Algebraic principles for the analysis of a biochemical system

✍ Scribed by Kenneth Krohn; Rudolph Langer; John Rhodes

• Book ID: 104147944
• Publisher: Elsevier Science
• Year: 1967
• Tongue: English
• Weight: 734 KB
• Volume: 1
• Category: Article
• ISSN: 0022-0000
• DOI: 10.1016/s0022-0000(67)80010-2

✦ Synopsis

A new algebraic approach to the description and understanding of finite-state systems is given in the form of principles derived from the Krohn-Rhodes' prime decomposition theorem for finite semigroups. The principles are motivated by several examples from classical physics and a model for the analysis of intermediary metabolism as a finite-state system is described in detail.

Principle I: The Semigroup of an Experiment. Any experiment may be regarded as a set of transformations on a set of states induced by the action of a set of inputs. That is, for any experiment E one may define: O : a set of states (the phase space); A : a set of inputs (the perturbations or stimuli); f : A • Q --~ Q the action (the experimentally observed "effect" of each input on each state). Now define the semigroup of E, S(E), to be the semigroup generated under composition by the "input transformations" fa :Q---~Q, which are defined for each a~A by fo(q) = f (a, q). Denote the transformation semigroup S(E) acting on Q by (Q, S(E)).