Automated Probing and Inference of Analytical Models for Metabolic Network Dynamics*

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 \textit{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 \textit{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\cdot A_3 -\frac{\mbox{192.24}\cdot A_3 S_1 }{1+\mbox{12.50}\cdot A_3 ^4}+124.92\cdot S_3 +31.69\cdot A_3 S_3 $, where A$_{3}$ = [ATP], S$_{1}$= [glucose], and S$_{3}$ = [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, $e.g. \quad -k_1 N_2 +K_2 v_1 +k_2 S_1 A_3 -(k_4 -k_5 v_1 )A_3 ^4+k_6 \approx 0$. This approach may enable automated design, control and analysis of wet-lab experiments for model identification/refinement.