Rosen's (M,R) system in process algebra.

BACKGROUND: Robert Rosen's Metabolism-Replacement, or (M,R), system can be represented as a compact network structure with a single source and three products derived from that source in three consecutive reactions. (M,R) has been claimed to be non-reducible to its components and algorithmically non-computable, in the sense of not being evaluable as a function by a Turing machine. If (M,R)-like structures are present in real biological networks, this suggests that many biological networks will be non-computable, with implications for those branches of systems biology that rely on in silico modelling for predictive purposes. RESULTS: We instantiate (M,R) using the process algebra Bio-PEPA, and discuss the extent to which our model represents a true realization of (M,R). We observe that under some starting conditions and parameter values, stable states can be achieved. Although formal demonstration of algorithmic computability remains elusive for (M,R), we discuss the extent to which our Bio-PEPA representation of (M,R) allows us to sidestep Rosen's fundamental objections to computational systems biology. CONCLUSIONS: We argue that the behaviour of (M,R) in Bio-PEPA shows life-like properties.

Formal methods for checking the consistency of biological models.

Formal modeling approaches such as process algebras and Petri nets seek to provide insight into biological processes by using both symbolic and numerical methods to reveal the dynamics of the process under study. These formal approaches differ from classical methods of investigating the dynamics of the process through numerical integration of ODEs because they additionally provide alternative representations which are amenable to discrete-state analysis and logical reasoning. Backed by these additional analysis methods, formal modeling approaches have been able to identify errors in published and widely-cited biological models. This paper provides an introduction to these analysis methods, and explains the benefits which they can bring to ensuring the consistency of biological models.