Jump-Diffusion Approximation of Stochastic Reaction Dynamics: Error bounds and Algorithms

Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or to exploit this multi-scale nature, respectively. In this paper, we propose a jump-diffusion approximation for multi-scale Markov jump processes that couples the two modeling approaches. An error bound of the proposed approximation is derived and used to partition the reactions into fast and slow sets, where the fast set is simulated by a stochastic differential equation and the slow set is modeled by a discrete chain. The error bound leads to a very efficient dynamic partitioning algorithm which has been implemented for several multi-scale reaction systems. The gain in computational efficiency is illustrated by a realistically sized model of a signal transduction cascade coupled to a gene expression dynamics.Comment: 32 pages, 7 figure

Simulator adaptation at runtime for component-based simulation software

Component-based simulation software can provide many opportunities to compose and configure simulators, resulting in an algorithm selection problem for the user of this software. This thesis aims to automate the selection and adaptation of simulators at runtime in an application-independent manner. Further, it explores the potential of tailored and approximate simulators - in this thesis concretely developed for the modeling language ML-Rules - supporting the effectiveness of the adaptation scheme.Komponenten-basierte Simulationssoftware kann viele Möglichkeiten zur Komposition und Konfiguration von Simulatoren bieten und damit zu einem Konfigurationsproblem für Nutzer dieser Software führen. Das Ziel dieser Arbeit ist die Entwicklung einer generischen und automatisierten Auswahl- und Adaptionsmethode für Simulatoren. Darüber hinaus wird das Potential von spezifischen und approximativen Simulatoren anhand der Modellierungssprache ML-Rules untersucht, welche die Effektivität des entwickelten Adaptionsmechanismus erhöhen können

Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which uni¯es the qualita- tive, stochastic and continuous paradigms. Each perspective adds its con- tribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how quali- tative descriptions are abstractions over stochastic or continuous descrip- tions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks