Dendritic excitability modulates dendritic information processing in a purkinje cell model

Abstract

Using an electrophysiological compartmental model of a Purkinje cell we quantified the contribution of individual active dendritic currents to processing of synaptic activity from granule cells. We used mutual information as a measure to quantify the information from the total excitatory input current (I(Glu)) encoded in each dendritic current. In this context, each active current was considered an information channel. Our analyses showed that most of the information was encoded by the calcium (I(CaP)) and calcium activated potassium (I(Kc)) currents. Mutual information between I(Glu) and I(CaP) and I(Kc) was sensitive to different levels of excitatory and inhibitory synaptic activity that, at the same time, resulted in the same firing rate at the soma. Since dendritic excitability could be a mechanism to regulate information processing in neurons we quantified the changes in mutual information between I(Glu) and all Purkinje cell currents as a function of the density of dendritic Ca (g(CaP)) and Kca (g(Kc)) conductances. We extended our analysis to determine the window of temporal integration of I(Glu) by I(CaP) and I(Kc) as a function of channel density and synaptic activity. The window of information integration has a stronger dependence on increasing values of g(Kc) than on g(CaP), but at high levels of synaptic stimulation information integration is reduced to a few milliseconds. Overall, our results show that different dendritic conductances differentially encode synaptic activity and that dendritic excitability and the level of synaptic activity regulate the flow of information in dendrites.

Keywords: cerebellum; compartmental modeling; dendritic computation; dendritic conductances; firing rate; information theory; modulatory synapses; synaptic plasticity.

Figure 1

(A) Morphology of the Purkinje cell model. (B) Schematic representation of the channel types incorporated into the Purkinje cell model.

Figure 2

Probability distribution of synaptic and dendritic currents. (A) The Purkinje cell model was stimulated with pairs of excitatory and inhibitory synaptic activity. The total excitatory synaptic current (I_Glu) remained practically constant for all the combinations of excitatory and inhibitory activity (activity in Hz). (B) Probability distribution of the I_CaP in response to the different combinations of excitatory and inhibitory activity in (A). (C) Probability distribution of I_Kc for the same simulations in (B). (D–F) The probability distribution of the other dendritic currents remained practically independent of level of synaptic activity. (G) The average firing rate at the soma remains constant for all combination of synaptic activity. (H) The Purkinje cell inter-spike distributions for each combination of synaptic activity in (A) have the same mean and standard deviation.

Figure 3

Calculating the amount of excitatory synaptic information being carried by dendritic currents. (A) Entropy of the I_Glu, I_CaP, and I_Kc. (B) Conditional entropy of H(I_CaP|I_Glu) and H(I_Kc|I_Glu). (C) Mutual information for I(I_CaP,I_Glu) and I(I_Kc, I_Glu) calculated from (A) and (B); e.g. I(I_CaP,I_Glu) = H(I_CaP)−H(I_CaP|I_Glu). B and C were calculated with a 1 ms time difference between I_Glu and the dendritic currents. All calculations were bias corrected using the Panzeri and Treves method.

Figure 4

Cross-correlation analysis of total synaptic excitatory input and dendritic currents. The figures show the auto-correlation of the synaptic current (I_Glu, blue), and the cross-correlation of I_Glu with I_CaP (green), and I_Kc (red). We repeated this analysis for all the combinations of synaptic activity (A–D).

Figure 5

Dependence of mutual information to previous activity. (A) I[I_CaP(t),I_Glu(t−Δt)] for Δt between 0–1 s. (B) I[I_Kc(t),I_Glu(t−Δt)] for Δt between 0–1 s. The different traces correspond to different combinations of synaptic activity. Mutual information was bias corrected using the Panzeri and Treves method.

Figure 6

Somatic firing rate varies as a function of dendritic excitability. (A) Firing rate as a function of homogenously changing the conductance of CaP (g_CaP). (B) Similar to A changing the conductance of Kc (g_Kc). The vertical lines correspond to the values of the control simulation.

Figure 7

Excitatory synaptic current information content in dendritic currents as a function of dendritic excitability. (A) Calculations H(I_CaP), H(I_CaP|I_Glu) and I(I_CaP,I_Glu) as a function of g_CaP. (B) Similar to (A) but with respect to I_Kc. (C,D) Identical calculations as (A) and (B) but varying g_Kc. Mutual information was bas corrected using the Panzeri and Treves method.

Figure 8

Excitatory synaptic current information content in dendritic currents as a function of dendritic excitability and time lags. (A) I[I_CaP(t),I_Glu(t−Δt)] for Δt from 0–1 s and varying g_CaP. (B) As in (A) for I_Kc. (C,D) Identical calculations as in (A–B) but varying g_Kc. The different panels correspond to different combinations of synaptic activity. Mutual information was bias corrected using the Panzeri and Treves method.