Yuriy V. Sereda

Multiscale simulation of microbe structure and dynamics.

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.

Prospective on multiscale simulation of virus-like particles: Application to computer-aided vaccine design

Simulations of virus-like particles needed for computer-aided vaccine design highlight the need for new algorithms that accelerate molecular dynamics. Such simulations via conventional molecular dynamics present a practical challenge due to the millions of atoms involved and the long timescales of the phenomena of interest. These phenomena include structural transitions, self-assembly, and interaction with a cell surface. A promising approach for addressing this challenge is multiscale factorization. The approach is distinct from coarse-graining techniques in that it (1) avoids the need for conjecturing phenomenological governing equations for coarse-grained variables, (2) provides simulations with atomic resolution, (3) captures the cross-talk between disturbances at the atomic and the whole virus-like particle scale, and (4) achieves significant speedup over molecular dynamics. A brief review of multiscale factorization method is provided, as is a prospective on its development.

Energy transfer between a nanosystem and its host fluid: A multiscale factorization approach

Energy transfer between a macromolecule or supramolecular assembly and a host medium is considered from the perspective of Newtons equations and Lie-Trotter factorization. The development starts by demonstrating that the energy of the molecule evolves slowly relative to the time scale of atomic collisions-vibrations. The energy is envisioned to be a coarse-grained variable that coevolves with the rapidly fluctuating atomistic degrees of freedom. Lie-Trotter factorization is shown to be a natural framework for expressing this coevolution. A mathematical formalism and workflow for efficient multiscale simulation of energy transfer is presented. Lactoferrin and human papilloma virus capsid-like structure are used for validation.

Discovering free energy basins for macromolecular systems via guided multiscale simulation.

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).

Broad spectrum assessment of the epitope fluctuation—Immunogenicity hypothesis

Prediction of immunogenicity is a substantial barrier in vaccine design. Here, a molecular dynamics approach to assessing the immunogenicity of nanoparticles based on structure is presented. Molecular properties of epitopes on nonenveloped viral particles are quantified via a set of metrics. One such metric, epitope fluctuation (and implied flexibility), is shown to be inversely correlated with immunogenicity for each of a broad spectrum of nonenveloped viruses. The molecular metrics and experimentally determined immunogenicities for these viruses are archived in the open-source vaccine computer-aided design database. Results indicate the promise of computer-aided vaccine design to bring greater efficiency to traditional lab-based vaccine discovery approaches.

Early Stage P22 Viral Capsid Self-Assembly Mediated by Scaffolding Protein: Atom-Resolved Model and Molecular Dynamics Simulation

Molecular dynamics simulation of an atom-resolved bacteriophage P22 capsid model is used to delineate the underlying mechanism of early stage P22 self-assembly. A dimer formed by the C-terminal fragment of scaffolding protein with a new conformation is demonstrated to catalyze capsomer (hexamer and pentamer) aggregation efficiently. Effects of scaffolding protein/coat protein binding patterns and scaffolding protein concentration on efficiency, fidelity, and capsid curvature of P22 self-assembly are identified.

Multiscale Molecular Dynamics Approach to Energy Transfer in Nanomaterials

After local transient fluctuations are dissipated, in an energy transfer process, a system evolves to a state where the energy density field varies slowly in time relative to the dynamics of atomic collisions and vibrations. Furthermore, the energy density field remains strongly coupled to the atomic scale processes (collisions and vibrations), and it can serve as the basis of a multiscale theory of energy transfer. Here, a method is introduced to capture the long scale energy density variations as they coevolve with the atomistic state in a way that yields insights into the basic physics and implies an efficient algorithm for energy transfer simulations. The approach is developed based on the N-atom Liouville equation and an interatomic force field and avoids the need for conjectured phenomenological equations for energy transfer and other processes. The theory is demonstrated for sodium chloride and silicon dioxide nanoparticles immersed in a water bath via molecular dynamics simulations of the energy transfer between a nanoparticle and its aqueous host fluid. The energy density field is computed for different sets of symmetric grid densities, and the multiscale theory holds when slowly varying energy densities at the nodes are obtained. Results strongly depend on grid density and nanoparticle constituent material. A nonuniform temperature distribution, larger thermal fluctuations in the nanoparticle than in the bath, and enhancement of fluctuations at the surface, which are expressed due to the atomic nature of the systems, are captured by this method rather than by phenomenological continuum energy transfer models.

A multiscale variational approach to the kinetics of viscous classical liquids: The coarse-grained mean field approximation

A closed kinetic equation for the single-particle density of a viscous simple liquid is derived using a variational method for the Liouville equation and a coarse-grained mean-field (CGMF) ansatz. The CGMF ansatz is based on the notion that during the characteristic time of deformation a given particle interacts with many others so that it experiences an average interaction. A trial function for the N-particle probability density is constructed using a multiscale perturbation method and the CGMF ansatz is applied to it. The multiscale perturbation scheme is based on the ratio of the average nearest-neighbor atom distance to the total size of the assembly. A constraint on the initial condition is discovered which guarantees that the kinetic equation is mass-conserving and closed in the single-particle density. The kinetic equation has much of the character of the Vlasov equation except that true viscous, and not Landau, damping is accounted for. The theory captures condensation kinetics and takes much of the character of the Gross-Pitaevskii equation in the weak-gradient short-range force limit.