Fractional-order dynamics of bacterial adaptation to fluctuating nutrient environments

Bacteria possess the remarkable ability to dynamically regulate physiological functions to adapt to environmental changes. Recent experiments have shown that fluctuation-induced growth physiology is distinct from growth physiology in constant environments. Specifically, bacteria maintain memory of past nutrient environments, resulting in decreased cellular response time to fluctuations at the expense of growth. Existing models for bacterial growth control are unable to capture this adaptive behavior to fluctuating environments, highlighting the need for better understanding of the feedback mechanisms which underlie bacterial adaptation to stress. To this end, we introduce a variable-order fractional calculus model of growth control in which growth is dependent not only on the current metabolic state but also on previous history. We connect the strength of this memory to the time-profile of environmental fluctuations through a Bayesian inference scheme. Furthermore, we show that this regulatory behavior can emerge mechanistically from multiple groups of ribosomes with different relaxation timescales. The model captures experimentally-observed E. coli growth control under pulsatile nutrient exposure, and predicts that the dynamics of adaptation are dictated by the time period of nutrient switching.