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

Derek Gatherer, Vashti Galpin

Research output: Contribution to journalArticlepeer-review



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.

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.

We argue that the behaviour of (M,R) in Bio-PEPA shows life-like properties.
Original languageEnglish
Number of pages10
JournalMolecular Systems Biology
Issue number1
Publication statusPublished - 2013


  • Robert Rosen
  • (M,R)
  • Metabolism-replacement
  • Metabolism-repair
  • Relational biology
  • Process algebra
  • Bio-PEPA
  • Computability
  • Turing machine


Dive into the research topics of 'Rosen's (M,R) system in process algebra'. Together they form a unique fingerprint.

Cite this