Modelling the cAMP pathway using BioNessie, and the use of BVP techniques for solving ODEs (Poster Presentation)

Copyright @ 2007 Gu et al; licensee BioMed Central LtdBiochemists often conduct experiments in-vivo in order to explore observable behaviours and understand the dynamics of many intercellular and intracellular processes. However an intuitive understanding of their dynamics is hard to obtain because most pathways of interest involve components connected via interlocking loops. Formal methods for modelling and analysis of biochemical pathways are therefore indispensable. To this end, ODEs (ordinary differential equations) have been widely adopted as a method to model biochemical pathways because they have an unambiguous mathematical format and are amenable to rigorous quantitative analysis. BioNessie http://www.bionessie.com webcite is a workbench for the composition, simulation and analysis of biochemical networks which is being developed in by the Systems Biology team at the Bioinformatics Research Centre as a part of a large DTI funded project 'BPS: A Software Tool for the Simulation and Analysis of Biochemical Networks' http://www.brc.dcs.gla.ac.uk/projects/dti_beacon webcite. BioNessie is written in Java using NetBeans Platform libraries that makes it platform independent. The software employs specialised differential equations solvers for stiff and non-stiff systems to produce model simulation traces. BioNessie provides a user-friendly interfact that comes up with an intuitive tree-based graphical layout, an edition function to SBML-compatible models and feature of data output

Algae Population Self-Replenishment

This modeling scenario investigates the massive algal blooms that struck Lake Chapala, Mexico, in 1994. After reading a summary of news articles on the incident, students create an ODE system model from a verbal description of the factors, visualize this system using an executable Java applet (PPLANE) to predict overall behavior, and then analyze the nonlinear system using the Jacobian matrix, eigenvalues, phase plane, and feasibility conditions on parameters to fully describe the system behavior. Students are expected to be familiar with systems of differential equations, equilibria, jacobian matrices, and eigenvalues. Students will learn modeling from qualitative descriptions, nondimensionalization, applying feasibility conditions to parameters, and how to use technology to interactively analyze a system of differential equations

A Class of Three Stage Implicit Rational Runge-Kutta Schemes for Approximation of Second Order Ordinary Differential Equations

In this paper, 3 – stage Implicit Rational Runge – Kutta methods are derived using Taylor and Binomial series expansion for the direct solution of general second order initial value problems of ordinary differential equations with constant step length. The basic properties of the developed method were investigated and found to be consistent and convergent. The efficiency of the method were tested on some numerical examples and found to give better approximations than the existing methods. Keywords: Java Programming Language, Implicit Rational Runge Kutta scheme, Second order equations

Qualitative Simulation of Genetic Regulatory Networks Using Piecewise-Linear Models

In order to cope with the large amounts of data that have become available in genomics, mathematical tools for the analysis of networks of interactions between genes, proteins, and other molecules are indispensable. We present a method for the qualitative simulation of genetic regulatory networks, based on a class of piecewise-linear (PL) differential equations that has been well-studied in mathematical biology. The simulation method is well-adapted to state-of-the-art measurement techniques in genomics which often provide qualitative and coarse-grained descriptions of genetic regulatory networks. The method is able to deal with nontrivial mathematical problems induced by the discontinuous right-hand sides of the differential equations. Furthermore, it guarantees that the simulation covers all possible solutions of quantitative PL models corresponding to the qualitative PL model used by the method. The qualitative simulation method has been implemented in Java

'BioNessie(G) - a grid enabled biochemical networks simulation environment

The simulation of biochemical networks provides insight and understanding about the underlying biochemical processes and pathways used by cells and organisms. BioNessie is a biochemical network simulator which has been developed at the University of Glasgow. This paper describes the simulator and focuses in particular on how it has been extended to benefit from a wide variety of high performance compute resources across the UK through Grid technologies to support larger scale simulations

BioNessie - a grid enabled biochemical networks simulation environment

The simulation of biochemical networks provides insight and understanding about the underlying biochemical processes and pathways used by cells and organisms. BioNessie is a biochemical network simulator which has been developed at the University of Glasgow. This paper describes the simulator and focuses in particular on how it has been extended to benefit from a wide variety of high performance compute resources across the UK through Grid technologies to support larger scale simulations

Language-based Abstractions for Dynamical Systems

Ordinary differential equations (ODEs) are the primary means to modelling dynamical systems in many natural and engineering sciences. The number of equations required to describe a system with high heterogeneity limits our capability of effectively performing analyses. This has motivated a large body of research, across many disciplines, into abstraction techniques that provide smaller ODE systems while preserving the original dynamics in some appropriate sense. In this paper we give an overview of a recently proposed computer-science perspective to this problem, where ODE reduction is recast to finding an appropriate equivalence relation over ODE variables, akin to classical models of computation based on labelled transition systems.Comment: In Proceedings QAPL 2017, arXiv:1707.0366