Firing rate distributions in a feedforward network of neural oscillators with intrinsic and network heterogeneity

Kyle Wendling; Cheng Ly; Kyle Wendling; Cheng Ly

doi:10.3934/mbe.2019099

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 4: 2023-2048. doi: 10.3934/mbe.2019099

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Research article

Firing rate distributions in a feedforward network of neural oscillators with intrinsic and network heterogeneity

Kyle Wendling ^,,
Cheng Ly ^,

Department of Statistical Sciences and Operations Research, Virginia Commonwealth University, Richmond, VA 23284, USA

Received: 12 September 2018 Accepted: 28 January 2019 Published: 08 March 2019

The level of firing rate heterogeneity in a population of cortical neurons has consequences for how stimuli are processed. Recent studies have shown that the right amount of firing rate heterogeneity (not too much or too little) is a signature of efficient coding, thus quantifying the relative amount of firing rate heterogeneity is important. In a feedforward network of stochastic neural oscillators, we study the firing rate heterogeneity stemming from two sources: intrinsic (different individual cells) and network (different effects from presynaptic inputs). We find that the relationship between these two forms of heterogeneity can lead to significant changes in firing rate heterogeneity. We consider several networks, including noisy excitatory synaptic inputs, and noisy inputs with both excitatory and inhibitory inputs. To mathematically explain these results, we apply a phase reduction and derive asymptotic approximations of the firing rate statistics assuming weak noise and coupling. Our analytic calculations reveals how the interaction between intrinsic and network heterogeneity results in different firing rate distributions. Our work shows the importance of the phase-resetting curve (and various transformations of it revealed by our analytic calculations) in controlling firing rate statistics.
- phase oscillators,
- PRC,
- heterogeneity,
- population firing rate,
- phase reduction
Citation: Kyle Wendling, Cheng Ly. Firing rate distributions in a feedforward network of neural oscillators with intrinsic and network heterogeneity[J]. Mathematical Biosciences and Engineering, 2019, 16(4): 2023-2048. doi: 10.3934/mbe.2019099

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Abstract

The level of firing rate heterogeneity in a population of cortical neurons has consequences for how stimuli are processed. Recent studies have shown that the right amount of firing rate heterogeneity (not too much or too little) is a signature of efficient coding, thus quantifying the relative amount of firing rate heterogeneity is important. In a feedforward network of stochastic neural oscillators, we study the firing rate heterogeneity stemming from two sources: intrinsic (different individual cells) and network (different effects from presynaptic inputs). We find that the relationship between these two forms of heterogeneity can lead to significant changes in firing rate heterogeneity. We consider several networks, including noisy excitatory synaptic inputs, and noisy inputs with both excitatory and inhibitory inputs. To mathematically explain these results, we apply a phase reduction and derive asymptotic approximations of the firing rate statistics assuming weak noise and coupling. Our analytic calculations reveals how the interaction between intrinsic and network heterogeneity results in different firing rate distributions. Our work shows the importance of the phase-resetting curve (and various transformations of it revealed by our analytic calculations) in controlling firing rate statistics.

References

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