Analysis of family structures reveals robustness or sensitivity of bursting activity to parameter variations in a half-center oscillator (HCO) model

Abstract

The underlying mechanisms that support robustness in neuronal networks are as yet unknown. However, recent studies provide evidence that neuronal networks are robust to natural variations, modulation, and environmental perturbations of parameters such as maximal conductances of intrinsic membrane and synaptic currents. Here we sought a method for assessing robustness, which might easily be applied to large brute-force databases of model instances. Starting with groups of instances with appropriate activity (e.g. tonic spiking), our method classifies instances into much smaller sub-groups, called families, in which all members vary only by the one parameter that defines the family. By analyzing the structures of families, we developed measures of robustness for activity type. Then, we applied these measures to our previously developed model database, HCO-db, of a two neuron half-center oscillator (HCO), a neuronal microcircuit from the leech heartbeat central pattern generator where the appropriate activity type is alternating bursting. In HCO-db the maximal conductances of 5 intrinsic and two synaptic currents were varied over 8 values (Leak reversal potential also varied, 5 values). We focused on how variations of particular conductance parameters maintain normal alternating bursting activity while still allowing for functional modulation of period and spike frequency. We explored the trade-off between robustness of activity type and desirable change in activity characteristics when intrinsic conductances are altered and identified the hyperpolarization-activated (h) current as an ideal target for modulation. We also identified ensembles of model instances that closely approximate physiological activity and can be used in future modeling studies.

Significance Statement: Robustness is an attribute of living systems and mathematical models that describe them. We developed a method for assessing robustness of activity types (e.g., bursting), which can be applied to brute-force databases of neuronal model instances in which biologically relevant parameters are varied and where sensitivity analyses are conceptually and practically difficult to apply. By organizing all instances with appropriate activity into families, in which all members vary only by the one parameter defining the family, we developed measures of robustness for activity type based on family structure and address a fundamental challenge to robustness, modulation, which by changing parameters may alter activity type. The method determines which parameters predictably alter activity characteristics, (e.g., burst period), without changing activity type.