Fig 1.
Encoding and odor signal processing in the early olfactory system of the fruit fly brain.
(A) Computational logic of the olfactory system. Encoding of odorant waveforms in the Antenna is confounded between odorant object identity and odorant concentration waveform. For robust downstream odor signal processing, recognition and associative learning, the Antennal Lobe transforms the confounded Antenna odorant representation into the identity and the on/off timing information of the odorant object. (B) Input/Output (I/O) characteristics of the early olfactory system along a single channel. Shown from left to right are Acetone staircase odorant concentration waveforms, Or59b OSN Peri-Stimulus Time Histograms (PSTHs) and DM4 PN PSTHs, respectively. Data taken from [35].
Fig 2.
Essential temporal encoding/processing characteristics of the DM4 PNs.
(A) Acetone concentration waveform (first published in [35]) and concentration contrast. (B) Or59b OSN and DM4 PN spike train data in response to an Acetone staircase waveform. Each neuron response is decomposed into steady-state and transient responses—where the steady-state response is computed as the average PSTH within a 500 miliseconds window before a jump in odorant concentration. The transient response is the residual obtained by subtracting the steady-state response from the overall response. See the text for more details. (C) Or59b OSN and DM4 PN normalized transient response compared against normalized concentration contrast. Note that the PN transient response agrees very well with the concentration contrast.
Fig 3.
An Example of Concentration-Invariance and Contrast-Boosting in a Single-Channel Antennal Lobe Circuit.
(A1) Model architecture of a single-channel (glomerulus) Antennal Lobe circuit. (A2) Functional equivalent model of the single-channel AL circuit in (A1) with each branch replaced in part by a differential DNP. For Post-LN pathways, BSGs are included to capture the spike generation of Post-LNs. (B, left) Input and output relationships for each of the three branches shown in (A1, A2). The odorant concentration waveform and Pre-LN, Post-eLN and Post-iLN to PN synaptic currents estimated from physiology recording data are shown in grey. Response of each DNP (and DNP-BSG cascade) pathway in (A2) is shown in red. (B, top right) Acetone staircase concentration waveform. (B, bottom right) Model DM4 PN PSTH (red) compared with the DM4 PN physiology recording (grey).
Fig 4.
An Example of Concentration-Invariance and Contrast-Boosting in a Multi-Channel Antennal Lobe Circuit.
(A1) Model architecture of multi-channel AL circuit. (A2) Functionally equivalent model of the multi-channel AL circuit, with each branch in (A1) replaced in part by a corresponding differential DNP model. (B) Input and output relationships of the multi-channel AL circuit. (B[i,v]) Acetone staircase odorant concentration waveform. (B[ii]) Post-eLN to PN synaptic currents. Different hues of red indicate strengths of synaptic current, with strongest due to the Post-eLN receiving input from the Or59b OSN indicated in dark red. (B[iii]) Post-iLN to PN synaptic currents. Different hues of blue indicate strengths of synaptic current, with strongest due to the Post-iLN receiving input from the Or59b OSN indicated in dark blue. (B[iv]) OSN Axon-Terminal to PN synaptic current shown as a heatmap. Different hues of grey indicate strengths of synaptic current. Refer to colorbar for scale. (B[vi]) Multi-channel PN PSTH, with synaptic current of ON and OFF pathways along Or59b/DM4 channel shown as blue and red arrows, respectively.
Fig 5.
Recovery of odorant semantics via angular distance minimization.
(A[i]) Acetone concentration waveform. (A[ii]) Acetone affinity vector shown as a heatmap. (A[iii]) PN multi-channel PSTH in response to Acetone input. (A[iv]) Angular distance between OSN/PN multi-channel PSTH and affinity vector shown in orange/black, respectively. Note that the angular distance between the PN multi-channel PSTH and affinity vector is lower (closer to 0) than that between the OSN multi-channel PSTH and affinity vector. (B) Similar results in (A) but shown for an Ethyl Acetate concentration waveform.
Fig 6.
Mapping of odorant semantics into PN BSG limit cycle manifolds.
(A) Limit cycles of the PN BSG for selected channels for Acetone. In each panel, the limit cycle occupied by PN in the corresponding channel is highlighted in red. Note that all 3d plots share the same axis limits and labels as the left-most plot. Other limit cycles of the Noisy ConnorStevens neuron model are shown in grey for reference. (B) Affinity vector of Acetone shown as bar plot indexed by the receptor type and the corresponding glomerulus along the x-axis. Note that the y-axis is in log-scale. (C) Limit cycles of the PN BSG for selected channels for Ethyl Acetate. Note that all 3d plots share the same axis limits and labels as the left-most plot. (D) Affinity vector of Ethyl Acetate shown as bar plot.
Fig 7.
Representation of semantic timing in the phase space of the PN BSG.
(A) The dynamics induced by odorant timing events in the phase space of the DM4 PN BSG. (A[i]) Acetone odorant concentration waveform with 4 segments corresponding to onset, first steady-state, first offset and second steady-state labeled as 1, 2, 3, 4. (A[ii]) DM4 PN PSTH in response to the Acetone stimulus with the corresponding PN PSTH values at time points 1, 2, 3, 4 are labeled accordingly. (A[iii]) Transitions between limit cycles of the DM4 PN BSG corresponding to the timing of the onset transient (1), steady-state (2), offset transient (3) and back to steady-state (4). (B) The dynamics induced by the Ethyl Acetate stimulus in the phase space of the DM4 PN BSG. (C-D) The dynamics induced by the Acetone and Ethyl Acetate stimuli in the phase space of the VM2 PN BSG, respectively. Note that in (C), VM2 PN does not respond to Acetone due to the low affinity of the upstream Or43B receptor to Acetone.
Fig 8.
Robustness of Concentration-Invariance and Contrast-Boosting of the multi-channel AL circuit.
(A [i]) Acetone staircase concentration waveform. (A [ii, iii]) Post-eLN/Post-iLN to PN synaptic current. (A [iv]) DM4 PN PSTH from physiology recording data (in grey) and model response (in red). (A [v]) Stable attractor limit cycle (in black) in DM4 PN BSG phase space and an example response trajectory of the DM4 PN BSG for 800 milliseconds between 2.2 second and 3 second, corresponding to the green shaded rectangles in (A[iv]). (B) Same as in (A) for Acetone step concentration waveform with additive white noise. Note that in the presence of strong additive white noise, the responses of the Post-eLN, Post-iLN pathways, as well as the overall DM4 PN PSTH remain similar to that in the noise-free case.
Fig 9.
Robust recovery of the identity of 110 mono-molecular odorants by the multi-channel AL circuit.
(A) Angular distance between [i] OSN and [ii] PN population responses to step concentration waveform and affinity vectors for 110 odorants for a range of 10 ∼ 10, 000 [ppm] concentration levels (log scale). Refer to the colorbar on the right for the scale of the angular distance from low (blue) to high (red). In (A[ii]), three concentration levels and three odorants are labeled corresponding to the 9 sets of PN BSG stable attractor limit cycles shown in (B,C,D). (B) Limit cycle manifolds for all 24 channels (color-coded by channel as indicated by the legend on the far right) at for Butyric Acid concentration levels of [i] 1000 ppm, [ii] 498 ppm and [iii] 100 ppm. (C, D) Same as in (B), respectively, for Acetone and Benzyl Alcohol.
Fig 10.
(left) Example single-channel AL circuit and (right) the associated model DNP circuit.
Refer to Table 1 for details on the circuit component parameterizations and the correspondence between circuit component models and the differential DNP models of Eq (3).
Fig 11.
(left) Example multi-channel AL circuit with feedforward Pre-LN pathway across glomeruli and (right) the associated model DNP circuit.
The multi-channel AL circuit has R channels, receiving input from OSNs expressing R receptor types. Shown above on the left are channels 1 and R. The Pre-LN pathway receives spiking input from OSNs across channels and outputs a single Pre-LN spike train. As opposed to the cross-channel integration of the Pre-LN pathway, the Post-eLN and Post-iLN pathways are repeated for each channel and only perform computation local to their corresponding glomerulus. The same distinction of global vs. local computations are shown for the model differential DNP circuit on the right. Here the multi-channel Pre-LN pathway is modeled as a Global DNP-FF. Note that the Post-eLN and Post-iLN pathways correspond to the same DNP-FF[II] and DNP-FF[III] models as in the single-channel AL circuit in Fig 10. Refer to Table 2 for model details.
Table 1.
Model description of the AL circuit in Fig 10(left), and its correspondence with the DNP circuit in Fig 10(right).
Note that for notational simplicity the free parameter values for θ are omitted. Indices under the Model column refer to the following detailed models: (1) OSN to Pre-LN Synapse, (2) Pre-LN BSG, (3) OSN Axon-Terminal, (4) OSN to Post-eLN Synapse, (5) Post-eLN BSG, (6) OSN to Post-iLN Synapse, (7) Post-iLN BSG, (8) OSN to PN Synapse, (9) Post-eLN to PN Synapse, (10) Post-iLN to PN Synapse, (11) PN BSG. The differential equations for each model are detailed under the Equation column, with the corresponding parameters summarized under the Parameters column. Note that under the Parameters column, values for a number of fixed parameters are shown. The circuit has a total of 23 free parameters denoted by the vector θ. For models that correspond to the three differential DNP components shown in Fig 10(right), the correspondences are made explicit on the right side of rows (1–3), (4–5), (6–7) for, respectively, DNP-FF[I], DNP-FF[II] and DNP-FF[III].
Table 2.
Model description of Fig 11(left), and its correspondence with the DNP circuit in Fig 11(right).
Note that for notational simplicity the parameter values for θ are omitted. Indices under the Model column refer to the following detailed models: (1) OSN to Pre-LN Synapse in the r-th channel, (2) Pre-LN BSG, (3) OSN Axon-Terminal in the r-th channel. Note that only components in the Global DNP-FF pathway are specified as the other circuit components are the same as in Fig 10(left) for each of the R channels. The differential equations for each model are detailed under the Equation column, with the corresponding parameters summarized under the Parameters column. Note that under the Parameters column, values for fixed parameters are shown. The circuit has a total of 23 free parameters denoted by vector θ, the same as the single-channel AL circuit in Fig 10. The correspondence between the Pre-LN pathway and the Global DNP-FF model is made explicit on the right side of rows (1–3).
Fig 12.
Evaluation of the angular distance objective functions for the single- and multi-channel AL circuit models.
(A[i]) Single-channel AL circuit model. (A[ii]) Synaptic currents injected by the (top) OSN Axon-Terminal into the PN, (middle) Post-eLN into the PN and (bottom) Post-iLN into the PN. The synaptic current estimated from the physiology dataset [35] is shown in grey, and the synaptic current obtained from the circuit model is shown in red. (A[iii]) Objective functions of each of the three pathways in (A[ii]) respectively described by Eqs (8), (9) and (10). (B[i]) Pre-LN pathway in the multi-channel AL circuit model in Figs 4 and 11 and Table 2. The O59b OSN is highlighted in blue. (B[ii]) Synaptic current injected by the OSN Axon-Terminal into the PN shown as a heatmap. The synaptic current was estimated from (left) the physiology recording dataset in [35] and (right) the multi-channel AL circuit model. (B[iii]) Objective function for the multi-channel Pre-LN pathway.
Fig 13.
Comparative analysis of AL circuit architectures for odor semantic information recovery.
(A) Circuit architectures of 5 different AL circuits: [i] no inhibition, [ii] feedback single-channel inhibition, [iii] feedforward single-channel inhibition, [iv] feedback multi-channel inhibition, [v] feedforward multi-channel inhibition. (B) Angular distance matrices between the PN population responses produced by the models [i-v] in (A) to 110 odorants with step concentration levels in the range of 10 ∼ 1, 000 [ppm] (log scale). Refer to the colourbar on the right of Fig 9A for the scale of the angular distance from low (blue) to high (red). The x-axis corresponds to odorant indices, for a total of 110 odorants with known affinity rates. The y-axis corresponds to concentration levels across 2 orders of magnitude, from 10 ppm to 1000 ppm (log scale). See caption of Fig 9A for more details. (C) Empirical distributions of the objective function J2(θ1) for randomly sampled parameter sets θ1 for the 5 different AL circuits compared. Each violinplot along the x-axis corresponds to a different model in (A).