How memory and adaptation cost shape cell phenotypic dynamics in response to fluctuating environments

Cells invariably encounter unpredictable changes in their microenvironment and undergo adaptation by orchestrating considerable alterations in their molecular states that often result in appreciable phenotypic changes. The timescale of molecular and, therefore, cellular adaptation depends on how quickly the memory of past environmental encounters is lost (and therefore forgotten) by the cell (e.g., degradation rate of proteins unfavorable to the current environment). Here, we study the dynamical implications of two distinct memory mechanisms on cellular responses to a changing environment. The two phenomenological models considered are - 1) Undated memory, wherein each prior environmental exposure has an equal probability to dissipate in the next time step, and 2) Dated memory, wherein each experience is dated and erased according to its order of encounter. We observed that while dated memory leads to faster adaptation in single-step environmental perturbations and helps in quick recovery of cellular benefit, the optimal memory type in the periodic environment depends on the period and cell memory capacity. However, both memory types confer comparable cellular benefits in stochastic environments. We extend the results with these memory types to show how the cost incurred during cellular adaptation (e.g., energetic cost of mRNA and protein production) improves cellular decision-making by delaying the phenotypic response until enough environmental change is experienced by the cells. However, such delayed adaptation proves detrimental to the cells under one-step environmental perturbations. Together, these results elucidate the intricate roles of memory and adaptation cost in phenotypic adaptation in fluctuating environments.