Rate Reduction for Associative Memory Model in Hodgkin–Huxley-Type Network

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  • Oizumi Masafumi
    Graduate School of Frontier Sciences, The University of Tokyo
  • Miyawaki Yoichi
    NICT, Computational Neuroscience Laboratories ATR, Computational Neuroscience Laboratories
  • Okada Masato
    Graduate School of Frontier Sciences, The University of Tokyo RIKEN, Brain Science Institute

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Abstract

We proposed a systematic method for reducing Hodgkin–Huxley-type networks to networks of rate equations on the basis of Shriki et al.’s formulation. Our rate model predicts the results of numerical simulations of the Hodgkin–Huxley-type network model very precisely over a broad range of synaptic conductances. However, in the proposed framework, we ad hoc assumed that the firing threshold and the gain of the f–I curve of the Hodgkin–Huxley-type conductance-based model have a second-order dependence on leak conductance. Here, we discuss optimal model selection with respect to the dependence of the threshold and the gain on the f–I curve, using the Akaike information criterion. We then apply our rate reduction method to an associative memory model of Hodgkin–Huxley neurons. Most associative memory models have been studied using two-state neurons or graded-response neurons. We check the correspondence between an associative memory model of Hodgkin–Huxley neurons and that of graded-response neurons, particularly in terms of phase diagrams. We store correlated patterns in the network and investigate the phase transition between the memory state and the mixed state. We demonstrate that our rate model, which is obtained by the reduction method, explains the phase diagram of the Hodgkin–Huxley-type network very well.

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