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Parallel Computational Subunits in Dentate Granule Cells Generate Multiple Place Fields

Figure 2

Input strength encoding with uniform synapses.

(A) The figure shows two neurons (or the same neuron with two different input sets). We calculated the probability of firing (H(U)) given that one of the branches has exactly U synaptic input (e.g., U₁ = U) while inputs of other branches (U₂, U₃, …, U_N) are drawn independently from the input distribution. Second, we calculated the distribution of the maximal input (K(U^*)) given the depolarization of the soma exceeds the firing threshold. (B) Color coded joint probability distribution of the somatic activation and the maximal dendritic input, with the linear integration function. Red is maximum, dark blue is zero. The color-code emphasizes low probability events and it is not linear. The horizontal line is the firing threshold; the yellow line shows the conditional expectation of a_s given U^*. If dendrites were independent high and low U^* values could be separated by a somatic threshold of action potential generation. (C–D) Dendritic independence with linear (C) and quadratic (D) integration functions. Left axis, red: K(U^*), the distribution of the maximal dendritic inputs during firing. Right axis, blue: the H(U) function, which is the probability of firing given that one of the dendrites has U total input. The probability of triggering output by a single branch is low (H(U)<0.25) even with reasonably large input (as revealed by the low H(U) values at the probability mass of K(U^*)). This indicates that a single dendritic subunit is unable to reliably activate the neuron with these integration functions. Background light gray is the distribution of U while dark grey shows the distribution of U^*. Parameters: R = 0.01, N = 30.

doi: https://doi.org/10.1371/journal.pcbi.1000500.g002