10 research outputs found
Inhibition is subtractive for large A-channel conductance or weak synaptic excitation.
<p><b>A, B</b>: Firing rates computed from simulations with inhibition (<i>g</i><sub><i>Syn</i>,<i>I</i></sub> = 1, <i>r</i><sub><i>I</i></sub> = 50 Hz, abscissa) plotted as a function of firing rates computed from simulations without inhibition (<i>g</i><sub><i>Syn</i>,<i>I</i></sub> = 0, ordinate). In <b>A</b>: Three values of A-channel conductance are compared (<i>g</i><sub><i>A</i></sub> = 20, 30, 40) with synaptic excitation strength fixed at <i>g</i><sub><i>Syn</i>,<i>E</i></sub> = 0.5. Inhibition is subtractive for large <i>g</i><sub><i>A</i></sub> evident in the rightward shift of the threshold-linear relationship between firing rates for <i>g</i><sub><i>A</i></sub> = 40. In <b>B</b>: Three values of synaptic excitation strength are compared (<i>g</i><sub><i>Syn</i>,<i>E</i></sub> = 0.4, 0.5, 0.7) with A-channel conductance fixed at <i>g</i><sub><i>A</i></sub> = 30. Inhibition is subtractive for weaker excitation, evident in the rightward shift of the threshold-linear relationship between firing rates for <i>g</i><sub><i>Syn</i>,<i>E</i></sub> = 0.4.</p
The slope of the input/output firing rate curves at <i>r</i><sub><i>E</i></sub> = 0 computed from both the theoretical prediction Eq 15 and simulations of the full model.
<p>The slope of the input/output firing rate curves at <i>r</i><sub><i>E</i></sub> = 0 computed from both the theoretical prediction <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1006292#pcbi.1006292.e054" target="_blank">Eq 15</a> and simulations of the full model.</p
Approximation of <i>b</i> (a slow variable) by its average value.
<p><b>A</b>: Plots of <i>b</i><sub><i>av</i></sub> vs. <i>r</i><sub><i>E</i></sub> for different values of <i>g</i><sub><i>A</i></sub>. <b>B</b>: Plots of , and <i>b</i><sub><i>av</i></sub>(<i>r</i><sub><i>E</i></sub>, <i>g</i><sub><i>A</i></sub>) with <i>g</i><sub><i>A</i></sub> = 40. In both panels, <i>g</i><sub><i>Syn</i>,<i>E</i></sub> = 3, <i>g</i><sub><i>Syn</i>,<i>I</i></sub> = 5 and <i>r</i><sub><i>I</i></sub> = 50 Hz.</p
Output firing rates approximated as dead-time modified Poisson process with firing threshold.
<p><b>Top row</b>: Firing rate as a function of input rate obtained from simulations (circles) and theoretical approximation (lines); for <i>g</i><sub><i>A</i></sub> = 15 (A1), <i>g</i><sub><i>A</i></sub> = 25 (B1), and <i>g</i><sub><i>A</i></sub> = 35 (C1). Simulations and theory show transition from divisive to subtractive inhibition as <i>g</i><sub><i>A</i></sub> increases. <b>Bottom row</b>: Theoretical approximation of firing threshold <i>θ</i> (lines), and the largest observed values of <i>s</i><sub><i>I</i></sub> for which excitatory inputs elicited spikes in simulations (circles), plotted as functions of input rate; for <i>g</i><sub><i>A</i></sub> = 15 (A2), <i>g</i><sub><i>A</i></sub> = 25 (B2), and <i>g</i><sub><i>A</i></sub> = 35 (C2).</p
Boundary between subtractive and divisive inhibition in (<i>g</i><sub><i>Syn</i>,<i>E</i></sub>, <i>g</i><sub><i>A</i></sub>) parameter space.
<p><b>A, B</b>: For each parameter set, we fit threshold-linear functions to characterize the relationship between output firing rates in the presence and absence of inhibition. Dots in each panel identify the smallest value of <i>g</i><sub><i>A</i></sub> (for a given parameter set) at which inhibition is subtractive. In <b>A</b>: We vary inhibition strength (<i>g</i><sub><i>Syn</i>,<i>I</i></sub> = 0.5, 1, 2) and keep inhibition rate fixed at 50 Hz. In <b>B</b>: We vary inhibition rate (<i>r</i><sub><i>I</i></sub> = 30, 50, 70 Hz) and keep inhibition strength fixed at <i>g</i><sub><i>Syn</i>,<i>I</i></sub> = 1. The values of <i>g</i><sub><i>A</i></sub> that define the boundary between subtractive and divisive inhibition decrease with increases in either inhibition parameter (<i>g</i><sub><i>Syn</i>,<i>I</i></sub> or <i>r</i><sub><i>I</i></sub>).</p
Examples of divisive and subtractive effects of inhibition in the one-compartment model.
<p><b>A, B</b>: Output firing rates as a function of excitatory input rate, computed from simulations without inhibition (empty circles, <i>g</i><sub><i>Syn</i>,<i>I</i></sub> = 0) and with inhibition (filled circles, <i>g</i><sub><i>Syn</i>,<i>I</i></sub> = 1 and <i>r</i><sub><i>I</i></sub> = 50 Hz). Excitatory synaptic strength is <i>g</i><sub><i>Syn</i>,<i>E</i></sub> = 0.5. In <b>A</b>: Divisive rescaling of the input/output relation with <i>g</i><sub><i>A</i></sub> = 20. In <b>B</b>: Subtractive shifting of the input/output relation with <i>g</i><sub><i>A</i></sub> = 40. <b>C</b>: Data from <b>A</b> and <b>B</b> are replotted with output firing rates in the absence of inhibition on the ordinate and output firing rates in the presence of inhibition on the abscissa. Threshold-linear functions are fit to simulation data (black lines). Rightward shift of threshold-linear function for <i>g</i><sub><i>A</i></sub> = 40 is characteristic of subtractive inhibition.</p
Comparison of firing rate input/output relations for subtractive and divisive inhibition (illustration only, not actual data).
<p><b>A</b>: Subtractive inhibition: output rate without inhibition is , and output rate with inhibition is , where <i>c</i> is a constant with <i>c</i> > 0. <b>B</b>: Divisive inhibition: output rate without inhibition is (same as in <b>A</b>), and output rate with with inhibition is , where <i>α</i> is a constant with 0 < <i>α</i> < 1.</p
Divisive and subtractive inhibition in a multi-compartment neuron model.
<p><b>A</b>: Voltage traces in response to excitatory inputs at varying input locations along the dendrite. Parameter values in these simulations: <i>g</i><sub><i>Syn</i>,<i>E</i></sub> = 3, <i>g</i><sub><i>Syn</i>,<i>I</i></sub> = 0, and <i>g</i><sub><i>A</i></sub> = 0. Inputs distant from the soma lead to spike initiation with millisecond-scale delay between excitatory input and spike onset. <b>B</b>: Threshold-linear relation between output firing rates in simulations of the multi-compartment model with and without inhibition for varying input location and <i>g</i><sub><i>A</i></sub> = 20. For simulations with inhibition: <i>g</i><sub><i>Syn</i>,<i>I</i></sub> = 1 and <i>r</i><sub><i>I</i></sub> = 50. Inhibition is subtractive for distal excitatory input (<i>cpt</i><sub><i>in</i></sub> = 6). <b>C</b>: Critical values of <i>g</i><sub><i>A</i></sub> that define boundary between subtractive and divisive inhibition in (<i>g</i><sub><i>Syn</i>,<i>E</i></sub>, <i>g</i><sub><i>A</i></sub>) parameter space. The boundary shifts downward as excitatory inputs are moved to more distal locations, indicating that inhibition has a subtractive effect for lower values of <i>g</i><sub><i>A</i></sub> for more distal inputs.</p
Dependence of the <i>V</i>-nullcline on A: <i>g</i><sub><i>A</i></sub>, B: <i>b</i>, C: <i>s</i><sub><i>I</i></sub> and D: <i>s</i><sub><i>E</i></sub>.
<p>Default values of the parameters are <i>g</i><sub><i>A</i></sub> = 20, <i>b</i> = .5, <i>s</i><sub><i>I</i></sub> = .5 and <i>s</i><sub><i>E</i></sub> = 1. Moreover, <i>g</i><sub><i>Syn</i>,<i>E</i></sub> = 3 and <i>g</i><sub><i>Syn</i>,<i>I</i></sub> = 5. Thin blue line is <i>n</i><sub>∞</sub>(<i>V</i>), the <i>n</i>-nullcline.</p
Response to an excitatory input.
<p><b>A</b>. The neuron will or will not fire an action potential if, at the time of the excitatory input, it lies below or above the left knee of the <i>s</i><sub><i>E</i></sub> = 1 cubic, respectively. <b>B</b>. The neuron cannot respond with an action potential if the left knee of the <i>s</i><sub><i>E</i></sub> = 1 cubic lies below the <i>n</i> = 0 axis.</p