On Discovering Low Order Models in Biochemical Reaction Kinetics

We develop a method by which a large number of differential equations representing biochemical reaction kinetics may be represented by a smaller number of differential equations. The basis of our technique is a conjecture that the high dimension equations of biochemical kinetics, which involve reaction terms of specific forms, are actually implementing a low dimension system whose behavior requires right hand sides that can not be biochemically implemented. For systems that satisfy this conjecture, we develop a simple approximation scheme based on multilinear algebra that extracts the low dimensional system from simulations of the high dimension system. We demonstrate this technique on a standard 10 dimensional model of circadian oscillations and obtain a 3 dimensional sub-model that has the same rhythmic, birhythmic and chaotic behavior of the original model.