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

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

An overview of existing modeling tools making use of model checking in the analysis of biochemical networks

Model checking is a well-established technique for automaticallyverifying complex systems. Recently, model checkers have appearedin computer tools for the analysis of biochemical (and generegulatory) networks. We survey several such tools to assess thepotential of model checking in computational biology. Next, our overviewfocuses on direct applications of existing model checkers, as well ason algorithms for biochemical network analysis influenced by modelchecking, such as those using binary decision diagrams or Booleansatisfiability solvers. We conclude with advantages and drawbacks ofmodel checking for the analysis of biochemical networks

Analyzing various models of Circadian Clock and Cell Cycle coupling

The daily rhythm can influence the proliferation rate of many cell types. In the mammalian system the transcription of the cell cycle regulatory protein Wee1 is controlled by the circadian clock. Zamborszky et al. (2007) present a computational model coupling the cell cycle and circadian rhythm, showing that this coupling can lead to multimodal cell cycle time distributions. Biological data points to additional couplings, including a link back from the cell cycle to the circadian clock. Proper modelling of this coupling requires a more detailed description of both parts of the model. Hence, we aim at further extending and analysing earlier models using a combination of modelling techniques and computer software, including CoSBI lab, BIOCHAM, and GINsim

A graphical method for reducing and relating models in systems biology

Motivation: In Systems Biology, an increasing collection of models of various biological processes is currently developed and made available in publicly accessible repositories, such as biomodels.net for instance, through common exchange formats such as SBML. To date, however, there is no general method to relate different models to each other by abstraction or reduction relationships, and this task is left to the modeler for re-using and coupling models. In mathematical biology, model reduction techniques have been studied for a long time, mainly in the case where a model exhibits different time scales, or different spatial phases, which can be analyzed separately. These techniques are however far too restrictive to be applied on a large scale in systems biology, and do not take into account abstractions other than time or phase decompositions. Our purpose here is to propose a general computational method for relating models together, by considering primarily the structure of the interactions and abstracting from their dynamics in a first step

Computational Modeling, Formal Analysis, and Tools for Systems Biology.

As the amount of biological data in the public domain grows, so does the range of modeling and analysis techniques employed in systems biology. In recent years, a number of theoretical computer science developments have enabled modeling methodology to keep pace. The growing interest in systems biology in executable models and their analysis has necessitated the borrowing of terms and methods from computer science, such as formal analysis, model checking, static analysis, and runtime verification. Here, we discuss the most important and exciting computational methods and tools currently available to systems biologists. We believe that a deeper understanding of the concepts and theory highlighted in this review will produce better software practice, improved investigation of complex biological processes, and even new ideas and better feedback into computer science

A general computational method for robustness analysis with applications to synthetic gene networks

Motivation: Robustness is the capacity of a system to maintain a function in the face of perturbations. It is essential for the correct functioning of natural and engineered biological systems. Robustness is generally defined in an ad hoc, problem-dependent manner, thus hampering the fruitful development of a theory of biological robustness, recently advocated by Kitano

Model Revision from Temporal Logic Properties in Computational Systems Biology

International audienceSystems biologists build models of bio-molecular processes from knowledge acquired both at the gene and protein levels, and at the phenotype level through experiments done in wildlife and mutated organisms. In this chapter, we present qualitative and quantitative logic learning tools, and illustrate how they can be useful to the modeler. We focus on biochemical reaction models written in the Systems Biology Markup Language SBML, and interpreted in the Biochemical Abstract Machine BIOCHAM. We first present a model revision algorithm for inferring reaction rules from biological properties expressed in temporal logic. Then we discuss the representations of kinetic models with ordinary differential equations (ODEs) and with stochastic logic programs (SLPs), and describe a parameter search algorithm for finding parameter values satisfying quantitative temporal properties. These methods are illustrated by a simple model of the cell cycle control, and by an application to the modelling of the conditions of synchronization in period of the cell cycle by the circadian cycle

Compiling Elementary Mathematical Functions into Finite Chemical Reaction Networks via a Polynomialization Algorithm for ODEs

The Turing completeness result for continuous chemical reaction networks (CRN) shows that any computable function over the real numbers can be computed by a CRN over a finite set of formal molecular species using at most bimolecular reactions with mass action law kinetics. The proof uses a previous result of Turing completeness for functions defined by polynomial ordinary differential equations (PODE), the dualrail encoding of real variables by the difference of concentration between two molecular species, and a back-end quadratization transformation to restrict to elementary reactions with at most two reactants. In this paper, we present a polynomialization algorithm of quadratic time complexity to transform a system of elementary differential equations in PODE. This algorithm is used as a front-end transformation to compile any elementary mathematical function, either of time or of some input species, into a finite CRN. We illustrate the performance of our compiler on a benchmark of elementary functions relevant to CRN design problems in synthetic biology specified by mathematical functions. In particular, the abstract CRN obtained by compilation of the Hill function of order 5 is compared to the natural CRN structure of MAPK signalling networks