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The effects of electromagnetic fields (EMF) have been widely debated concerning their role in chemical reactions. Reactions, usually took hours or days to complete, have been shown to happen a thousand times faster using EMF radiations. This work develops a formalism and a computer program to evaluate and quantify the EMF effects in chemical reactions. The master equation employed in this program solves the internal energy of the reaction under EMFs while including collisional effects. Multiphoton absorption and emission are made possible with the transitioning energy close to the EMF and are influenced by the dielectric properties of the system. Dimethyl Sulfoxide and Benzyl Chloride are simulated under different EMF intensities. The results show that EMF absorption is closely related to the collisional redistribution of energy in molecules. The EMF effect can be interpreted as a shift of the thermodynamic equilibrium. Under such nonequilibrium energy distribution, the 'temperature' is not a reliable quantity for defining the state of the system. [ABSTRACT FROM AUTHOR]

Cell chemotaxis is an important characteristic of cellular migration, which takes part in crucial aspects of life and development. In this work, we propose a novelin silicomodel of mesenchymal 3D migration with competing protrusions under a chemotactic gradient. Based on recent experimental observations, we identify three main stages that can regulate mesenchymal chemotaxis: chemosensing, dendritic protrusion dynamics and cell–matrix interactions. Therefore, each of these features is considered as a different module of the main regulatory computational algorithm. The numerical model was particularized for the case of fibroblast chemotaxis under a PDGF-bb gradient. Fibroblasts migration was simulated embedded in two different 3D matrices – collagen and fibrin – and under several PDGF-bb concentrations. Validation of the model results was provided through qualitative and quantitative comparison within vitrostudies. Our numerical predictions of cell trajectories and speeds were within the measuredin vitroranges in both collagen and fibrin matrices. Although in fibrin, the migration speed of fibroblasts is very low, because fibrin is a stiffer and more entangling matrix. Testing PDGF-bb concentrations, we noticed that an increment of this factor produces a speed increment. At 1 ng mL−1a speed peak is reached after which the migration speed diminishes again. Moreover, we observed that fibrin exerts a dampening behavior on migration, significantly affecting the migration efficiency. [ABSTRACT FROM AUTHOR]

Background: The concept of Petri nets (PN) is widely used in systems biology and allows modeling of complex biochemical systems like metabolic systems, signal transduction pathways, and gene expression networks. In particular, PN allows the topological analysis based on structural properties, which is important and useful when quantitative (kinetic) data are incomplete or unknown. Knowing the kinetic parameters, the simulation of time evolution of such models can help to study the dynamic behavior of the underlying system. If the number of involved entities (molecules) is low, a stochastic simulation should be preferred against the classical deterministic approach of solving ordinary differential equations. The Stochastic Simulation Algorithm (SSA) is a common method for such simulations. The combination of the qualitative and semi-quantitative PN modeling and stochastic analysis techniques provides a valuable approach in the field of systems biology. Results: Here, we describe the implementation of stochastic analysis in a PN environment. We extended MONALISA - an open-source software for creation, visualization and analysis of PN - by several stochastic simulation methods. The simulation module offers four simulation modes, among them the stochastic mode with constant firing rates and Gillespie's algorithm as exact and approximate versions. The simulator is operated by a user-friendly graphical interface and accepts input data such as concentrations and reaction rate constants that are common parameters in the biological context. The key features of the simulation module are visualization of simulation, interactive plotting, export of results into a text file, mathematical expressions for describing simulation parameters, and up to 500 parallel simulations of the same parameter sets. To illustrate the method we discuss a model for insulin receptor recycling as case study. Conclusions: We present a software that combines the modeling power of Petri nets with stochastic simulation of dynamic processes in a user-friendly environment supported by an intuitive graphical interface. The program offers a valuable alternative to modeling, using ordinary differential equations, especially when simulating single-cell experiments with low molecule counts. The ability to use mathematical expressions provides an additional flexibility in describing the simulation parameters. The open-source distribution allows further extensions by third-party developers. The software is cross-platform and is licensed under the Artistic License 2.0. [ABSTRACT FROM AUTHOR]

It is well known that firings of a well-stirred chemically reacting system can be described by a continuous-time Markov chain. The currently-used exact implementations of Gillespie's algorithm simulate every reaction event individually and thus the computational cost is inevitably high. In this paper, we present an exact implementation of a continuous-time Markov chain with bounded intensity which can simulate the process at given time points. The implementation involves rejection sampling, with a trajectory either accepted or rejected based on just a few reaction events. A simulation study on the Schlögl model is presented and supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

We discuss two independent methods of solution of a master equation whose biased jump transition rates account for long jumps of Lévy-stable type and admit a Boltzmannian (thermal) equilibrium to arise in the large time asymptotics of a probability density function ρ( x, t). Our main goal is to demonstrate a compatibility of a direct solution method (an explicit, albeit numerically assisted, integration of the master equation) with an indirect pathwise procedure, recently proposed in [Physica A 392, 3485, (2013)] as a valid tool for a dynamical analysis of non-Langevin jump-type processes. The path-wise method heavily relies on an accumulation of large sample path data, that are generated by means of a properly tailored Gillespie's algorithm. Their statistical analysis in turn allows to infer the dynamics of ρ( x, t). However, no consistency check has been completed so far to demonstrate that both methods are fully compatible and indeed provide a solution of the same dynamical problem. Presently we remove this gap, with a focus on potential deficiencies (various cutoffs, including those upon the jump size) of approximations involved in simulation routines and solutions protocols. [ABSTRACT FROM AUTHOR]

We give the description for the Nondeterministic Waiting Time (NWT) algorithm, a biochemical modeling approach based on the Membrane Systems paradigm of computation. This simulation technique provides a unique perspective on the biochemical evolution of the cell different from Gillespie's algorithm and different from ODE-based simulations. That is, depending on the reactions and molecular multiplicities of a given model, our simulator is capable of producing results comparable to the alternative techniques - continuous and deterministic or discrete and stochastic. Some results for a few models are given, illustrating the differences between the NWT algorithm, the Gillespie algorithm, and the solutions to systems of ordinary differential equations. We are able to show that in some cases the NWT technique yields results closer to Gillespie, while for other models the results of the NWT simulator are much closer to the results of the ODE simulator. [ABSTRACT FROM AUTHOR]

We analyze a specific class of random systems that, while being driven by a symmetric Lévy stable noise, asymptotically set down at the Boltzmann-type equilibrium, represented by a probability density function (pdf) . This behavior needs to be contrasted with the standard Langevin representation of Lévy jump-type processes. It is known that the choice of the drift function in the Newtonian form excludes the existence of the Boltzmannian pdf (Eliazar–Klafter no go theorem). In view of this incompatibility statement, our main goal here is to establish the appropriate path-wise description of the equilibrating jump-type process. A priori given inputs are (i) jump transition rates entering the master equation for and (ii) the target (invariant) pdf of that equation, in the Boltzmannian form. We resort to numerical methods and construct a suitable modification of the Gillespie algorithm, originally invented in the chemical kinetics context. The generated sample trajectories show up a qualitative typicality, e.g. they display structural features of jumping paths (predominance of small vs large jumps) specific to particular stability indices . The obtained random paths statistical data allow us to infer an associated pdf dynamics which stands for a validity check of our procedure. The considered exemplary Boltzmannian equilibria refer to (i) harmonic potential , (ii) logarithmic potential with and (iii) locally periodic confining potential , . [ABSTRACT FROM AUTHOR]

The simplest, and most common, stochastic model for population processes, including those from biochemistry and cell biology, are continuous time Markov chains. Simulation of such models is often relatively straightforward, as there are easily implementable methods for the generation of exact sample paths. However, when using ensemble averages to approximate expected values, the computational complexity can become prohibitive as the number of computations per path scales linearly with the number of jumps of the process. When such methods become computationally intractable, approximate methods, which introduce a bias, can become advantageous. In this paper, we provide a general framework for understanding the weak error, or bias, induced by different numerical approximation techniques in the current setting. The analysis takes into account both the natural scalings within a given system and the step size of the numerical method. Examples are provided to demonstrate the main analytical results as well as the reduction in computational complexity achieved by the approximate methods. [ABSTRACT FROM AUTHOR]

In this article we consider a new derivation mode for generalized communicating P systems (GCPS) corresponding to the functioning of population protocols (PP) and based on the sequential derivation mode and a fairness condition that permits to ensure a particular sequence of configurations. We show that PP can be seen as a particular variant of GCPS. We also consider several stochastic evolutions satisfying different fairness conditions and particularly focus on those corresponding to the run of a Gillespie's SSA. This permits to further describe the dynamics of GCPS by a system of ODEs when the population size goes to the infinity. [ABSTRACT FROM AUTHOR]

We analyze a hierarchy of three regimes for modeling gene regulation. The most complete model is a continuous time, discrete state space, Markov jump process. An intermediate "switch plus diffusion" model takes the form of a stochastic differential equation driven by an independent continuous time Markov switch. In the third "switch plus ODE" model the switch remains, but the diffusion is removed. The latter two models allow for multiscale simulation where, for the sake of computational efficiency, system components are treated differently according to their abundance. The switch plus ODE regime was proposed by Paszek [Bull. Math. Biol., 69 (2007), pp. 1567-1601], who analyzed the steady state behavior, showing that the mean was preserved, but the variance only approximated that of the full model. Here, we show that the tools of stochastic calculus can be used to analyze first and second moments for all time. A technical issue to be addressed is that the state space for the discrete-valued switch is infinite. We show that the new switch plus diffusion regime preserves the biologically relevant measures of mean and variance, whereas the switch plus ODE model uniformly underestimates the variance in the protein level. We also show that, for biologically relevant parameters, the transient behavior can differ significantly from the steady state, justifying our time-dependent analysis. Extra computational results are also given for a protein dimerization model that is beyond the scope of the current analysis. [ABSTRACT FROM AUTHOR]

Objectives: P-selectin binding to P-selectin glycoprotein ligand-1 (PSGL)-1 mediates leukocyte rolling under conditions of inflammation and injury. The aims of this study were to develop an efficient, high temporal resolution model for direct simulation of leukocyte rolling and conduct a study of load-bearing bonds using the model. Materials and Methods: A stochastic π-calculus-driven event-tracking model of adhesion (ETMA) was developed and compared with experimental data. Multiple simulations for each case were conducted to obtain high-confidence numerical characteristics of leukocyte rolling. Results: Leukocyte rolling and the underlying P-selectin—PSGL-1 bonds were studied under low wall shear rate (25-50 s-1) conditions from measured parameters of leukocyte rolling and bond properties. For the first time, the location, number, lifetime, history, and kinetics of load-bearing bonds and their influence on cell rolling were identified and instantaneous cell displacements, translational and rotational velocities, and cell-substrate distances derived. The model explains the commonly observed “stop-start” type rolling behavior and reveals that a few load-bearing bonds are sufficient to support rolling, while a large number of bonds dissociate before becoming load bearing. Conclusions: ETMA provides a method for more precise, direct simulation of leukocyte rolling at low wall shear rates and sets a foundation upon which further refinements can be introduced. [ABSTRACT FROM AUTHOR]

Abstract: In this paper P systems are used as a formal framework for the specification and simulation of biological systems. In particular, we will deal with gene regulation systems consisting of protein–protein and protein–DNA interactions that take place in different compartments of the hierarchical structure of the living cell or in different individual cells from a colony. We will explicitly model transcription and translation as concurrent and discrete processes using rewriting rules on multisets of objects and strings. Our approach takes into account the discrete character of the components of the system, its random behaviour and the key role played by membranes in processes involving signalling at the cell surface and selective uptake of substances from the environment. Our systems will evolve according to an extension of Gillespie’s algorithm, called Multicompartmental Gillespie’s Algorithm. The well known gene regulation system in the Lac Operon in Escherichia coli will be modelled as a case study to benchmark our approach. [Copyright &y& Elsevier]

Quorum sensing is a cell-density-dependent gene regulation system that allows an entire population of bacterial cells to communicate in order to regulate the expression of certain or specific genes in a coordinated way depending on the size of the population. We present a model of the quorum sensing system in Vibrio fischeri using a variant of membrane systems called P systems. In this framework each bacterium and the environment are represented by membranes, and the rules are applied according to an extension of Gillespie's algorithm called the multicompartmental Gillespie's algorithm. This algorithm runs on more than one compartment and takes into account the disturbance produced when chemical substances diffuse from one compartment or region to another one. Our approach allows us to examine the individual behavior of each bacterium as an agent as well as the emergent behavior of the colony as a whole and the processes of swarming and recruitment. Our simulations show that at low cell densities bacteria remain dark, while at high cell densities some bacteria start to produce light and a recruitment process takes place that makes the whole colony of bacteria do so. Our computational modeling of quorum sensing could provide insights leading to new applications where multiple agents need to robustly and efficiently coordinate their collective behavior based only on very limited information about the local environment. [ABSTRACT FROM AUTHOR]

Abstract: Oscillations in the transcriptional activator NF- localized in the nucleus have been observed when a cell is stimulated by an external agent. A negative feedback based on the protein whose expression is controlled by NF- is known to be responsible for these oscillations. We study NF- oscillations, which have been observed both for cell populations by Hoffmann et al. [2002. The -- signaling module: temporal control and selective gene activation. Science 298, 1241–1245] and for single cells by Nelson et al. [2004. Oscillations in - signaling control the dynamics of gene expression. Science 306, 704–708]. In order to study cell-to-cell variability we use Gillespie''s algorithm, applied to a simplified version of the model proposed by Hoffmann et al. (2002). We consider the amounts of cellular NF- and activated IKK as external parameters. When these are fixed, we show that intrinsic fluctuations are small in a model with strong transcription, as is the case of the Hoffmann et al. (2002) model, whether transcription is quadratic or linear in the number of NF- molecules. Intrinsic fluctuations can however be large when transcription is weak, as we illustrate in a model variant. The effect of extrinsic fluctuations can be significant: cell-to-cell fluctuations of the initial amount of cellular NF- affect mainly the amplitude of nuclear NF- oscillations, at least when transcription is linear in the number of NF- molecules, while fluctuations in the amount of activated IKK affect both their amplitude and period, whatever the mode of transcription. In this case model results are in qualitative agreement with the considerable cell-to-cell variability of NF- oscillations observed by Nelson et al. (2004). [Copyright &y& Elsevier]