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Abstract

Living organisms are constantly exposed to a huge range of sensory stimuli. The ability of an organism to cope with the variability of inputs determines how well they thrive. One measure for the capability of a system to distinguish stimuli is the dynamic range. It was shown in theory and experiments that the dynamic range is maximized close to a non-equilibrium phase transition (NEPT)[1,2]. A tractable model that shows such a NEPT and describes activity propagation is the branching network with control parameter m. In this model the dynamic range is indeed maximal at the NEPT (m=1). However, for small deviations from the NEPT, as observed for cortex in vivo [3], the dynamic range is virtually indistinguishable from the optimal one and covers the same interval of stimuli (discriminable interval, Fig. 1A). We identify this to be a result from convergence effects in the branching network, i.e., the simultaneous transmission of activation to the same unit from multiple sources in the system. When we correct for convergences in the model using biologically plausible adaptation, the discriminable interval becomes a function of m (Fig. 1B). Considering an ensemble of such networks enables us to extend the discriminable interval and realize a diverging dynamic range in the limit of an infinite ensemble of networks. The same effect can be achieved by rapidly adapting the control parameter of the modified model to the intensity of the incoming stimuli. Our results allow to dissect the mechanisms of sensitivity optimization. They can be applied for better understanding of biological networks as well as to optimize machine learning algorithms.