Abstract
With the advancement in computer technology, it has become possible to fit complex models to neuronal data. In this work, we test how two methods can estimate parameters of simple neuron models (passive soma) to more complex ones (neuron with one dendritic cylinder and two active conductances). The first method uses classical voltage traces resulting from current pulses injection (time domain), while the second uses measures of the neuron's response to sinusoidal stimuli (frequency domain). Both methods estimate correctly the parameters in all cases studied. However, the time-domain method is slower and more prone to estimation errors in the cable parameters than the frequency-domain method. Because with noisy data the goodness of fit does not distinguish between different solutions, we suggest that running the estimation procedure a large number of times might help find a good solution and can provide information about the interactions between parameters. Also, because the formulation used for the model's response in the frequency domain is analytical, one can derive a local sensitivity analysis for each parameter. This analysis indicates how well a parameter is likely to be estimated and helps choose an optimal stimulation protocol. Finally, the tests suggest a strategy for fitting single-cell models using the two methods examined.
Similar content being viewed by others
References
Ali-Hassan WA, Saidel GM, Durand D (1992) Estimation of electrotonic parameters of neurons using an inverse fourier transform technique. IEEE Transactions on Biomedical Engineering 39:493-501.
Bhalla US, Bower JM (1993) Exploring parameter space in detailed single neuron models: Simulations of the mitral and granule cell of the olfactory bulb. Journal of Neurophysiology 69:1948-1965.
Borst A, Haag J (1996) The intrinsic electrophysiological characteristics of fly lobula plate tangential cells: I. Passive membrane properties. Journal of Computational Neuroscience 3:313-336.
Burke RE, ten Bruggencate G (1971) Electrotonic characteristics of alpha motoneurones of varying size. Journal of Physiology 212: 1-20.
Byrne GD, Hindmarsh AC (1975) A polyalgorithm for the numerical solution of ordinary differential equations. ACM Transactions on Mathematical Software 1:71-96.
Dennis JE, Gay DM, Welsch RE (1981) An adaptive nonlinear least-squares algorithm. ACM Transactions on Mathematical Software 7:348-368.
Durand D (1984) The somatic shunt cable model for neurons. Biophysical Journal 46:645-653.
Foster WR, Ungar LH, Schwaber JS (1993) Significance of conductances in Hodgkin-Huxley models. Journal of Neurophysiology 70:2502-2518.
Hodgkin AL, Huxley AF (1952) A quantitative description of membrane currents and its application to conduction and excitation in nerve. Journal of Physiology 117:500-544.
Kawato M (1984) Cable properties of a neuron model with nonuniform resistivity. Journal of Theoretical Biology 111:149-169.
Major G, Larkman AU, Jack JJB (1990) Constraining nonuniqueness in passive electrical models of cortical pyramidal neurones. Journal of Physiology 430:13P.
Major G, Larkman AU, Jonas P, Sakmann B, Jack JJB (1994) Detailed passive models of whole-cell recorded CA3 pyramidal neurons in rat hippocampal slices. Journal of Neuroscience 14:4613-4638.
Mauro A, Conti F, Dodge F, Schor R (1970) Subthreshold behavior and phenomenological impedance of the squid giant axon. Journal of General Physiology 55:497-523.
Moore LE, Christensen BN (1985) White noise analysis of cable properties of neuroblastoma cells and lamprey central neurons. Journal of Neurophysiology 53:636-651.
Moore LE, Hill RH, Grillner S (1993) Voltage-clamp frequency domain analysis of NMDA-activated neurons. Journal of Experimental Biology 175:59-87.
Murphey CR, Moore LE, Buchanan JT (1995) Quantitative analysis of electrotonic structure and membrane properties of NMDA-activated lamprey spinal neurones. Neural Computation 7:486-506.
Murphey CR, Tabak J, Moore LE, Buchanan J (1996) Estimation of membrane properties from step current measurement of Xenopus neurons. In: Bower J, ed. Computational Neuroscience. Academic Press, New York, pp. 107-112.
Nelder JA, Mead J (1965) A simplex algorithm for function minimization. Computer Journal 7:308-313.
Press WH, Flannery BP, Teukolsky SA, Vetterling WT (1988) Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, Cambridge.
Rall W (1969) Time constants and electronic length of membrane cylinders and neurons. Biophysical Journal 9:1483-1508.
Staley KJ, Otis TS, Mody I (1992) Membrane properties of dentate gyrus cells: Comparison of sharp microelectrode and whole-cell recording. Journal of Neurophysiology 67:1346-1358.
Stratford K, Mason A, Larkman A, Major G, Jack J (1989) The modelling of pyramidal neurones in the visual cortex. In: Durbin R, Miall C, Mitchison G, eds. The Computing Neuron. Addison-Wesley, Reading, MA. pp. 296-321.
Surkis A, Peskin CS, Tranchina D, Leonard CS (1998) Recovery of cable properties through active and passive modeling of subthreshold membrane responses from laterodorsal tegmental neurons. Journal of Neurophysiology 80:2593-2607.
Tabak J, Moore LE (1998) Simulation and parameter estimation study of a simple neuronal model for rhythm generation: Role of NMDA and non-NMDA receptors. Journal of Computational Neuroscience 5:209-235.
Tabak J, Murphey CR, Moore LE (1996) Estimation methods in locomotion network activity. Society for Neuroscience Abstract 22:1372.
Weyhing H, Borst A (1997) Parameter search in compartmental models using genetic algorithms. Society for Neuroscience Abstract 23:655.
White JA, Manis PB, Young ED (1992) The parameter estimation problem for the somatic shunt model. Biological Cybernetics 66:307-318.
Wright WN, Bardakjian BL, Valiante TA, Perez-Velazquez JL, Carlen P (1996) White noise approach for estimating the passive electrical properties of neurons. Journal of Neurophysiology 76:3442-3450.
Zipser D (1992) Identification models of the nervous system. Neuroscience 47:853-862.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Tabak, J., Murphey, C.R. & Moore, L. Parameter Estimation Methods for Single Neuron Models. J Comput Neurosci 9, 215–236 (2000). https://doi.org/10.1023/A:1026531603628
Issue Date:
DOI: https://doi.org/10.1023/A:1026531603628