Among the most striking aspects of movement many animal groups are their sudden coherent changes in direction. Recent observations locusts and starlings have shown that this directional switching is an intrinsic property motion. Similar direction switches seen self-propelled particle other models group Comprehending factors determine such key to understanding these groups. Here, we adopt a coarse-grained approach study model assuming underlying one-dimensional Fokker-Planck equation for mean...

Several stochastic simulation algorithms (SSAs) have been recently proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this paper, two commonly used SSAs are studied. The first SSA is an on-lattice model described by the master equation. second off-lattice based on of Brownian motion individual molecules their reactive collisions. both cases, it shown that implementation bimolecular reactions (i.e. form A + B -> C, or C) might lead to incorrect results....

Bacterial chemotaxis is widely studied from both the microscopic (cell) and macroscopic (population) points of view, here we connect these very different levels description by deriving classical for a model behavior individual cells. The analysis based on velocity jump process describing motion individuals such as bacteria, wherein each carries an internal state that evolves according to system ordinary differential equations forced time- and/or space-dependent external signal. In problem...

Many cellular and subcellular biological processes can be described in terms of diffusing chemically reacting species (e.g. enzymes). Such reaction–diffusion mathematically modelled using either deterministic partial-differential equations or stochastic simulation algorithms. The latter provide a more detailed precise picture, several algorithms have been proposed recent years. models typically give the same description far from boundary simulated domain, but behaviour close to reactive...

A practical introduction to stochastic modelling of reaction-diffusion processes is presented. No prior knowledge simulations assumed. The methods are explained using illustrative examples. article starts with the classical Gillespie algorithm for chemical reactions. Then algorithms molecular diffusion given. Finally, basic connections between and deterministic models mathematical tools (e.g. master equation) concludes an overview more advanced problems.

A generalization of the Cucker--Smale model for collective animal behavior is investigated. The formulated as a system delayed stochastic differential equations. It incorporates two additional processes which are present in decision making, but often neglected modeling: (i) stochasticity (imperfections) individual and (ii) responses individuals to signals their environment. Sufficient conditions flocking generalized derived by using suitable Lyapunov functional. As by-product, new result...

Nonlinear independent component analysis is combined with diffusion-map data techniques to detect good observables in high-dimensional dynamic data. These detections are achieved by integrating local principal of simulation bursts using eigenvectors a Markov matrix describing anisotropic diffusion. The widely applicable procedure, crucial step model reduction approaches, illustrated on stochastic chemical reaction network simulations.

The collective behavior of bacterial populations provides an example how cell-level decision making translates into population-level and illustrates clearly the difficult multiscale mathematical problem incorporating individual-level models. Here we focus on flagellated bacterium E. coli, for which a great deal is known about signal detection, transduction, swimming behavior. We review biological background individual- processes discuss velocity-jump approach used describing based...

Spatial organization and noise play an important role in molecular systems biology. In recent years, a number of software packages have been developed for stochastic spatio-temporal simulation, ranging from detailed molecular-based approaches to less compartment-based simulations. Compartment-based yield quick accurate mesoscopic results, but lack the level detail that is characteristic computationally intensive models. Often microscopic only required small region (e.g. close cell membrane)....

We present computer-assisted methods for analyzing stochastic models of gene regulatory networks. The main idea that underlies this equation-free analysis is the design and execution appropriately-initialized short bursts simulations; results these are processed to estimate coarse-grained quantities interest, such as mesoscopic transport coefficients. In particular, using a simple model genetic toggle switch, we illustrate computation an effective free energy state-dependent diffusion...

A class of Brownian dynamics algorithms for stochastic reaction-diffusion models which include reversible bimolecular reactions is presented and analyzed. The method a generalization the $\lambda$–$\overline{\varrho}$ model irreversible was introduced in [R. Erban S. J. Chapman, Phys. Biol., 6 (2009), 046001]. formulae relating experimentally measurable quantities (reaction rate constants diffusion constants) with algorithm parameters are derived. probability geminate recombination also investigated.

A planar bistable liquid crystal device, reported in Tsakonas et al. [Appl. Phys. Lett. 90, 111913 (2007)], is modeled within the Landau-de Gennes theory for nematic crystals. This device consists of an array square micrometer-sized wells. We obtain six different classes equilibrium profiles and these are classified as diagonal or rotated solutions. In strong anchoring case, we propose a Dirichlet boundary condition that mimics experimentally imposed tangent conditions. weak present suitable...

Two algorithms that combine Brownian dynamics (BD) simulations with mean-field partial differential equations (PDEs) are presented. This PDE-assisted (PBD) methodology provides exact particle tracking data in parts of the domain, whilst making use a reaction-diffusion PDE description elsewhere. The first PBD algorithm couples BD PDEs by randomly creating new particles close to interface, which partitions and reincorporating into continuum PDE-description when they cross interface. second...

The noisy dynamics of chemical systems is commonly studied using either the master equation (CME) or Fokker-Planck (CFPE). latter a continuum approximation discrete CME approach. It has recently been shown that for particular system, CFPE captures noise-induced multistability predicted by CME. This phenomenon involves CME's marginal probability distribution changing from unimodal to multimodal as system size decreases below critical value. We here show does not always capture multistability....

We study nematic equilibria on a square with tangent Dirichlet conditions the edges, in three different modelling frameworks: (i) off-lattice Hard Gaussian Overlap and Gay–Berne models; (ii) lattice-based Lebwohl–Lasher model; (iii) two-dimensional Landau-de Gennes model. compare predictions, identify regimes of agreement case, find up to 21 equilibria. Of these, two are physically stable.

Three coarse-grained molecular dynamics (MD) models are investigated with the aim of developing and analysing multi-scale methods which use MD simulations in parts computational domain (less detailed) Brownian (BD) remainder domain. The first model is formulated one spatial dimension. It based on elastic collisions heavy molecules (e.g. proteins) light point particles water molecules). Two three-dimensional then investigated. obtained results applied to a simplified protein binding receptors...

Stochastic modelling of gene regulatory networks provides an indispensable tool for understanding how random events at the molecular level influence cellular functions. A common challenge stochastic models is to calibrate a large number model parameters against experimental data. Another difficulty study behaviour depends on its parameters, i.e. whether change in can lead significant qualitative (bifurcation). In this paper, tensor-structured parametric analysis (TPA) developed address these...

Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled Markov typically simulated using the Gillespie Stochastic Simulation Algorithm (SSA). While easy to implement exact, computational cost of SSA simulate become prohibitive frequency reaction events increases. This has motivated numerous coarse-grained schemes, where "fast" reactions are approximated either Langevin...

Abstract Summary: Smoldyn is a software package for stochastic modelling of spatial biochemical networks and intracellular systems. It was originally developed with an accurate off-lattice particle-based model at its core. This has recently been enhanced the addition computationally efficient on-lattice model, which can be run stand-alone or coupled together multiscale simulations using both models in regions where they are most required, increasing applicability to larger molecule numbers...

Finding coarse-grained, low-dimensional descriptions is an important task in the analysis of complex, stochastic models gene regulatory networks. This involves (a) identifying observables that best describe state these complex systems and (b) characterizing dynamics observables. In a previous paper [R. Erban et al., J. Chem. Phys. 124, 084106 (2006)] authors assumed good were known priori, presented equation-free approach to approximate coarse-grained quantities (i.e., effective drift...

A framework for the analysis of stochastic models chemical systems which deterministic mean-field description is undergoing a saddle-node infinite period (SNIPER) bifurcation presented. Such occurs, example, in modeling cell-cycle regulation. It shown that system possesses oscillatory solutions even parameter values model does not oscillate. The dependence mean these oscillations on parameters (kinetic rate constants) and size (number molecules present) are studied. Our approach based...