Three-dimensional Stochastic Simulation Research Articles

Chiral Thermodynamics in Tailored Chiral Optical Environments

We present an optomechanical model that describes the stochastic motion of an overdamped chiral nanoparticle diffusing in the optical bistable potential formed in the standing-wave of two counter-propagating Gaussian beams. We show how chiral optical environments can be induced in the standing-wave with no modification of the initial bistability by controlling the polarizations of each beam. Under this control, optical chiral densities and/or an optical chiral fluxes are generated, associated respectively with reactive vs. dissipative chiral optical forces exerted on the diffusing chiral nanoparticle. This optomechanical chiral coupling bias the thermodynamics of the thermal activation of the barrier crossing, in ways that depend on the nanoparticle enantiomer and on the optical field enantiomorph. We show that reactive chiral forces, being conservative, contribute to a global, enantiospecific, change of the Helmholtz free energy bistable landscape. In contrast, when the chiral nanoparticle is immersed in a dissipative chiral environment, the symmetry of the bistable potential is broken by non-conservative chiral optical forces. In this case, the chiral electromagnetic fields continuously transfer, through dissipation, mechanical energy to the chiral nanoparticle. For this chiral nonequilibrium steady-state, the thermodynamic changes of the barrier crossing take the form of heat transferred to the thermal bath and yield chiral deracemization schemes that can be explicitly calculated within the framework of our model. Three-dimensional stochastic simulations confirm and further illustrate the thermodynamic impact of chirality. Our results reveal how chiral degrees of freedom both of the nanoparticle and of the optical fields can be transformed into true thermodynamics control parameters, thereby demonstrating the significance of optomechanical chiral coupling in stochastic thermodynamics.

Three-dimensional stochastic simulation of chemoattractant-mediated excitability in cells.

During the last decade, a consensus has emerged that the stochastic triggering of an excitable system drives pseudopod formation and subsequent migration of amoeboid cells. The presence of chemoattractant stimuli alters the threshold for triggering this activity and can bias the direction of migration. Though noise plays an important role in these behaviors, mathematical models have typically ignored its origin and merely introduced it as an external signal into a series of reaction-diffusion equations. Here we consider a more realistic description based on a reaction-diffusion master equation formalism to implement these networks. In this scheme, noise arises naturally from a stochastic description of the various reaction and diffusion terms. Working on a three-dimensional geometry in which separate compartments are divided into a tetrahedral mesh, we implement a modular description of the system, consisting of G-protein coupled receptor signaling (GPCR), a local excitation-global inhibition mechanism (LEGI), and signal transduction excitable network (STEN). Our models implement detailed biochemical descriptions whenever this information is available, such as in the GPCR and G-protein interactions. In contrast, where the biochemical entities are less certain, such as the LEGI mechanism, we consider various possible schemes and highlight the differences between them. Our simulations show that even when the LEGI mechanism displays perfect adaptation in terms of the mean level of proteins, the variance shows a dose-dependence. This differs between the various models considered, suggesting a possible means for determining experimentally among the various potential networks. Overall, our simulations recreate temporal and spatial patterns observed experimentally in both wild-type and perturbed cells, providing further evidence for the excitable system paradigm. Moreover, because of the overall importance and ubiquity of the modules we consider, including GPCR signaling and adaptation, our results will be of interest beyond the field of directed migration.

Three-dimensional stochastic simulations of soil clay and its response to sampling density

Clay is an active component in the mechanical composition of soil. The quantitative study of the spatial distribution of soil clay content is crucial to soil microecological research and agricultural or environmental management. The main purpose of the paper was to simulate soil clay content in three dimensions and reveal its response to sampling density based on sequential Gaussian simulation. The results showed the following: (1) With a reduction in samples, especially in the A horizon, spatial correlation was relatively enhanced and randomness weakened. (2) The spatial distribution of soil clay showed soil had high clay content in the mid-eastern region of the Haidian District, Beijing, and clay content was generally low in the other areas; (3) With a decrease of sampling density, the simulated spatial distribution of clay became gradually more homogeneous. The stochastic simulation results for two kinds of sampling densities, i.e., SD1 and SD4 were closer to the original measured values; the general distribution was discrete and could more accurately reflect the local volatility of the original data distribution; (4) Considering the root mean square error (RMSE), accurate plot, standard error map, and quartile deviation map, SD1 had the best effect of three-dimensional stochastic simulation, followed by SD4; (5) For soil clay, three-dimensional sampling can be applicable to reduce samples required in the lower horizon in order to reduce the sampling workload.

Mechanism of nuclear movements in a multinucleated cell.

Multinucleated cells are important in many organisms, but the mechanisms governing the movements of nuclei sharing a common cytoplasm are not understood. In the hyphae of the plant pathogenic fungus Ashbya gossypii, nuclei move back and forth, occasionally bypassing each other, preventing the formation of nuclear clusters. This is essential for genetic stability. These movements depend on cytoplasmic microtubules emanating from the nuclei that are pulled by dynein motors anchored at the cortex. Using three-dimensional stochastic simulations with parameters constrained by the literature, we predict the cortical anchor density from the characteristics of nuclear movements. The model accounts for the complex nuclear movements seen in vivo, using a minimal set of experimentally determined ingredients. Of interest, these ingredients power the oscillations of the anaphase spindle in budding yeast, but in A.gossypii, this system is not restricted to a specific nuclear cycle stage, possibly as a result of adaptation to hyphal growth and multinuclearity.

3-Dimensional Stochastic Seepage Analysis of a Yangtze River Embankment

Three-dimensional stochastic simulation was performed to investigate the complexity of the seepage field of an embankment. Three-dimensional anisotropic heterogeneous steady state random seepage finite element model was developed. The material input data were derived from a statistical analysis of strata soil characteristics and geological columns. The Kolmogorov-Smirnov test was used to validate the hypothesis that the Gaussian probability distribution is applicable to the random permeability tensors. A stochastic boundary condition, the random variation of upstream and downstream water level, was taken into account in the three-dimensional finite element modelling. Furthermore, the functions of sheet-pile breakwater and catchwater were also incorporated as turbulent sources. This case, together with the variability of soil permeability, has been analyzed to investigate their influence on the hydraulic potential distributed and the random evolution of stochastic seepage field. Results from stochastic analyses have also been compared against those of deterministic analyses. The insights gained in this study suggest it is necessary, feasible, and practical to employ stochastic studies in seepage field problems. The method provides a more comprehensive stochastic algorithm than conventional ones to characterize and analyze three-dimensional random seepage field problems.

A first look at Bottomonium melting via a stochastic potential

We investigate the phenomenon of Bottomonium melting in a thermal quark-gluon plasma using three-dimensional stochastic simulations based on the concept of open-quantum systems. In this non-relativistic framework, introduced in [Phys.Rev. D85 (2012) 105011], which makes close contact to the potentials derived in effective field theory, the $b\bar{b}$ system evolves unitarily under the incessant kicks by the constituents of the surrounding heat bath. In particular thermal fluctuations and the presence of a complex potential in the EFT are naturally related. An intricate interplay between state mixing and thermal excitations emerges as we show how non-thermal initial conditions of Bottomonium states evolve over time. We emphasize that the dynamics of these states gives us access to information beyond what is encoded in the thermal Bottomonium spectral functions. Assumptions underlying our approach and their limitations, as well as the refinements necessary to connect to experimental measurements under more realistic conditions are discussed.

Theoretical evaluation of methods for extracting retention factors and kinetic rate constants in liquid chromatography

A three-dimensional stochastic simulation is used to provide a detailed understanding of mass transfer processes in liquid chromatography. In this simulation, the migration of individual molecules is established through diffusion and laminar convection within the mobile phase. The molecules interact with the stationary phase by a partition (absorption) mechanism. For these studies, the column length, linear velocity, stationary-phase diffusion coefficient, interfacial mass transfer coefficient, and equilibrium constant are varied in a system with a homogeneous surface. Heterogeneous surfaces are also investigated by having multiple types of interaction sites that are equally or unequally distributed. For each simulation, the molecular distribution is examined and characterized at specified times or column lengths. Five individual methods are then applied to extract the thermodynamic and kinetic information for transport between the mobile and stationary phases. In the first method, all of the molecules are initially distributed in the mobile phase and the fraction remaining is monitored as a function of time. These simulation data are fit to a single exponential decay by nonlinear regression to determine the “true” retention factors and rate constants. The other methods rely on evaluating the shape of the zone profiles along the column. The statistical moments of the profiles are used to calculate the mean and the variance, which are related to the retention factors and the rate constants, respectively. The profiles are also fit to the exponentially modified Gaussian equation, the Giddings equation, and the Thomas equation. The fitting parameters from these equations are then used to calculate the retention factors and rate constants. Comparisons of the accuracy relative to the “true” retention factors and “true” rate constants, as well as the advantages and limitations of each method are discussed.

Stochastic simulation of the partition mechanism under diffusion-limited conditions in chromatography and electrochromatography

A three-dimensional stochastic simulation has been used to study the kinetics of the partition mechanism in a homogeneous system under diffusion-limited conditions. By nonlinear regression of the simulation data, the rate constants for transport between the fluid and surface phases ( k fs and k sf) are determined with ±0.49% average relative standard deviation, and the ratio of the rate constants ( k fs/ k sf) with ±0.70% average relative standard deviation and ±2.25% average relative error. The results of these simulations are used to elucidate the relationship between the rate constants and the fundamental parameters of the system, including the equilibrium constant ( K), the diffusion coefficients ( D f and D s), and the radius of the fluid and surface phases ( R f and R s). In addition, the influence of slow kinetics on the solute zone profile is characterized under the conditions of laminar and electroosmotic flow. The mean, variance, and asymmetry of the zone profile are shown to vary systematically with the rate constants, the linear velocity, and the distance travelled.

Three-Dimensional Molecular Simulation of Electrophoretic Separations

A three-dimensional stochastic simulation has been developed for electrophoretic separations. This simulation follows the trajectories of individual molecules by applying the fundamental equations of motion for diffusion, electroosmotic flow, and electrophoretic migration. The molecular zone profile may then be examined and characterized at any specified time or distance. The stochastic simulation has been validated by comparison with classical transport models, having average relative errors for the mean zone distance and variance of 0.01−0.04% and 2.67−4.36%, respectively. The simulation also shows excellent agreement with experimental results for the electrophoretic separation of the nucleotide monophosphates in phosphate buffer solution, having average relative errors for the mean zone distance and variance of 1.65% and 12.99%, respectively. This stochastic simulation provides an accurate and versatile means to examine and characterize transport processes in complex electrophoretic systems.