1Department of Neuroscience, Baylor College of Medicine, Houston, USA 2Department of Computation Applied Mathematics & Operations Research, Rice University, Houston, USA *Email:gabbiani@bcm.edu
Introduction
Much work has been devoted to fitting the biophysical properties of neurons in compartmental models with Hodgkin-Huxley type conductances. Yet, little is known on how reliable model parameters are, and their possible degeneracy. For example, when characterizing a membrane conductance through voltage-clamp (VC) experiments, one would like to know if the data will constrain the parameters and how reliable their estimates are. Similarly, when studying the responses of a neuron with multiple conductances in current clamp (CC), how robust is the model to changes in peak conductances. Such degeneracy is linked to biological robustness [1] and is key in understanding the constraints posed by conductance distributions on dendritic computation [2].
Methods A one-compartment model with Hodgkin-Huxley (HH) type conductances was used. We studied synthetic and experimental VC data of the H-type conductance (gH) that is widely expressed in neuronal dendrites. We also studied the original HH model in VC and CC. Finally, we considered a stomatogastric ganglion (STG) neuron model in CC. The ordinary differential equation solutions, parameters, and their sensitivities were simultaneously estimated using collocation methods and automatic differentiation. This allowed to solve the non-linear least squares (NLLS) problem associated with each model. Parameter degeneracy manifold iterative tracing was performed based on the singular value decomposition (SVD) of the NLLS residual Jacobian. Results &Discussion We identified parameter degeneracy using an SVD-based subset selection algorithm [3] applied to the objective function Jacobian. In the gH model in VC, the 2 least identifiable parameters were the leak conductance (gL) and gHreversal potentials, ELand EH. EHwas constrained by tail current experiments. This left a 1-dimensional (1-D) non-linear solution manifold for the remaining 7 parameters: gL, EH, and peak gHat 5 VC values. In the HH model in VC, 3 parameters were least identifiable: EK, gNaand EL. The HH model in CC exhibited approximate parameter degeneracy with a 1-D solution manifold. Similar results were obtained for the STG model. The role of ELin degeneracy was unexpected. Our results generalize to multi-compartment models.
Acknowledgements Supported by NIH grant R01 NS130917.
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