Generalized end-product feedback circuit can sense high-dimensional environmental fluctuations

Understanding computational capabilities of simple biological circuits, such as the regulatory circuits of single-cell organisms, remains an active area of research. Recent theoretical work has shown that a simple cross-talk architecture based on end-product inhibition can exhibit predictive behavior by learning fluctuation statistics of one or two environmental parameters. Here we extend this analysis to higher dimensions, i.e., a large number of fluctuating inputs. We show that a generalized version of the cross-talk architecture can learn not only the dominant direction of fluctuations, as shown previously, but also the subdominant modes, orienting its responsiveness spectrum to the fluctuation eigenmodes. We comment on the relevance of our results to living systems at other scales of organization, such as ecosystems of species competing for fluctuating resources.