scholarly journals Compartmental and spatial rule-based modeling with Virtual Cell (VCell)

2017 ◽  
Author(s):  
M. L. Blinov ◽  
J. C. Schaff ◽  
D. Vasilescu ◽  
I. I. Moraru ◽  
J. E. Bloom ◽  
...  
Keyword(s):  
Reaction Diffusion ◽  
Molecular Complexes ◽  
Reaction Diffusion Equations ◽  
Reaction Networks ◽  
The Novel ◽  
Modeling Framework ◽  
Rule Based ◽  
Agent Based ◽  
Virtual Cell ◽  
Stochastic Simulator

AbstractIn rule-based modeling, molecular interactions are systematically specified in the form of reaction rules that serve as generators of reactions. This provides a way to account for all the potential molecular complexes and interactions among multivalent or multistate molecules. Recently, we introduced rule-based modeling into the Virtual Cell (VCell) modeling framework, permitting graphical specification of rules and merger of networks generated automatically (using the BioNetGen modeling engine) with hand-specified reaction networks. VCell provides a number of ordinary differential equation (ODE) and stochastic numerical solvers for single-compartment simulations of the kinetic systems derived from these networks, and agent-based network-free simulation of the rules. In this work, compartmental and spatial modeling of rule-based models has been implemented within VCell. To enable rule-based deterministic and stochastic spatial simulations and network-free agent-based compartmental simulations, the BioNetGen and NFSim engines were each modified to support compartments. In the new rule-based formalism, every reactant and product pattern and every reaction rule are assigned locations. We also introduce the novel rule-based concept of molecular anchors. This assures that any species that has a molecule anchored to a predefined compartment will remain in this compartment. Importantly, in addition to formulation of compartmental models, this now permits VCell users to seamlessly connect reaction networks derived from rules to explicit geometries to automatically generate a system of reaction-diffusion equations. These may then be simulated using either the VCell partial differential equations (PDE) deterministic solvers or the Smoldyn stochastic simulator.

scholarly journals On-lattice agent-based simulation of populations of cells within the open-source Chaste framework

2013 ◽  
Vol 3 (2) ◽  
pp. 20120081 ◽  
Author(s):  
Grazziela P. Figueredo ◽  
Tanvi V. Joshi ◽  
James M. Osborne ◽  
Helen M. Byrne ◽  
Markus R. Owen
Keyword(s):  
Tumour Growth ◽  
Current System ◽  
Reaction Diffusion ◽  
Multiple Scale ◽  
Reaction Diffusion Equations ◽  
Scale Model ◽  
Low Oxygen ◽  
Model Framework ◽  
Agent Based ◽  
Multi Scale

Over the years, agent-based models have been developed that combine cell division and reinforced random walks of cells on a regular lattice, reaction–diffusion equations for nutrients and growth factors; and ordinary differential equations for the subcellular networks regulating the cell cycle. When linked to a vascular layer, this multiple scale model framework has been applied to tumour growth and therapy. Here, we report on the creation of an agent-based multi-scale environment amalgamating the characteristics of these models within a Virtual Physiological Human (VPH) Exemplar Project. This project enables reuse, integration, expansion and sharing of the model and relevant data. The agent-based and reaction–diffusion parts of the multi-scale model have been implemented and are available for download as part of the latest public release of Chaste (Cancer, Heart and Soft Tissue Environment; http://www.cs.ox.ac.uk/chaste/), part of the VPH Toolkit (http://toolkit.vph-noe.eu/). The environment functionalities are verified against the original models, in addition to extra validation of all aspects of the code. In this work, we present the details of the implementation of the agent-based environment, including the system description, the conceptual model, the development of the simulation model and the processes of verification and validation of the simulation results. We explore the potential use of the environment by presenting exemplar applications of the ‘what if’ scenarios that can easily be studied in the environment. These examples relate to tumour growth, cellular competition for resources and tumour responses to hypoxia (low oxygen levels). We conclude our work by summarizing the future steps for the expansion of the current system.

scholarly journals Quantifying the driving factors for language shift in a bilingual region

2017 ◽  
Vol 114 (17) ◽  
pp. 4365-4369 ◽  
Author(s):  
Katharina Prochazka ◽  
Gero Vogl
Keyword(s):  
Cellular Automata ◽  
Differential Equations ◽  
Large Scale ◽  
Language Shift ◽  
Reaction Diffusion ◽  
Agent Based Modeling ◽  
Reaction Diffusion Equations ◽  
Agent Based ◽  
Using Data ◽  
A Minor

Many of the world’s around 6,000 languages are in danger of disappearing as people give up use of a minority language in favor of the majority language in a process called language shift. Language shift can be monitored on a large scale through the use of mathematical models by way of differential equations, for example, reaction–diffusion equations. Here, we use a different approach: we propose a model for language dynamics based on the principles of cellular automata/agent-based modeling and combine it with very detailed empirical data. Our model makes it possible to follow language dynamics over space and time, whereas existing models based on differential equations average over space and consequently provide no information on local changes in language use. Additionally, cellular automata models can be used even in cases where models based on differential equations are not applicable, for example, in situations where one language has become dispersed and retreated to language islands. Using data from a bilingual region in Austria, we show that the most important factor in determining the spread and retreat of a language is the interaction with speakers of the same language. External factors like bilingual schools or parish language have only a minor influence.

scholarly journals On the linear stability of some finite difference schemes for nonlinear reaction-diffusion models of chemical reaction networks

2018 ◽  
Vol 9 (1) ◽  
pp. 121-140
Author(s):  
Nathan Muyinda ◽  
Bernard De Baets ◽  
Shodhan Rao
Keyword(s):  
Finite Difference ◽  
Chemical Reaction ◽  
Jacobian Matrix ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Chemical Reaction Networks ◽  
Difference Schemes ◽  
Reaction Diffusion Equations ◽  
Reaction Networks ◽  
Finite Difference Schemes

Abstract We identify sufficient conditions for the stability of some well-known finite difference schemes for the solution of the multivariable reaction-diffusion equations that model chemical reaction networks. Since the equations are mainly nonlinear, these conditions are obtained through local linearization. A recurrent condition is that the Jacobian matrix of the reaction part evaluated at some positive unknown solution is either D-semi-stable or semi-stable. We demonstrate that for a single reversible chemical reaction whose kinetics are monotone, the Jacobian matrix is D-semi-stable and therefore such schemes are guaranteed to work well.

Using the Virtual Cell Simulation Environment for Extracting Quantitative Parameters from Live Cell Fluorescence Imaging Data

2009 ◽  
Vol 17 (6) ◽  
pp. 36-39 ◽  
Author(s):  
A. E. Cowan ◽  
Y. Li ◽  
F. R. Morgan ◽  
D. E. Koppel ◽  
B. M. Slepchenko ◽  
...  
Keyword(s):  
Fluorescence Imaging ◽  
Fluorescence Probe ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Reaction ◽  
Simulation Environment ◽  
Imaging Data ◽  
Virtual Cell ◽  
Spatiotemporal Information ◽  
Cell Simulation

Rapid advances in fluorescence probe and imaging technologies now provide easily accessible tools for biologists to perform highly detailed analysis of molecular interactions in living cells. However it can be difficult to extract accurate parameters from these experiments because of the complex interplay of diffusion-reaction events with the morphology of the cell. As a result, only a small fraction of the available spatiotemporal information is utilized, and in many cases analysis remains at a qualitative level. The Virtual Cell (VCell, http://vcell.org) simulation environment is uniquely suited to analyzing these types of fluorescence imaging experiments because it is designed to solve reaction-diffusion equations within any given geometry [1]

PATTERN DYNAMICS OF A MULTI-COMPONENT REACTION–DIFFUSION SYSTEM: DIFFERENTIATION OF REPLICATING SPOTS

2002 ◽  
Vol 12 (11) ◽  
pp. 2579-2598 ◽  
Author(s):  
HIROAKI TAKAGI ◽  
KUNIHIKO KANEKO
Keyword(s):  
Cell Biology ◽  
Chemical Species ◽  
Reaction Diffusion ◽  
Chemical Diversity ◽  
Reaction Diffusion Equations ◽  
Condition Dependence ◽  
Reaction Networks ◽  
Initial Condition ◽  
Pattern Dynamics ◽  
System Differentiation

Replication and differentiation of spots in a class of reaction–diffusion equations are studied by extending the Gray–Scott model with self-replicating spots so that it includes many chemical species. By examining many possible reaction networks, the behavior of this model is categorized into three types: replication of homogeneous fixed spots, replication of oscillatory spots, and differentiation from "multipotent spots". These multipotent spots either replicate or differentiate into other types of spots with different fixed-point dynamics, and as a result, an inhomogeneous pattern of spots is formed. This differentiation process of spots is analyzed in terms of the loss of chemical diversity and decrease of the local Kolmogorov–Sinai entropy. Initial condition dependence and robustness of a pattern against macroscopic perturbation are also analyzed. Relevance of the results to developmental cell biology is also discussed.

On a Nonlinear System of Reaction-Diffusion Equations

2006 ◽  
Vol 11 (2) ◽  
pp. 115-121 ◽  
Author(s):  
G. A. Afrouzi ◽  
S. H. Rasouli
Keyword(s):  
Weak Solution ◽  
Dirichlet Boundary ◽  
Smooth Boundary ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Dirichlet Boundary Conditions ◽  
Nonlinear Elliptic System ◽  
Positive Parameter ◽  
Nonlinear Elliptic ◽  
Positive Weak Solution

The aim of this article is to study the existence of positive weak solution for a quasilinear reaction-diffusion system with Dirichlet boundary conditions,− div(|∇u1|p1−2∇u1) = λu1α11u2α12... unα1n,   x ∈ Ω,− div(|∇u2|p2−2∇u2) = λu1α21u2α22... unα2n,   x ∈ Ω, ... , − div(|∇un|pn−2∇un) = λu1αn1u2αn2... unαnn,   x ∈ Ω,ui = 0,   x ∈ ∂Ω,   i = 1, 2, ..., n,  where λ is a positive parameter, Ω is a bounded domain in RN (N > 1) with smooth boundary ∂Ω. In addition, we assume that 1 < pi < N for i = 1, 2, ..., n. For λ large by applying the method of sub-super solutions the existence of a large positive weak solution is established for the above nonlinear elliptic system.

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