Trainable computation in molecular networks.

Reports of learning in single cells without genetic change span decades yet remain controversial, in part because there is no accepted general molecular mechanism for training comparable to gradient-based training or Hebbian learning in neural circuits. Here we identify a minimal set of ingredients sufficient to realize non-genetic learning, drawing inspiration from Boltzmann neural networks. First, dense reversible interaction networks provide an expressive substrate in which modulating the concentrations of a small set of mediator species can reprogram function without altering the underlying interaction parameters. Second, a simple rate-sensitive autoregulatory scheme that adjusts these mediator levels provides a local Hebbian-like training rule that can train the same network for diverse tasks, including Pavlovian conditioning, supervised classification, and generative tuning of bet-hedging ratios to match environmental statistics. We show that this autoregulatory training rule is model free and applies to reversible multimerization networks of arbitrary complexity, so training can compensate for unknown or unmodeled interactions present in vivo. These results suggest design principles for trainable synthetic cellular circuits and indicate how molecular systems could learn statistical features of their environments through experience.