Abstract
BackgroundRobert 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.ResultsWe 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.ConclusionsWe argue that the behaviour of (M,R) in Bio-PEPA shows life-like properties.
Highlights
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
Relational biology is a discipline founded by Robert Rosen (1934–1998) [1,2,3], based on the previous work of Nicolas Rashevsky (1899–1972), which considers biological network structures using the mathematical tools of category theory
It is immediately evident that the Bio-PEPA (M,R) model has dynamic behaviour
Summary
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. Systems biologists attempt to represent biological network systems as software objects for simulation on computers. These network structures may vary in their degree of complexity, but the difference between simple and complex networks is treated as one of degree rather than of. A Turing machine is a formal mathematical model of computation, which has a notion of its internal state, an unbounded tape and a read-write head for that tape [4]. A function is (Turing-) computable if it can be evaluated by a Turing machine which, when given an input to the function, eventually writes the value of the function for that input on its output tape, assuming that the function is defined for the input. No time bound can be imposed on how long the Turing machine will take to output the value
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