Multiscale macromolecular simulation: role of evolving ensembles.

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.

Scaling behavior of electronic excitations in assemblies of molecules with degenerate ground states.

The behavior of long space-time excitations in many-electron systems with ground state degeneracy is explored via multiscale analysis. The analysis starts with an ansatz for the wave function's dual dependence on the N-electron configuration (i.e., both by direct means and by indirect means via a set of order parameters). It is shown that a Dirac-like equation form of the wave equation emerges in the limit where the ratio epsilon (of the average nearest-neighbor distance to the characteristic length of the long-scale phenomenon of interest) is small. Examples of the long scale are the size of a quantum dot, nanotube, or wavelength of a density disturbance. The velocities in the Dirac-like equation are the transition moments of the single-particle momentum operator connecting degenerate ground states. While detailed band structure and the independent quasi-particle picture could underlie the behavior of some systems (as commonly suggested for graphene), the present scaling law results show it is not necessarily the only explanation. Rather, it can follow from the scaling properties of low-lying, long spatial scale excitations and ground state degeneracy, even in strongly interacting systems. The generality of our findings suggests graphene may be just one of many examples of Dirac-like equation behavior. A preliminary validation of our quantum scaling law for molecular arrays is presented. As our scaling law constitutes a coarse-grained wave equation, path integral or other methods derived from it hold great promise for calibration-free, long-time simulation of many-particle quantum systems.

Chromosome segregation in Escherichia coli division: a free energy-driven string model.

Although the mechanisms of eukaryotic chromosome segregation and cell division have been elucidated to a certain extent, those for bacteria remain largely unknown. Here we present a computational string model for simulating the dynamics of Escherichia coli chromosome segregation. A novel thermal-average force field accounting for stretching, bending, volume exclusion, friction and random fluctuation is introduced. A Langevin equation is used to simulate the chromosome structural changes. The mechanism of chromosome segregation is thereby postulated as a result of free energy-driven structural optimization with replication introduced chromosomal mass increase. Predictions of the model agree well with observations of fluorescence labeled chromosome loci movement in living cells. The results demonstrate the possibility of a mechanism of chromosome segregation that does not involve cytoskeletal guidance or advanced apparatus in an E. coli cell. The model also shows that DNA condensation of locally compacted domains is a requirement for successful chromosome segregation. Simulations also imply that the shape-determining protein MreB may play a role in the segregation via modification of the membrane pressure.

A plausible model for reversal of neoplastic transformations in plants based on multiple steady states.

We offer a plausible interpretation of some experiments on the reversal of neoplastic transformations in plants. We suggest that normal cells and tumorous cells represent multiple stable-steady states corresponding to a reaction feedback mechanism. The (autocatalytic) feedback loop is constructed from observations on the role played by myo-inositol: it increases the permeability of ions through the membrane and the biosynthetic pathway to myo-inositol is activated by ions. Provided that the permeabilities of nutrients (sugars and salts) are a product-enhanced function of myo-inositol, then we have a (oversimplified) model that can exhibit multiple stationary stable states, one or two depending on the exogenous nutrients and myo-inositol concentrations, and reversible and irreversible transitions from one of these states to the other are possible. From this model, straightforward simple experiments are suggested. We also propose that recent models dealing with the intracellular calcium regulation by hormones, where one key step requires the hydrolysis of inositol phospholipids, take into account free myo-inositol and endogenous hormone concentrations (e.g., auxins).