Limits...
Modulation of a Single Neuron Has State-Dependent Actions on Circuit Dynamics(,.)

Gutierrez GJ, Marder E - eNeuro (2014)

Bottom Line: We determined the effects of varying ḡCa , ḡK , and ḡh on the frequency, amplitude, and duty cycle of a single neuron oscillator.For a different set of network parameters, circuit behavior varied with the maximal conductances of the hub neuron.This demonstrates that neuromodulation of a single target neuron may dramatically alter the performance of an entire network when the network is in one state, but have almost no effect when the circuit is in a different state.

View Article: PubMed Central - HTML - PubMed

Affiliation: Volen Center for Complex Systems and Biology Department, Brandeis University, Waltham, Massachusetts 02454.

ABSTRACT

When does neuromodulation of a single neuron influence the output of the entire network? We constructed a five-cell circuit in which a neuron is at the center of the circuit and the remaining neurons form two distinct oscillatory subnetworks. All neurons were modeled as modified Morris-Lecar models with a hyperpolarization-activated conductance (ḡh ) in addition to calcium (ḡCa ), potassium (ḡK ), and leak conductances. We determined the effects of varying ḡCa , ḡK , and ḡh on the frequency, amplitude, and duty cycle of a single neuron oscillator. The frequency of the single neuron was highest when the ḡK and ḡh conductances were high and ḡCa was moderate whereas, in the traditional Morris-Lecar model, the highest frequencies occur when both ḡK and ḡCa are high. We randomly sampled parameter space to find 143 hub oscillators with nearly identical frequencies but with disparate maximal conductance, duty cycles, and burst amplitudes, and then embedded each of these hub neurons into networks with different sets of synaptic parameters. For one set of network parameters, circuit behavior was virtually identical regardless of the underlying conductances of the hub neuron. For a different set of network parameters, circuit behavior varied with the maximal conductances of the hub neuron. This demonstrates that neuromodulation of a single target neuron may dramatically alter the performance of an entire network when the network is in one state, but have almost no effect when the circuit is in a different state.

No MeSH data available.


Comparison of two database neurons. A, A selected panel from the neuron database is displayed in which K+ conductance is 40 nS. Two neurons in this plane have frequencies very close to each other despite their disparate ionic conductances [ḡh = 5 nS, ḡCa = 45 nS, 0.5705 Hz; ḡh = 10 nS, ḡCa = 10 nS, 0.5787 Hz]. B, These two neurons differ in their wave form profile, however, as shown in the traces. C, A plot of duty cycles illustrates how much these two neurons differ in that respect. Duty cycle is depicted as the percentage of the cycle in which the neuron is above threshold. D, Phase response curves. One full period is plotted (top) for each of the two neurons highlighted above. The neuron with the higher maximal calcium conductance is in black and the lower calcium neuron is shown in gray. PRCs in response to positive current pulses of 50 nA (middle) and PRCs in response to negative current pulses of −50 nA (bottom) are shown.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4596081&req=5

Figure 3: Comparison of two database neurons. A, A selected panel from the neuron database is displayed in which K+ conductance is 40 nS. Two neurons in this plane have frequencies very close to each other despite their disparate ionic conductances [ḡh = 5 nS, ḡCa = 45 nS, 0.5705 Hz; ḡh = 10 nS, ḡCa = 10 nS, 0.5787 Hz]. B, These two neurons differ in their wave form profile, however, as shown in the traces. C, A plot of duty cycles illustrates how much these two neurons differ in that respect. Duty cycle is depicted as the percentage of the cycle in which the neuron is above threshold. D, Phase response curves. One full period is plotted (top) for each of the two neurons highlighted above. The neuron with the higher maximal calcium conductance is in black and the lower calcium neuron is shown in gray. PRCs in response to positive current pulses of 50 nA (middle) and PRCs in response to negative current pulses of −50 nA (bottom) are shown.

Mentions: We took two neurons with intrinsic frequencies within 1.5% of each other (0.0083 Hz difference) from among model neurons with a maximal potassium conductance of 40 nS. In Figure 3A, these are shown with dashed outlines at the two sets of parameters that give rise to these neurons. The voltage traces (Fig. 3B) reveal that, although these two neurons have similar frequencies, they have very different peak voltages, amplitudes, and duty cycles. Figure 3C shows the duty cycles for all of the model neurons with ḡK = 40 nS and indicates that duty cycle in the isolated neurons increases steadily as ḡCa increases. This increase in duty cycle effectively explains the rotated U shape of the frequencies seen in Figure 3A, because as the plateau phase of the oscillator increases, eventually the oscillator period must extend because the interburst interval has to be long enough to allow the next burst to occur (Skinner et al., 1993, 1994).


Modulation of a Single Neuron Has State-Dependent Actions on Circuit Dynamics(,.)

Gutierrez GJ, Marder E - eNeuro (2014)

Comparison of two database neurons. A, A selected panel from the neuron database is displayed in which K+ conductance is 40 nS. Two neurons in this plane have frequencies very close to each other despite their disparate ionic conductances [ḡh = 5 nS, ḡCa = 45 nS, 0.5705 Hz; ḡh = 10 nS, ḡCa = 10 nS, 0.5787 Hz]. B, These two neurons differ in their wave form profile, however, as shown in the traces. C, A plot of duty cycles illustrates how much these two neurons differ in that respect. Duty cycle is depicted as the percentage of the cycle in which the neuron is above threshold. D, Phase response curves. One full period is plotted (top) for each of the two neurons highlighted above. The neuron with the higher maximal calcium conductance is in black and the lower calcium neuron is shown in gray. PRCs in response to positive current pulses of 50 nA (middle) and PRCs in response to negative current pulses of −50 nA (bottom) are shown.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4596081&req=5

Figure 3: Comparison of two database neurons. A, A selected panel from the neuron database is displayed in which K+ conductance is 40 nS. Two neurons in this plane have frequencies very close to each other despite their disparate ionic conductances [ḡh = 5 nS, ḡCa = 45 nS, 0.5705 Hz; ḡh = 10 nS, ḡCa = 10 nS, 0.5787 Hz]. B, These two neurons differ in their wave form profile, however, as shown in the traces. C, A plot of duty cycles illustrates how much these two neurons differ in that respect. Duty cycle is depicted as the percentage of the cycle in which the neuron is above threshold. D, Phase response curves. One full period is plotted (top) for each of the two neurons highlighted above. The neuron with the higher maximal calcium conductance is in black and the lower calcium neuron is shown in gray. PRCs in response to positive current pulses of 50 nA (middle) and PRCs in response to negative current pulses of −50 nA (bottom) are shown.
Mentions: We took two neurons with intrinsic frequencies within 1.5% of each other (0.0083 Hz difference) from among model neurons with a maximal potassium conductance of 40 nS. In Figure 3A, these are shown with dashed outlines at the two sets of parameters that give rise to these neurons. The voltage traces (Fig. 3B) reveal that, although these two neurons have similar frequencies, they have very different peak voltages, amplitudes, and duty cycles. Figure 3C shows the duty cycles for all of the model neurons with ḡK = 40 nS and indicates that duty cycle in the isolated neurons increases steadily as ḡCa increases. This increase in duty cycle effectively explains the rotated U shape of the frequencies seen in Figure 3A, because as the plateau phase of the oscillator increases, eventually the oscillator period must extend because the interburst interval has to be long enough to allow the next burst to occur (Skinner et al., 1993, 1994).

Bottom Line: We determined the effects of varying ḡCa , ḡK , and ḡh on the frequency, amplitude, and duty cycle of a single neuron oscillator.For a different set of network parameters, circuit behavior varied with the maximal conductances of the hub neuron.This demonstrates that neuromodulation of a single target neuron may dramatically alter the performance of an entire network when the network is in one state, but have almost no effect when the circuit is in a different state.

View Article: PubMed Central - HTML - PubMed

Affiliation: Volen Center for Complex Systems and Biology Department, Brandeis University, Waltham, Massachusetts 02454.

ABSTRACT

When does neuromodulation of a single neuron influence the output of the entire network? We constructed a five-cell circuit in which a neuron is at the center of the circuit and the remaining neurons form two distinct oscillatory subnetworks. All neurons were modeled as modified Morris-Lecar models with a hyperpolarization-activated conductance (ḡh ) in addition to calcium (ḡCa ), potassium (ḡK ), and leak conductances. We determined the effects of varying ḡCa , ḡK , and ḡh on the frequency, amplitude, and duty cycle of a single neuron oscillator. The frequency of the single neuron was highest when the ḡK and ḡh conductances were high and ḡCa was moderate whereas, in the traditional Morris-Lecar model, the highest frequencies occur when both ḡK and ḡCa are high. We randomly sampled parameter space to find 143 hub oscillators with nearly identical frequencies but with disparate maximal conductance, duty cycles, and burst amplitudes, and then embedded each of these hub neurons into networks with different sets of synaptic parameters. For one set of network parameters, circuit behavior was virtually identical regardless of the underlying conductances of the hub neuron. For a different set of network parameters, circuit behavior varied with the maximal conductances of the hub neuron. This demonstrates that neuromodulation of a single target neuron may dramatically alter the performance of an entire network when the network is in one state, but have almost no effect when the circuit is in a different state.

No MeSH data available.