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Oscillations and Synchrony in Large-scale Cortical Network Models

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Abstract

Intrinsic neuronal and circuit properties control the responses of large ensembles of neurons by creating spatiotemporal patterns of activity that are used for sensory processing, memory formation, and other cognitive tasks. The modeling of such systems requires computationally efficient single-neuron models capable of displaying realistic response properties. We developed a set of reduced models based on difference equations (map-based models) to simulate the intrinsic dynamics of biological neurons. These phenomenological models were designed to capture the main response properties of specific types of neurons while ensuring realistic model behavior across a sufficient dynamic range of inputs. This approach allows for fast simulations and efficient parameter space analysis of networks containing hundreds of thousands of neurons of different types using a conventional workstation. Drawing on results obtained using large-scale networks of map-based neurons, we discuss spatiotemporal cortical network dynamics as a function of parameters that affect synaptic interactions and intrinsic states of the neurons.

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Notes

  1. More often than not, neuronal dynamics is simulated using differential equations rather than difference equations (for example, the Hodgkin–Huxley model [1], the IF model [17–19], and the Izhikevich model [22]). However, it is important to emphasize that to solve a differential equation numerically, it is usually rewritten in the form of a difference equation (e.g., using the Euler scheme, the time derivative dV/dt is replaced by (V n + 1 − V n )/τ).

  2. One can simplify the condition for the threshold by introducing a new control parameter \(\sigma^{\mathrm{new}}= \sigma - 2+\sqrt{\alpha/(1-\mu)}\). In this case, the threshold value occurs at \(\sigma^{\mathrm{new}}_{\mathrm{th}}=0\). In this paper, we do not use this change of the control parameter.

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Acknowledgement

Partially supported by grant from ONR, N00014-07-1-0741 (NR) and by grant from NIDCD (MB).

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Authors and Affiliations

  1. UCSD and Information Systems Labs. Inc., San Diego, CA, USA

    Nikolai F. Rulkov

  2. The Salk Institute, San Diego, CA, USA

    Maxim Bazhenov

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Correspondence to Nikolai F. Rulkov.

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Rulkov, N.F., Bazhenov, M. Oscillations and Synchrony in Large-scale Cortical Network Models. J Biol Phys 34, 279–299 (2008). https://doi.org/10.1007/s10867-008-9079-y

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