# Dynamic metabolic resource allocation based on the maximum entropy principle

## TL;DR

This paper develops a dynamic metabolic model based on maximum entropy principles, unifying existing approaches and explaining cellular strategies under environmental uncertainty, with practical implications for metabolic engineering.

## Contribution

It introduces a novel framework combining maximum entropy with optimal control for dynamic metabolic modeling, extending previous models to account for uncertainty and heterogeneity.

## Key findings

- Describes bet-hedging strategies in cell populations.
- Models resource allocation and reserve accumulation.
- Aligns with observed yeast growth behaviors.

## Abstract

Organisms have evolved a variety of mechanisms to cope with the unpredictability of environmental conditions, and yet mainstream models of metabolic regulation are typically based on strict optimality principles that do not account for uncertainty. This paper introduces a dynamic metabolic modelling framework that is a synthesis of recent ideas on resource allocation and the powerful optimal control formulation of Ramkrishna and colleagues. In particular, their work is extended based on the hypothesis that cellular resources are allocated among elementary flux modes according to the principle of maximum entropy. These concepts both generalise and unify prior approaches to dynamic metabolic modelling by establishing a smooth interpolation between dynamic flux balance analysis and dynamic metabolic models without regulation. The resulting theory is successful in describing `bet-hedging' strategies employed by cell populations dealing with uncertainty in a fluctuating environment, including heterogenous resource investment, accumulation of reserves in growth-limiting conditions, and the observed behaviour of yeast growing in batch and continuous cultures. The maximum entropy principle is also shown to yield an optimal control law consistent with partitioning resources between elementary flux mode families, which has important practical implications for model reduction, selection, and simulation.