Bulbar Microcircuit Model Predicts Connectivity and Roles of Interneurons in Odor Coding

<div><p>Stimulus encoding by primary sensory brain areas provides a data-rich context for understanding their circuit mechanisms. The vertebrate olfactory bulb is an input area having unusual two-layer dendro-dendritic connections whose roles in odor coding are unclear. To clarify these roles, we built a detailed compartmental model of the rat olfactory bulb that synthesizes a much wider range of experimental observations on bulbar physiology and response dynamics than has hitherto been modeled. We predict that superficial-layer inhibitory interneurons (periglomerular cells) linearize the input-output transformation of the principal neurons (mitral cells), unlike previous models of contrast enhancement. The linearization is required to replicate observed linear summation of mitral odor responses. Further, in our model, action-potentials back-propagate along lateral dendrites of mitral cells and activate deep-layer inhibitory interneurons (granule cells). Using this, we propose sparse, long-range inhibition between mitral cells, mediated by granule cells, to explain how the respiratory phases of odor responses of sister mitral cells can be sometimes decorrelated as observed, despite receiving similar receptor input. We also rule out some alternative mechanisms. In our mechanism, we predict that a few distant mitral cells receiving input from different receptors, inhibit sister mitral cells differentially, by activating disjoint subsets of granule cells. This differential inhibition is strong enough to decorrelate their firing rate phases, and not merely modulate their spike timing. Thus our well-constrained model suggests novel computational roles for the two most numerous classes of interneurons in the bulb.</p></div

Mechanism of decorrelation.

<p>A-E. Distribution of correlations between phasic responses of two central mitral sisters (50 mitral-pair—odor combinations, but 350 for D) in different connectivities namely A. <i>Random</i> connectivity, B. <i>Directed</i> connectivity, C. <i>Directed</i> with different leak reversal potentials: -58 and -70 mV (effectively different thresholds) for the sister pair, D. <i>Default</i> ‘super-inhibitory’ connectivity with two lateral odor-responsive glomeruli, E. <i>Default ‘</i>super-inhibitory<i>’</i> connectivity with six lateral odor-responsive glomeruli. The delta-rate correlation is noted at top left of each histogram for each connectivity. For A-C, the receptor spike rate to central glomerulus was halved for odor compared to default i.e. D; while for E, it was quadrupled for air and doubled for odor, to get similar mean firing rate as D. Only the default model in D had substantial decorrelation: note the negative correlation bins, which have been shaded; and the delta-rate correlation values.</p

Model connectivity.

<p>A. Synaptic schematic: Each glomerulus (dotted ellipse) receives input from olfactory receptor neurons (ORNs) expressing a single type of receptor out of many (different colors). Mitral/tufted (M/T) cells take excitatory input onto their dendritic tufts within one glomerulus, directly from ORNs (and via ET cells). ET cells have not been modeled (crossed out) and their input to M/T and PG cells is considered folded into the ORN input. Periglomerular (PG) cells are excited by ORNs (and via ET cells), and in turn inhibit M/T cells within the same glomerulus, thus causing feed-forward inhibition. PG cells also get excitation from M/T cells at reciprocal synapses, thus mediating recurrent inhibition. Further, M/T cells form reciprocal synapses with granule cells on their soma, primary and lateral dendrites, where they excite granule (G) cells which cause recurrent and lateral inhibition. Short-axon (SA) cells have not been modeled (crossed out). B. Visualization of <i>default</i> model having 3 glomeruli each with 2 sister mitral cells, and connecting interneurons. Singly connected granule cells are shown in purple. The jointly and multiply connected (shared) granule cells are shown in yellow and cyan respectively. PG cells are shown in orange. Synaptic connections are not shown, but granule and PG cells connect to nearby mitral dendrites, within their small dendritic extents.</p

. Factors affecting linearity.

<p>A-E: Mitral input-output curves simulated in a <i>default</i> network (Figs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0098045#pone.0098045.g002" target="_blank">2D</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0098045#pone.0098045.g004" target="_blank">4D</a>(i)) and modifications thereof. In each case mitral firing rate is plotted against ORN firing rate to the tuft of mitral cell A. Activity-dependent lateral inhibition to A, mediated by granule cells, is assessed in each case by considering a lateral ‘super-inhibiting’ mitral cell B receiving Poisson ORN input at 0 Hz (black squares), 5 Hz (red diamonds) and 10 Hz (blue circles). A. <i>default</i>. B. PG cells removed. C. granule cells removed. D, E: The <i>default</i> network is modified to have stronger PG cell excitation yielding half-Mexican-hat profiles i.e. suppression of mitral firing for low ORN input. D. ORN→PG and mitral→PG synaptic strengths are increased by 2.4 times for both plateau-ing and low threshold spiking PG cells. E. ORN→PG and mitral→PG synaptic strengths are increased by 6 times for plateau-ing PG cells but unchanged for low threshold spiking PG cells. F-J. The histograms of <math><mrow><msqrt><mrow><mi>r</mi><mi>e</mi><mi>s</mi><mi>i</mi><mi>d</mi><mi>u</mi><mi>a</mi><mi>l</mi><mo>/</mo><mi>n</mi><mi>o</mi><mi>i</mi><mi>s</mi><mi>e</mi></mrow></msqrt></mrow></math> for fits to single odor random pulse-trains (top row) and for predictions to two-odor random pulse-trains (bottom row) corresponding to above A-E cases respectively, from 30 network instances, each with different two odors. All values for <math><mrow><msqrt><mrow><mi>r</mi><mi>e</mi><mi>s</mi><mi>i</mi><mi>d</mi><mi>u</mi><mi>a</mi><mi>l</mi><mo>/</mo><mi>n</mi><mi>o</mi><mi>i</mi><mi>s</mi><mi>e</mi></mrow></msqrt><mo>></mo><mn>2</mn></mrow></math> are in the right-most bin. The mitral input-output curve saturated to a small extent on removing granule cells (C) causing a worsening of the linear fits and predictions. But on removing PG cells (B), the saturation was much stronger and the lateral inhibition for 10 Hz input to lateral mitral cell B was less than that for 5 Hz. On modifying the input-output curve to have an initial supra-linear region (half-Mexican-hat) (D,E), the predictions were often seen to be supra-linear compared to the fits. Also, the lateral inhibition turned on with a threshold, i.e. negligible for 5 Hz input to mitral cell B but large for 10 Hz, since the lateral mitral cell B had the same non-linear input-output curve.</p

Hierarchical construction of model by replicating and predicting network properties at each stage.

<p>Hierarchical construction of model by replicating and predicting network properties at each stage.</p

Channel kinetics and parameters (temperature T = 35°C, relevant units for numerical values are specified).

<p>Channel kinetics and parameters (temperature T = 35°C, relevant units for numerical values are specified).</p

Summary of network connectivity patterns used in different variants of the olfactory bulb model.

<p>Summary of network connectivity patterns used in different variants of the olfactory bulb model.</p

Long-range inhibition between mitral cells.

<p>A-C. Connectivity patterns: Central mitral cell A in red, and lateral mitral cell B in green, with a few shared granule cells (PG cells not shown). A. <i>Random</i> connectivity schematic: mitral cells’ dendrites are randomly rotated and B’s dendrites usually do not pass near the soma of A, leading to few and distal shared granule cells. B. <i>Directed</i> connectivity schematic: a dendrite of lateral mitral cell B is oriented to pass near soma of A, leading to a few shared granule cells proximal to A’s soma. C. <i>Default</i> / ‘Super-inhibitory’ connectivity schematic: Building on directed connectivity, extra shared granule cells with strengthened synapses are recruited between A and B, proximal to A’s soma. Synaptic strength distributions: D(i). Schematic of <i>default</i> network (same as C) where lateral mitral cell B ‘super-inhibits’ central mitral cell A. D(ii-v). Mean strength of synapses on a mitral cell compartment as a function of distance from soma. Blue lines and markers are for <i>random</i> and <i>directed</i> connectivity, while red/green are for <i>default</i> (i.e. ‘super-inhibitory’) connectivity. Solid lines represent means across 10 network seeds for a given connectivity; scatter plots are for a specific seed. (ii). Inhibitory granule —┤mitral synapses along the primary dendrite of mitral cell A. (iii). Inhibitory granule —┤mitral synapses along all lateral dendrites of mitral cell A. (iv). Excitatory mitral → granule synapses along all lateral dendrites of mitral cell A. (v). Excitatory mitral → granule synapses along the lateral dendrite of mitral B, which is super-inhibitory on mitral cell A. Long range activity dependent inhibition <i>in vivo</i>: Both mitral cells A and B receive ORN input as Poisson spikes on their tufts. E. Inhibition on B due to A: mean change in firing rate of B (mean across 0–19 Hz ORN inputs to B, and across 10 network instances—Materials and Methods), due to 10Hz ORN input to A, as the separation between cells A and B is increased for: <i>random</i> (green circles), <i>directed</i> (blue crosses), and <i>default</i> (red squares) connections. F. Inhibition on A due to B: as for E, but with A and B interchanged.</p

Single neuron model electrophysiological properties.

<p>Mitral cell: A. Visualization of a simulated <i>slice</i> network. We simulated ORN shock input to mitral cell A and its associated PG cells (Materials and Methods), while recording voltages in soma, base of tuft and tuft compartments (large arrows). B. Weak shock: action potential started at the soma (red solid) and spread to tuft base (blue dotted) and tuft (black dashed). C. Strong shock: action potential started at the tuft (black dashed) and propagated forward to tuft base (blue dotted) and soma (red solid). D. <i>Default</i> network <i>in vivo</i>, with mitral cells B and A, 400 μm apart (Materials and Methods). Recording electrodes are shown on mitral cell B at three locations. E. Spike propagation of cell B in circuit in D shown by voltage: at B’s soma (red solid), at the site of maximal inhibition on its lateral dendrite near soma of A (blue dashed), and farther along the same dendrite (black dotted). F. Granule cell physiology: Voltage at soma of granule cell (morphology at right) with a mitral → granule excitatory post-synaptic potential (EPSP) event delivered every 6 ms in a train totaling 100. This made the cell fire after a long latency. Inset shows integration of EPSPs. G, H: PG cell physiology: Somatic voltages of two PG cell models (same morphology at right) showing: (1) depolarizing ‘sag’ on hyperpolarization; (2) rebound burst with shoulder on recovery; and (3) low-threshold spike in G, or burst with plateau in H, on current injection. I. Input-output curve of mitral cell without lateral inhibition: Firing rate output of mitral cell A versus ORN firing rate input to its glomerulus, without input to mitral cell B, in <i>default</i> network shown in D with: all cells present (red diamonds); granule cells removed (cyan discs); PG cells removed (blue triangles); all interneurons removed (black squares).</p

Phase decorrelation.

<p>A. Experimental odor responses of two sister mitral cells (squares vs discs), periodic with respiration, that were negatively correlated, re-plotted from data [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0098045#pone.0098045.ref018" target="_blank">18</a>]. Firing rate is only approximate since we obtained respiration phase data instead of time data from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0098045#pone.0098045.ref018" target="_blank">18</a>]. B. Distribution of phase-correlations between responses of sister mitral cells to air (dotted) and odor (solid), (840 sister-pair—odor combinations, neglecting zero responses) re-plotted from data [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0098045#pone.0098045.ref018" target="_blank">18</a>]. C. Respiratory odor input: air and odor kernels were convolved with ~2 cycles of rectified respiratory waveform, and added (along with constant background) yielding firing rate of ORNs in freely-breathing condition, for an odor input at a glomerulus. The kernels have arbitrary units, as they are convolved with air-flow rate and odor-concentration profile, which have normalized units (to obtain mean air and odor firing rates), yielding ORN firing rate in Hz. D. Proposed mechanism of decorrelation by super-inhibitory i.e. <i>default</i> connectivity with ORN firing rates to glomeruli for 1 respiration cycle (top), and subsequent mitral responses (bottom). The central mitral sisters received same excitatory input from ORNs, but differential inhibition from lateral mitral cells, at different phases of the respiration cycle (denoted by! vs #), which caused their outputs to be phase-decorrelated. E. Simulated responses of two sister mitral cells, in a <i>default</i> network instance, analogous to the experimental responses in A. F. Correlation distribution of simulated responses of sister mitral cells (350 sister-pair—odor combinations, neglecting zero responses) using same analysis as in B.</p