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Temporal integration by calcium dynamics in a model neuron

Nature Neuroscience volume 6, pages 961–967 (2003)Cite this article

Abstract

The calculation and memory of position variables by temporal integration of velocity signals is essential for posture, the vestibulo-ocular reflex (VOR) and navigation. Integrator neurons exhibit persistent firing at multiple rates, which represent the values of memorized position variables. A widespread hypothesis is that temporal integration is the outcome of reverberating feedback loops within recurrent networks, but this hypothesis has not been proven experimentally. Here we present a single-cell model of a neural integrator. The nonlinear dynamics of calcium gives rise to propagating calcium wave-fronts along dendritic processes. The wave-front velocity is modulated by synaptic inputs such that the front location covaries with the temporal sum of its previous inputs. Calcium-dependent currents convert this information into concomitant persistent firing. Calcium dynamics in single neurons could thus be the physiological basis of the graded persistent activity and temporal integration observed in neurons during analog memory tasks.

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Figure 1: The generation of a [Ca2+]i front.
Figure 2: The effect of homogeneous synaptic input on the calcium front (equation (5) in Methods).
Figure 3: The conversion of [Ca2+]i into spikes.
Figure 4: Integration of a time-dependent spatially homogeneous stimulus.
Figure 5: The velocity of the front as a function of the constant external input in a granular dendrite.
Figure 6: Parallel integration of input by multiple dendritic branches in the presence of noise.

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Acknowledgements

We thank M. Goldman, D. Hansel, H.G. Rotstein, M. Spira and Y. Yarom for discussions. This work was supported in part by the Israeli Science Foundation (Center of Excellence 8006-00). Y.L. was supported by the Yeshaya Horowitz Association.

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  1. Racah Institute of Physics, and Center for Neural Computation, Hebrew University, Jerusalem, 91904, Israel

    Yonatan Loewenstein & Haim Sompolinsky

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Correspondence to Yonatan Loewenstein.

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Loewenstein, Y., Sompolinsky, H. Temporal integration by calcium dynamics in a model neuron. Nat Neurosci 6, 961–967 (2003). https://doi.org/10.1038/nn1109

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