Cell Cycle Control in Eukaryotes: a BioSpi model

This paper presents a stochastic model of the cell cycle control in eukaryotes. The framework used is based on stochastic process algebras for mobile systems. The automatic tool used in the simulation is the BioSpi. We compare our approach with classical ODE specications

A Type System for a Stochastic CLS

The Stochastic Calculus of Looping Sequences is suitable to describe the evolution of microbiological systems, taking into account the speed of the described activities. We propose a type system for this calculus that models how the presence of positive and negative catalysers can modify these speeds. We claim that types are the right abstraction in order to represent the interaction between elements without specifying exactly the element positions. Our claim is supported through an example modelling the lactose operon

06161 Abstracts Collection -- Simulation and Verification of Dynamic Systems

From 17.04.06 to 22.04.06, the Dagstuhl Seminar 06161 ``Simulation and Verification of Dynamic Systems\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Modelling Cell Cycle using Different Levels of Representation

Understanding the behaviour of biological systems requires a complex setting of in vitro and in vivo experiments, which attracts high costs in terms of time and resources. The use of mathematical models allows researchers to perform computerised simulations of biological systems, which are called in silico experiments, to attain important insights and predictions about the system behaviour with a considerably lower cost. Computer visualisation is an important part of this approach, since it provides a realistic representation of the system behaviour. We define a formal methodology to model biological systems using different levels of representation: a purely formal representation, which we call molecular level, models the biochemical dynamics of the system; visualisation-oriented representations, which we call visual levels, provide views of the biological system at a higher level of organisation and are equipped with the necessary spatial information to generate the appropriate visualisation. We choose Spatial CLS, a formal language belonging to the class of Calculi of Looping Sequences, as the formalism for modelling all representation levels. We illustrate our approach using the budding yeast cell cycle as a case study

Studying the effects of adding spatiality to a process algebra model

We use NetLogo to create simulations of two models of disease transmission originally expressed in WSCCS. This allows us to introduce spatiality into the models and explore the consequences of having different contact structures among the agents. In previous work, mean field equations were derived from the WSCCS models, giving a description of the aggregate behaviour of the overall population of agents. These results turned out to differ from results obtained by another team using cellular automata models, which differ from process algebra by being inherently spatial. By using NetLogo we are able to explore whether spatiality, and resulting differences in the contact structures in the two kinds of models, are the reason for this different results. Our tentative conclusions, based at this point on informal observations of simulation results, are that space does indeed make a big difference. If space is ignored and individuals are allowed to mix randomly, then the simulations yield results that closely match the mean field equations, and consequently also match the associated global transmission terms (explained below). At the opposite extreme, if individuals can only contact their immediate neighbours, the simulation results are very different from the mean field equations (and also do not match the global transmission terms). These results are not surprising, and are consistent with other cellular automata-based approaches. We found that it was easy and convenient to implement and simulate the WSCCS models within NetLogo, and we recommend this approach to anyone wishing to explore the effects of introducing spatiality into a process algebra model

Stochastic ordinary differential equations in applied and computational mathematics

Using concrete examples, we discuss the current and potential use of stochastic ordinary differential equations (SDEs) from the perspective of applied and computational mathematics. Assuming only a minimal background knowledge in probability and stochastic processes, we focus on aspects that distinguish SDEs from their deterministic counterparts. To illustrate a multiscale modelling framework, we explain how SDEs arise naturally as diffusion limits in the type of discrete-valued stochastic models used in chemical kinetics, population dynamics, and, most topically, systems biology. We outline some key issues in existence, uniqueness and stability that arise when SDEs are used as physical models, and point out possible pitfalls. We also discuss the use of numerical methods to simulate trajectories of an SDE and explain how both weak and strong convergence properties are relevant for highly-efficient multilevel Monte Carlo simulations. We flag up what we believe to be key topics for future research, focussing especially on nonlinear models, parameter estimation, model comparison and multiscale simulation

Modelling and simulating in systems biology: an approach based on multi-agent systems

Systems Biology is an innovative way of doing biology recently raised in bio-informatics contexts, characterised by the study of biological systems as complex systems with a strong focus on the system level and on the interaction dimension. In other words, the objective is to understand biological systems as a whole, putting on the foreground not only the study of the individual parts as standalone parts, but also of their interaction and of the global properties that emerge at the system level by means of the interaction among the parts. This thesis focuses on the adoption of multi-agent systems (MAS) as a suitable paradigm for Systems Biology, for developing models and simulation of complex biological systems. Multi-agent system have been recently introduced in informatics context as a suitabe paradigm for modelling and engineering complex systems. Roughly speaking, a MAS can be conceived as a set of autonomous and interacting entities, called agents, situated in some kind of nvironment, where they fruitfully interact and coordinate so as to obtain a coherent global system behaviour. The claim of this work is that the general properties of MAS make them an effective approach for modelling and building simulations of complex biological systems, following the methodological principles identified by Systems Biology. In particular, the thesis focuses on cell populations as biological systems. In order to support the claim, the thesis introduces and describes (i) a MAS-based model conceived for modelling the dynamics of systems of cells interacting inside cell environment called niches. (ii) a computational tool, developed for implementing the models and executing the simulations. The tool is meant to work as a kind of virtual laboratory, on top of which kinds of virtual experiments can be performed, characterised by the definition and execution of specific models implemented as MASs, so as to support the validation, falsification and improvement of the models through the observation and analysis of the simulations. A hematopoietic stem cell system is taken as reference case study for formulating a specific model and executing virtual experiments

Multi-Level Kinetic Model of mRNA Delivery via Transfection of Lipoplexes

Recent work on the use of mRNA lipoplexes for gene delivery demonstrates the need for a mathematical model that simulates and predicts kinetics and transfection efficiency. The small copy numbers involved make it necessary to use stochastic models and include statistical analysis of the variation observed in the experimental data. The modeling requirements are further complicated by the multi-level nature of the problem, where mRNA molecules are contained in lipoplexes, which are in turn contained in endosomes, where each of these entities displays a behavior of its own. We have created a mathematical model that reproduces both the time courses and the statistical variance observed in recent experiments using single-cell tracking of GFP expression after transfection. By applying a few key simplifications and assumptions, we have limited the number of free parameters to five, which we optimize to match five experimental determinants by means of a simulated annealing algorithm. The models demonstrate the need for modeling of nested species in order to reproduce the shape of the dose-response and expression-level curves