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Cytochrome c(2) (cyt. c(2)) is a major element in electron transfer between redox proteins in bioenergetic membranes. While the interaction between cyt. c(2) and anionic lipids abundant in bioenergetic membranes has been reported, their effect on the shuttling activity of cyt. c(2) remains elusive. Here, the effect of anionic lipids on interaction and binding of cyt. c(2) to cytochrome bc(1) complex (bc(1)) is investigated using a combination of molecular dynamics (MD) and Brownian dynamics (BD) simulations. MD is used to generate thermally accessible conformations of cyt. c(2) and membrane-embedded bc(1), which were subsequently used in multi-replica BD simulations of cyt. c(2) diffusion from solution to bc(1), in the presence of various lipids. We show that, counterintuitively, anionic lipids facilitate association of cyt. c(2) to bc(1) by localizing its diffusion to the membrane surface. The observed lipid-mediated bc(1)-association is further enhanced by the oxidized state of cyt. c(2) in line with its physiological function. This lipid-mediated enhancement is salinity-dependent, and anionic lipids can disrupt cyt. c(2) - bc(1) interaction at non-physiological levels of salt. Our data highlight the importance of the redox state of cyt. c(2), the lipid composition of the chromatophore membrane, and the salinity of the chromatophore in regulating the efficiency of the electron shuttling process mediated by cyt. c(2). The conclusions can be extrapolated to mitochondrial systems and processes, or any bioenergetic membrane, given the structural similarity between cyt. c(2) and bc(1) and their mitochondrial counterparts.

Influenza A viruses (IAVs) exploit host glycans in airway epithelial mucosa to gain entry and initiate infection. Rapid detection of changes in IAV specificity towards host glycan classes can provide early indication of virus transmissibility and infection potential. IAVs use hemagglutinins (HA) to bind sialic acids linked to larger glycan structures and a switch in HA specificity from α2,3-to α2,6-linked sialoglycans is considered a prerequisite for viral transmission from birds to humans. While the changes in HA structure associated with the evolution of binding phenotype have been mapped, the influence of glycan receptor presentation on IAV specificity remains obscured. Here, we describe a glycan array platform which uses synthetic mimetics of mucin glycoproteins to model how receptor presentation in the mucinous glycocalyx, including glycan type and valency of the glycoconjugates and their surface density, impact IAV binding. We found that H1N1 virus produced in embryonated chicken eggs, which recognizes both receptor types, exclusively engaged mucin-mimetics carrying α2,3-linked sialic acids in their soluble form. The virus was able utilize both receptor structures when the probes were immobilized on the array; however, increasing density in the mucin-mimetic brush diminished viral adhesion. Propagation in mammalian cells produced a change in receptor pattern recognition by the virus, without altering its HA affinity, toward improved binding of α2,6-sialylated mucin mimetics and reduced sensitivity to surface crowding of the probes. Application of a support vector machine (SVM) learning algorithm as part of the glycan array binding analysis efficiently characterized this shift in binding preference and may prove useful to study the evolution of viral responses to a new host.

Cryo-electron microscopy (EM) requires molecular modeling to refine structural details from data. Ensemble models arrive at low free-energy molecular structures, but are computationally expensive and limited to resolving only small proteins that cannot be resolved by cryo-EM. Here, we introduce CryoFold - a pipeline of molecular dynamics simulations that determines ensembles of protein structures directly from sequence by integrating density data of varying sparsity at 3-5 Å resolution with coarse-grained topological knowledge of the protein folds. We present six examples showing its broad applicability for folding proteins between 72 to 2000 residues, including large membrane and multi-domain systems, and results from two EMDB competitions. Driven by data from a single state, CryoFold discovers ensembles of common low-energy models together with rare low-probability structures that capture the equilibrium distribution of proteins constrained by the density maps. Many of these conformations, unseen by traditional methods, are experimentally validated and functionally relevant. We arrive at a set of best practices for data-guided protein folding that are controlled using a Python GUI.

Cryo-electron microscopy (cryo-EM) has produced a number of structural models of the SARS-CoV-2 spike, already prompting biomedical outcomes. However, these reported models and their associated electrostatic potential maps represent an unknown admixture of conformations stemming from the underlying energy landscape of the spike protein. As for any protein, some of the spike’s conformational motions are expected to be biophysically relevant, but cannot be interpreted only by static models. Using experimental cryo-EM images, we present the energy landscape of the spike protein conformations, and identify molecular rearrangements along the most-likely conformational path in the vicinity of the open (so called 1RBD-up) state. The resulting global and local atomic refinements reveal larger movements than those expected by comparing the reported 1RBD-up and 1RBD-down cryo-EM models. Here we report greater degrees of “openness” in global conformations of the 1RBD-up state, not revealed in the single-model interpretations of the density maps, together with conformations that overlap with the reported models. We discover how the glycan shield contributes to the stability of these conformations along the minimum free-energy pathway. A local analysis of seven key binding pockets reveals that six out them, including those for engaging ACE2, therapeutic mini-proteins, linoleic acid, two different kinds of antibodies, and protein-glycan interaction sites, switch conformations between their known apo- and holo-conformations, even when the global spike conformation is 1RBD-up. This is reminiscent of a conformational pre-equilibrium. We found only one binding pocket, namely antibody AB-C135 to remain closed along the entire minimum free energy path, suggesting an induced fit mechanism for this enzyme.

A primary reason for the intense interest in structural biology is the fact that knowledge of structure can elucidate macromolecular functions in living organisms. Sustained effort has resulted in an impressive arsenal of tools for determining the static structures. But under physiological conditions, macromolecules undergo continuous conformational changes, a subset of which are functionally important. Techniques for capturing the continuous conformational changes underlying function are essential for further progress. Here, we present chemically-detailed conformational movies of biological function, extracted data-analytically from experimental single-particle cryo-electron microscopy (cryo-EM) snapshots of ryanodine receptor type 1 (RyR1), a calcium-activated calcium channel engaged in the binding of ligands. The functional motions differ substantially from those inferred from static structures in the nature of conformationally active structural domains, the sequence and extent of conformational motions, and the way allosteric signals are transduced within and between domains. Our approach highlights the importance of combining experiment, advanced data analysis, and molecular simulations., There is a great interest in retrieving functional pathways from cryo-EM single-particle data. Here, the authors present an approach that combines cryo-EM with advanced data-analytical methods and molecular dynamics simulations to reveal the functional pathways traversed on experimentally derived energy landscapes using the ryanodine receptor type 1 as an example.

Despite significant advances in resolution, the potential for cryo-electron microscopy (EM) to be used in determining the structures of protein-drug complexes remains unrealized. Determination of accurate structures and coordination of bound ligands necessitates simultaneous fitting of the models into the density envelopes, exhaustive sampling of the ligand geometries, and, most importantly, concomitant rearrangements in the side chains to optimize the binding energy changes. In this article, we present a flexible-fitting pipeline where molecular dynamics flexible fitting (MDFF) is used to refine structures of protein-ligand complexes from 3 to 5 A electron density data. Enhanced sampling is employed to explore the binding pocket rearrangements. To provide a model that can accurately describe the conformational dynamics of the chemically diverse set of small-molecule drugs inside MDFF, we use QM/MM and neural-network potential (NNP)/MM models of protein-ligand complexes, where the ligand is represented using the QM or NNP model, and the protein is represented using established molecular mechanical force fields (e.g., CHARMM). This pipeline offers structures commensurate to or better than recently submitted high-resolution cryo-EM or X-ray models, even when given medium to low-resolution data as input. The use of the NNPs makes the algorithm more robust to the choice of search models, offering a radius of convergence of 6.5 A for ligand structure determination. The quality of the predicted structures was also judged by density functional theory calculations of ligand strain energy. This strain potential energy is found to systematically decrease with better fitting to density and improved ligand coordination, indicating correct binding interactions. A computationally inexpensive protocol for computing strain energy is reported as part of the model analysis protocol that monitors both the ligand fit as well as model quality.

X-ray crystallography and cryo-electron microscopy are two popular methods for the structure determination of biological molecules. Atomic structures are derived through the fitting and refinement of an initial model into electron density maps constructed by both experiments. Two computational approaches, MDFF and xMDFF, have been developed to facilitate this process by integrating the experimental data with molecular dynamics simulation. However, the set-up of an MDFF/xMDFF simulation requires knowledge of both experimental and computational methods, which is not straightforward for non-expert users. In addition, sometimes it is desirable to include realistic environments such as explicit solvent and lipid bilayers during the simulation, which poses another challenge even for expert users. To alleviate these difficulties, we have developed MDFF/xMDFF Utilizer in CHARMM-GUI that helps users to set up an MDFF/xMDFF simulation. The capability of MDFF/xMDFF Utilizer is greatly enhanced by integration with other CHARMM-GUI modules, including protein structure manipulation, a diverse set of lipid types, and all-atom CHARMM and coarse-grained PACE force fields. With this integration, various simulation environments are available for MDFF Utilizer (vacuum, implicit/explicit solvent, and bilayers) and xMDFF Utilizer (vacuum and solution). In this work, three examples are shown to demonstrate the usage of MDFF/xMDFF Utilizer (http://www.charmm-gui.org/input/mdff and http://www.charmm-gui.org/input/xmdff).

The widely-conserved natural resistance associated macrophage protein (Nramp) family of divalent metal transporters enables manganese import in bacteria and dietary iron uptake in mammals. We determined the crystal structure of the Deinococcus radiodurans Nramp homolog (DraNramp) in an inward-facing apo state, including the complete transmembrane (TM) segment 1a—absent from a previous Nramp structure. Mapping our cysteine accessibility scanning results onto this structure, we identified the metal permeation pathway in the alternate outward-open conformation. We investigated the functional impact of two natural anemia-causing glycine-to-arginine mutations, which impaired transition metal transport in both human Nramp2 and DraNramp. The TM4 G153R mutation perturbs the closing of the outward metal permeation pathway and alters the selectivity of the conserved metal-binding site. In contrast, the TM1a G45R mutation prevents conformational change by sterically blocking the essential movement of that helix, thus locking the transporter in an inward-facing state.

Summary Francisella tularensis is the causative agent for the potentially fatal disease tularemia. The lipoprotein Flpp3 has been identified as a virulence determinant of tularemia with no sequence homology outside the Francisella genus. We report a room temperature structure of Flpp3 determined by serial femtosecond crystallography that exists in a significantly different conformation than previously described by the NMR-determined structure. Furthermore, we investigated the conformational space and energy barriers between these two structures by molecular dynamics umbrella sampling and identified three low-energy intermediate states, transitions between which readily occur at room temperature. We have also begun to investigate organic compounds in silico that may act as inhibitors to Flpp3. This work paves the road to developing targeted therapeutics against tularemia and aides in our understanding of the disease mechanisms of tularemia.

Polymorphisms in MHC-I protein sequences across human populations significantly affect viral peptide binding capacity, and thus alter T cell immunity to infection. In the present study, we assess the relationship between observed SARS-CoV-2 population mortality and the predicted viral binding capacities of 52 common MHC-I alleles. Potential SARS-CoV-2 MHC-I peptides are identified using a consensus MHC-I binding and presentation prediction algorithm called EnsembleMHC. Starting with nearly 3.5 million candidates, we resolve a few hundred highly probable MHC-I peptides. By weighing individual MHC allele-specific SARS-CoV-2 binding capacity with population frequency in 23 countries, we discover a strong inverse correlation between predicted population SARS-CoV-2 peptide binding capacity and mortality rate. Our computations reveal that peptides derived from the structural proteins of the virus produce a stronger association with observed mortality rate, highlighting the importance of S, N, M, and E proteins in driving productive immune responses., Wilson et al. define a predicted MHC allele-specific hierarchy for the presentation of peptides derived from SARS-CoV-2 viral proteins. They find that a composite population-level metric combining predicted MHC allele SARS-CoV-2 binding capacity and endemic allele frequencies is inversely correlated with deaths per million.

The rise of the computer as a powerful tool for model building and refinement has revolutionized the field of structure determination for large biomolecular systems. Despite the wide availability of robust experimental methods capable of resolving structural details across a range of spatiotemporal resolutions, computational hybrid methods have the unique ability to integrate the diverse data from multimodal techniques such as X-ray crystallography and electron microscopy into consistent, fully atomistic structures. Here, commonly employed strategies for computational real-space structural refinement are reviewed, and their specific applications are illustrated for several large macromolecular complexes: ribosome, virus capsids, chemosensory array, and photosynthetic chromatophore. The increasingly important role of computational methods in large-scale structural refinement, along with current and future challenges, is discussed.

The cellular process responsible for providing energy for most life on Earth, namely, photosynthetic light-harvesting, requires the cooperation of hundreds of proteins across an organelle, involving length and time scales spanning several orders of magnitude over quantum and classical regimes. Simulation and visualization of this fundamental energy conversion process pose many unique methodological and computational challenges. We present, in two accompanying movies, light-harvesting in the photosynthetic apparatus found in purple bacteria, the so-called chromatophore. The movies are the culmination of three decades of modeling efforts, featuring the collaboration of theoretical, experimental, and computational scientists. We describe the techniques that were used to build, simulate, analyze, and visualize the structures shown in the movies, and we highlight cases where scientific needs spurred the development of new parallel algorithms that efficiently harness GPU accelerators and petascale computers.

Shape-persistent macrocycles are attractive functional targets for synthesis, molecular recognition, and hierarchical self-assembly. Such macrocycles are noncollapsible and geometrically well-defined, and they are traditionally characterized by having repeat units and low conformational flexibility. Here, we find it necessary to refine these ideas in the face of highly flexible yet shape-persistent macrocycles. A molecule is shape-persistent if it has a small change in shape when perturbed by external stimuli (e.g., heat, light, and redox chemistry). In support of this idea, we provide the first examination of the relationships between a macrocycle's shape persistence, its conformational space, and the resulting functions. We do this with a star-shaped macrocycle called cyanostar that is flexible as well as being shape-persistent. We employed molecular dynamics (MD), density functional theory (DFT), and NMR experiments. Considering a thermal bath as a stimulus, we found a single macrocycle has 332 accessible conformers with olefins undergoing rapid interconversion by up-down and in-out motions on short time scales (0.2 ns). These many interconverting conformations classify single cyanostars as flexible. To determine and confirm that cyanostars are shape-persistent, we show that they have a high 87% shape similarity across these conformations. To further test the idea, we use the binding of diglyme to the single macrocycle as guest-induced stimulation. This guest has almost no effect on the conformational space. However, formation of a 2:1 sandwich complex involving two macrocycles enhances rigidity and dramatically shifts the conformer distribution toward perfect bowls. Overall, the present study expands the scope of shape-persistent macrocycles to include flexible macrocycles if, and only if, their conformers have similar shapes.

Accurate structure determination from electron density maps at 3–5 A resolution necessitates a balance between extensive global and local sampling of atomistic models, yet with the stereochemical correctness of backbone and sidechain geometries. Molecular Dynamics Flexible Fitting (MDFF), particularly through a resolution-exchange scheme, ReMDFF, provides a robust way of achieving this balance for hybrid structure determination. Employing two high-resolution density maps, namely that of β -galactosidase at 3.2 A and TRPV1 at 3.4 A, we showcase the quality of ReMDFF-generated models, comparing them against ones submitted by independent research groups for the 2015–2016 Cryo-EM Model Challenge. This comparison offers a clear evaluation of ReMDFF’s strengths and shortcomings, and those of data-guided real-space refinements in general. ReMDFF results scored highly on the various metric for judging the quality-of-fit and quality-of-model. However, some systematic discrepancies are also noted employing a Molprobity analysis, that are reproducible across multiple competition entries. A space of key refinement parameters is explored within ReMDFF to observe their impact within the final model. Choice of force field parameters and initial model seem to have the most significant impact on ReMDFF model-quality. To this end, very recently developed CHARMM36m force field parameters provide now more refined ReMDFF models than the ones originally submitted to the Cryo-EM challenge. Finally, a set of good-practices is prescribed for the community to benefit from the MDFF developments.

Millisecond-scale conformational transitions represent a seminal challenge for traditional molecular dynamics simulations, even with the help of high-end supercomputer architectures. Such events are particularly relevant to the study of molecular motors-proteins or abiological constructs that convert chemical energy into mechanical work. Here, we present a hybrid-simulation scheme combining an array of methods including elastic network models, transition path sampling, and advanced free-energy methods, possibly in conjunction with generalized-ensemble schemes to deliver a viable option for capturing the millisecond-scale motor steps of biological motors. The methodology is already implemented in large measure in popular molecular dynamics programs, and it can leverage the massively parallel capabilities of petascale computers. The applicability of the hybrid method is demonstrated with two examples, namely cyclodextrin-based motors and V-type ATPases.

The transduction of transmembrane electric fields into protein motion plays an essential role in the generation and propagation of cellular signals. Voltage-sensing domains (VSD) carry out these functions through reorientations of S4 helix with discrete gating charges. Here, crystal structures of the VSD from Ci-VSP were determined in both, active (Up) and resting (Down) conformations. The S4 undergoes a ~5 Å displacement along its main axis accompanied by a ~60o rotation, consistent with the helix-screw gating mechanism. This movement is stabilized by a change in countercharge partners in helices S1 and S3, generating an estimated net charge transfer of ~1 eo. Gating charges move relative to a “hydrophobic gasket” that electrically divides intra and extracellular compartments. EPR spectroscopy confirms the limited nature of S4 movement in a membrane environment. These results provide an explicit mechanism for voltage sensing and set the basis for electromechanical coupling in voltage-dependent cellular activities.

ATP synthase is the most prominent bioenergetic macromolecular motor in all life-forms, utilizing the proton gradient across the cell membrane to fuel the synthesis of ATP. Notwithstanding the wealth of available biochemical and structural information inferred from years of experiments, the precise molecular mechanism whereby vacuolar (V–type) ATP synthase fulfills its biological function remains largely fragmentary. Recently, crystallographers provided the first high-resolution view of ATP activity in Enterococcus hirae V1–ATPase. Employing a combination of transition-path sampling and high-performance free-energy methods, the sequence of conformational transitions involved in a functional cycle accompanying ATP hydrolysis has been investigated in unprecedented detail over an aggregate simulation time of 65 μs. Our simulated pathways reveal that the chemical energy produced by ATP hydrolysis is harnessed via the concerted motion of the protein–protein interfaces in the V1-ring, and is nearly entirely consumed in the rotation of the central stalk. Surprisingly, in an ATPase devoid of a central stalk, the interfaces of this ring are perfectly designed for inducing ATP hydrolysis. Yet, in a complete V1-ATPase, the mechanical property of the central stalk is a key determinant of the rate of ATP turnover. The simulations further unveil a sequence of events, whereby unbinding of the hydrolysis product (ADP+Pi) is followed by ATP uptake, which, in turn, leads to the torque generation step and rotation of the center stalk. Molecular trajectories also bring to light multiple intermediates, two of which have been isolated in independent crystallography experiments.

Bioenergetic membranes are the key cellular structures responsible for coupled energy-conversion processes, which supply ATP and important metabolites to the cell. Here, we report the first 100-million atom-scale model of an entire photosynthetic organelle, a chromatophore membrane vesicle from a purple bacterium, which reveals the rate-determining steps of membrane-mediated energy conversion. Molecular dynamics simulations of this bioenergetic organelle elucidate how the network of bioenergetic proteins influences membrane curvature and demonstrates the impact of thermal disorder on photosynthetic excitation transfer. Brownian dynamics simulations of the quinone and cytochrome c(2) charge carriers within the chromatophore interior probe the mechanisms of nanoscale charge transport under various pH and salinity conditions. Reproducing phenotypic properties from atomistic details, a rate-kinetic model evinces that low-light adaptations of the bacterium emerge as a spontaneous outcome of optimizing the balance between the chromatophore’s structural integrity and robust energy conversion. Put together, the hybrid structure determination and systems-level modeling of the chromatophore, in conjunction with optical spectroscopy, illuminate the chemical and organizational design principles of biological membranes that foster energy storage and transduction in living cells. Parallels are drawn with the more universal mitochondrial bioenergetic machinery, from whence molecular-scale insights on the mechanism of cellular aging are inferred. This endeavor made feasible through the advent of petascale supercomputers, paves the way to first-principles modeling of whole living cells.

Small diffusible redox proteins facilitate electron transfer in respiration and photosynthesis by alternately binding to their redox partners, integral membrane proteins, and exchanging electrons. Diffusive search, recognition, binding and unbinding of these proteins amount often to kinetic bottlenecks in cellular energy conversion, but despite the availability of structures and intense study, the physical mechanisms controlling redox partner interactions remain largely unknown. The present molecular dynamics study provides an all-atom description of the cytochrome c2 - docked bc1 complex in Rhodobacter sphaeroides in terms of an ensemble of favorable docking conformations, and reveals an intricate series of conformational changes that allow cytochrome c2 to recognize the bc1 complex and bind or unbind in a redox state-dependent manner. In particular, the role of electron transfer in triggering a molecular switch, and in altering water-mediated interface mobility, thereby strengthening and weakening complex formation, is described. The results resolve long-standing discrepancies between structural and functional data.

Multiscale analysis provides an algorithm for the efficient simulation of macromolecular assemblies. This algorithm involves the coevolution of a quasiequilibrium probability density of atomic configurations and the Langevin dynamics of spatial coarse-grained variables denoted order parameters (OPs) characterizing nanoscale system features. In practice, implementation of the probability density involves the generation of constant OP ensembles of atomic configurations. Such ensembles are used to construct thermal forces and diffusion factors that mediate the stochastic OP dynamics. Generation of all-atom ensembles at every Langevin time step is computationally expensive. Here, multiscale computation for macromolecular systems is made more efficient by a method that self-consistently folds in ensembles of all-atom configurations constructed in an earlier step, history, of the Langevin evolution. This procedure accounts for the temporal evolution of these ensembles, accurately providing thermal forces and diffusions. It is shown that efficiency and accuracy of the OP-based simulations is increased via the integration of this historical information. Accuracy improves with the square root of the number of historical timesteps included in the calculation. As a result, CPU usage can be decreased by a factor of 3-8 without loss of accuracy. The algorithm is implemented into our existing force-field based multiscale simulation platform and demonstrated via the structural dynamics of viral capsomers.

An approach for the automated discovery of low free energy states of macromolecular systems is presented. The method does not involve delineating the entire free energy landscape but proceeds in a sequential free energy minimizing state discovery, i.e., it first discovers one low free energy state and then automatically seeks a distinct neighboring one. These states and the associated ensembles of atomistic configurations are characterized by coarse-grained variables capturing the large-scale structure of the system. A key facet of our approach is the identification of such coarse-grained variables. Evolution of these variables is governed by Langevin dynamics driven by thermal-average forces and mediated by diffusivities, both of which are constructed by an ensemble of short molecular dynamics runs. In the present approach, the thermal-average forces are modified to account for the entropy changes following from our knowledge of the free energy basins already discovered. Such forces guide the system away from the known free energy minima, over free energy barriers, and to a new one. The theory is demonstrated for lactoferrin, known to have multiple energy-minimizing structures. The approach is validated using experimental structures and traditional molecular dynamics. The method can be generalized to enable the interpretation of nanocharacterization data (e.g., ion mobility – mass spectrometry, atomic force microscopy, chemical labeling, and nanopore measurements).

Coarse-grained features of macromolecular assemblies are understood via a set of order parameters (OPs) constructed in terms of their all-atom configuration. OPs are shown to be slowly changing in time and capture the large-scale spatial features of macromolecular assemblies. The relationship of these variables to the classic notion of OPs based on symmetry breaking phase transitions is discussed. OPs based on space warping transformations are analyzed in detail as they naturally provide a connection between overall structure of an assembly and all-atom configuration. These OPs serve as the basis of a multiscale analysis that yields Langevin equations for OP dynamics. In this context, the characteristics of OPs and PCA modes are compared. The OPs enable efficient all-atom multiscale simulations of the dynamics of macromolecular assemblies in response to changes in microenvironmental conditions, as demonstrated on the structural transitions of cowpea chlorotic mottle virus capsid (CCMV) and RNA of the satellite tobacco mosaic virus (STMV).

Molecular Dynamics Flexible Fitting (MDFF) is an established technique for fitting all-atom structures of molecules into corresponding cryo-electron microscopy (cryo-EM) densities. The practical application of MDFF is simple but requires a user to be aware of and take measures against a variety of possible challenges presented by each individual case. Some of these challenges arise from the complexity of a molecular structure or the limited quality of available structural models and densities to be interpreted, while others stem from the intricacies of MDFF itself. The current article serves as an overview of the strategies that have been developed since MDFF’s inception to overcome common challenges and successfully perform MDFF simulations.

Soft materials (e.g., enveloped viruses, liposomes, membranes and supercooled liquids) simultaneously deform or display collective behaviors, while undergoing atomic scale vibrations and collisions. While the multiple space-time character of such systems often makes traditional molecular dynamics simulation impractical, a multiscale approach has been presented that allows for long-time simulation with atomic detail based on the co-evolution of slowly varying order parameters (OPs) with the quasi-equilibrium probability density of atomic configurations. However, this approach breaks down when the structural change is extreme, e.g., when nearest-neighbor connectivity between structural subsystems is not maintained. In the current study, a self-consistent approach is presented wherein OPs and a reference structure co-evolve slowly to yield long-time simulation for dynamical soft-matter phenomena such as structural transitions and self-assembly. The development begins with the Liouville equation for N classical atoms and an ansatz on the form of the associated N-atom probability density. Multiscale techniques are used to derive Langevin equations for the coupled OP-configurational dynamics. The net result is a set of equations for the coupled stochastic dynamics of the OPs and centers of mass of the subsystems that constitute a soft material body. The theory is based on an all-atom methodology and an interatomic force field, and therefore enables calibration-free simulations of soft matter, such as macromolecular assemblies.

Macromolecular assemblies often display a hierarchical organization of macromolecules or their sub-assemblies. To model this, we have formulated a space warping method that enables capturing overall macromolecular structure and dynamics via a set of coarse-grained order parameters (OPs). This article is the first of two describing the construction and computational implementation of an additional class of OPs that has built into them the hierarchical architecture of macromolecular assemblies. To accomplish this, first, the system is divided into subsystems, each of which is described via a representative set of OPs. Then, a global set of variables is constructed from these subsystem-centered OPs to capture overall system organization. Dynamical properties of the resulting OPs are compared to those of our previous nonhierarchical ones, and implied conceptual and computational advantages are discussed for a 100ns, 2 million atom solvated Human Papillomavirus-like particle simulation. In the second article, the hierarchical OPs are shown to enable a multiscale analysis that starts with the N-atom Liouville equation and yields rigorous Langevin equations of stochastic OP dynamics. The latter is demonstrated via a force-field based simulation algorithm that probes key structural transition pathways, simultaneously accounting for all-atom details and overall structure.

A multiscale mathematical and computational approach is developed that captures the hierarchical organization of a microbe. It is found that a natural perspective for understanding a microbe is in terms of a hierarchy of variables at various levels of resolution. This hierarchy starts with the N -atom description and terminates with order parameters characterizing a whole microbe. This conceptual framework is used to guide the analysis of the Liouville equation for the probability density of the positions and momenta of the N atoms constituting the microbe and its environment. Using multiscale mathematical techniques, we derive equations for the co-evolution of the order parameters and the probability density of the N-atom state. This approach yields a rigorous way to transfer information between variables on different space-time scales. It elucidates the interplay between equilibrium and far-from-equilibrium processes underlying microbial behavior. It also provides framework for using coarse-grained nanocharacterization data to guide microbial simulation. It enables a methodical search for free-energy minimizing structures, many of which are typically supported by the set of macromolecules and membranes constituting a given microbe. This suite of capabilities provides a natural framework for arriving at a fundamental understanding of microbial behavior, the analysis of nanocharacterization data, and the computer-aided design of nanostructures for biotechnical and medical purposes. Selected features of the methodology are demonstrated using our multiscale bionanosystem simulator DeductiveMultiscaleSimulator. Systems used to demonstrate the approach are structural transitions in the cowpea chlorotic mosaic virus, RNA of satellite tobacco mosaic virus, virus-like particles related to human papillomavirus, and iron-binding protein lactoferrin.