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)

Quantification of Short Term Signaling by the Epidermal Growth Factor Receptor

“…A model by itself is not an objective "truth," but it can be used to falsify a specific hypothesis. Therefore, good modeling practice requires a systematic exploration of parameter variance ranges compatible with experimentally observed behavior (96).…”

Degeneracy in hippocampal physiology and plasticity

“…Therefore, a widely employed alternate interpretation (Foster et al, 1993;Goldman et al, 2001;Marder, 2011;Marder and Goaillard, 2006;Marder et al, 2015;Marder and Taylor, 2011;Prinz et al, 2004;Narayanan, 2012a, 2014;Srikanth and Narayanan, 2015;Taylor et al, 2009) is where degeneracy is assessed as the ability of different structural components to elicit quantitatively similar functional measurements. With reference to our chosen example, this would translate to assessing degeneracy as the ability to achieve a specific range of values of resonance frequency with disparate combinations of parameters (Fig.…”

“…First, cellular-or network-scale functions could robustly emerge with disparate combinations of molecular-or cellular-scale parameters, with experimentally demonstrated variability (Foster et al, 1993;Golowasch et al, 2002;Golowasch and Marder, 1992;Katz, 2016;MacLean et al, 2005;Marder, 2011;Marder and Goaillard, 2006;Prinz et al, 2004;Narayanan, 2012a, 2014;Schulz et al, 2006;Schulz et al, 2007;Taylor et al, 2009). These observations suggest that precise homeostatic balance at a lower scale (e.g., ion channels expressed to exact conductance values) is not essential for maintaining functional homeostasis at a higher scale.…”

“…The advantages of biological variability, degeneracy and complexity have been widely studied and recognized in simple nervous systems (Edelman and Gally, 2001;Foster et al, 1993;Gjorgjieva et al, 2016;Goldman et al, 2001;Katz, 2016;Marder, 2011;Marder and Goaillard, 2006;Marder et al, 2015;Marder and Taylor, 2011;Prinz et al, 2004;Taylor et al, 2009). However, this recognition has been very limited in the mammalian neuroscience literature, where the focus is predominantly on explicitly assigning (or implicitly assuming) unique causal mechanistic relationships between constituent components and emergent functions.…”

“…1B) through interactions among disparate parametric combinations in a lower scale (Edelman and Gally, 2001;Foster et al, 1993;Gjorgjieva et al, 2016;Goldman et al, 2001;Marder, 2011;Marder and Goaillard, 2006;Marder et al, 2015;Marder and Taylor, 2011; parameters (at the molecular scale) to achieve activity homeostasis (Gjorgjieva et al, 2016;Hengen et al, 2016;Nelson and Turrigiano, 2008;Turrigiano, 2011;Turrigiano, 1999Turrigiano, , 2008Turrigiano and Nelson, 2004). Thus, under the degeneracy framework, different uncorrelated clusters in the lower-scale parametric space could result in similar, if not identical, functional outcomes in the higher-scale measurement space, thereby suggesting a many-to-one relationship between the lower-and higher-scale manifolds (Edelman and Gally, 2001;Jazayeri and Afraz, 2017;Krakauer et al, 2017).…”