Phenomenological models.

<p><b>(a)</b> (Top) Different phenomenological models of a L5 pyramidal cell (left to right): the detailed multi-compartmental simulation; a composite model where the maximum and threshold of the sigmoidal transformation of basal input to spike frequency are defined by tuft input; a multiplicative model which multiplies the independent sigmoidal transformations of basal and tuft output, and an additive model that adds the sigmoidal transformations of basal and tuft output. (Bottom) The output frequencies of the simulation and nonlinear least-squares best-fit models for each of the model types as a function of tuft and basal input. Note that in the composite model, the sigmoid relating tuft input to high-frequency threshold is decreasing while the sigmoid relating tuft input to maximum frequency is increasing, since tuft input acts to lower the threshold and increase the frequency of somatic output. <b>(b)</b> The percentage of variance explained of each of the three phenomenological model types. <b>(c)</b> The parameters of the composite model can be interpreted as defining the sigmoidal transformation of basal input to output frequency, where the maximum (M) and threshold (T) of that transformation is defined by the tuft input. <b>(d)</b> Plotting the maximum (left) and threshold (right) of the nonlinear least-squares fit to the simulation data (curves) agrees with tuft-constant slices of the simulation (open circles). This gives a method for interpreting and deriving the parameters of the phenomenological model. Colors refer to apical dendrite Ca²⁺ conductance amounts, as defined in (b).