Multi-timescale adaptation and emergent learning in single bacterial cells

How do single-celled organisms adapt and learn to survive in dynamic environments without a nervous system? We provide experimental evidence and a theoretical model demonstrating the emergence of learning-like behavior by single bacterial cells in fluctuating nutrient environments. Using a custom microfluidic platform, we tracked individual E. colicells in dynamic nutrient environments and found that bacteria adapt on multiple timescales, tuning their growth control behavior based on prior environmental experience. We find that the adaptation dynamics are scale-free, a hallmark of systems with distributed timescales. We develop a theoretical framework based on fractional-order dynamics, demonstrating that a dynamic, power-law memory governs how cells integrate environmental history. We propose that these fractional dynamics emerge from a microscopic model of heterogeneous ribosomal activity, where a broad spectrum of relaxation times naturally gives rise to the observed non-local memory kernel. This reveals an inherent tradeoff between adaptation speed and growth rate, 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.