Extended Data Fig. 3: Temporal scaling as opposed to shifting provided a better account of temperature’s effect on neural activity.

(a) Top: Simulated spike density functions exhibiting bidirectional and dose-dependent temporal scaling with temperature. Middle: Templates built by warping a control spike density function (thicker black line) in time by scale factors ranging from 0.625 (maximum contraction) to 1.75 (maximum dilation). Note that when applying this method to data, this control response is not the same as the one shown in the top panel, as the two are built using two non-overlapping random sets of control trials. Bottom: Thick lines represent the coefficient of determination (R²) for all scaled templates in the middle panel regressed against each of the target spike density functions shown at the top. We computed this objective function for each neuron-temperature condition pair and took its global maximum as the corresponding temporal scaling factor, highlighted here by the larger markers. Thinner lines and smaller markers depict R² values for a similar regression procedure applied to a series of shifted, as opposed to scaled, templates. (b) Same as (A), except that for artificially temporally shifted responses relative to control (top), temporally shifted templates (middle), and their regression outcomes (bottom). The thinner lines and smaller markers respectively represent the R² curves and maxima resulting from regressing the scaled templates from A (middle) against the shifted targets in B (top). Conversely, the result of regressing shifted templates against scaled targets is plotted in the same manner in (A, bottom). (c) To assess whether the effects of temperature on individual striatal responses were better accounted for by temporal scaling or shifting, we built two separate spiking models in which we either injected one effect or the other. Briefly, we modeled 500 control firing rate functions as gaussian bumps defined over 1.5 s with means spanning the interval from 150 ms to 750 ms (Fig. 1e) and a standard deviation of 50 ms. The amplitudes of the resulting probability density functions were rescaled so that their distribution of mean firing rates matched that of striatal data. Next, we created one additional rate function per neuron per manipulation condition by either shifting or scaling its control response in time. Again, the distribution of generative temporal scaling factors and shifts used was informed by the empirical distributions of these metrics extracted from striatal data. We then generated 150 spike trains of each condition per neuron by sampling spike times from inhomogeneous Poisson point processes with the aforementioned condition-specific responses as their time-dependent rate parameters. From this point on, we proceeded to analyze the resulting surrogate spike data in the exact same way we did for the striatal data, by first averaging trials within condition, generating libraries of templates and then computing temporal scaling factors and shifts. Finally, for each ‘neuron’-condition pair within each model, we stored the R² values corresponding to the best-matching scaled and shifted templates and subtracted the former from the latter to build the distributions shown here at the top (scaling model) and middle (shifting model) panels. Thick solid sigmoidal lines represent the CDFs of each condition’s R² difference. Thin vertical black lines denote control mean differences. Small horizontal colored lines link the respective means of the corresponding manipulation and control distributions. (d) Same as (C), but for striatal data.