Abstract
We demonstrate a parameter-space search algorithm using a computational model of a single-compartment neuron with conductance-based Hodgkin–Huxley dynamics. To classify bursting (the desired behavior), we use a simple cost function whose inputs are derived from the frequency content of the neural output. Our method involves the repeated use of a stochastic gradient descent-type algorithm to locate parameter values that allow the neural model to produce bursting within a specified tolerance. We demonstrate good results, including those showing that the utility of our algorithm improves as the pre-defined allowable parameter ranges increase and that the initial approach to our method is computationally efficient.
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Butera R Jr, Rinzel J, Smith JC (1999) Models of respiratory rhythm generation in the Pre-Bötzinger complex. I. Bursting pacemaker neurons. J Neurophysiol 82(1):382–397
Foster W, Ungar L, Schwaber J (1993) Significance of conductances in Hodgkin–Huxley models. J Neurophysiol 70(6):2502–2518
Golowasch J, Goldman MS, Abbott L, Marder E (2002) Failure of averaging in the construction of a conductance-based neuron model. J Neurophysiol 87:1129–1131
Hill A, Hooser SV, Calbrese R (2002) Half-center oscillators underlying rhythmic movements. In: Arbib M (ed) The handbook of brain theory and neural networks. The MIT Press, pp 507–510
Hille B (2001) Ion channels of excitable membranes, 3rd edn. Sinauer Associates, Sunderland
Hodgkin A, Huxley A (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol (London) 117:500–544
Izhikevich EM (2000) Neural excitability, spiking and bursting. Int J Bifurcation Chaos 10(6):1171–1266
Marder E, Calabrese RL (1996) Principles of rhythmic motor pattern generation. Physiol Rev 76(3):687–717
Mead CA (1989) Analog VLSI and neural systems. Addison-Wesley, Reading
Nelson M, Rinzel J (1998) The Hodgkin–Huxley model. In: Bower JM, Beeman D (eds) The book of genesis: exploring realistic neural models with the general neural simulation system, Chap 4. Springer, Heidelberg, pp 29–49
Oppenheim AV, Schafer RW, Buck JR (1999) Discrete-time signal processing, 2nd edn. Prentice Hall, Upper Saddle River
Prinz AA, Billimoria CP, Marder E (2003) Alternative to hand-tuning conductance-based models: construction and analysis of databases of model neurons. J Neurophysiol 90:3998–4015
Tsallis C, Stariolo DA (1996) Generalized simulated annealing. Physica A 233(1–2):395–406
Wolpert D, Macready W (1997) No free lunch theorems for optimization. IEEE Trans Evolut Comput 1:67–82
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Reid, M.S., Brown, E.A. & DeWeerth, S.P. A parameter-space search algorithm tested on a Hodgkin–Huxley model. Biol Cybern 96, 625–634 (2007). https://doi.org/10.1007/s00422-007-0156-2
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DOI: https://doi.org/10.1007/s00422-007-0156-2