Stochastic Dynamics of Bionanosystems: Multiscale Analysis and Specialized Ensembles

An approach for simulating bionanosystems, such as viruses and ribosomes, is presented. This calibration-free approach is based on an all-atom description for bionanosystems, a universal interatomic force field, and a multiscale perspective. The supramillion-atom nature of these bionanosystems prohibits the use of a direct molecular dynamics approach for phenomena like viral structural transitions or self-assembly that develop over milliseconds or longer. A key element of these multiscale systems is the cross-talk between, and consequent strong coupling of, processes over many scales in space and time. We elucidate the role of interscale cross-talk and overcome bionanosystem simulation difficulties with automated construction of order parameters (OPs) describing supra-nanometer scale structural features, construction of OP dependent ensembles describing the statistical properties of atomistic variables that ultimately contribute to the entropies driving the dynamics of the OPs, and the derivation of a rigorous equation for the stochastic dynamics of the OPs. Since the atomic scale features of the system are treated statistically, several ensembles are constructed that reflect various experimental conditions. The theory provides a basis for a practical, quantitative bionanosystem modeling approach that preserves the cross-talk between the atomic and nanoscale features. A method for integrating information from nanotechnical experimental data in the derivation of equations of stochastic OP dynamics is also introduced.Comment: 24 page

Self-Assembly of Nanocomponents into Composite Structures: Derivation and Simulation of Langevin Equations

The kinetics of the self-assembly of nanocomponents into a virus, nanocapsule, or other composite structure is analyzed via a multiscale approach. The objective is to achieve predictability and to preserve key atomic-scale features that underlie the formation and stability of the composite structures. We start with an all-atom description, the Liouville equation, and the order parameters characterizing nanoscale features of the system. An equation of Smoluchowski type for the stochastic dynamics of the order parameters is derived from the Liouville equation via a multiscale perturbation technique. The self-assembly of composite structures from nanocomponents with internal atomic structure is analyzed and growth rates are derived. Applications include the assembly of a viral capsid from capsomers, a ribosome from its major subunits, and composite materials from fibers and nanoparticles. Our approach overcomes errors in other coarse-graining methods which neglect the influence of the nanoscale configuration on the atomistic fluctuations. We account for the effect of order parameters on the statistics of the atomistic fluctuations which contribute to the entropic and average forces driving order parameter evolution. This approach enables an efficient algorithm for computer simulation of self-assembly, whereas other methods severely limit the timestep due to the separation of diffusional and complexing characteristic times. Given that our approach does not require recalibration with each new application, it provides a way to estimate assembly rates and thereby facilitate the discovery of self-assembly pathways and kinetic dead-end structures.Comment: 34 pages, 11 figure

Multiscaling for Classical Nanosystems: Derivation of Smoluchowski and Fokker-Planck Equations

Using multiscale analysis and methods of statistical physics, we show that a solution to the N-atom Liouville Equation can be decomposed via an expansion in terms of a smallness parameter epsilon, wherein the long scale time behavior depends upon a reduced probability density that is a function of slow-evolving order parameters. This reduced probability density is shown to satisfy the Smoluchowski equation up to order epsilon squared for a given range of initial conditions. Furthermore, under the additional assumption that the nanoparticle momentum evolves on a slow time scale, we show that this reduced probability density satisfies a Fokker-Planck equation up to the same order in epsilon. This approach applies to a broad range of problems in the nanosciences.Comment: 23 page

Mesoscopic model of nucleation and Ostwald ripening/stepping: Application to the silica polymorph system

Precipitation is modeled using a particle size distribution ~PSD! approach for the single or multiple polymorph system. A chemical kinetic-type model for the construction of the molecular clusters of each polymorph is formulated that accounts for adsorption at a heterogeneous site, nucleation, growth, and Ostwald ripening. When multiple polymorphs are accounted for, Ostwald stepping is also predicted. The challenge of simulating the 23 order of magnitude in cluster size ~monomer, dimer, . . . , 1023-mer! is met by a new formalism that accounts for the macroscopic behavior of large clusters as well as the structure of small ones. The theory is set forth for the surface kinetic controlled growth systems and it involves corrections to the Lifshitz–Slyozov, Wagner ~LSW! equation and preserves the monomer addition kinetics for small clusters. A time independent, scaled PSD behavior is achieved both analytically and numerically, and the average radius grows with Rave}t1/2 law for smooth particles. Applications are presented for the silica system that involves five polymorphs. Effects of the adsorption energetics and the smooth or fractal nature of clusters on the nucleation, ripening, and stepping behavior are analyzed. The Ostwald stepping scenario is found to be highly sensitive to adsorption energetics. Long time scaling behavior of the PSD reveals time exponents greater than those for the classical theory when particles are fractal. Exact scaling solutions for the PSD are compared with numerical results to assess the accuracy and convergence of our numerical technique. © 2000 American Institute of Physics. @S0021-9606~00!70123-1

Mechanical failure of cavities in poroelastic media

The stress-induced failure of cavities in poroelastic media is investigated using an analytical solution of the elastic matrix inclusion problem of Eshelby and a rock failure criterion. The elastic properties of the porous matrix surrounding the cavity are modeled using a self-consistent version of the theory of Berryman while the cavity collapse criterion is based on a failure condition calibrated as a function of matrix mineralogy, grain size and porosity. The influence of the latter textural variables as well as pore fluid pressure and cavity shape and orientation relative to the far-field stress are evaluated. The region of failure on the cavity surface is identified. These results are applied to the prediction of vug stability in a sedimentary basin in the context of vuggy reservoir exploration and production

Visual attention modulates the into ration of goal-relevant evidence and not value

When choosing between options, such as food items presented in plain view, people tend to choose the option they spend longer looking at. The prevailing interpretation is that visual attention increases value. However, in previous studies, ‘value’ was coupled to a behavioural goal, since subjects had to choose the item they preferred. This makes it impossible to discern if visual attention has an effect on value, or, instead, if attention modulates the information most relevant for the goal of the decision-maker. Here, we present the results of two independent studies—a perceptual and a value-based task—that allow us to decouple value from goal-relevant information using specific task-framing. Combining psychophysics with computational modelling, we show that, contrary to the current interpretation, attention does not boost value, but instead it modulates goal-relevant information. This work provides a novel and more general mechanism by which attention interacts with choice

Multiscale Theory of Finite Size Bose Systems: Implications for Collective and Single-Particle Excitations

Boson droplets (i.e., dense assemblies of bosons at low temperature) are shown to mask a significant amount of single-particle behavior and to manifest collective, droplet-wide excitations. To investigate the balance between single-particle and collective behavior, solutions to the wave equation for a finite size Bose system are constructed in the limit where the ratio \varepsilon of the average nearest-neighbor boson distance to the size of the droplet or the wavelength of density disturbances is small. In this limit, the lowest order wave function varies smoothly across the system, i.e., is devoid of structure on the scale of the average nearest-neighbor distance. The amplitude of short range structure in the wave function is shown to vanish as a power of \varepsilon when the interatomic forces are relatively weak. However, there is residual short range structure that increases with the strength of interatomic forces. While the multiscale approach is applied to boson droplets, the methodology is applicable to any finite size bose system and is shown to be more direct than field theoretic methods. Conclusions for Helium-4 nanodroplets are drawn.Comment: 28 pages, 5 figure

Multiscaling for Systems with a Broad Continuum of Characteristic Lengths and Times: Structural Transitions in Nanocomposites

The multiscale approach to N-body systems is generalized to address the broad continuum of long time and length scales associated with collective behaviors. A technique is developed based on the concept of an uncountable set of time variables and of order parameters (OPs) specifying major features of the system. We adopt this perspective as a natural extension of the commonly used discrete set of timescales and OPs which is practical when only a few, widely-separated scales exist. The existence of a gap in the spectrum of timescales for such a system (under quasiequilibrium conditions) is used to introduce a continuous scaling and perform a multiscale analysis of the Liouville equation. A functional-differential Smoluchowski equation is derived for the stochastic dynamics of the continuum of Fourier component order parameters. A continuum of spatially non-local Langevin equations for the OPs is also derived. The theory is demonstrated via the analysis of structural transitions in a composite material, as occurs for viral capsids and molecular circuits.Comment: 28 pages, 1 figur

Instabilities in the dissolution of a porous matrix

A reactive fluid dissolving the surrounding rock matrix can trigger an instability in the dissolution front, leading to spontaneous formation of pronounced channels or wormholes. Theoretical investigations of this instability have typically focused on a steadily propagating dissolution front that separates regions of high and low porosity. In this paper we show that this is not the only possible dissolutional instability in porous rocks; there is another instability that operates instantaneously on any initial porosity field, including an entirely uniform one. The relative importance of the two mechanisms depends on the ratio of the porosity increase to the initial porosity. We show that the "inlet" instability is likely to be important in limestone formations where the initial porosity is small and there is the possibility of a large increase in permeability. In quartz-rich sandstones, where the proportion of easily soluble material (e.g. carbonate cements) is small, the instability in the steady-state equations is dominant.Comment: to be published in Geophysical Research Letter

Overview of the structural geology and tectonics of the Central Basin Platform, Delaware Basin, and Midland Basin, West Texas and New Mexico

The structural geology and tectonics of the Permian Basin were investigated using an integrated approach incorporating satellite imagery, aeromagnetics, gravity, seismic, regional subsurface mapping and published literature. The two primary emphases were on: (1) delineating the temporal and spatial evolution of the regional stress state; and (2) calculating the amount of regional shortening or contraction. Secondary objectives included delineation of basement and shallower fault zones, identification of structural style, characterization of fractured zones, analysis of surficial linear features on satellite imagery and their correlation to deeper structures. Gandu Unit, also known as Andector Field at the Ellenburger level and Goldsmith Field at Permian and younger reservoir horizons, is the primary area of interest and lies in the northern part of Ector county. The field trends northwest across the county line into Andrews County. The field(s) are located along an Ellenburger thrust anticline trap on the eastern margin of the Central Basin Platform