Determining the contributions of divisive and subtractive feedback in the Hodgkin-Huxley model

Abstract

The Hodgkin-Huxley (HH) model is the basis for numerous neural models. There are two negative feedback processes in the HH model that regulate rhythmic spiking. The first is an outward current with an activation variable n that has an opposite influence to the excitatory inward current and therefore provides subtractive negative feedback. The other is the inactivation of an inward current with an inactivation variable h that reduces the amount of positive feedback and therefore provides divisive feedback. Rhythmic spiking can be obtained with either negative feedback process, so we ask what is gained by having two feedback processes. We also ask how the different negative feedback processes contribute to spiking. We show that having two negative feedback processes makes the HH model more robust to changes in applied currents and conductance densities than models that possess only one negative feedback variable. We also show that the contributions made by the subtractive and divisive feedback variables are not static, but depend on time scales and conductance values. In particular, they contribute differently to the dynamics in Type I versus Type II neurons.

Phasic Firing and Coincidence Detection by Subthreshold Negative Feedback: Divisive or Subtractive or, Better, Both

“…To counteract a strong non-inactivating inward current with a strong outward current constrains the allowable channel density. However, controlling the effect of autocatalysis by a divisive mechanism, makes the system less sensitive and more flexible to changes in channel density (Sengül et al, 2014 ). Spiking, crucial for neuronal communication and computation, needs to be preserved with respect to variations in channel density.…”

Analysis of parameter changes of a neuronal network model using transfer entropy

“…As a result, input coming to Neuron 2 from Neuron 1 dominates the information flow and causes the change of the direction from 1-to-2 to 2-to-1 ( Figure 4A). The characteristic of the TE curves for varying 2 does not cross each other meaning that the information flow does not change direction according to the strength of the subtractive feedback due to K + current of Neuron 2 [25]. To be able to change the information flow in this coupled system, we should support Neuron 2, but increasing 2 will do the inverse and the phase locked system is not affected as illustrated in Figure 5C&5D.…”

Quantitative roles of ion channel dynamics on ventricular action potential

“…Furthermore, quantitative approaches are needed to answer the question of “how much” each parameter affects the change of membrane potential. Quantitative analysis methods including dominant scale analysis [ 23 , 24 ], lead potential analysis [ 25 ], and relative contribution analysis [ 26 ] focus on understanding the role of each component in a complex cell model. Dominant scale analysis calculates which components are dominant in a specific time interval of AP by using an equilibrium membrane potential value.…”