Bryce Chung

J Rubin

R Clewley

RH Clewley

Robert Clewley

S Druckmann

BMC Neuroscience

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POSTER PRESENTATION Open AccessGeometric analysis of soft thresholds in actionpotential initiation and the consequences forunderstanding phase response curves and modeltuningRobert Clewley1,2*, Bryce Chung1From Twenty First Annual Computational Neuroscience Meeting: CNS*2012Decatur, GA, USA. 21-26 July 2012Recent mathematical and computational work on thespace-clamped Hodgkin-Huxley (H-H) model of neuralexcitability identifies major dynamic features of thechanging nullclines in 2D phase plane projections dur-ing action potential (AP) initiation [1,2]. Such analysisprovides novel mechanistic and geometric understand-ing (in terms of interplay between variables and cur-rents) of the “soft threshold” dynamics. We performvisualization of the nullcline dynamics around threshold,and characterize important geometric properties via“dominant scale analysis” [3], which avoids the need tomake asymptotic approximations. In particular, we ana-lyze the transient dynamics during the passage throughthe ghost of a saddle-node bifurcation in the (V, m)phase-plane projection of a local 3D approximation tothe 4D H-H equations (where sodium inactivation h isheld constant). Linear analysis of the moving V-nullclinein these projections indicates that a necessary conditionfor AP initiation is the eventual holding of the followinginequalities in the neighborhood of the ghost of the sad-dle node:     V V VmmVnn V n        0 0 and ,where the asymptotic steady state voltage V∞(m, n) isfor constant h. Given that  Vm 0 and   Vn 0 in thisneighborhood, the first inequality can be interpreted assaying that the fast sodium current must dominate theeffect of the growing delayed rectifier potassium current,but not in such a way that V becomes large too rapidly.We find that the curvature of the nullclines in thisregion is responsible for the truth of this condition (forstandard parameter values used for Type I and II modesof H-H excitability).We compare different parameter regimes for periodicand transient trajectories using our analysis. Under mildvariation of parameters and initial conditions, andexcept in pathological circumstances that are related tothe generation of sub-threshold oscillations and canards(e.g., see ref. [2]), we can predict the onset of AP initia-tion and its timing as the result of parameter changes orsmall voltage perturbations. This leads to insight aboutthe origin of phase response curve shape in Type I vs.Type II neural excitability. Geometric features of thenullclines are measured during this analysis using PyD-STool [4], and the curvature conditions can be used toguide objective function choice for parameter tuningtasks where AP generation is found to be incomplete orimperfect (e.g., compare refs. [5,6]). This has applica-tions in situations where APs are pathologically changeddue to genetic channel defects (especially in potassiumchannels), or where unwanted depolarization blockoccurs.AcknowledgementThis research is supported in part by NSF EMT/BSSE award #0829742.Author details1Neuroscience Institute, Georgia State University, Atlanta, GA 30303, USA.2Department of Mathematics and Statistics, Georgia State University, Atlanta,GA 30303, USA.* Correspondence: rclewley@gsu.edu1Neuroscience Institute, Georgia State University, Atlanta, GA 30303, USAFull list of author information is available at the end of the articleClewley and Chung BMC Neuroscience 2012, 13(Suppl 1):P165http://www.biomedcentral.com/1471-2202/13/S1/P165© 2012 Clewley and Chung; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the CreativeCommons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, andreproduction in any medium, provided the original work is properly cited.Published: 16 July 2012References1. Clewley R: Encoding the Fine-Structured Mechanism of Action PotentialDynamics with Qualitative Motifs. J Comput Neurosci 2011, 30(2):391-408.2. Rubin J, Wechselberger M: Giant squid-hidden canard: the 3D geometryof the Hodgkin-Huxley model. Biol Cybern 2007, 97:5-32.3. Clewley R, Soto-Trevino C, Nadim F: Dominant ionic mechanisms exploredin the transition between spiking and bursting using local low-dimensional reductions of a biophysically realistic model neuron. JComput Neurosci 2009, 26(1):75-90.4. Clewley RH, Sherwood WE, LaMar MD, Guckenheimer JM: PyDSTool, asoftware environment for dynamical systems modeling. 2007 [http://pydstool.sf.net].5. Druckmann S, Banitt Y, Gidon A, Schurmann F, Markram H, Segev I: A NovelMultiple Objective Optimization Framework for ConstrainingConductance-Based Neuron Models by Experimental Data. Frontiers inNeuroscience 2007, 1(1):7-18.6. Clewley R, Dobric M: A qualitative optimization technique for biophysicalneuron models with many parameters. BMC Neuroscience 2010, 11(Suppl1):P39, doi:10.1186/1471-2202-11-S1-P39.doi:10.1186/1471-2202-13-S1-P165Cite this article as: Clewley and Chung: Geometric analysis of softthresholds in action potential initiation and the consequences forunderstanding phase response curves and model tuning. BMCNeuroscience 2012 13(Suppl 1):P165.Submit your next manuscript to BioMed Centraland take full advantage of: • Convenient online submission• Thorough peer review• No space constraints or color figure charges• Immediate publication on acceptance• Inclusion in PubMed, CAS, Scopus and Google Scholar• Research which is freely available for redistributionSubmit your manuscript at www.biomedcentral.com/submitClewley and Chung BMC Neuroscience 2012, 13(Suppl 1):P165http://www.biomedcentral.com/1471-2202/13/S1/P165Page 2 of 2

Geometric analysis of soft thresholds in action potential initiation and the consequences for understanding phase response curves and model tuning

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Geometric analysis of soft thresholds in action potential initiation and the consequences for understanding phase response curves and model tuning

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