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.

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.

Energy transfer between a macromolecule or supramolecular assembly and a host medium is considered from the perspective of Newton's 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.

The ability of a dinucleotide-step based elastic-rod model of DNA to predict nucleosome binding free energies is investigated using four available sets of elastic parameters. We compare the predicted free energies to experimental values derived from nucleosome reconstitution experiments for 84 DNA sequences. Elastic parameters (conformation and stiffnessess) obtained from MD simulations are shown to be the most reliable predictors, as compared to those obtained from analysis of base-pair step melting temperatures, or from analysis of x-ray structures. We have also studied the effect of varying the folded conformation of nucleosomal DNA by means of our Fourier - filtering knock-out and knock-in procedure. This study confirmed the above ranking of elastic parameters, and helped to reveal problems inherent in models using only a local elastic energy function. Long-range interactions were added to the elastic-rod model in an effort to improve its predictive ability. For this purpose a Debye-Huckel energy term with a single, homogenous point charge per base-pair was introduced. This term contains only three parameters, - its weight relative to the elastic energy, the Debye screening length, and a minimum sequence distance for including pairwise interactions between charges. After optimization of these parameters, our Debye-Huckel term is attractive, and yields the same level of correlation with experiment (R=0.75) as was achieved merely by varying the nucleosomal shape in the elastic-rod model. We suggest this result indicates a linker DNA - histone attraction or, possibly, entropic effects, that lead to a stabilization of a nucleosome away from the ends of DNA segments longer than 147 bp. Such effects are not accounted for by a localized elastic energy model.

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