(744g) Revisiting the Foundations of Cybernetic Modeling Using Systems Engineering Methods

The cybernetic modeling framework for the growth of microorganisms provides an elegant methodology to account for unknown regulatory interactions using principles of optimal control theory[1, 2]. In this work, we revisit the various assumptions used in the cybernetic modeling framework. We first propose a generalized Monod model incorporating control variables, formulate various optimal control problems involving the generalized Monod model and solve them analytically to show that the long-term objective of maximizing cellular concentration at a fixed final time is equivalent to maximizing instantaneous growth rate during the growth of microorganisms in a single/two substrate batch environment. We then show that reformulation of the state and adjoint equations of the above optimal control problems result in generalized governing dynamic equations of the cybernetic model. We illustrate the influence of various constraints in the cybernetic model on the optimal growth behavior of microorganisms by solving several dynamic optimization problems using genetic algorithms. Finally, we will present a methodology for inferring the values of control variables for enzyme induction u_iof cybernetic models from experimental data.

References:

1. Ramkrishna D, Song HS: Dynamic models of metabolism: Review of the cybernetic approach. AlChE J 2012, 58(4):986-997.

2. Young JD, Ramkrishna D: On the matching and proportional laws of cybernetic models. Biotechnol Prog 2007, 23(1):83-99.