Metabolic Pathway Optimization with Data Driven Approaches

Abstract

The flux control coefficient (FCC) is a sensitivity coefficient that measures the percent change in flux as a result of a given percentage change in the activity of the enzyme. The higher the FFC the more controlling the step. However, the value for a flux control coefficient for a specific enzyme is determined by all the other enzymes in the pathway. Most kinetic rate laws for pathway models are generally nonlinear, which makes an analytical analysis virtually impossible. Previous studies have explored linearization under assumptions such as non-saturation, which limit all steps to the first order region, however these assumptions are not realistic for all situations. Here we present a statistical approach to predict the probability distribution of dominance of each enzyme step in a linear section of metabolic flux, and in the meantime, to identify key system parameters that could maximally reduce the uncertainty of the distribution. Generalized linear models are applied to predict the probability of dominance of each step, while L1 regularization is applied to select system parameters that contribute most to the prediction. For better predictions, a neural network is used for the prediction of distribution of control coefficients based on the FCC summation property. The models are trained on synthetic datasets generated using fully reversible Michaelis-Menten kinetics. All parameters are randomly sampled from a maximum entropy distribution assuming no prior knowledge on the system. For a pathway up to 15 nodes, the results show over 90% accuracy in predicting step with the largest control coefficient at the extreme regularization condition, where total enzyme, the equilibrium constant, and forward Michaelis-Menten constant are identified as key system parameters. Similar patterns can be generated for pathways with different number of nodes. The approach is also tested under noisy data, and shows higher accuracy when noise increase compared with numerical simulation. These results offer a means to determine the FCCs of a pathway given minimal information under noise. It will make it easier for metabolic engineers to target the most promising enzymatic steps to maximize pathway flux.