Loss of phase-locking in non-weakly coupled inhibitory networks of type-I model neurons

Oh, Myongkeun; Matveev, Victor

doi:10.1007/s10827-008-0112-8

Cited by 34 publications

(34 citation statements)

References 35 publications

(82 reference statements)

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“…The linear nature of the experimental PRCs in Fig. 5 has been reported in a computational model of Hermissenda photoreceptors (Butson and Clark 2008a,b) and other common biophysically realistic computational models of neurons given strong inputs (Oh and Matveev 2009;Maran and Canavier 2008). Therefore, we consider linear-like PRCs to be a generic property of oscillators given strong inputs.…”

Section: Phase-resetting Theorymentioning

confidence: 77%

“…We based our PRC on expected spike time delays; however, investigations involving timescale separation and analysis of stochastic maps derived from biophysical neural models have been analyzed (Rubin and Josić 2007). Theoretical investigations of biophysical neural models in the strong coupling regime have reported similar linear-like PRCs (Oh and Matveev 2009;Maran and Canavier 2008;Butson and Clark 2008a,b). Therefore, we consider linear PRCs to be a generic property of oscillators given strong inputs.…”

Section: Discussionmentioning

confidence: 99%

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Relative spike timing in stochastic oscillator networks of the Hermissenda eye

Nesse

Clark

2010

Biol Cybern

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The role of relative spike timing on sensory coding and stochastic dynamics of small pulse-coupled oscillator networks is investigated physiologically and mathematically, based on the small biological eye network of the marine invertebrate Hermissenda. Without network interactions, the five inhibitory photoreceptors of the eye network exhibit quasi-regular rhythmic spiking; in contrast, within the active network, they display more irregular spiking but collective network rhythmicity. We investigate the source of this emergent network behavior first analyzing the role of relative input to spike-timing relationships in individual cells. We use a stochastic phase oscillator equation to model photoreceptor spike sequences in response to sequences of inhibitory current pulses. Although spike sequences can be complex and irregular in response to inputs, we show that spike timing is better predicted if relative timing of spikes to inputs is accounted for in the model. Further, we establish that greater noise levels in the model serve to destroy network phase-locked states that induce non-monotonic stimulus rate-coding, as predicted in Butson and Clark (J Neurophysiol 99:146-154, 2008a; J Neurophysiol 99:155-165, 2008b). Hence, rate-coding can function better in noisy spiking cells relative to non-noisy cells. We then study how relative input to spike-timing dynamics of single oscillators contribute to network-level dynamics. Relative timing interactions in the network sharpen the stimulus window that can trigger a spike, affecting stimulus encoding. Also, we derive analytical inter-spike interval distributions of cells in the model network, revealing that irregular Poisson-like spike emission and collective network rhythmicity are emergent properties of network dynamics, consistent with experimental observations. Our theoretical results generate experimental predictions about the nature of spike patterns in the Hermissenda eye.

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Section: Phase-resetting Theorymentioning

confidence: 77%

Section: Discussionmentioning

confidence: 99%

Relative spike timing in stochastic oscillator networks of the Hermissenda eye

Nesse

Clark

2010

Biol Cybern

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“…In fact, Maran and Canavier (2008) demonstrated qualitatively new dynamical states such as stable "leap-frog" spiking (leader-switching) exhibited by two Wang-Buzsáki model neurons (Wang and Buzsáki 1996) coupled by non-weak inhibition, which arise when phase variable is negative during part of each oscillation cycle. Recently we examined similar leader-switching in a homogeneous network of simpler Morris-Lecar model neurons pulse-coupled by non-weak inhibition (Oh and Matveev 2009), and Canavier and coworkers further generalized the STRC approach to describe more complex phase-locked and clustered solutions in larger networks of non-weak coupled cells Achuthan and Canavier 2009;Canavier and Achuthan 2010).…”

Section: Introductionmentioning

confidence: 99%

“…In Oh and Matveev (2009) we analyzed stable leader-switching associated with the condition (φ) > φ, and demonstrated its geometric meaning in terms of isochrons that curl around the limit cycle, as shown in Fig. 1.…”

Section: Introductionmentioning

confidence: 99%

Non-weak inhibition and phase resetting at negative values of phase in cells with fast-slow dynamics at hyperpolarized potentials

Matveev

2010

J Comput Neurosci

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Phase response is a powerful concept in the analysis of both weakly and non-weakly perturbed oscillators such as regularly spiking neurons, and is applicable if the oscillator returns to its limit cycle trajectory between successive perturbations. When the latter condition is violated, a formal application of the phase return map may yield phase values outside of its definition domain; in particular, strong synaptic inhibition may result in negative values of phase. The effect of a second perturbation arriving close to the first one is undetermined in this case. However, here we show that for a Morris-Lecar model of a spiking cell with strong time scale separation, extending the phase response function definition domain to an additional negative value branch allows to retain the accuracy of the phase response approach in the face of such strong inhibitory coupling. We use the resulting extended phase response function to accurately describe the response of a Morris-Lecar oscillator to consecutive non-weak synaptic inputs. This method is particularly useful when analyzing the dynamics of three or more non-weakly coupled cells, whereby more than one synaptic perturbation arrives per oscillation cycle into each cell. The method of perturbation prediction based on the negative-phase extension of the phase response function may be applicable to other excitable cell models characterized by slow voltage dynamics at hyperpolarized potentials.

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“…In our previous work [3], we have shown that for some biophysical models of spiking cells, a one-dimensional phase reduction of a non-weakly perturbed limit cycle oscillator may require the extension of the phase variable defining the state of the oscillator to a multi-branched phase domain. Such multi-branched domain is most easily implemented by extending the [0, 1] phase interval to negative values.…”

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confidence: 99%

Negative phase and extended spike-time response curve

Matveev

2009

BMC Neurosci

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The phase response curve (PRC) approach is a powerful tool in analyzing response of spiking cell to synaptic or other perturbations. The PRC-based analysis of the cell response involves describing the effect of perturbation as a change of the phase variable characterizing the state of the spiking cell, whereby the phase is always bounded on the interval [0, 1] or [0, 2π]. However, the extension of phase domain to negative values naturally arises when deriving phase return maps in the case of non-weak inhibition or larger networks coupled by three or more cells, as previously shown by Canavier and coworkers [1,2].In our previous work [3], we have shown that for some biophysical models of spiking cells, a one-dimensional phase reduction of a non-weakly perturbed limit cycle oscillator may require the extension of the phase variable defining the state of the oscillator to a multi-branched phase domain. Such multi-branched domain is most easily implemented by extending the [0, 1] phase interval to negative values. The simplest illustration of such negative phase is provided by the integrate-and-fire model when it is hyperpolarized below its reset potential. This notion of negative phase enables us to extend the phase return map analysis based on the spike-time response curve (STRC) characteristic to describe novel dynamical states of nonweakly coupled oscillators, in particular the alternatingorder spiking state.Here we examine the geometric meaning of such negative phase domain for the first time in terms of the phase space of the model and show that the extension of STRC to negative values of phase is necessary to accurately predict the response of a model cell to several close non-weak perturbations, as shown in Figure 1. Such an extended STRC can then be used to analyze the dynamics of three or more non-weakly coupled cells, whereby more than one synaptic perturbation arrives per oscillation cycle into each cell. Also, we reproduce the entire bifurcation structure of the Morris-Lecar network dynamics using the α-function STRC to examine a qualitative effect of changing the shape of STRC with negative phase domain.

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Loss of phase-locking in non-weakly coupled inhibitory networks of type-I model neurons

Cited by 34 publications

References 35 publications

Relative spike timing in stochastic oscillator networks of the Hermissenda eye

Relative spike timing in stochastic oscillator networks of the Hermissenda eye

Non-weak inhibition and phase resetting at negative values of phase in cells with fast-slow dynamics at hyperpolarized potentials

Negative phase and extended spike-time response curve

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