Classification of biological networks by their qualitative dynamics
Abstract
Techniques are given to classify biological networks into classes having similar qualitative dynamics. The following steps are used: (1) A discretization is proposed which identifies a sequence of Boolean N-vectors, each of which differs from the preceding one in one locus, with transients and cycles in continuous N variable biological systems. (2) The sequences are represented as directed edges on Boolean N-cubes. (3) Any two dynamical systems which have identical steady states and cycles on the Boolean N-cube, under some symmetry operation of the N-cube, are defined to be in the same dynamical equivalence class and to have the same deep structure.
We consider systems in which there is no self-input (each edge of the N-cube representation is directed in only one orientation) and enumerate the three deep structures for N = 2 and the 13 deep structures with at least a single steady state for N = 3. We illustrate these techniques by considering dynamic data from a number of biological systems and showing how the deep structure of each system can be determined.- Publication:
-
Journal of Theoretical Biology
- Pub Date:
- 1975
- DOI:
- 10.1016/S0022-5193(75)80056-7
- Bibcode:
- 1975JThBi..54...85G