(a,b,c,d) Examples of 1 second DC current injections into the dendrites of a L5 pyramidal neuron in V1 in experiments and computer simulations. Red traces show dendritic and black traces show somatic membrane potentials. Insets show details of individual action potentials and dendritic responses. (a,b) Membrane response to dendritic current injections at 135 μm from the soma show somatic spiking with relatively constant ISIs giving rise to bAPs in the dendrite. (c,d) Membrane response to dendritic current injections 442 μm from the soma show burst firing at the soma and dendritic electrogenesis that precedes action potential firing at the soma. Like in experiments (a,c), in simulations (b,d), injections close to the soma give rise to APs at a regular frequency that backpropagate, while injections farther into the apical dendrite give rise to large dendritic potentials that precede bursts of APs. (e) Dendritic potential width (illustrated as red dotted lines in (a,c)) and ISI coefficient of variations as a function of distance of the dendritic current injection from the soma in experiment and simulation. Filled circles corresponds to cases where dendritic spikes precede the somatic spike (e.g. inset c,d), while open circles correspond to cases where somatic spikes precede the dendritic event (e.g. inset a,b). Red and blue circles denote experiment and simulation results respectively. Lines are linear fits. (f) Comparison of the DP width and coefficient of variation of the ISIs of cases where somatic spiking preceded dendritic events (open bars) and where dendritic electrogenesis preceded somatic spiking (filled bars). Experimental data is in red and simulation data is in blue. *, **, *** Indicate significant differences between the two bars.

(a) The somatic (black) and dendritic (red) response to three short current pulses at the soma at a slow frequency (70 Hz). Analysis of experimental and simulation data are given in rows 1 and 2 respectively. (b) As in (a) except for three pulses above the critical frequency (100 Hz). Note the slow dendritic signal following the last somatic spike as well as the elongated somatic afterdepolarization (ADP) compared to (a). (c) Ten somatic responses to increasing frequencies of 3 short DC current injections at the soma, aligned at the final AP. Note the sharp nonlinear jump in ADP shape (broken line) (d) ADP size shown at the time of the dotted line in (c) as a function of frequency. The critical frequency is defined as the inflection point of the sigmoidal fit, and ADP size is defined as the difference between the two plateaus. The inset in d1 shows a histogram of the critical frequency for all 66 cells. Simulation results of the critical frequency analysis are shown in the bottom row.

(a) 100 tuft and 175 basal NMDA/AMPA synapses are distributed randomly across the apical tuft and basal dendrites of a multi-compartmental L5 pyramidal neuron model. All synapses are randomly and uniformly elicited in time across 100 ms. In the following, somatic traces are in black and dendritic (location shown by the red arrow in a), are in red. (b) Simultaneous tuft and basal inputs triggers a burst of somatic APs and a dendritic Ca²⁺ spike, while (c) basal inputs alone evoke only a single somatic spike. (d) Apical tuft inputs alone do not evoke somatic spiking. (e) Reducing Ca²⁺ channel conductance by 50% during tuft and basal input gives rise to a single somatic spike. (f) When applying a 200 pA hyperpolarizing DC current to the soma, the subthreshold response of the tuft and basal inputs are similar to the case with Ca²⁺ conductances reduced shown in (g), even though the suprathreshold (b,c) cases are remarkably different.

(a) The output frequency of the L5 simulated cell over a wide range of tuft and basal inputs into a control cell (left), a cell with half (middle), and a quarter (right) of the Ca²⁺ conductance along the apical tuft. In each plot we systematically vary the number of basal and tuft inputs and report the output frequency at the soma in color. Open red circles correspond to . (b) The modulation of the input-output relationship as function of basal and apical tuft input. Different lines correspond to different amounts of tuft input (from light to dark, 0–200 tuft inputs).

(a) (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) The percentage of variance explained of each of the three phenomenological model types. (c) 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. (d) 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).

(a) Four mechanisms are compared (from left to right): composite sigmoid, purely multiplicative where the amount of tuft and basal input are simply multiplied to arrive at the final output, purely additive, where the amount of tuft and basal input are simply added to arrive at the final output, and single-sigmoid, where either the tuft or the basal input is input into a sigmoid function to arrive at the final output. (b) The input into these mechanisms is given by a von Mises distribution (circular analog of a normal distribution) with varying compression parameter (k) and the preferred orientation always set to 0 radians. An example of tuft and basal input distributions as a function of stimulus orientation is shown with tuft input k = 1.0 and basal input k = 0.5. (c) The output of the different mechanisms with the inputs shown in (b). Colors indicate the different mechanisms as defined in (a). The single-sigmoid mechanism acts on either the tuft (solid purple) or basal (dashed purple) inputs. (d) The circular variance of the output of the different mechanisms as a function of the width of inputs. In this plot, both tuft and basal inputs have the same k, given on the x-axis. The circular variance of the input is shown in black. Note the additive mechanism has the same output variance as the input. At all parameters of the input tested, the composite sigmoid mechanism features the tightest tuning.