Origin of heterogeneous spiking patterns from continuously distributed ion channel densities: a computational study in spinal dorsal horn neurons

Abstract

Key points Distinct spiking patterns may arise from qualitative differences in ion channel expression (i.e. when different neurons express distinct ion channels) and/or when quantitative differences in expression levels qualitatively alter the spike generation process.We hypothesized that spiking patterns in neurons of the superficial dorsal horn (SDH) of spinal cord reflect both mechanisms.We reproduced SDH neuron spiking patterns by varying densities of KV1‐ and A‐type potassium conductances. Plotting the spiking patterns that emerge from different density combinations revealed spiking‐pattern regions separated by boundaries (bifurcations).This map suggests that certain spiking pattern combinations occur when the distribution of potassium channel densities straddle boundaries, whereas other spiking patterns reflect distinct patterns of ion channel expression. The former mechanism may explain why certain spiking patterns co‐occur in genetically identified neuron types.We also present algorithms to predict spiking pattern proportions from ion channel density distributions, and vice versa. AbstractNeurons are often classified by spiking pattern. Yet, some neurons exhibit distinct patterns under subtly different test conditions, which suggests that they operate near an abrupt transition, or bifurcation. A set of such neurons may exhibit heterogeneous spiking patterns not because of qualitative differences in which ion channels they express, but rather because quantitative differences in expression levels cause neurons to operate on opposite sides of a bifurcation. Neurons in the spinal dorsal horn, for example, respond to somatic current injection with patterns that include tonic, single, gap, delayed and reluctant spiking. It is unclear whether these patterns reflect five cell populations (defined by distinct ion channel expression patterns), heterogeneity within a single population, or some combination thereof. We reproduced all five spiking patterns in a computational model by varying the densities of a low‐threshold (KV1‐type) potassium conductance and an inactivating (A‐type) potassium conductance and found that single, gap, delayed and reluctant spiking arise when the joint probability distribution of those channel densities spans two intersecting bifurcations that divide the parameter space into quadrants, each associated with a different spiking pattern. Tonic spiking likely arises from a separate distribution of potassium channel densities. These results argue in favour of two cell populations, one characterized by tonic spiking and the other by heterogeneous spiking patterns. We present algorithms to predict spiking pattern proportions based on ion channel density distributions and, conversely, to estimate ion channel density distributions based on spiking pattern proportions. The implications for classifying cells based on spiking pattern are discussed.

Recent advances in our understanding of the organization of dorsal horn neuron populations and their contribution to cutaneous mechanical allodynia

“…However, in addition to be tonic, phasic, delayed or single spike, lamina II neurons also include gap (a.k.a. irregular)-which have a delay between two spikes that is greater than 1.5 times the delay between two previous or two following spikes, and reluctant (which do not spike upon depolarization current) neurons (Balachandar and Prescott 2018).…”

“…Most importantly, these transcriptomic analyses provide putative markers for cell clusters located in the superficial, but also deep DH, and may reveal the as-yet unknown chemical phenotype of several superficial neurons and most of deep DH neurons. Additionally, it has recently been shown that ion channel density distributions, and particularly densities of K V 1-and A-type potassium conductances, can predict neuronal firing pattern in the DH (Balachandar and Prescott 2018). It will be thus very interesting to see if transcriptomic expression of potassium conductance-related channels from the newly identified cell clusters can predict the firing pattern properties of previously recorded DH neurons, in physiological conditions but also during persistent pain states.…”

Excitability of Rat Superficial Dorsal Horn Neurons Following a Neonatal Immune Challenge

“…Delayed firing, however, was rarely observed in our sample of neurons. This is best explained by reference to a recent computational study showing that the density and relative ratios of potassium channels can alter the phenotypical AP discharge pattern of SDH neurons ( 40 , 41 ). Given our findings of altered channel expression during development, it is possible that the critical level of I Ar channels required for delayed firing has not yet been reached and may continue to rise during the subsequent postnatal period.…”

Visualization of the relative contributions of conductances in neuronal models with similar behavior and different conductance densities

“…Because of the intrinsic variability, canonical models that capture the mean behavior of a set of observations are not sufficient to address these issues (Golowasch et al, 2002;Balachandar and Prescott, 2018). In order to incorporate intrinsic biophysical variability Prinz et al (2004) introduced an ensemble modeling approach.…”