# Modeling multiple time scale firing rate adaptation in a neural network of local field potentials

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## Abstract

In response to stimulus changes, the firing rates of many neurons adapt, such that stimulus change is emphasized. Previous work has emphasized that rate adaptation can span a wide range of time scales and produce time scale invariant power law adaptation. However, neuronal rate adaptation is typically modeled using single time scale dynamics, and constructing a conductance-based model with arbitrary adaptation dynamics is nontrivial. Here, a modeling approach is developed in which firing rate adaptation, or spike frequency adaptation, can be understood as a filtering of slow stimulus statistics. Adaptation dynamics are modeled by a stimulus filter, and quantified by measuring the phase leads of the firing rate in response to varying input frequencies. Arbitrary adaptation dynamics are approximated by a set of weighted exponentials with parameters obtained by fitting to a desired filter. With this approach it is straightforward to assess the effect of multiple time scale adaptation dynamics on neural networks. To demonstrate this, single time scale and power law adaptation were added to a network model of local field potentials. Rate adaptation enhanced the slow oscillations of the network and flattened the output power spectrum, dampening intrinsic network frequencies. Thus, rate adaptation may play an important role in network dynamics.

## Keywords

Neural networks Rate adaptation Local field potentials Slow oscillations Multiple time scale## Notes

### Acknowledgments

To Adrienne Fairhall, Matt Higgs, and John Oakley for insightful discussions and comments on the manuscript, and to the University of Washington Department of Neurology for support.

### Conflict of interest

The author declares that he has no conflict of interest.

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