Figure 1. Effects of temperature in a model pyloric network.

(A) Schematic diagram of the model pyloric network in Prinz et al., 2004. The three groups interact via seven inhibitory chemical synapses. The red synapses are cholinergic from the PD neurons and all others are glutamatergic. The traces below show a representative solution that exhibits a triphasic rhythm: the activity is approximately periodic and the cells burst in a specific sequence: $PD$-$LP$-$PY$. (B) Activity of a temperature robust model network at 10°C - 25°C. As temperature increases the frequency of the rhythm increases but the duty cycle of the cells (the burst duration in units of the period) remains approximately constant. (C) Top: average burst frequency of each cell over temperature (values are nearly identical so dots overlap). Middle: average duty cycle of each cell (cell type indicated in colors). Bottom: average phases of the cycle at which bursts begin and terminate using the start of the PD burst as reference (indicated by label $B_{REF}$ in magenta). As temperature increases these phases remain approximately constant. The panels show average values over 30 s for 16 values of temperature between 10°C - 25°C.

Figure 1—figure supplement 1. Equivalent phenotype for different sets of maximal conductances and temperature sensitivities.

For each set of maximal conductances we studied, it was possible to find multiple sets of $Q_{10}$ that yielded temperature compensated solutions. (A) Burst frequency (top), duty cycle (middle), and phases (bottom) over the working temperature range for three different models (indicated in colors). (B) Values of the maximal conductances (in $\mu S$) and $Q_{10}$ for each model indicated by symbols (triangle, square, rectangle).

Figure 1—figure supplement 2. Spiking patterns during temperature ramps.

The spiking patterns of the cells exhibit interesting dependencies with temperature. (A) Schematic representation of the temperature ramp used in these simulations. Temperature was increased linearly between 10°C and 25°C over 60 min. (B) ISI of each cell over temperature (y-axis is logarithmic). The spiking patterns consist of one large ISI corresponding to the inter-burst interval (≥ 200 ms) and several smaller values produced by spikes within bursts. There are ranges of temperature over which the ISI takes almost the same values and the patterns result in nearly identical sets of points, and there are ranges where there is more variability. (C) Instantaneous frequency of each burst of the $PD$ cell. (D) Duty cycle of each burst in each cell. While the duty cycle remains approximately constant on average, there are ranges of temperature for which the duty cycle alternates between two or more values (pink shaded box in $PD$. (E) Traces of the $PD$ cell at 10°C (blue box) and 20°C (pink box). The brown filled and empty triangles indicate the prescence/abscence of a last spike in the burst which results in different duty cycle values for consecutive bursts.

Figure 1—figure supplement 3. Duty cycle distributions of all models.

Variability across models in duty cycle distributions of the LP cell as a function of temperature, during the same temperature ramp as in Figure 3. The precise shape of these patterns depends on the values of the maximal conductances and temperature sensitivities. Note that at all temperatures, the duty cycle of each burst remains close to the average duty cycle across temperatures (red dashed line), and thus is temperature invariant.