Power-law memory governs bacterial adaptation and learning in fluctuating environments

How do single-celled organisms adapt and learn to survive in dynamic environments without a nervous system? Here, we provide experimental evidence and a theoretical model demon-strating learning-like behavior by single bacterial cells in fluctuating environments. Using a custom microfluidic platform, we tracked individual E. coli cells in dynamic nutrient environments and found that bacteria adapt on multiple timescales, tuning their growth control behavior based on prior environmental experience. Motivated by our observation that cellular adaptation dynamics are approximately scale-free, we built a theoretical framework for bacterial growth control with dynamic power-law memory to explain how bacteria integrate environmental information over a range of timescales to enable growth rate adaptation. We show how this behavior arises naturally from heterogeneous ribosomal relaxation dynamics within a bacterial cell. Using this model, we identify an inherent trade-off between growth rate maximization and adaptation speed, which we validate experimentally in pulsatile nutrient environments. Finally, we connect our mechanistic reaction-network model to descriptions of artificial recurrent neural networks, identifying a minimal network architecture capable of exhibiting adaptation and learning at the single-cell level.