Geometric analysis of soft thresholds in action potential initiation and the consequences for understanding phase response curves and model tuning
© Clewley and Chung; licensee BioMed Central Ltd. 2012
Published: 16 July 2012
where the asymptotic steady state voltage V ∞ (m, n) is for constant h. Given that and in this neighborhood, the first inequality can be interpreted as saying that the fast sodium current must dominate the effect of the growing delayed rectifier potassium current, but not in such a way that becomes large too rapidly. We find that the curvature of the nullclines in this region is responsible for the truth of this condition (for standard parameter values used for Type I and II modes of H-H excitability).
We compare different parameter regimes for periodic and transient trajectories using our analysis. Under mild variation of parameters and initial conditions, and except in pathological circumstances that are related to the generation of sub-threshold oscillations and canards (e.g., see ref. ), we can predict the onset of AP initiation and its timing as the result of parameter changes or small voltage perturbations. This leads to insight about the origin of phase response curve shape in Type I vs. Type II neural excitability. Geometric features of the nullclines are measured during this analysis using PyDSTool , and the curvature conditions can be used to guide objective function choice for parameter tuning tasks where AP generation is found to be incomplete or imperfect (e.g., compare refs. [5, 6]). This has applications in situations where APs are pathologically changed due to genetic channel defects (especially in potassium channels), or where unwanted depolarization block occurs.
This research is supported in part by NSF EMT/BSSE award #0829742.
- Clewley R: Encoding the Fine-Structured Mechanism of Action Potential Dynamics with Qualitative Motifs. J Comput Neurosci. 2011, 30 (2): 391-408. 10.1007/s10827-010-0267-y.View ArticlePubMedGoogle Scholar
- Rubin J, Wechselberger M: Giant squid-hidden canard: the 3D geometry of the Hodgkin-Huxley model. Biol Cybern. 2007, 97: 5-32. 10.1007/s00422-007-0153-5.View ArticlePubMedGoogle Scholar
- Clewley R, Soto-Trevino C, Nadim F: Dominant ionic mechanisms explored in the transition between spiking and bursting using local low-dimensional reductions of a biophysically realistic model neuron. J Comput Neurosci. 2009, 26 (1): 75-90. 10.1007/s10827-008-0099-1.PubMed CentralView ArticlePubMedGoogle Scholar
- Clewley RH, Sherwood WE, LaMar MD, Guckenheimer JM: PyDSTool, a software environment for dynamical systems modeling. 2007, [http://pydstool.sf.net]Google Scholar
- Druckmann S, Banitt Y, Gidon A, Schurmann F, Markram H, Segev I: A Novel Multiple Objective Optimization Framework for Constraining Conductance-Based Neuron Models by Experimental Data. Frontiers in Neuroscience. 2007, 1 (1): 7-18. 10.3389/neuro.01.1.1.001.2007.PubMed CentralView ArticlePubMedGoogle Scholar
- Clewley R, Dobric M: A qualitative optimization technique for biophysical neuron models with many parameters. BMC Neuroscience. 2010, 11 (Suppl 1): P39-10.1186/1471-2202-11-S1-P39. doi:10.1186/1471-2202-11-S1-P39PubMed CentralView ArticleGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.