The neuronal code arising from the coordinated activity of grid cells in the rodent entorhinal cortex can uniquely represent space across a large range of distances, but the precise conditions for optimal coding capacity are known only for environments with finite size.Here we consider a coding scheme that is suitable for unbounded environments, and present a novel, number theoretic approach to derive the grid parameters that maximise the coding range in the presence of noise.We derive an analytic upper bound on the coding range and provide examples for grid scales that achieve this bound and hence are optimal for encoding in unbounded environments.We show that in the absence of neuronal noise, the capacity of the system is extremely sensitive to the choice of the grid periods.However, when the accuracy of the representation is limited by neuronal noise, the capacity quickly becomes more robust against the choice of grid scales as the number of modules increases.Importantly, we found that the capacity of the system is near optimal even for random scale choices already for a realistic number of grid modules.Our study demonstrates that robust and efficient coding can be achieved without parameter tuning in the case of grid cell representation and provides a solid theoretical explanation for the large diversity of the grid scales observed in experimental studies.Moreover, we suggest that having multiple grid modules in the entorhinal cortex is not only required for the exponentially large coding capacity, but is also a prerequisite for the robustness of the system. Author summaryNavigation in natural, open environments poses serious challenges to animals as the distances to be represented may span several orders of magnitudes and are potentially unbounded.The recently discovered grid cells in the rodent brain are though to play a crucial role in generating unique representations for a large number of spatial locations.However, it is unknown how to choose the parameters of the grid cells to achieve maximal capacity, i.e., to uniquely encode the utmost locations in an open environment.In our manuscript, we demonstrate the surprising robustness of the grid cell coding system: The population code realised by grid cells is close to optimal for unique space representation irrespective of the choices of grid parameters.Thus, our study reveals a remarkable

Schizophrenia is often regarded as a set of symptoms caused by impairments in the cognitive control in macro-networks of the brain. To investigate this hypothesis, an fMRI study involving an associative learning task was conducted with schizophrenia patients and controls. A set of generative models of the BOLD signal generation were defined to describe the interaction of five brain regions (Primary Visual Cortex, Superior Parietal and Inferior Temporal Cortex, Hippocampus and Dorsal Prefrontal Cortex) and the experimental conditions. The models were fitted to the data using Bayesian model inversion. The comparison of different model connectivity structures lead to the finding that in schizophrenia, there are significant impairments in backward connections from prefrontal cortex to hippocampal and temporal regions in patients. These findings fit very well with the predictions of a neuron network model of encoding-recall switching dynamics we have described previously.

Computational analyses of dendritic computations often assume stationary inputs to neurons, ignoring the pulsatile nature of spike-based communication between neurons and the moment-to-moment fluctuations caused by such spiking inputs. Conversely, circuit computations with spiking neurons are usually formalized without regard to the rich nonlinear nature of dendritic processing. Here we address the computational challenge faced by neurons that compute and represent analogue quantities but communicate with digital spikes, and show that reliable computation of even purely linear functions of inputs can require the interplay of strongly nonlinear subunits within the postsynaptic dendritic tree. Our theory predicts a matching of dendritic nonlinearities and synaptic weight distributions to the joint statistics of presynaptic inputs. This approach suggests normative roles for some puzzling forms of nonlinear dendritic dynamics and plasticity.

A fundamental question in understanding neuronal computations is how dendritic events influence the output of the neuron. Different forms of integration of neighbouring and distributed synaptic inputs, isolated dendritic spikes and local regulation of synaptic efficacy suggest that individual dendritic branches may function as independent computational subunits. In the present paper, we study how these local computations influence the output of the neuron. Using a simple cascade model, we demonstrate that triggering somatic firing by a relatively small dendritic branch requires the amplification of local events by dendritic spiking and synaptic plasticity. The moderately branching dendritic tree of granule cells seems optimal for this computation since larger dendritic trees favor local plasticity by isolating dendritic compartments, while reliable detection of individual dendritic spikes in the soma requires a low branch number. Finally, we demonstrate that these parallel dendritic computations could contribute to the generation of multiple independent place fields of hippocampal granule cells.