Limits on the computational expressivity of non-equilibrium biophysical processes

Many biological decision-making tasks require classifying high-dimensional chemical states. The biophysical and computational mechanisms that enable classification remain enigmatic. In this work, using Markov jump processes as an abstraction of general biochemical networks, we reveal several unanticipated and universal limitations on the classification ability of generic biophysical processes. These limits arise from a fundamental non-equilibrium thermodynamic constraint that we have derived. Importantly, we show that these limitations can be overcome using common biochemical mechanisms that we term input multiplicity, examples of which include enzymes acting on multiple targets. Analogous to how increasing depth enhances the expressivity and classification ability of neural networks, our work demonstrates how tuning input multiplicity can potentially enable an exponential increase in a biological system's ability to classify and process information.