The role of dendritic inhibition in shaping the plasticity of excitatory synapses

Abstract

Using computational tools we explored the impact of local synaptic inhibition on the plasticity of excitatory synapses in dendrites. The latter critically depends on the intracellular concentration of calcium, which in turn, depends on membrane potential and thus on inhibitory activity in particular dendritic compartments. We systematically characterized the dependence of excitatory synaptic plasticity on dendritic morphology, loci and strength, as well as on the spatial distribution of inhibitory synapses and on the level of excitatory activity. Plasticity of excitatory synapses may attain three states: "protected" (unchanged), potentiated (long-term potentiation; LTP), or depressed (long-term depression; LTD). The transition between these three plasticity states could be finely tuned by synaptic inhibition with high spatial resolution. Strategic placement of inhibition could give rise to the co-existence of all three states over short dendritic branches. We compared the plasticity effect of the innervation patterns typical of different inhibitory subclasses-Chandelier, Basket, Martinotti, and Double Bouquet-in a detailed model of a layer 5 pyramidal cell. Our study suggests that dendritic inhibition plays a key role in shaping and fine-tuning excitatory synaptic plasticity in dendrites.

Keywords: compartmental model; dendritic cable; dendritic calcium; dendritic inhibition; synaptic plasticity.

Figure 1

The [Ca²⁺]_i-based learning rule and the shaping of the [Ca²⁺]_i spatial profile in dendrites by inhibition. (A) The plasticity function, Ω, depends on intracellular calcium concentration, [Ca²⁺]_i. Below θ_d, the synaptic weights stay at a basal level (PROT. = protected); for θ_d < [Ca²⁺]_i < θ_p, the synapse undergoes long term depression, LTD; above θ_p, it undergoes long term potentiation, LTP. (B) The learning rate η as a function of intracellular calcium (adapted from Shouval et al., 2002). (C) Model of a somatic compartment coupled to a 2λ long cylindrical cable with inhibitory input (I) at X = 0.6 and 21 excitatory (AMPA/NMDA-receptor-mediated) synapses activated synchronously at 10 Hz each (E). Cyan and red excitatory synapses located at X = 0.6 and X = 1.6, respectively. (D) Intracellular calcium concentration along the dendritic cable in the absence of inhibition (black) and with a steady 5 nS inhibition (orange). The thresholds for potentiation (θ_p) and depression (θ_d) are marked by horizontal lines. (E) Left: Time course of changes in synaptic weights (w_exc) and [Ca²⁺]_i for distal and proximal excitatory synapses [cyan and red, respectively; colors correspond to the synapses in (C)] throughout 60 s of simulation. Right: EPSPs of the two synapses at the beginning (dashed line) and the end (filled line) of the simulations.

Figure 2

The local synaptic plasticity rule is spatially mapped onto the dendrites. (A) Calcium concentration, [Ca²⁺]_i, for the model shown in Figure 1C, at various electrical distances from the soma with inhibitory conductance, g_GABA, of 0 nS (black), 5 nS (orange), 10 nS (green), and 15 nS (purple). (B–D) Synaptic weights following 0, 6, 12, and 60 s of simulation, with the [Ca²⁺]_i-dependent plasticity rule depicted in Figure 1. Inhibition was activated at X = 0.6. Insets demonstrate which of the three states comprising the plasticity rule is mapped onto the dendritic cable. (B) Small GABAergic conductance (g_GABA = 5 nS) switched synaptic plasticity in the vicinity of inhibition from LTP to LTD. Black—synaptic weights in the absence of inhibition after 60 s of simulation. (C) Intermediate inhibitory conductance (g_GABA = 10 nS) caused a strong local decrease in [Ca²⁺]_i, leading to the absence of synaptic plasticity (w_exc = 1) in the dendritic region near the soma (between X = 0 and X = 0.3). To the right of the protected region, synapses were depressed due to lowered [Ca²⁺]_i, and further away to the right, synapses remain potentiated. (D) Strong inhibition (g_GABA = 15 nS) resulted in a large protected zone whereas further away to the right excitatory synapse were depressed.

Figure 3

Inhibitory impact on excitatory plasticity depends on the dendritic morphology. (A) Model of a reconstructed L5 pyramidal cell. Inhibition was activated with a conductance of g_inh = 1 nS in the middle of a distal apical dendritic tuft branch and multiple excitatory inputs were distributed uniformly on this branch (enlarged in circle) and activated at 10 Hz. Excitatory synapses near the bifurcation were depressed (cyan circles), whereas more distal synapses were potentiated (red). (B) Top: A simplified model emulating the encircled distal branch in (A) Excitatory synapses (E) were evenly distributed in this modeled branch and inhibitory input (I) was placed at either X = 0 (orange), X = 0.07 (green), or X = 0.14 (purple). Bottom: [Ca²⁺]_i versus electrical distance from the bifurcation point for the case without inhibition (black) and with inhibition at the three locations depicted at the top. The thresholds for potentiation (θ_p) and depression (θ_d) are marked by horizontal lines. (C) Weights for the excitatory synapses as a function of the electrical distance of the synapse from the bifurcation point for the three inhibitory loci [colors correspond to locations depicted in (B)]. Location of inhibition determines the transition point between synapses undergoing LTD and LTP. (D) The main apical trunk was endowed with an inhibitory synapse at X = 0.5 (I) and uniformly distributed excitatory synapses (active at 10 Hz). Excitatory synapses at the center of the branch were depressed (cyan region) whereas synapses at both ends were protected (black region). (E) Top: A simplified cylindrical model emulating the dendritic branch in (D) Bottom: [Ca²⁺]_i versus electrical distance in the simplified model. (F) Synaptic weights versus electrical distance for the case depicted in (E).

Figure 4

Overall activity level in the modeled cell modifies the inhibitory effect on excitatory plasticity. (A) Model of a L5 Pyramidal cell with low synaptic activity throughout the entire cell (2366 uniformly distributed excitatory synapses, each activated at 1 Hz). A basal branch consisting of an inhibitory synapse with a conductance of g_inh = 1 nS at X = 0.5 (I) and with multiple excitatory inputs (each activated at 10 Hz). The considerable electrical length of this branch and the significant load at the proximal end allowed for the simultaneous occurrence of all three plasticity states (protected—black, depressed—cyan, and potentiated—red) throughout the branch. (B) Top: A simplified model emulating the dendritic branch in (A). Inhibitory input (I) was activated at X = 0 (orange), X = 0.07 (green), or X = 0.14 (purple). Bottom: [Ca²⁺]_i versus electrical distance from the bifurcation point without inhibition (black) and with inhibition at three different locations (colors corresponding to top figure). Thresholds for potentiation (θ_p) and depression (θ_d) are marked by horizontal lines. (C) Weights of the excitatory synapses as a function of distance from the bifurcation point for three loci of the inhibitory synapses [colors as in (B)]. (D) Same L5 pyramidal cell model as in (A) but now the excitatory synapses were simulated at a high rate (10 Hz). Synapses near the soma (X=0) switched from a protected state to LTP [red, compare to (A)]. (E,F) As in (B,C). Synaptic weight distribution is determined not only by the location of inhibition, but by the level of cell activity as well.

Figure 5

An inhibitory synapse differentially impacts plasticity in different adjacent branches. (A) Excitatory synapses (circles in inset) were activated at 10 Hz on a distal basal bifurcating branch (parent and two daughter branches) in the pyramidal cell model. Inhibition (I) on one of the daughter branches (at X = 0.08 with g_inh = 5 nS) generated a local protected region (black) whereas LTD ensued at the more proximal region and at the father branch (cyan). Synapses on the sister branch were strengthened (LTP, red). (B) Synaptic weights in all three branches versus electrical distance of the synapse from the soma in the absence of inhibition (black), with weak inhibition (g_inh = 2 nS; green) or with stronger inhibition (g_inh = 20 nS; orange). Dashed lines represent the inhibited daughter branch. (C–E) Top: A reduced model for the distal Y structure in (A) with the location of inhibition (I) and an exemplar excitatory synapse (E). Bottom: The weight of the exemplar excitatory synapse (denoted above) as a function of increasing inhibitory conductance. Insets show the plasticity states that were expressed in the corresponding cases.

Figure 6

Domain-specific dendritic inhibition shapes regional excitatory plasticity. Four inhibitory subclasses impinging on the postsynaptic layer 5 cortical pyramidal cell are modeled: (A) Chandelier; (B) basket; (C) Martinotti; and (D) double bouquet. In each case the schemes on the left depict the locations of the inhibitory synapses (orange circles). The conductance of the Chandelier inhibition in (A) was g_inh = 25 nS. In (B–D) each inhibitory contact exerted g_inh = 1 nS [with 25 contacts in (B,C) and 10 contacts in (D)]. Two thousand three hundred and sixty-six excitatory synapses were uniformly distributed over the modeled tree and randomly activated either at 7 Hz (middle) or at 10 Hz (right). The strength of the excitatory synapses after 60 s of simulation is color-coded, superimposed on the modeled L5 dendrite. Black—protected region (w_exc = 1), cyan—LTD (w_exc < 1), and red—LTP (w_exc > 1).