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Complete Firing-Rate Response of Neurons with Complex Intrinsic Dynamics.

Puelma Touzel M, Wolf F - PLoS Comput. Biol. (2015)

Bottom Line: While resonator cell types exist in a variety of brain areas, few models incorporate this feature and fewer have investigated its effects.We find that resonance arises primarily due to slow adaptation with an intrinsic frequency acting to sharpen and adjust the location of the resonant peak.The expressions and analysis presented here provide an account of how intrinsic neuron dynamics shape dynamic population response properties and can facilitate the construction of an exact theory of correlations and stability of population activity in networks containing populations of resonator neurons.

View Article: PubMed Central - PubMed

Affiliation: Department for Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Goettingen, Germany.

ABSTRACT
The response of a neuronal population over a space of inputs depends on the intrinsic properties of its constituent neurons. Two main modes of single neuron dynamics-integration and resonance-have been distinguished. While resonator cell types exist in a variety of brain areas, few models incorporate this feature and fewer have investigated its effects. To understand better how a resonator's frequency preference emerges from its intrinsic dynamics and contributes to its local area's population firing rate dynamics, we analyze the dynamic gain of an analytically solvable two-degree of freedom neuron model. In the Fokker-Planck approach, the dynamic gain is intractable. The alternative Gauss-Rice approach lifts the resetting of the voltage after a spike. This allows us to derive a complete expression for the dynamic gain of a resonator neuron model in terms of a cascade of filters on the input. We find six distinct response types and use them to fully characterize the routes to resonance across all values of the relevant timescales. We find that resonance arises primarily due to slow adaptation with an intrinsic frequency acting to sharpen and adjust the location of the resonant peak. We determine the parameter regions for the existence of an intrinsic frequency and for subthreshold and spiking resonance, finding all possible intersections of the three. The expressions and analysis presented here provide an account of how intrinsic neuron dynamics shape dynamic population response properties and can facilitate the construction of an exact theory of correlations and stability of population activity in networks containing populations of resonator neurons.

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A resonance frequency emerges in the voltage response in one of two ways depending on the intrinsic timescale.For slow intrinsic current (), a response exhibiting a maximum at ωmax already exists at Ω = 0. For fast intrinsic current (), a resonance emerges at finite Ω, whose value converges for vanishing ωLτw.
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pcbi.1004636.g005: A resonance frequency emerges in the voltage response in one of two ways depending on the intrinsic timescale.For slow intrinsic current (), a response exhibiting a maximum at ωmax already exists at Ω = 0. For fast intrinsic current (), a resonance emerges at finite Ω, whose value converges for vanishing ωLτw.

Mentions: In this section, we take the general result of the previous section, Eq (23), and go through its explicit calculation for a population of Gauss-Rice GIF neurons to obtain the result Eq (41). A work taking a similar approach, partly inspired by this work, though with with less intermediate analysis has recently appeared [25]. Our novel findings arise from an exhaustive characterization of the parameter dependence across the phase diagram of the voltage response, Fig 3. We calculate the current-to-voltage filter, expressing it in each of the three representations listed in Table 1, Eqs (25, 26 and 27) respectively. We show (Fig 4) how the low pass component of the filter undergoes a qualitative change from second-order low pass to first-order low pass to resonant as QL is increased. We find the voltage resonance condition, , where the resonance has a contribution from slow adaptation and from the frequency, Ω. Either can exist without the other (Fig 5). We then compute the voltage correlation function, Eq (37)), whose envelope depends on the relaxation time, τr (Fig 6). From this, the variances are calculated and an expression for the differential correlation time, τs, Eq (39) is obtained. We show a characteristic dependence on the ratio τw/τI (Fig 7). Finally, we show in Fig 8 how the stationary firing rate has unimodal dependence on the time constants, τV and τI, monotonic rise with input variance, , and monotonic decay with intrinsic frequency, Ω.


Complete Firing-Rate Response of Neurons with Complex Intrinsic Dynamics.

Puelma Touzel M, Wolf F - PLoS Comput. Biol. (2015)

A resonance frequency emerges in the voltage response in one of two ways depending on the intrinsic timescale.For slow intrinsic current (), a response exhibiting a maximum at ωmax already exists at Ω = 0. For fast intrinsic current (), a resonance emerges at finite Ω, whose value converges for vanishing ωLτw.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4697854&req=5

pcbi.1004636.g005: A resonance frequency emerges in the voltage response in one of two ways depending on the intrinsic timescale.For slow intrinsic current (), a response exhibiting a maximum at ωmax already exists at Ω = 0. For fast intrinsic current (), a resonance emerges at finite Ω, whose value converges for vanishing ωLτw.
Mentions: In this section, we take the general result of the previous section, Eq (23), and go through its explicit calculation for a population of Gauss-Rice GIF neurons to obtain the result Eq (41). A work taking a similar approach, partly inspired by this work, though with with less intermediate analysis has recently appeared [25]. Our novel findings arise from an exhaustive characterization of the parameter dependence across the phase diagram of the voltage response, Fig 3. We calculate the current-to-voltage filter, expressing it in each of the three representations listed in Table 1, Eqs (25, 26 and 27) respectively. We show (Fig 4) how the low pass component of the filter undergoes a qualitative change from second-order low pass to first-order low pass to resonant as QL is increased. We find the voltage resonance condition, , where the resonance has a contribution from slow adaptation and from the frequency, Ω. Either can exist without the other (Fig 5). We then compute the voltage correlation function, Eq (37)), whose envelope depends on the relaxation time, τr (Fig 6). From this, the variances are calculated and an expression for the differential correlation time, τs, Eq (39) is obtained. We show a characteristic dependence on the ratio τw/τI (Fig 7). Finally, we show in Fig 8 how the stationary firing rate has unimodal dependence on the time constants, τV and τI, monotonic rise with input variance, , and monotonic decay with intrinsic frequency, Ω.

Bottom Line: While resonator cell types exist in a variety of brain areas, few models incorporate this feature and fewer have investigated its effects.We find that resonance arises primarily due to slow adaptation with an intrinsic frequency acting to sharpen and adjust the location of the resonant peak.The expressions and analysis presented here provide an account of how intrinsic neuron dynamics shape dynamic population response properties and can facilitate the construction of an exact theory of correlations and stability of population activity in networks containing populations of resonator neurons.

View Article: PubMed Central - PubMed

Affiliation: Department for Nonlinear Dynamics, Max Planck Institute for Dynamics and Self-Organization, Goettingen, Germany.

ABSTRACT
The response of a neuronal population over a space of inputs depends on the intrinsic properties of its constituent neurons. Two main modes of single neuron dynamics-integration and resonance-have been distinguished. While resonator cell types exist in a variety of brain areas, few models incorporate this feature and fewer have investigated its effects. To understand better how a resonator's frequency preference emerges from its intrinsic dynamics and contributes to its local area's population firing rate dynamics, we analyze the dynamic gain of an analytically solvable two-degree of freedom neuron model. In the Fokker-Planck approach, the dynamic gain is intractable. The alternative Gauss-Rice approach lifts the resetting of the voltage after a spike. This allows us to derive a complete expression for the dynamic gain of a resonator neuron model in terms of a cascade of filters on the input. We find six distinct response types and use them to fully characterize the routes to resonance across all values of the relevant timescales. We find that resonance arises primarily due to slow adaptation with an intrinsic frequency acting to sharpen and adjust the location of the resonant peak. We determine the parameter regions for the existence of an intrinsic frequency and for subthreshold and spiking resonance, finding all possible intersections of the three. The expressions and analysis presented here provide an account of how intrinsic neuron dynamics shape dynamic population response properties and can facilitate the construction of an exact theory of correlations and stability of population activity in networks containing populations of resonator neurons.

Show MeSH
Related in: MedlinePlus