Significance of conductances in Hodgkin-Huxley models

Abstract

1. We explore the roles of conductances in Hodgkin-Huxley (HH) models using a method that allows the explicit linking of HH model input-output behavior to parameter values for maximal conductances, voltage shifts, and time constants. The procedure can be used to identify not only the parameter values most critical to supporting a neuronal activity pattern of interest but also the relationships between parameters which may be required, e.g., limited ranges of relative magnitudes. 2. The method is the repeated use of stochastic search to find hundreds or even thousands of different sets of model parameter values that allow a HH model to produce a desired behavior, such as current-frequency transduction, to within a desired tolerance, e.g., frequency match to within 10 Hz. Graphical or other analysis may then be performed to reveal the shape and boundaries of the parameter solution regions that support the desired behavior. 3. The shape of these parameter regions can reveal parameter values and relationships essential to the behavior. For instance, graphical display may reveal covariances between maximal conductance values, or a much wider range of variation in some maximal conductance values than in others. 4. We demonstrate the use of these techniques with simple, representative HH models, primarily that of Connor et al. for crustacean walking leg axons, but also some extensions of the results are explored using the more complex model of McCormick and Huguenard for thalamocortical relay neurons. Both models are single compartment. Behaviors studied include current-to-frequency transduction, the time delay to first action potential in response to current steps, and the timing of action potential occurrences in response to both square-wave current injection and the injection of currents derived from in vitro records of excitatory postsynaptic currents. 5. Using these simple models, we find that relatively general behaviors such as current-frequency (I/F) curves may be supported by very broad, but bounded parameter solution regions, with the shape of the solution regions revealing the relative importance of the maximal conductances of a model in creating the behavior. Furthermore, we find that a focus on increasingly specific behaviors, such as I/F behavior, defined by tolerances of only a few hertz combined with strict requirements for action potential height, inevitably leads to increasingly narrow, and eventually nonphysiologically narrow, regions of acceptable parameter values. 6. We use the Connor et al. model to reproduce the in vitro action potential timing responses of a rat brain stem neuron to various stimuli.(ABSTRACT TRUNCATED AT 400 WORDS)