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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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Related in: MedlinePlus

Optimal scaling factor for sinusoidal input compared with equlibrium scaling factor.The red line is the optimal scaling factor  (11) of the equilibrium input/output curves computed for , and the black line with dots is the optimal scaling factor  (14) of the two dynamical responses with sinusoidal input . The scaling factors match very well for a variety of pairs of balanced background synaptic inputs. Top panels to bottom panels have background synaptic input rates of: (A) , (B) , (C) , (D) . See Equation (4) for corresponding  background balance of excitation and inhibition.
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pcbi-1000365-g007: Optimal scaling factor for sinusoidal input compared with equlibrium scaling factor.The red line is the optimal scaling factor (11) of the equilibrium input/output curves computed for , and the black line with dots is the optimal scaling factor (14) of the two dynamical responses with sinusoidal input . The scaling factors match very well for a variety of pairs of balanced background synaptic inputs. Top panels to bottom panels have background synaptic input rates of: (A) , (B) , (C) , (D) . See Equation (4) for corresponding background balance of excitation and inhibition.

Mentions: A gain control scheme will be effective in unpredictable environments if it is quantitatively insensitive to the timescales of the input, or in other words the degree to which the response is scaled should not depend on the spectral content of the signal. For fluctuation induced gain control we then require that the scaling factor associated with a specific background state would need to be independent of the temporal frequencies in the driver input . To test this we compare the optimal scaling factor between two dynamical responses (each with a distinct balanced background state) where the synaptic driving input is:Notice the specified varies from 0 to , so that synaptic input rates are non-negative. Let us denote by for two given background rates driven by sinusoidal input with frequency in Hz (here is not the conventional radian frequency). When is in a low range the differences between and are negligible over a wide range of (Fig. 7). This result is robust for a range of background states (Fig. 7A–D). The quantitative match between the divisive scaling of equilibrium and nonequlibrium responses extends to more complicated temporal modulations of the driving input (Fig. 3A). Specifically, we find that for the results shown previously ( and in Figs. 2 and 3). Thus, fluctuation induced gain control is quantitatively insensitive to the timescales of the driving input.


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

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

Optimal scaling factor for sinusoidal input compared with equlibrium scaling factor.The red line is the optimal scaling factor  (11) of the equilibrium input/output curves computed for , and the black line with dots is the optimal scaling factor  (14) of the two dynamical responses with sinusoidal input . The scaling factors match very well for a variety of pairs of balanced background synaptic inputs. Top panels to bottom panels have background synaptic input rates of: (A) , (B) , (C) , (D) . See Equation (4) for corresponding  background balance of excitation and inhibition.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2667215&req=5

pcbi-1000365-g007: Optimal scaling factor for sinusoidal input compared with equlibrium scaling factor.The red line is the optimal scaling factor (11) of the equilibrium input/output curves computed for , and the black line with dots is the optimal scaling factor (14) of the two dynamical responses with sinusoidal input . The scaling factors match very well for a variety of pairs of balanced background synaptic inputs. Top panels to bottom panels have background synaptic input rates of: (A) , (B) , (C) , (D) . See Equation (4) for corresponding background balance of excitation and inhibition.
Mentions: A gain control scheme will be effective in unpredictable environments if it is quantitatively insensitive to the timescales of the input, or in other words the degree to which the response is scaled should not depend on the spectral content of the signal. For fluctuation induced gain control we then require that the scaling factor associated with a specific background state would need to be independent of the temporal frequencies in the driver input . To test this we compare the optimal scaling factor between two dynamical responses (each with a distinct balanced background state) where the synaptic driving input is:Notice the specified varies from 0 to , so that synaptic input rates are non-negative. Let us denote by for two given background rates driven by sinusoidal input with frequency in Hz (here is not the conventional radian frequency). When is in a low range the differences between and are negligible over a wide range of (Fig. 7). This result is robust for a range of background states (Fig. 7A–D). The quantitative match between the divisive scaling of equilibrium and nonequlibrium responses extends to more complicated temporal modulations of the driving input (Fig. 3A). Specifically, we find that for the results shown previously ( and in Figs. 2 and 3). Thus, fluctuation induced gain control is quantitatively insensitive to the timescales of the driving input.

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