Fig 1.
Spike statistics from in vivo multi-electrode array recordings.
Population average spike statistics for orthonasal (blue) and retronasal (red) with stimulus onset at time t = 0 s as indicated by black arrow for 1 s duration. A) Firing rate (Hz) is statistically significantly different between ortho and retro for the duration of the evoked period (0.4 ≤ t ≤ 1.1 s). B) Spike count variance has no statistically significant difference between ortho and retro. C) Covariance of spike counts are statistically significant different throughout the evoked state (0 ≤ t ≤ 2) with ortho having larger values. Scaled measures of variability shown for completeness: Fano Factor (D) is the variance divided by mean spike count, and Pearson’s correlation (E) is the covariance divided by the product of the standard deviations; both are also different with ortho versus retro. Spike counts in 100 ms half-overlapping time windows averaging over all 10 trials. Significance: two-sample t-tests (assuming unequal variances) for each time bin to assess differences in population means, p < 0.01, also see S1 and S2 Figs. From 94 total cells and 1435 simultaneously recorded cell pairs; shaded regions show relative population heterogeneity: μ ± 0.2std (standard deviation across the population/pairs after trial-averaging; 0.2 scale for visualization).
Fig 2.
A) Dynamics of the 3 uncoupled cell models. MC voltage dynamics with current step inputs in Li & Cleland models (black curves on the left, copied from Li & Cleland [29]) are captured by our single-compartment model (blue on the right). Rows 5–8 show expanded time view of first 4 rows to highlight spike cluster sizes and sub-threshold oscillations (same voltage axis for each). GC voltage responses to three different levels of current injection in the Li & Cleland model (black curves on the left) is similar to our model (green on the right). PGC responses with depolarizing current steps again are similar in both models. Note that release from a hyperpolarizing current injection leads to transient spiking in both models (bottom). B) Coupled OB network model of 2 glomeruli with ORN inputs. ORN synapses are driven by correlated inhomogeneous Poisson Processes (Eqs (10)–(12)). C) Based on ORN imaging studies, we set λO(t) to increase and decay faster than λR(t) with odor onset at time 0s (i). Similarly, we set the input correlation of ORN synapses to the 2 MCs to cR/O(t) where cR(t) < cO(t) and cO(t) rises quicker than cR(t) (ii).
Fig 3.
OB model captures trends in our data.
Comparison of all first and second-order statistics of coupled OB network model to our data. A) Firing rate of ortho increases and decays faster than retro in both data and model. B) Variance of spike counts for ortho and retro shown for completeness, but recall that in experimental data that they are not statistically different. C) Covariance of spike counts is larger for ortho than retro in both data and model (left), but the magnitudes of data and model differ. Comparison of the ratio of retro covariance to ortho covariance in the evoked state (right) shows that the model captures the relative differences between ortho and retro—here μ (resp. σ) is the average (resp. standard deviation) ratio over 20 time bins in the evoked state. For A–C, top shaded error regions of data (retro in A, ortho in B,C) are cut-off to better compare model and data. Comparisons of the (D) Fano factor and (E) Pearson’s spike count correlation shown for completeness despite both measures depending on spike count variance. D) The model has slightly larger Fano factor with ortho, consistent with the data. E) The model does qualitatively capture the spike count correlation for both ortho and retro, at least in the evoked state.
Fig 4.
LN framework used to analyze OB transfer of input statistics.
A) Schematic of the phenomenological linear-nonlinear (LN) model to approximate how the OB network transfers input statistics. B) The actual ortho (top row) and retro (bottom row) input synapses used in the biophysical OB model results in Fig 3. Comparisons of the Monte Carlo simulations (Eqs (11) and (12)) and theoretical calculations (Eqs (13), (18) and (22) for respective columns) show smooth curve matches even for correlated time-varying (inhomogeneous) Poisson processes.
Fig 5.
LN model shows that retronasal input results in linear filters with larger magnitudes.
A) Comparison of LN model output (dashed black curves) to OB network model output statistics for ortho (solid blue curves in top panels) and retro (solid red curves in bottom panels) stimulus with onset at t = 0 s. The LN output qualitatively captures OB model output statistics. B) Linear filters k(t) in LN model for ortho (in blue) and retro (in red) stimulus over time (−5 ≤ t ≤ 0 ms). Linear filters for retro have larger positive and negative values than with ortho.
Table 1.
Parameter b for LN model fits to MC spiking statistics in Fig 5.
Fig 6.
Temporal profile is crucial for larger magnitude filters.
A) Different combinations of input rates (left) including slower increase and decay (retro-like) and faster increase and decay (ortho-like) as well as high and low amplitude as labelled. Two different input correlations (right), with high correlation in gray, and lower correlation in black. B) Resulting linear filters k(t) have consistently larger absolute values when temporal profile of ORN inputs is slower (retro-like), compared to faster (ortho-like).
Table 2.
Parameter b for LN model fits to MC spiking statistics in Fig 6.
Fig 7.
Comparison of all 8 OB model results.
The 8 different OB model results are from varying temporal profile, amplitude height, and input correlation (2 ways each, see Fig 6A). Different temporal profiles is key for both having different model spike statistics and for best matching qualitative differences in our data (see Fig 3). A) Firing rate in Hz (left) is slightly lower with low input rate amplitude, but no significant difference with different input correlations. B) Spike count variance, similar to firing rate, has only slightly lower values with low input rate amplitude. C) Spike count covariance is lower with lower input correlation for all of ortho evoked state (not surprisingly). However, retro (fast) with lower amplitude steadily increases above higher amplitude after about 1 s in the evoked state. D) Fano Factor model results only change modestly. E) Pearson’s spike count correlation, similar to spike count covariance, is lower with lower input correlation and similarly for retro (fast), there is an increase with higher input correlation.
Table 3.
Description of model parameters.
Table 4.
Parameter values for each cell type.
Each of these values are the same as defined by [30] with the exception of maximal conductance values which are the sum of all cell compartments (soma, dendrite, axon, etc.) as defined by [30]. Additionally, any conductance value denoted by − implies that this ionic current is not included in the associated cell.