Automated Probing and Inference of Analytical Models for Metabolic Network Dynamics

Authors

John Wikswo, Vanderbilt University

Michael Schmidt, Hod Lipson, Cornell University

Jerry Jenkins, Hudson Alpha Institute

Jonathan Hood, CFD Research Corp

Abstract

We introduce a method to automatically construct mathematical models of a biological system, and apply this technique to infer a seven-dimensional nonlinear model of glycolytic oscillations in yeast – based only on noisy observational data obtained from in silico experiments. Graph-based symbolic encoding, fitness prediction, and estimation-exploration can for the first time provide the level of symbolic regression required for biological applications. With no a priori knowledge of the system, the Cornell algorithm in several hours of computation correctly identified all seven ordinary nonlinear differential equations, the most complicated of which was $\frac{dA_3}{dt} = -1.12 A_3 -\frac{192.24·A_3S_1}{1+12.50A^4_3} +124.92 S_3 +31.69·A_3S_3$, where where A₃ = [ATP], S₁ = [glucose], and S₃ = [cytosolic pyruvate and acetaldehyde pool]. Errors on the 26 parameters ranged from 0 to 14.5%. The algorithm also automatically identified new and potentially useful chemical constants of the motion, e.g. $-k_1N_2 +K_2v_1 +k_2S_1A_3 -(k_4 -k_5v_1)A^4_3 + k_6 \approx 0$. This approach may enable automated design, control and analysis of wet-lab experiments for model identification/refinement.

Back to APS March Meeting 2010 Focus Session on Physics of Behavior -- From Molecules to Organisms.