The authors have declared that no competing interests exist.
Conceived and designed the experiments: AG USB. Performed the experiments: AG. Analyzed the data: AG. Contributed reagents/materials/analysis tools: AG USB. Wrote the paper: AG USB.
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.
Primary sensory encoding provides a particularly direct framework for studying input-output computations in the brain. In sensory systems like vision, there is a direct topological mapping of the two-dimensional visual field onto a two-dimensional neuronal substrate. In contrast [
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
There is a distinguished history of models that explore the implications of this dendro-dendritic circuitry [
Here, we report a detailed model of micro-circuits in the rat olfactory bulb to understand and predict the circuit mechanisms that account for its major odor coding properties. Our model has been constrained hierarchically, using multiple single-cell and coupled-cell recordings, both
We used multi-scale compartmental modeling to first match cell- and synapse-level observations of bulbar anatomy and physiology, and then to build a microcircuit network model to replicate
In order to span the range from cellular physiology to single- and cross-glomerular mitral cell coding, our model included simulated olfactory receptor neuron (ORN) input, periglomerular (PG) cells, mitral/tufted (henceforth termed mitral) cells, and granule cells. To study the odor responses of single or coupled mitral cells, we organized our model into a central odor-responsive glomerulus with two representative sister mitral cells, and 0 to 6 odor-responsive lateral glomeruli, each with two mitral cells, that could strongly influence via interneurons the two central sister mitral cells of interest. These mitral cells were coupled with physiological numbers of PG and granule cells to complete the dendro-dendritic microcircuits.
We tried various connectivities:
Cell | Number | Synapse | Number of synapses per cell | Experiment: PSP / PSC amplitude, peak / fall times | Modeling strategy | Model: max conductance & time constants; Simulated PSP amplitude & peak / fall times |
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104 / glomerulus | As Poisson spikes | |||||
70–85% of juxtaglomerular (JG) cells (1500–2000 [ |
ORN→PG | ~50 spines (estimated from 25 in mice [ |
EPSP 3 mV [ |
1000 PG / glomerulus; 50 ORN→PG synapses per PG. | gmax = 0.45 nS for plateauing and 1.25 nS for low-threshold spiking PG cell, τ1 = 1 ms, τ2 = 1 ms (same for both synapses); simulated EPSP: ~7-8 mV, τp ~ 2 ms, τf ~ 5 ms. | |
M/T→PG or ET→PG | Similar to above. | EPSP 6–10 mV [ |
25 M→PG per PG. | Same as above. | ||
10% of JG cells (M.T. Shipley, email, 2010) [ |
ORN→ET; SA─┤ET | Absorbed into ORN Poisson spikes. | ||||
15–20% of JG cells are ET / SA [ |
Not much inter-glomerular inhibition |
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25 M / 50 T per glomerulus [ |
ORN→M | 460–1500 [ |
Conflicting EPSP amplitudes: ~3 mV [ |
2 mitral cells / glomerulus; 400 ORN→M on mitral tuft. | gmax = 6 nS, τ1 = 1 ms, τ2 = 1 ms; simulated EPSP: ~1 mV, τp ~ 7 ms, τf ~ 80 ms (Large time constant of our mitral cell model caused long EPSPs) | |
G ─┤M | 104 [ |
IPSC amplitude decays with distance [ |
104 G ─┤M on mitral soma, apical and lateral dendrites. | proximal gmax = 1 nS but 4× if |
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PG ─┤M | ~100 (PG spines are connected to both M/T and ET i.e. ~250 cells) | IPSCs are similar to above G ─┤M synapse [ |
100 PG ─┤M on mitral tuft, | gmax = 1 nS, τ1 = 1 ms, τ2 = 20 ms; simulated IPSP: ~ –0.2 mV, τp ~ 28 ms, τf ~ 117 ms; (as above, we verified that setting τ2 = 1 ms with gmax = 30 nS did not change our results qualitatively.) | ||
50 to 100 G per M/T [ |
M→G | 100 spines [ |
EPSP ~3.5 mV |
2500 G-s per glomerulus: shared G-s were retained 1:1; but non-shared were aggregated 100:1; unconnected were pruned. | AMPA: gmax = 0.2 nS, τ1 = 1 ms, τ2 = 4 ms; NMDA: gmax = 0.26 × AMPA gmax, τ1 = 25 ms, τ2 = 200 ms; (3× for distal ‘super-inhibitory’ synapses); simulated EPSP: ~2 mV, τp ~ 13 ms, τf ~ 50 ms. |
τp is the time to peak, and τf the time to fall (to 20% of peak) in the relevant cell. All synaptic conductances were modeled as dual exponential
for
Sl. | Phenomenon replicated | Network adjustments | Replication / explanation / prediction |
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Mean firing rate of odor responses of mitral cells in anesthetized, freely-breathing rats and mice is ~12 Hz (calculated from experimental data [ |
We adjusted ORN→M strength to get mean odor / air mitral rate in freely-breathing simulations of ~14 Hz / ~8 Hz with input of experimentally typical receptor firing ranges for odor (1% saturated vapor) / air (see |
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PG cells respond to odor in anesthetized freely-breathing rats [ |
We adjusted ORN→PG and M→PG strengths so that PG cells fire with odor [ |
Mitral output vs receptor input plots with and without PG inhibition in |
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Action potential is generated in mitral tuft for weak nerve shock and in mitral soma for strong nerve shock |
To the Bhalla and Bower mitral cell model [ |
Replication in |
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Activity dependent inhibition between two mitral cells ~50 μm apart, observed in 15 of 29 mitral cell pairs probed |
We adjusted the M→G strength so that only when both mitral cells fire at intermediate rates, the shared granule cells spike. This set the point of onset of inhibition in |
Replication in |
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G—┤M conductance density drops along the primary and secondary dendrites exponentially [ |
We set the observed decay in the model as shown in |
1. Replicates spike travelling along the lateral dendrites even with local inhibition en route [ |
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Linearity of responses in time and between odors [ |
PG ─┤M should not be so strong as to quench mitral firing and make the |
Replication in |
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Phase and delta-rate decorrelation of sister mitral cells [ |
Strengthened and created extra M→G and G ─┤M between central sister and a non-sister odor responsive mitral cell. Similarly between other central sister and non-sister mitral cell of a third glomerulus. Proximal strengths are set by activity dependent inhibition. Also self-inhibition should not be too strong. This enforces M→G to be stronger away from the soma, to deliver strong inhibition, yet not self-inhibit. | Strengthened synapses in the |
We first modeled three cell types based on physiological data. Mitral cells were modeled with 286 compartments including 7 voltage-gated ion channels and calcium dynamics distributed over the cell, adapted from the Bhalla and Bower model [
Mitral cell: A. Visualization of a simulated
Our two-compartment granule cell had a soma and a dendritic compartment, with Na, K and KA channels, adapted from Migliore and Shepherd’s model [
Periglomerular (PG) cells had 3 compartments with 5 types of channels, and calcium dynamics. Two types of PG cell firing, namely low-threshold spiking and plateauing, have been reported [
Thus, each of the mitral, granule, and PG cell models were able to replicate basic electrophysiological properties.
Using these cell models, we constructed our network with physiological cell and synapse numbers, and set the synaptic strengths and time constants from evoked / spontaneous post synaptic potentials / currents reported in the literature (
We simulated the input-output curve of a mitral cell
Thus, at this stage, we had parameterized the glomerular synaptic strengths and also the input-output relationship at two points for mitral cell firing (air and odor means).
We next parameterized the mitral-granule dendro-dendritic circuitry from observed lateral inhibition between nearby mitral cells, which is thought to be mediated by shared granule cells [
A. Schematic of model and experiment: Inhibition on mitral cell A due to mitral cell B ~50 μm apart is probed by simultaneous dual patch recordings [
We replicated these experiments in a
Connectivity | Description | # of lateral glomeruli | Modifications | Inputs |
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Mitral cells randomly rotated. | 2 | None. | ORN inputs scaled to get similar mean mitral firing as |
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Central mitral sisters had dendrites from different lateral mitral cells pass near their somas. | 2 | (i) None. (ii) Leak reversal potentials of sisters at -58 mV and -70 mV. | As above | |
B ‘super-inhibited’ A denotes: (a) B’s lateral dendrite passed near A’s soma; (b) 100 extra shared granule connections with A, proximal to B’s soma; (c) mitral → shared-granule strengthened 3× distally; (d) shared-granule ─┤ mitral strengthened 4×. Lateral mitral cells differentially ‘super-inhibited’ the two mitral cells of the central glomerulus. Most connections remained as in the |
2 |
(i) None. (ii) lateral mitral cells removed. (iii) PGs cells removed. (iv) granule cells removed. (v) all interneurons removed. (vi) non-linear input. | ORN inputs set to obtain mean mitral firing of ~10–15 Hz for odor and ~8 Hz for air. 35 Hz |
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Two mitral cells A and B, 50 μm apart. Granule cells farther than 100 μm from the plane containing primary dendrites of A and B were discarded. | 1 | Lateral dendrites of A and B oriented randomly (most connections in |
Current injected into somas of A and B. |
Most of the shared granule cells between nearby mitral cell pairs were proximal to both their somas, due to maximal overlap of the mitral cells’ dendrites in this region. Thus, this activity-dependent inhibition between nearby mitral cells [
Thus these pairwise recordings helped to define the crucial mitral├→ granule synaptic strengths for the model.
We next addressed a long-standing question in the field about the computational role of lateral dendrites of mitral cells: are they input or output structures? This possible dual role emerges from the observation that dendro-dendritic synapses with granule cells are bi-directional [
In our
To address inhibition between mitral cells versus their separation, we examined three connectivity patterns:
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.
The
The
We performed activity-dependent inhibition calculations between pairs of mitral cells, for each of these three networks. Since these were
There were three factors contributing to the reduction in inhibition on B due to A in all three networks: 1) drop in number of shared granule cells; 2) decay in the strength of the inhibitory granule —┤mitral connections away from the soma (
We used the same three network configurations to examine how back-propagating action potentials along the lateral dendrite could mediate long-range inhibition. We repeated the calculations for activity-dependent inhibition at increasing cell separations, but this time from B to A (
Thus in our model, the mechanism for a lateral mitral cell B to strongly inhibit a distant mitral cell A, was by B’s action potentials propagating along its lateral dendrite and activating the column of granule cells on the soma, primary and proximal-secondary dendrites of A, where the granule —┤mitral synapses were strongest (
It is interesting to note that our model brings together two experimental observations, namely the decay of granule ─┤mitral synapses [
Thus, our model proposes that the distinctive, elongated mitral cell lateral dendrites deliver selective, long-range inhibition via back-propagating action potentials.
Having parameterized the model, and replicated several circuit-level observations, we now investigated whether it replicated results of
A-C. Experimental example. (Re-plotted from data [
To simulate odor responses, we generated input ORN responses that were linear with concentration and flow rate. For the ORNs of each glomerulus, we first randomly generated different linear kernels (impulse responses) for air and two odors, as Gaussians in time (latency-to-peak = 150 to 350 ms, width = 250 to 450 ms). These were used to generate the random on-off pulse single-odor ORN input (
For completeness, we also tested: (1) a sigmoidal output non-linearity appended to the linear ORN model (
Fifty random instances of the
We also ran simulations with peak 2% saturated vapor. The fits and predictions were comparable to those from experiments with 1% saturated vapor, but the corresponding kernels at 1% differed in temporal structure from those at 2% (
Here, the ORN input underwent an approximately linear transformation by the mitral cell’s ‘dynamic’ input-output function (averaged over 400 ms in
A-E: Mitral input-output curves simulated in a
We also simulated freely breathing mitral responses using the same ORN kernels for 1% saturated vapor, convolved with a periodic respiration waveform as input (
Thus, with physiological settings of PG and granule cell inhibition, our model replicated two freely-breathing anesthetized rat experiments, demonstrating linear odor coding by mitral cells for respiration tuned input also.
A. Experimental odor responses of two sister mitral cells (squares vs discs), periodic with respiration, that were negatively correlated, re-plotted from data [
We next asked if mitral responses were linear over larger variations in concentration. We simulated the responses to odor pulses of 200 ms duration at 1/3, 2/3, 1, 2 and 5% saturated vapor, generated similar to random pulses (
The responses at higher concentration had a shorter latency to first spike after odor onset (
Responses at concentrations different from 1% were decorrelated i.e. changed time profile, from the 1% response (similar to that seen with pulse trains above), and saturated at high concentrations (
Thus, the network exhibited degraded linearity when probed with pulses of odor scaled over a wide concentration range, even though it remained linear when summing pulse-trains at any given fixed concentration.
We next manipulated the inhibitory circuits in the
We tested stronger input to PG cells to create a half-Mexican-hat mitral input-output curve as proposed in some models [
Thus through the use of simulated cell knockout and circuit manipulation ‘experiments’, we found that PG cells are instrumental in linearizing olfactory bulb responses.
Having analyzed emergent single-neuron coding, we next asked how cross-neuron coding features might emerge from the bulbar circuit. Specifically, Dhawale et al. found that ~30% of respiration-phase locked odor responses in sister mitral/tufted cells of freely breathing mice were negatively correlated [
To simulate these experiments in the
Through model parameter exploration, we determined that the 3× distal strengthening of mitral → granule connections was necessary for the lateral mitral cell to excite shared granule cells at typical low mitral firing rates, and the 4× strengthening of granule ─┤mitral connections was necessary to strongly modulate central mitral firing. Recall that the mean proximal weights were constrained by activity dependent inhibition [
The distribution of phase-correlations between the simulated odor and air responses of the sister pairs in 350 instances of the
Thus, super-inhibitory differential lateral connectivity is a sufficient network explanation for multiple aspects of decorrelation between sister mitral cells connected to the same glomerulus.
While we cannot rigorously show that our
In all connectivities other than
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.
In addition to granule-cell connectivities, we tested that intrinsic differences in resting potentials (hence different spike thresholds) between sister cells could not decorrelate responses (
Hence, from our simulations, we predict that there should be sparse, strong, proximal and differential lateral inhibition on sister mitral cells in order to decorrelate their responses to the extent observed experimentally.
We have developed a detailed compartmental model of olfactory bulb microcircuits incorporating a few odor-responsive glomerular column microcircuits and their interconnections. This model provides a mechanistic account of individual and cross neuron olfactory coding for identity, intensity, and mixtures. It specifically addresses the contrasting computational roles of mitral cell apical tufts versus lateral dendrites, especially their dendro-dendritic contacts, and supports the hypothesis that the lateral dendrites are primarily output structures. We have summarized the network-level constraints, replications of various experiments, and our predictions in Tables
In a series of increasingly detailed models, Shepherd, Migliore and colleagues have looked at the generation of granule cell modules [
We propose that, complementary to the above role of spike time modulation, granule cells mediate sparse and strong lateral inhibitory connections (currently unobserved) that can radically alter the respiratory phase of mitral firing compared to its primary glomerular input, causing phase decorrelation between sister mitral cells [
In our study, we have only looked at phase decorrelation between sister mitral cells which receive the same excitatory glomerular input, not at phase decorrelation between mitral cells belonging to different glomeruli which in any case receive receptor input at different phases. While odor coding by spike latencies essentially between glomeruli has been studied in simplified models [
Based on our results, we expect phases of sister mitral cells to become highly correlated if granule cells are selectively silenced. If phase decorrelation is still seen, then other mechanisms must be considered, say (1) differential inhibition at the glomerulus, or (2) intrinsic differences between sister mitral cells. However, the former is unlikely given the averaging in the glomerulus via shared ET cells and gap junctions. For the latter, we specifically tested leak reversal potential (and hence spike threshold) as one intrinsic difference and did not find any resultant phase decorrelation (
In the spatial domain, the decrease in granule ─┤mitral strength with distance, coupled with the jump in mitral → granule strength beyond 100–200 μm, suggests that a major role of the lateral dendrites is to inhibit distal mitral cells. This distal inhibition is directed and sparse.
While granule cells play a primary role in phase decorrelation, PG cells linearize the mitral input-output curve. Hence if PG cells are selectively silenced, we expect strong saturation effects to show up in the mitral firing rate response versus odor concentration. Indeed, we expect PG cells to compensate for both receptor and mitral saturation / non-linearities. If linearity is maintained on silencing PG cells, then the ORN-mitral pathway may be fairly linear on its own, or the external-tufted—short-axon cell network may be involved in linearizing (see below). However, given the firing rates of PG cells, and their effectiveness in inhibiting the input at the tuft itself [
Contrary to this, Cleland, Sethupathy, and Linster have proposed that intra-glomerular PG cell inhibition suppresses low mitral firing, causing a half-Mexican-hat mitral input-output curve, leading to contrast enhancement [
We propose that the linearity of the feed-forward circuitry can be tested by light-activating axons of olfactory receptor neurons (which activate both mitral and PG cells) at a glomerulus at respiratory time-scales, and checking if the mitral rate response versus activation intensity is linear or not. The bulbar circuitry does offer alternative possibilities to obtain the observed linear summation [
Thus our model proposes a testable role for the PG cells in linearization, and its falsification would implicate other mechanisms.
We propose that lateral inhibition not only sculpts the mitral responses spatially and temporally, but also differentially between sister mitral cells, while maintaining limited linearity. Our prediction of strong, sparse and differential inhibition on sister mitral cells is corroborated by the recent observation of sparse lateral connections and the non-sharing of granule cells between neighboring or sister mitral cells (differential connections) [
Based on our model and bulbar anatomy, we compute an upper bound and also a tighter, model-constrained estimate of the fraction of ‘super-inhibitory’ connections in the bulb. Given ~400 granule ←┤ M1 synapses proximal to a mitral M1’s soma in our model, and ~100 spines (reciprocal synapses) on a granule cell [
From our model we found that super-inhibition on central mitral sisters from too few (0) or too many (6+) odor-activated mitral cells (of different lateral glomeruli) did not yield the observed decorrelation [
These estimates of connectivity are strong quantitative predictions from our model that can be experimentally tested using retroviral and other tracing methods.
The experimental literature provides numerous constraints on bulbar anatomy and physiology at the cellular, micro-circuit and macro-circuit level. Our study synthesizes many such constraints, and marries these to odor response data from a range of
We have been able to account for key, broad-brush coding features of mitral cells despite glossing over the role of several bulbar circuit elements. These circuit details may likely have network implications too. We did not model external-tufted, short-axon and other interneurons, nor gap junctions between mitral cells, and it will be interesting to see if future studies reveal a larger contribution to linearity or decorrelation from these components than our model suggests (Materials and Methods: ‘What was simplified in the model, and why’). We also did not include centrifugal modulation or learning, since our experimental references were in anesthetized preparations. We modeled only a few activated and connected columnar micro-circuits in the olfactory bulb, with the rest replaced by background activity to granule cells. Thus there is considerable scope to include more realism and detail; to study larger-scale functional organization, and to examine the roles of modulatory inputs, plasticity, homeostasis, and additional circuit elements.
Our model shows how many aspects of mitral coding emerge as the sum of a primary excitatory and a few lateral inhibitory temporal inputs from the glomerular representation. As an abstraction of our model circuit, the receptor neurons reduce the high-dimensional odor space to a lower-dimensional glomerular representation. Each mitral cell combines a few dimensions of the glomerular representation via coupled lateral mitral microcircuits. Sister mitral cells send different / decorrelated limited-linear combinations, disambiguating similar stimuli. Many mitral cells converge on each of the large number of pyramidal neurons in the olfactory cortex, mapping the glomerular representation somewhat linearly to the cortical one. Pyramidal neurons in the olfactory cortex require a number of possibly coincident (same phase) inputs from mitral cells to fire [
We used the Multi-scale Object Oriented Simulation Environment (MOOSE,
We extended MOOSE to load NeuroML files along with input spike trains. We farmed multiple trials with the same network instance, but different ORN and baseline granule cell input on a cluster. Simulation setup and post-simulation analysis code was in Python (
We constructed a biophysical model of coupled odor-responsive microcircuits in the rat olfactory bulb, using compartmental models for mitral, granule and periglomerular (PG) cells. Input from olfactory receptor neurons (ORNs) was represented as time-varying Poisson spike trains. These inputs were afferent onto mitral tufts and PG dendrites. Since we were interested in simulating odor responses of two sister mitral cells, we modeled a central glomerulus containing the two mitral cells of interest, and zero to six lateral glomeruli in its dendritic field, that were activated by odor and inhibited the central mitral cells.
At concentrations of interest (~1% saturated vapor), an odor activates glomeruli sparsely [
In our model, PG cells mediated feed-forward (ORN → PG ─┤mitral) and recurrent (mitral├→ PG) intra-glomerular inhibition, and granule cells mediated self / recurrent (mitral├→ granule) and lateral (mitral1 → granule ─┤mitral2) inhibition. We used spatial scales and connectivity from rat, but we constrained the model and reproduced results from experiments on both rats and mice. We ignored centrifugal inputs to the bulb, restricting the model to experiments on anaesthetized animals, where centrifugal modulation is low [
A summary of cell numbers, synaptic numbers, modeling strategies for each, and experimental and simulated synaptic strengths and time scales is provided in
We used a modified version of Bhalla and Bower’s 286 compartment model of the mitral cell [
Our two-compartment granule cell had a soma and a dendritic compartment, with Na, K and KA channels, adapted from Migliore and Shepherd’s model [
PG cell models had a soma and two dendritic shaft compartments from the soma. Their resting Vm was set to −65 mV [
We provide a summary of / references for the channel parameters in
Channel / Ion-Pool name (cell name) | Kinetics |
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Same as in Bhalla and Bower’s model [ |
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As above, except: |
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Same as Kca_mit_usb of Bhalla and Bower’s model [ |
For a given network connectivity (
Hence, for a network instance, we first generated positions for a ‘central’ glomerulus and 0–6 ‘lateral’ glomeruli in an 850×850 μm2 area around it i.e. within mitral dendritic reach. Then we placed 2 mitral cells with their primary tufts in each glomerulus, and their somas in the mitral cell layer below. Due to computational constraints, we retained only two mitral cells per glomerulus. We rotated one mitral cell from each lateral glomerulus, so that one of its lateral dendrites passed close to alternately one or the other central sister’s soma (Figs
At each glomerulus, we placed 1000 PG cells in a 2D array. For each mitral cell, we created 100 reciprocal mitral├→ PG synapses, each between a randomly-chosen tuft compartment of the mitral cell in that glomerulus, and any of the two dendrites of a randomly chosen PG cell. We repeated these mitral → PG synapses, to complete 25 synapses per PG cell, distributing their delays uniformly from 0 ms to 40 ms. PG ─┤mitral synaptic delays were distributed exponentially with a mean of 160 ms.
We next created a granule cell layer with realistic density: 2500 granule cells per (100 μm)2, beneath the mitral cell layer. For each mitral cell, we formed 104 reciprocal (mitral├→ granule) synapses [
Further, for the
The strong proximal granule ─┤mitral synapses around each central sister’s soma due to super-inhibitory connections effectively created a ‘column’ of granule cells. We also strengthened the proximal granule ─┤mitral synapses of the lateral mitral cells to create columns of granule cells around them in lieu of additional lateral mitral cells ‘super-inhibiting’ these lateral mitral cells,
We modeled only those odor-responsive mitral cells that strongly inhibited the central sister mitral cells, via shared granule cells. We incorporated the average inhibitory effects of the large number of mitral cells that we did not model, by a 3.45 Hz
We estimated synaptic numbers from reported numbers of PG & granule cells (vis-à-vis mitral cells), and their spine counts, assuming one connection per spine (
Leak reversal potentials of granule cells were spread normally with a standard deviation (SD) of 2.25 mV similar to experiment [
The
For the
The different connectivities we probed are listed in
After creating the reciprocal mitral├→ granule synapses as above, unconnected granule cells were pruned. Shared granule cells connected to two or more mitral cells were left 1:1, and not aggregated, so as not to average out lateral inhibition effects. In the
For each such 100:1 aggregated granule cell, the excitatory mitral → granule input synapse was maintained the same, but the inhibition to the connected mitral cell was increased corresponding to the effect of 100 granule cells. However, just multiplying granule ─┤mitral synaptic strength, would make this proxy inhibition too large and synchronous. So instead of a single synapse of 100× weight, we set up 10 synapses, each of strength 10×, with staggered delays, triggered by the same pre-synaptic granule cell spike. The staggered delays were distributed exponentially with a standard deviation of 160 ms similar to experiment [
We confirmed that simulations with 100:1 aggregation gave qualitatively similar results to 20:1 aggregation for activity dependent inhibition
Typical model-construction approaches start out with a reduced number of cells and connect them up via proportionally stronger synapses. By contrast, we first created a model with realistic numbers of mitral, granule and PG cells, connected them up with realistic numbers of synapses, and then discarded, neglected, or aggregated cells based on their connectivity. The advantage with our method of cell number reduction is that (1) differential connectivity effects are not averaged out as only unshared granule cells are aggregated, not shared ones, (2) synaptic strengths and integration effects are partly maintained using non-synchronous scaling of synapses, and (3) proxy background (in our case excitation to granules cells) is provided in lieu of the discarded (mitral) cells.
We modeled synapses as dual exponential conductances. Excitatory glutamatergic mitral→granule synapses had both AMPA and NMDA components. Magnesium-block voltage-dependence and NMDA to AMPA ratio were taken from experiment [
All synapses in our model were spike-based. Dendro-dendritic synapses are usually considered graded, however the mitral → granule synapse was modeled as spike-based because in the presence of TTX, “graded depolarization [of the mitral cell] below threshold for calcium spike initiation failed to activate the reciprocal synapse” [
We implemented the inhibitory effect of the Ca transient in the granule cell spine, on the mitral cell, by creating a weak auto-inhibitory synapse on the mitral cell, at each reciprocal mitral├→ granule synapse, which was activated when the mitral cell fired. The strength of this auto-inhibitory synapse should be the same as the inhibitory part of the reciprocal synapse as it is indeed the same synapse, just its activation is different. However, spinal neuro-transmitter release is expected to be stochastic and dependent on the number of pre-synaptic action potentials, whereas with our auto-inhibitory synapse all 104 synapses per mitral cell get activated on each spike. Thus a weak, effective synaptic strength of 5 pS was used to avoid strongly inhibiting the mitral cell.
Apart from this, the usual granule ─┤mitral synapse in our model was spike-based, to represent the activation due to global Ca transient following a granule cell spike. We reduced granule ─┤mitral synaptic strengths exponentially along the dendrites (length constant 100 μm on primary and 150 μm on secondary dendrites), and further reduced them proportionally with diameter, both as measured experimentally (after space clamp correction) [
For
Each individual synaptic weight was finally set log-normally [
Focal GABA uncaging on the mitral lateral dendrite did not block spike propagation in the rest of the dendrite and revealed reduction in granule ─┤mitral strength with distance [
When we naively set synaptic weights based on evoked / spontaneous post synaptic potentials / currents, network effects like mean firing rates and activity dependent inhibition were quantitatively different from experiment. Therefore, we replicated various network level experiments, at each stage refining a subset of synaptic weights or connectivity, while maintaining previous results (
Most input to mitral and PG cells, is via ET cells [
The non-synaptic inhibitory action of PG cells on ORN terminals [
Various papers report long-lasting depolarizations and/or all-or-none mitral responses in slice to nerve shock [
We have not modeled the inter-glomerular network formed by short-axon cells. Short axon cells have been reported to inhibit ET cells in glomeruli up to 600 μm away [
We have not modeled PG cell axons inhibiting nearby glomeruli, as they are rare but can extend over 4–5 glomeruli [
We also did not model gap junctions between M/T cells, between M/T and ET cells, and between M/T and PG cells in the glomerulus [
Granule cells in our model were activated asynchronously since their leak reversal potentials were distributed normally (see ‘
Tufted cells are similar to mitral cells, just smaller, and have not been modeled explicitly. For purposes of summation and lateral inhibition, we expect tufted cells to function similar to mitral cells. Though, recent studies indicate that tufted cells fire with lower latencies compared to mitral cells [
We also did not include the parvalbumin-expressing (PV) interneurons in the external plexiform layer, which form reciprocal dendrodentritic connections with mitral cells. These have been recently reported to take input from multiple mitral cells and are broadly tuned to odors, unlike granule cells which are more selective and narrowly tuned [
We have also neglected Blanes cells that inhibit granule cells [
We also did not include centrifugal input to the bulb in our model, as we considered only anesthetized preparations where centrifugal input may not play as strong a role as in awake animals [
We did not include any learning in our model, again since we were focusing on recordings from anesthetized preparations, which have lower centrifugal input that is critical for learning [
We modeled only a small number of microcircuits, and only a small number of mitral cells within each, as we were computationally limited.
We combined experiments on rats and mice. Our model dimensions, cellular and synaptic numbers, and synaptic time constants were largely those of rat. Synaptic weights were fine-tuned from experiments on both rats and mice. We used an anesthetized respiration period of 0.5 s as for mice. Firing rates of mouse and rat mitral cells for air and odor were not too dissimilar (using data of [
Whenever replicating experiments, we broadly followed the analogous experimental protocol and analysis, in particular for activity dependent inhibition [
For action potential initiation in the mitral cell (
For action potential propagation in a mitral cell B (
For activity dependent inhibition
For activity dependent inhibition
We distributed 400 ORN → mitral synapses on each mitral tuft, randomly on the tuft compartments, consistent with observations [
We did not model ORNs biophysically, rather as Poisson spike trains afferent on to above mitral and PG cell synapses. For simulating activity dependent inhibition
For the ORNs of each glomerulus, we first generated linear kernels for air and two odors, as Gaussians in time with latency-to-peak
The amplitude
We used the same set of ORN air and odor kernels for both the tracheotomized and the freely-breathing protocols, to compare the two in the same network instance. The set of air and odor ORN kernels along with the corresponding network instance was analogous to a distinct rat / mouse. For the tracheotomized and freely-breathing protocols (details in sections below), first an odor concentration time-series was generated as a random pulse-train or a respiratory waveform respectively. Similarly an air flow-rate time-series was generated. The concentration time-series was convolved with the odor kernel, while the air flow-rate time-series was convolved with the air kernel. Their sum along with a constant 0.5 Hz baseline gave the firing rate time-series of the ORNs of a given glomerulus (Figs
For most of the simulations we assumed that the ORN responses scaled linearly with odor concentration and air-flow. There is some evidence that ORN responses scale linearly with odor concentration roughly over 1 order of magnitude around 1% saturated vapor [
For the tracheotomized protocol (
We then convolved this true concentration time-series with the ORN odor kernel to obtain the ORN firing rate waveform for this protocol. This odor m-sequence rode on a constant air/suction pedestal. The constant pedestal was convolved with the air kernel to get the air firing waveform which was added to that of the odor, along with a constant 0.5 Hz background.
The flow rate used in the experiment [
For every network instance, we ran 2 random pulse-train stimuli for each of two odors, and 1 two-odor overlapping random pulse-train stimulus (2 of the 4 single-odor pulse-train responses are shown in
We fit the responses to the 2 random pulses stimuli per odor for each central sister, after subtracting a constant air background, with a 2 s long odor kernel discretized at 50 ms. We predicted each sister’s response to the sum of random pulses of two odors, using fitted kernels for the two odors. This analysis closely followed experiment [
For the freely-breathing protocols we replicated [
We had set the glomerular input and inhibitory synaptic strengths (Tables
For air and for each odor in every network instance, we ran 8 trials in parallel on the cluster with each trial having 2 respiratory cycles. We averaged over the second cycles of the trials and binned the average cycle response into 5 bins. Since typical mitral kernels had duration between 0.5 to 1 s [
As in the experimental analysis, we calculated the Pearson correlation of the mean single-cycle odor response of one central sister versus the other. We did the same for the air responses.
We calculated the delta-rate for each odor i.e. odor mean—air mean, with the mean over the bins of all the second cycles. We strung together the delta-rates for every odor in every network instance of one central sister into one vector, and for the other central sister into another. The Pearson correlation between these two vectors gave us the delta-rate correlation which measures how much the sisters co-vary in their mean rate responses to odor, compared to their air baselines.
Since we used the same input ORN kernels to generate the freely-breathing and tracheotomized stimuli, we could use the mitral odor kernel fitted from the tracheotomized protocol to see how well it predicted the freely-breathing response. We convolved the fitted mitral odor kernel with the rectified respiration waveform / time-series and compared this prediction, using the
Following the replicated experiment [
We also tested a model similar to the pulse-trains experiment [
In the experimental analysis [
To compare responses across a larger concentration scale, we used 200 ms pulses of odor scaled to 0%, 1/3%, 2/3%, 1%, 2% and 5% saturated vapor. The protocol was the same as the tracheotomized protocol (
For
For
For
(TIF)
(TIF)
Goodness of fits and predictions, and kernels of simulated responses to 2% saturated vapor random pulse-trains compared with 1%: A-B. Distributions of
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Mitral cell responses to 200 ms long odor pulse input, scaled at 1/3, 2/3, 1, 2, and 5% saturated vapor pressure, were simulated in 50 instances of the
(TIF)
Example simulated responses to scaled odor pulse input in
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(MP4)
We thank the MOOSE team, in particular Subhasis Ray and Niraj Dudani for help in using and extending the MOOSE simulator; the MOOGLI (