Competition-based model of pheromone component ratio detection in the moth

Abstract

For some moth species, especially those closely interrelated and sympatric, recognizing a specific pheromone component concentration ratio is essential for males to successfully locate conspecific females. We propose and determine the properties of a minimalist competition-based feed-forward neuronal model capable of detecting a certain ratio of pheromone components independently of overall concentration. This model represents an elementary recognition unit for the ratio of binary mixtures which we propose is entirely contained in the macroglomerular complex (MGC) of the male moth. A set of such units, along with projection neurons (PNs), can provide the input to higher brain centres. We found that (1) accuracy is mainly achieved by maintaining a certain ratio of connection strengths between olfactory receptor neurons (ORN) and local neurons (LN), much less by properties of the interconnections between the competing LNs proper. An exception to this rule is that it is beneficial if connections between generalist LNs (i.e. excited by either pheromone component) and specialist LNs (i.e. excited by one component only) have the same strength as the reciprocal specialist to generalist connections. (2) successful ratio recognition is achieved using latency-to-first-spike in the LN populations which, in contrast to expectations with a population rate code, leads to a broadening of responses for higher overall concentrations consistent with experimental observations. (3) when longer durations of the competition between LNs were observed it did not lead to higher recognition accuracy.

Figure 1. The structure of the elementary pheromone component ratio recognition unit in the MGC.

Two groups of ORNs (ORNa and ORNb), each tuned to a specific individual pheromone component, converge onto ipsilateral specialist LNs (LNa and LNb) and onto a generalist LN (LNc). All LNs are interconnected via inhibitory synapses. The response of the model is observed at the intermediary LNi and the PN.

Figure 2. The target profile matrix for the conductance-based setup, with the x axis referring to λ_a ⁱ = λ₀×1.3ⁱ, i = 0,…,9, the y axis to λ_b ^j = λ₀×1.3^j, j =  0,…,9 and λ₀ = 0.01 ms⁻¹.

Individual weights are for the target ratios R of 1∶1 (panel A), 1∶3 (B) and 1∶9 (C), where C_i = 2×1.3ⁱ and a = 18, b = 1.25 and c = 0.3. The functional form and parameters of this target response profile were chosen heuristically to ensure that a) highest firing rates on the diagonal are favoured, b) the “punishment” of off-diagonal responses increases gradually with the distance from the diagonal for ratios close to the diagonal and c) responses far off the diagonal are equally and strongly “punished” in the cost function.

Figure 3. The cloud of data points (with cost function <0, n = 159,180) obtained in the simplex annealing of a basic conductance-based model with an ORN∶LN convergence rate of 1000.

The colour of data points corresponds to the cost function value observed (see color bar). In each subfigure, the point with the best cost function is marked with a cross.

Figure 4. The balance of inter-LN connection strengths affects the ratio recognition accuracy.

A) Response profiles in the conductance-based setup. B) Response profiles in the rate-based setup. The three symbols in each panel indicate, in order, the synaptic strengths on LNsp-LNgen, LNsp-LNsp and LNgen-LNsp connections, where “_” is the value for that connection found in the annealing optimisation (Table 1), and “o” is that value times 1.3 (A) or 1.5 (B). The x- and y-axes represent the concentration of individual components in the blend as the log of the Poisson firing rate of ORNs; the colour code of the squares shows the SDF (spike-density function) (A) and the average spiking rate (B), see respective colour bars. ORN-LN convergence rate used was 1000.

Figure 5. Percentage of LNc responses as a function of the ratio g _ORN-LNsp/g _ORN-LNgen.

A–D, ORN∶LN convergence rates of 100, 200, 500 and 1000. The descending lines in each panel represent the percentage of responses to the 1∶1 ratio where LNc spikes first (true positives for 1∶1); ascending lines, the percentage of responses where an LNsp (specifically, LNb) fired first (true positives for non-1∶1 ratios immediately adjacent to the target 1∶1 ratio). The colours correspond to low (red), medium (green) and high (blue) pheromone blend concentrations. Note that there is no value of g _ORN-LNsp/g _ORN-LNgen where both true positives are high simultaneously.

Figure 6. Response profiles for the population models.

The grey scale plots show the spike density function of the PN in response to the different input frequencies in the stacked arrangement (A) and the grouped arrangement (B). These are the best outcomes of a total of 120 trials.Figure 7. Per-stimulus pair decision latencies (in ms) observed at the individual LNs, averaged over 120 trials (A, stacked arrangement, B, grouped arrangement).

Figure 7. Decision latencies of LNs.

The grey scale plots show the decision latency (in ms) per stimulus pair observed at the individual LNs, averaged over 120 trials. A) stacked arrangement. B) grouped arrangement.

Figure 8. Correlation of average per-trial PN latency and the cost function in the extended models.

(A, stacked arrangement, B, grouped arrangement).