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Divisive gain modulation with dynamic stimuli in integrate-and-fire neurons.

Ly C, Doiron B - PLoS Comput. Biol. (2009)

Bottom Line: It has been shown that divisive gain modulation of neural responses can result from a stochastic shunting from balanced (mixed excitation and inhibition) background activity.However, input statistics, such as the firing rates of pre-synaptic neurons, are often dynamic, varying on timescales comparable to typical membrane time constants.Using a population density approach for integrate-and-fire neurons with dynamic and temporally rich inputs, we find that the same fluctuation-induced divisive gain modulation is operative for dynamic inputs driving nonequilibrium responses.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania, USA. chengly@math.pitt.edu

ABSTRACT
The modulation of the sensitivity, or gain, of neural responses to input is an important component of neural computation. It has been shown that divisive gain modulation of neural responses can result from a stochastic shunting from balanced (mixed excitation and inhibition) background activity. This gain control scheme was developed and explored with static inputs, where the membrane and spike train statistics were stationary in time. However, input statistics, such as the firing rates of pre-synaptic neurons, are often dynamic, varying on timescales comparable to typical membrane time constants. Using a population density approach for integrate-and-fire neurons with dynamic and temporally rich inputs, we find that the same fluctuation-induced divisive gain modulation is operative for dynamic inputs driving nonequilibrium responses. Moreover, the degree of divisive scaling of the dynamic response is quantitatively the same as the steady-state responses--thus, gain modulation via balanced conductance fluctuations generalizes in a straight-forward way to a dynamic setting.

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Divisive gain modulation does not hold for high intensity input drivers.(A) Top Panel: Same stimulus in Figure 3, but magnified to include higher output firing rates. Bottom Panel: The response for different balanced background levels . (B) The three responses do not scale in a simple way.
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pcbi-1000365-g005: Divisive gain modulation does not hold for high intensity input drivers.(A) Top Panel: Same stimulus in Figure 3, but magnified to include higher output firing rates. Bottom Panel: The response for different balanced background levels . (B) The three responses do not scale in a simple way.

Mentions: When the dynamic stimuli are increased so that resulting output firing rates are larger, the neurons no longer exhibit divisive gain modulation. Increasing the overall intensity of the driving input (compare Fig. 5A with Fig. 3A) yields firing rates that are an order of magnitude larger (compare Fig. 5B with Fig. 3C). Increasing the overall background activity reduces the overall response magnitude (Fig. 5B), similar to what is observed in both the equilibrium and nonequlibrium regimes. However, when the response curves are scaled by computed for the low rate case pure divisive gain modulation is not observed for the high rate response. There is no trivial (a time independent ) or natural way to scale the output firing rate curves so that they lie on top of each other. Since divisive gain modulation does not hold in the equilibrium setting for high output firing rates (drift dominated regime), one would expect that it does not hold in the nonequilibrium state. However, both the equilibrium and nonequilibrium states are quite different and we present the failure of fluctuation induced division for the sake of completeness. It is interesting to note that for periods of time when the output firing rates are low, divisive gain modulation appears evident, likely owing to a transient excursion into the fluctuation driven regime.


Divisive gain modulation with dynamic stimuli in integrate-and-fire neurons.

Ly C, Doiron B - PLoS Comput. Biol. (2009)

Divisive gain modulation does not hold for high intensity input drivers.(A) Top Panel: Same stimulus in Figure 3, but magnified to include higher output firing rates. Bottom Panel: The response for different balanced background levels . (B) The three responses do not scale in a simple way.
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Related In: Results  -  Collection

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getmorefigures.php?uid=PMC2667215&req=5

pcbi-1000365-g005: Divisive gain modulation does not hold for high intensity input drivers.(A) Top Panel: Same stimulus in Figure 3, but magnified to include higher output firing rates. Bottom Panel: The response for different balanced background levels . (B) The three responses do not scale in a simple way.
Mentions: When the dynamic stimuli are increased so that resulting output firing rates are larger, the neurons no longer exhibit divisive gain modulation. Increasing the overall intensity of the driving input (compare Fig. 5A with Fig. 3A) yields firing rates that are an order of magnitude larger (compare Fig. 5B with Fig. 3C). Increasing the overall background activity reduces the overall response magnitude (Fig. 5B), similar to what is observed in both the equilibrium and nonequlibrium regimes. However, when the response curves are scaled by computed for the low rate case pure divisive gain modulation is not observed for the high rate response. There is no trivial (a time independent ) or natural way to scale the output firing rate curves so that they lie on top of each other. Since divisive gain modulation does not hold in the equilibrium setting for high output firing rates (drift dominated regime), one would expect that it does not hold in the nonequilibrium state. However, both the equilibrium and nonequilibrium states are quite different and we present the failure of fluctuation induced division for the sake of completeness. It is interesting to note that for periods of time when the output firing rates are low, divisive gain modulation appears evident, likely owing to a transient excursion into the fluctuation driven regime.

Bottom Line: It has been shown that divisive gain modulation of neural responses can result from a stochastic shunting from balanced (mixed excitation and inhibition) background activity.However, input statistics, such as the firing rates of pre-synaptic neurons, are often dynamic, varying on timescales comparable to typical membrane time constants.Using a population density approach for integrate-and-fire neurons with dynamic and temporally rich inputs, we find that the same fluctuation-induced divisive gain modulation is operative for dynamic inputs driving nonequilibrium responses.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania, USA. chengly@math.pitt.edu

ABSTRACT
The modulation of the sensitivity, or gain, of neural responses to input is an important component of neural computation. It has been shown that divisive gain modulation of neural responses can result from a stochastic shunting from balanced (mixed excitation and inhibition) background activity. This gain control scheme was developed and explored with static inputs, where the membrane and spike train statistics were stationary in time. However, input statistics, such as the firing rates of pre-synaptic neurons, are often dynamic, varying on timescales comparable to typical membrane time constants. Using a population density approach for integrate-and-fire neurons with dynamic and temporally rich inputs, we find that the same fluctuation-induced divisive gain modulation is operative for dynamic inputs driving nonequilibrium responses. Moreover, the degree of divisive scaling of the dynamic response is quantitatively the same as the steady-state responses--thus, gain modulation via balanced conductance fluctuations generalizes in a straight-forward way to a dynamic setting.

Show MeSH
Related in: MedlinePlus