by future experiments.

Data-Driven Molecular Dynamics: A Multifaceted Challenge

The big data concept is currently revolutionizing several fields of science including drug discovery and development. While opening up new perspectives for better drug design and related strategies, big data analysis strongly challenges our current ability to manage and exploit an extraordinarily large and possibly diverse amount of information. The recent renewal of machine learning (ML)-based algorithms is key in providing the proper framework for addressing this issue. In this respect, the impact on the exploitation of molecular dynamics (MD) simulations, which have recently reached mainstream status in computational drug discovery, can be remarkable. Here, we review the recent progress in the use of ML methods coupled to biomolecular simulations with potentially relevant implications for drug design. Specifically, we show how different ML-based strategies can be applied to the outcome of MD simulations for gaining knowledge and enhancing sampling. Finally, we discuss how intrinsic limitations of MD in accurately modeling biomolecular systems can be alleviated by including information coming from experimental data.

Conformational state switching and pathways of chromosome dynamics in cell cycle

The cell cycle is a process and function of a cell with different phases essential for cell growth, proliferation, and replication. It depends on the structure and dynamics of the underlying DNA molecule, which underpins the genome function. A microscopic structural-level understanding of how a genome or its functional module chromosome performs the cell cycle in terms of large-scale conformational transformation between different phases, such as the interphase and the mitotic phase, is still challenging. Here, we develop a non-equilibrium, excitation-relaxation energy landscape-switching model to quantify the underlying chromosome conformational transitions through (de-)condensation for a complete microscopic understanding of the cell cycle. We show that the chromosome conformational transition mechanism from the interphase to the mitotic phase follows a two-stage scenario, in good agreement with the experiments. In contrast, the mitotic exit pathways show the existence of an over-expanded chromosome that recapitulates the chromosome in the experimentally identified intermediate state at the telophase. We find the conformational pathways are heterogeneous and irreversible as a result of the non-equilibrium dynamics of the cell cycle from both structural and kinetic perspectives. We suggest that the irreversibility is mainly due to the distinct participation of the ATP-dependent structural maintenance of chromosomal protein complexes during the cell cycle. Our findings provide crucial insights into the microscopic molecular structural and dynamical physical mechanism for the cell cycle beyond the previous more macroscopic descriptions. Our non-equilibrium landscape framework is general and applicable to study diverse non-equilibrium physical and biological processes such as active matter, differentiation/development, and cancer.

A Perspective on Deep Learning for Molecular Modeling and Simulations

Deep learning is transforming many areas in science, and it has great potential in modeling molecular systems. However, unlike the mature deployment of deep learning in computer vision and natural language processing, its development in molecular modeling and simulations is still at an early stage, largely because the inductive biases of molecules are completely different from those of images or texts. Footed on these differences, we first reviewed the limitations of traditional deep learning models from the perspective of molecular physics and wrapped up some relevant technical advancement at the interface between molecular modeling and deep learning. We do not focus merely on the ever more complex neural network models; instead, we introduce various useful concepts and ideas brought by modern deep learning. We hope that transacting these ideas into molecular modeling will create new opportunities. For this purpose, we summarized several representative applications, ranging from supervised to unsupervised and reinforcement learning, and discussed their connections with the emerging trends in deep learning. Finally, we give an outlook for promising directions which may help address the existing issues in the current framework of deep molecular modeling.

Toward empirical force fields that match experimental observables

Biomolecular force fields have been traditionally derived based on a mixture of reference quantum chemistry data and experimental information obtained on small fragments. However, the possibility to run extensive molecular dynamics simulations on larger systems achieving ergodic sampling is paving the way to directly using such simulations along with solution experiments obtained on macromolecular systems. Recently, a number of methods have been introduced to automatize this approach. Here, we review these methods, highlight their relationship with machine learning methods, and discuss the open challenges in the field.

Assessing the accuracy of direct-coupling analysis for RNA contact prediction

Many noncoding RNAs are known to play a role in the cell directly linked to their structure. Structure prediction based on the sole sequence is, however, a challenging task. On the other hand, thanks to the low cost of sequencing technologies, a very large number of homologous sequences are becoming available for many RNA families. In the protein community, the idea of exploiting the covariance of mutations within a family to predict the protein structure using the direct-coupling-analysis (DCA) method has emerged in the last decade. The application of DCA to RNA systems has been limited so far. We here perform an assessment of the DCA method on 17 riboswitch families, comparing it with the commonly used mutual information analysis and with state-of-the-art R-scape covariance method. We also compare different flavors of DCA, including mean-field, pseudolikelihood, and a proposed stochastic procedure (Boltzmann learning) for solving exactly the DCA inverse problem. Boltzmann learning outperforms the other methods in predicting contacts observed in high-resolution crystal structures.

A novel high-dimensional NMR experiment for resolving protein backbone dihedral angle ambiguities

Intrinsically disordered proteins (IDPs) are challenging established structural biology perception and urge a reassessment of the conventional understanding of the subtle interplay between protein structure and dynamics. Due to their importance in eukaryotic life and central role in protein interaction networks, IDP research is a fascinating and highly relevant research area in which NMR spectroscopy is destined to be a key player. The flexible nature of IDPs, as a result of the sampling of a vast conformational space, however, poses a tremendous scientific challenge, both technically and theoretically. Pronounced signal averaging results in narrow signal dispersion and requires higher dimensionality NMR techniques. Moreover, a fundamental problem in the structural characterization of IDPs is the definition of the conformational ensemble sampled by the polypeptide chain in solution, where often the interpretation relies on the concept of 'residual structure' or 'conformational preference'. An important source of structural information is information-rich NMR experiments that probe protein backbone dihedral angles in a unique manner. Cross-correlated relaxation experiments have proven to fulfil this task as they provide unique information about protein backbones, particularly in IDPs. Here we present a novel cross-correlation experiment that utilizes non-uniform sampling detection schemes to resolve protein backbone dihedral ambiguities in IDPs. The sensitivity of this novel technique is illustrated with an application to the prototypical IDP [Formula: see text]-Synculein for which unexpected deviations from random-coil-like behaviour could be observed.