Figure 7. Diverse dynamics in fronto-parietal cortex could act as a temporal basis set for evidence accumulation.

(A) Pulse kernels for neurons in FOF, PPC and mV2 with positive-going responses to evidence. Periods when the response was statistically significant are colored in red. Waveforms were normalized to the magnitude of the peak response of the cell and sorted by the time of the peak. Periods when the response was not significant were set to zero (colored in black). (B) Schematic of the architecture of the neural network used to evaluate whether impulse response functions could form a basis set for evidence accumulation. Network output is a weighted sum of the deconvolved impulse response functions of each neuron. The weights for each neuron (W_i) were adjusted using gradient descent to minimize the distance between the network output and the target function. The target functions were constructed using predictions of the time course of the accumulator value, a, derived from a drift diffusion based behavioral model (Brunton et al 2013). The time course of the target function was defined by the function da=Fdt+λadt, in which F is the timing of the flashes on the preferred side and λ is a leak parameter that was fit to the behavioral data. (C) Examples of network output and target functions for λ = -1.7 (left panel), λ = 0.006 (right panel). (D) Performance of a neural network trained against a range of target functions λ values ranged from -1.7 to 0.5 which is the range observed in rats in our study. Network performance was quantified by the variance explained (r²) between the trained network output and the target function for λ = -1.7 through 0.5. (E) Schematic indicating two proposed models for the generation of diverse temporal responses in fronto-parietal cortex: delay lines (left panel) and iterative convolution (right panel). (F) Examples of the waveforms of seven successive simulated neurons in a chain shown for each model. For the iterative convolution model, (purple; middle panel), the waveform of the ith neuron was produced by convolving the waveform of i-1th neuron with the waveform of the first neuron in the chain. For the delay line model (blue; lower panel), the waveform of each neuron was produced by adding a 100ms delay to the response of the previous neuron’s waveform. Waveforms were then convolved with the GCaMP6f kernel to allow direct comparison with recorded GCaMP6f signal. (G) Left panel: Schematic of the approach used to quantify the timescale of the impulse response function for each neuron. Right panel: Correlation between impulse response function half-width and peak time across all neurons with significant visual components. Each red dot represents the time course of the visual filter on the preferred side for each neuron. Black line indicates the best fit (least squares) to the data. Purple line represents the prediction of the iterative convolution model and blue line represents the prediction of the delay line model.