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Abstract Neurons in the CA1 area of the mouse hippocampus encode the position of the animal in an environment. However, given the variability in individual neurons responses, the accuracy of this code is still poorly understood. It was proposed that downstream areas could achieve high spatial accuracy by integrating the activity of thousands of neurons, but theoretical studies point to shared fluctuations in the firing rate as a potential limitation. Using high-throughput calcium imaging in freely moving mice, we demonstrated the limiting factors in the accuracy of the CA1 spatial code. We found that noise correlations in the hippocampus bound the estimation error of spatial coding to ~10 cm (the size of a mouse). Maximal accuracy was obtained using approximately [300–1400] neurons, depending on the animal. These findings reveal intrinsic limits in the brain’s representations of space and suggest that single neurons downstream of the hippocampus can extract maximal spatial information from several hundred inputs. 

We combine stochastic thermodynamics, large deviation theory, and information theory to derive fundamental limits on the accuracy with which single cell receptors can estimate external concentrations. As expected, if the estimation is performed by an ideal observer of the entire trajectory of receptor states, then no energy consuming nonequilibrium receptor that can be divided into bound and unbound states can outperform an equilibrium two- state receptor. However, when the estimation is performed by a simple observer that measures the fraction of time the receptor is bound, we derive a fundamental limit on the accuracy of general nonequilibrium receptors as a function of energy consumption. We further derive and exploit explicit formulas to numerically estimate a Pareto-optimal tradeoff between accuracy and energy. We find this tradeoff can be achieved by nonuniform ring receptors with a number of states that necessarily increases with energy. Our results yield a thermodynamic uncertainty relation for the time a physical system spends in a pool of states and generalize the classic Berg- Purcell limit [H. C. Berg and E. M. Purcell, Biophys. J. 20, 193 (1977)] on cellular sensing along multiple dimensions.