Anatomical and Functional Connectivity at the Dendrodendritic Reciprocal Mitral Cell-Granule Cell Synapse: Impact on Recurrent and Lateral Inhibition

Abstract

In the vertebrate olfactory bulb, reciprocal dendrodendritic interactions between its principal neurons, the mitral and tufted cells, and inhibitory interneurons in the external plexiform layer mediate both recurrent and lateral inhibition, with the most numerous of these interneurons being granule cells. Here, we used recently established anatomical parameters and functional data on unitary synaptic transmission to simulate the strength of recurrent inhibition of mitral cells specifically from the reciprocal spines of rat olfactory bulb granule cells in a quantitative manner. Our functional data allowed us to derive a unitary synaptic conductance on the order of 0.2 nS. The simulations predicted that somatic voltage deflections by even proximal individual granule cell inputs are below the detection threshold and that attenuation with distance is roughly linear, with a passive length constant of 650 μm. However, since recurrent inhibition in the wake of a mitral cell action potential will originate from hundreds of reciprocal spines, the summated recurrent IPSP will be much larger, even though there will be substantial mutual shunting across the many inputs. Next, we updated and refined a preexisting model of connectivity within the entire rat olfactory bulb, first between pairs of mitral and granule cells, to estimate the likelihood and impact of recurrent inhibition depending on the distance between cells. Moreover, to characterize the substrate of lateral inhibition, we estimated the connectivity via granule cells between any two mitral cells or all the mitral cells that belong to a functional glomerular ensemble (i.e., which receive their input from the same glomerulus), again as a function of the distance between mitral cells and/or entire glomerular mitral cell ensembles. Our results predict the extent of the three regimes of anatomical connectivity between glomerular ensembles: high connectivity within a glomerular ensemble and across the first four rings of adjacent glomeruli, substantial connectivity to up to eleven glomeruli away, and negligible connectivity beyond. Finally, in a first attempt to estimate the functional strength of granule-cell mediated lateral inhibition, we combined this anatomical estimate with our above simulation results on attenuation with distance, resulting in slightly narrowed regimes of a functional impact compared to the anatomical connectivity.

Keywords: glomerular column; granule cell; lateral inhibition; mitral cell; network model; olfactory bulb; reciprocal synapse; recurrent inhibition.

FIGURE 1

Dendrodendritic interactions between mitral cells and granule cells. (A) Scheme of mitral cell–granule cell network. Glomerular column: Ensemble of mitral cells and granule cells that can be excited from a glomerulus. Recurrent inhibition will occur widely, lateral inhibition can happen only via the granule cells that are sufficiently excited within the columnar ensemble to generate a global or local spike (if at all, see Section “Discussion”). (B) Example double stain of juvenile rat mitral cell lateral dendrite segment and GABAergic presynapses (see Section “Materials and Methods”). Top left: Biocytin label. Bottom left: VGAT-stain. Both z-projections of 5 μm-deep image stack (sectioning at 0.2 μm). Right: Overlay of z-projections within a 1 μm selection of the stack. (C) Cumulative histochemical data: Left: Synaptic input density distribution for certain synapses and upper limit (n = 14 segments). Right: Density versus distance on the segment. Linear fit (significance of correlation 1-tailed for MC1 P = 0.012, MC2 P = 0.127, n = 7 data points each). (D) Unitary-like mitral cell IPSCs are evoked by uncaging of glutamate onto granule cell spines (data from Lage-Rupprecht et al., 2020). Top left: Averaged example traces from two mitral cells at two different holding potentials (−70 mV, +10 mV) and equilibrium potentials E_Cl (+16 mV, −130 mV). Top right, bottom: Distribution of amplitudes, response latencies, and release probabilities (modified from Figure 1 in Lage-Rupprecht et al., 2020).

FIGURE 2

Simulation of granule cell-mediated recurrent inhibition. (A) Model anatomy of one mitral cell lateral dendrite. Branchpoints at b₁ = 150 μm, b₂ = 550 μm, b₃ = 750 μm. Total length 850 μm, the total number of branchpoints 3. Tapering: first segment 4–2.5 μm, second segment 2.5–2 μm, third segment 2–1 μm, fourth segment 1–0.5 μm. (B) Top: Simulation of IPSC recorded at the soma under physiological conditions (10 μm from soma, g_syn = 200 pS, V_m = −60 mV, E_Cl = −80 mV). Middle: Simulation of IPSP generated at the same location and at various distances, as recorded at the soma. Bottom: IPSP at the same locations as in panel C but recorded at the distal site (810 μm). (C) Cumulative somatopetal attenuation along the dendrite, absolute (left axis) and normalized to the extrapolated amplitude at 0 μm (normalized IPSP, right axis). Gray line: Simulation in a cylindrical neurite without tapering. (D) Somatic recurrent inhibition exerted by 200 synapses distributed equally across 1 lateral dendrite of the mitral cell model (black trace) and with the proximal 80% of synapses shifted to another lateral dendrite (green trace). The difference between the traces indicates the reduced shunting of the distal 20% of synapses in the second case. (E) Recurrent summated IPSP amplitude at the soma versus a number of (equidistant) synapses on one dendrite. Dotted line: linear summation of unitary IPSP. Dashed line: saturation due to shunting and reduction in driving force. (F) Black trace: same simulation as in panel (D). Magenta trace: same, but with onset latencies distributed according to Figure 1D. Green trace: the temporal extent of latency values further expanded, to 500 ms.

FIGURE 3

Anatomical connectivity between individual mitral cells and granule cells. (A) Scheme of the MC-GC network, below the top view of the dendritic fields of MC A (magenta, field radius R_MC) and a GC (green, field radius R_GC). r_A: distance MC-GC. (B) Synaptic density for single mitral cell with branching secondary dendrites as described in Eq. 1. The top graph shows a schematic view of a branching neuron, and the middle graph illustrates how the synaptic density was calculated with the position of the steps corresponding to the average branchpoint position. The bottom graph shows the average radial synaptic density n(r) for a branching cell including smoothing of the branchpoint positions. The gray line corresponds to the unsmoothed density as given in Eq. 1. (C) Number of synapses of MC A that a given GC at position r_A can access (Eq. 3). 2R_GC indicates the distance at which there is no more overlap with the GC dendritic field with the peak of n(r). (D) Probability P_A that a GC at position r_A will indeed connect to MC A (Eq. 6) and effective inhibitory impact I_A (Eq. 7, from Figure 2C). The spacing of glomeruli is indicated (diameter of glomeruli scaled to fit all 4,000 glomeruli into A_EPL, see Section “Results”).

FIGURE 4

Anatomical connectivity between pairs of mitral cells via one granule cell. (A) Top: Top view of the dendritic fields of MC A (magenta), a second MC B (gray) at distance d_AB, and a GC (green) within the overlap area F of the MCs’ dendritic fields. Middle: Illustration of symmetry in N_A(r) and N_B(r). Bottom: Geometrical parameters relevant for the calculus in Eqs 9, 10 (see also Table 2). r_A, r_B: distance of GC from MC A resp. B. α: angle between the position of GC soma r_A and d_AB. α_MAX: maximally possible α for the respective d_AB. x: distance of projection of GC position onto d_AB from MC A; relevant for integration. The gray rectangles represent the integration increments dF. (B) Probability P_AB of a GC at position r_A to connect to both A and B (Eq. 6), plotted for a set of distances d_AB between mitral cells A and B (0–1400 μm). The righthand peak in the curves for 200–700 μm is due to the increased synaptic density around the soma of MC B. Parameters as given in Table 1. (C) I_AB: correction of P_AB for a distance-dependent reduction in IPSP impact because of attenuation (Figure 2C, Eq. 7).

FIGURE 5

Number of granule cells providing connectivity between two mitral cells or glomerular mitral cell ensemble. (A) Synaptic density distribution for single MC n(r) as in Figure 3B and for a glomerular ensemble of mitral cells n_GL(r) (see Section “Materials and Methods”). (B) Number of GCs N_AB that interconnects a pair of MCs versus their distance d_AB (Eq. 9). The gray bars illustrate the average dimensions of glomeruli within the network (2⋅r_GL = 120 μm). (C) Number of GCs that interconnect a pair of glomerular MC ensembles (blue line) or a single MC and an ensemble (green line), compared to the MC-MC case (black line). For better comparison, all three connectivity functions are scaled to the same size at d_AB = 0, with the respective maximal numbers indicated in the respective color. (D) Top: Number of GCs as above but corrected for their functional impact. Dotted lines: Functions from above for comparison. Arbitrary units on the y-scale. Bottom: Impact with varying degrees of attenuation. The slope of the linear attenuation (fit in Figure 2C) is increased or decreased by 25%. The spacing of glomeruli is indicated (diameter of glomeruli scaled to fit all 4000 glomeruli into A_EPL, see Section “Results”).