Programmability of Chemical Reaction Networks

Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri Nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior

Formal methods for biochemical signalling pathways

We apply quantitative formal methods to a domain from the life sciences: biochemical signalling pathways. The key idea is to model pathways as stochastic continuous time distributed systems. Components of the system are molecular species (rather than individual molecules) and are modelled by concurrent processes that interact with each other via biochemical reactions. Through an application, we show how high level languages and analysis techniques rooted in computer science theory add significantly to the analysis presently available to computational biologists

Formalizing a notion of concentration robustness for biochemical networks

The main goal of systems biology is to understand the dynamical properties of biological systems by investigating the interactions among the components of a biological system. In this work, we focus on the robustness property, a behaviour observed in several biological systems that allows them to preserve their functions despite external and internal perturbations. We first propose a new formal definition of robustness using the formalism of continuous Petri nets. In particular, we focus on robustness against perturbations to the initial concentrations of species. Then, we demonstrate the validity of our definition by applying it to the models of three different robust biochemical networks

Petri net models for the semi-automatic construction of large scale biological networks

Chen M, Hariharaputran S, Hofestädt R, Kormeier B, Spangardt S. Petri net models for the semi-automatic construction of large scale biological networks. Natural Computing. 2011;10(3):1077-1097.For the implementation of the virtual cell, the fundamental question is how to model and simulate complex biological networks. During the last 15 years, Petri nets have attracted more and more attention to help to solve this key problem. Regarding the published papers, it seems clear that hybrid functional Petri nets are the adequate method to model complex biological networks. Today, a Petri net model of biological networks is built manually by drawing places, transitions and arcs with mouse events. Therefore, based on relevant molecular database and information systems biological data integration is an essential step in constructing biological networks. In this paper, we will motivate the application of Petri nets for modeling and simulation of biological networks. Furthermore, we will present a type of access to relevant metabolic databases such as KEGG, BRENDA, etc. Based on this integration process, the system supports semi-automatic generation of the correlated hybrid Petri net model. A case study of the cardio-disease related gene-regulated biological network is also presented. MoVisPP is available at http://agbi.techfak.uni-bielefeld.de/movispp/