Figure 7. Inhibition enhances spatial specificity of spine calcium elevation.

(A–B) Stimulation of a single GABAergic synapse on the distal dendrite reduces the ratio of peak calcium in nonstimulated spines (A) and dendritic shaft (B) relative to the peak in synaptically stimulated spines for fast or slow GABA_A kinetics. For both fast and slow GABA_A kinetics, the GABAergic synapse is on the dendritic shaft, co-located with and synchronously stimulated with glutamatergic stimulation of a cluster of 16 distal dendritic spines (location of synaptic input indicated by blue arrowhead). Figure 7—figure supplement 1 shows the sensitivity of the effect of inhibition on spatial specificity to parameter variations. Figure 7—figure supplement 2 shows the robustness of this main finding to model assumptions. (C–D) Inhibition enhances synapse-specificity during stimulation of randomly distributed excitatory synaptic inputs. Distributions of integrated spine calcium concentration for stimulated (blue) and non-stimulated (green) spines are shown for randomly distributed excitatory Poisson input trains (2.5 Hz) for lower (C; n = 200) or higher (D; n = 300) numbers of independent excitatory synaptic inputs, either with (right columns) or without (left columns) 50 GABAergic Poisson input trains (2.5 Hz). Top row shows the log-scale distribution of integrated spine calcium elevation over the 1 s duration inputs; bottom row shows log-scale scatter plots of peak calcium (y axis) versus normalized calcium duration (i.e. integrated calcium/peak calcium) (x axis).

Figure 7—figure supplement 1. Parameter sensitivity analysis for enhancement of spatial specificity by inhibition.

Parameters listed on the left (ordered by type of mechanism: ligand-gated channels; inward currents through voltage-gated calcium or sodium channels; outward currents through potassium channels; calcium dynamics; spine neck resistance) were individually varied ±10 or 20% to evaluate sensitivity of the GABA/No-GABA specificity ratio (the ratio of the non-stim/stim spine ratio with GABAergic inhibition from the right panel to the non-stim/stim spine ratio without GABAergic inhibition from the middle panel; right and middle panels show peak calcium in non-stimulated spine/peak calcium in stimulated spine). The black vertical bars indicate the original values (i.e. with no varied parameters) for the GABA/No-GABA specificity ratio (left), or the non-stim/stim spine peak calcium ratio in the absence (middle) or presence (right) of inhibition. A GABA/No-GABA specificity ratio of 1 would indicate no effect of inhibition on the specificity ratio, whereas a value <1 indicates that inhibition enhances specificity, with smaller values corresponding to greater enhancement. For ion channel parameters, maximum conductance was varied; for buffers, the quantities were varied. NeckRA refers to the spine neck axial resistance. CaR and NMDAR were covaried (last row) with opposite sign (orange bar is +CaR/-NMDA; blue bar is -CaR/+NMDA).

Figure 7—figure supplement 2. Robustness of model assumptions for enhancement of spatial specificity by inhibition.

(A) The effects of varying calcium diffusion rate, pump density, and calcium flux through calcium permeable channels on the GABA/No-GABA specificity ratio are shown to evaluate model robustness to assumptions that may affect calcium dynamics. As in Figure 7—figure supplement 1, the black vertical bar indicates the original effect of inhibition with unvaried parameters; values <1 mean that inhibition enhances specificity, and smaller values correspond to greater enhancement. The response to fine discretization (timestep of 1 µs, voltage compartment length of 1 micron, six axial calcium diffusion slabs in each spine head and spine neck, and increased radial calcium diffusion shells in the dendritic shaft) is shown to confirm that finer discretization did not change the main result. Facilitated diffusion between spine neck and spine head or dendritic shaft using the geometric-mean method for computing the shared surface area between neck and shaft (Holmes and Poznanski, 2005) rather than the default smaller of the two surfaces areas, is also shown. Calcium fluxes refer to calcium influx through all calcium permeable channels, and these values were modulated independently of the contribution of these channels to membrane depolarization, to isolate effects mediated by calcium dynamics versus effects mediated by depolarization. (B) Comparisons of finer discretization to standard discretization are shown for membrane potential transients in the soma (top left) and a stimulated spine (top right), and spine calcium concentration transients in a stimulated spine (bottom left) and non-stimulated spine (bottom right) during synaptic stimulation of clustered, distal spines.