How linear response shaped models of neural circuits and the quest for alternatives

Herfurth, Tim; Tchumatchenko, Tatjana

doi:10.1016/j.conb.2017.09.001

“…Individual, pairwise CSDs between spike trains might still be non-linearly related to their pairwise external input CSDs. Recent work has called for looking beyond linear analysis of neuronal networks [81]. Our analysis shows that, even in networks where neural transfer of inputs is nonlinear, linear meanfield analysis can still be accurate and useful.…”

Section: Summary and Discussionmentioning

confidence: 87%

Correlated states in balanced neuronal networks

Baker

¹

,

Ebsch

²

,

Lampl

³

et al. 2019

View full text Add to dashboard Cite

Understanding the magnitude and structure of inter-neuronal correlations and their relationship to synaptic connectivity structure is an important and difficult problem in computational neuroscience. Early studies show that neuronal network models with excitatory-inhibitory balance naturally create very weak spike train correlations, defining the "asynchronous state." Later work showed that, under some connectivity structures, balanced networks can produce larger correlations between some neuron pairs, even when the average correlation is very small. All of these previous studies assume that the local network receives feedforward synaptic input from a population of uncorrelated spike trains. We show that when spike trains providing feedforward input are correlated, the downstream recurrent network produces much larger correlations. We provide an in-depth analysis of the resulting "correlated state" in balanced networks and show that, unlike the asynchronous state, it produces a tight excitatory-inhibitory balance consistent with in vivo cortical recordings.

show abstract

“…Individual, pairwise CSDs between spike trains might still be non-linearly related to their pairwise external input CSDs. Recent work has called for looking beyond linear analysis of neuronal networks [81]. Our analysis shows that, even in networks where neural transfer of inputs is nonlinear, linear mean-field analysis can still be accurate and useful.…”

Section: Summary and Discussionmentioning

confidence: 88%

The correlated state in balanced neuronal networks

Baker

¹

,

Ebsch

²

,

Lampl

³

et al. 2018

Preprint

View full text Add to dashboard Cite

Understanding the magnitude and structure of inter-neuronal correlations and their relationship to synaptic connectivity structure is an important and difficult problem in computational neuroscience. Early studies show that neuronal network models with excitatory-inhibitory balance naturally create very weak spike train correlations. Later work showed that, under some connectivity structures, balanced networks can produce larger correlations between some neuron pairs, even when the average correlation is very small. All of these previous studies assume that the local neuronal network receives feedforward synaptic input from a population of uncorrelated spike trains. We show that when spike trains providing feedforward input are correlated, the downstream recurrent neuronal network produces much larger correlations. We provide an in-depth analysis of the resulting "correlated state" in balanced networks and show that, unlike the asynchronous state of previous work, it produces "tight" excitatory-inhibitory balance, consistent with in vivo cortical recordings. Author summaryCorrelation and synchrony between the activity of neurons in the brain is known to play a crucial role in the dynamics and coding properties of neuronal networks, and also mediates synaptic plasticity and learning. Therefore, it is important to understand the relationship between the structure of connectivity in a neuronal networks and the correlations between the activity of neurons in the network. Previous theoretical work shows that this relationship is constrained by the widely observed balance between excitatory (positive) and inhibitory (negative) input received by neurons in the network. We extend this previous theoretical work to account for the fact that inputs coming from outside the local neuronal network might come from neural populations that are themselves correlated or partially synchronous. Including this biologically realistic assumption changes the basic operating state of the network and produces a tighter balance between excitatory and inhibitory synaptic inputs that is consistent with in vivo recordings.

show abstract

“…The intrinsic dynamics of neurons defines their computational properties 13 , 14 . For regularly firing neurons, an important part of their dynamics is reflected in the neuron’s temporal sensitivity to inputs, captured by the so-called phase-response curve (PRC).…”

Section: Resultsmentioning

confidence: 99%

Temperature elevations can induce switches to homoclinic action potentials that alter neural encoding and synchronization

Hesse

¹

,

Schleimer

²

,

Maier

³

et al. 2022

View full text Add to dashboard Cite

Almost seventy years after the discovery of the mechanisms of action potential generation, some aspects of their computational consequences are still not fully understood. Based on mathematical modeling, we here explore a type of action potential dynamics – arising from a saddle-node homoclinic orbit bifurcation - that so far has received little attention. We show that this type of dynamics is to be expected by specific changes in common physiological parameters, like an elevation of temperature. Moreover, we demonstrate that it favours synchronization patterns in networks – a feature that becomes particularly prominent when system parameters change such that homoclinic spiking is induced. Supported by in-vitro hallmarks for homoclinic spikes in the rodent brain, we hypothesize that the prevalence of homoclinic spikes in the brain may be underestimated and provide a missing link between the impact of biophysical parameters on abrupt transitions between asynchronous and synchronous states of electrical activity in the brain.

show abstract

How linear response shaped models of neural circuits and the quest for alternatives

Cited by 9 publications

References 69 publications

Correlated states in balanced neuronal networks

Correlated states in balanced neuronal networks

The correlated state in balanced neuronal networks

Temperature elevations can induce switches to homoclinic action potentials that alter neural encoding and synchronization

Contact Info

Product

Resources

About