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Response linearity determined by recruitment strategy in detailed model of nictitating membrane control

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Abstract

Many models of eyeblink conditioning assume that there is a simple linear relationship between the firing patterns of neurons in the interpositus nucleus and the time course of the conditioned response (CR). However, the complexities of muscle behaviour and plant dynamics call this assumption into question. We investigated the issue by implementing the most detailed model available of the rabbit nictitating membrane response (Bartha and Thompson in Biol Cybern 68:135–143, 1992a and in Biol Cybern 68:145–154, 1992b), in which each motor unit of the retractor bulbi muscle is represented by a Hill-type model, driven by a non-linear activation mechanism designed to reproduce the isometric force measurements of Lennerstrand (J Physiol 236:43–55, 1974). Globe retraction and NM extension are modelled as linked second order systems. We derived versions of the model that used a consistent set of SI units, were based on a physically realisable version of calcium kinetics, and used simulated muscle cross-bridges to produce force. All versions showed similar non-linear responses to two basic control strategies. (1) Rate-coding with no recruitment gave a sigmoidal relation between control signal and amplitude of CR, reflecting the measured relation between isometric muscle force and stimulation frequency. (2) Recruitment of similar strength motor units with no rate coding gave a sublinear relation between control signal and amplitude of CR, reflecting the increase in muscle stiffness produced by recruitment. However, the system response could be linearised by either a suitable combination of rate-coding and recruitment, or by simple recruitment of motor units in order of (exponentially) increasing strength. These plausible control strategies, either alone or in combination, would in effect present the cerebellum with the simplified virtual plant that is assumed in many models of eyeblink conditioning. Future work is therefore needed to determine the extent to which motor neuron firing is in fact linearly related to the nictitating membrane response.

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Abbreviations

CR:

Conditioned response

HG:

Harders gland

MN:

Motoneuron

MU:

Motor unit

NM:

Nictitating membrane

NMR:

Nictitating membrane response

RB:

Retractor bulbi

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Author notes

  1. Eirini Mavritsaki

    Present address: School of Psychology, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK

Authors and Affiliations

  1. Department of Psychology, Sheffield University, Sheffield, S10 2TP, UK

    Eirini Mavritsaki, Nathan Lepora, John Porrill & Paul Dean

  2. Department of Anatomy and Developmental Biology, University College London, Gower Street, London, WC1E 6BT, UK

    Christopher H. Yeo

Authors
  1. Eirini Mavritsaki
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  2. Nathan Lepora
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  3. John Porrill
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  4. Christopher H. Yeo
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  5. Paul Dean
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Corresponding author

Correspondence to Paul Dean.

Additional information

Codes for all figures are available from http://www.neuralalgorithms.com (and also http://www.lepora.com) or by email from N. Lepora.

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Mavritsaki, E., Lepora, N., Porrill, J. et al. Response linearity determined by recruitment strategy in detailed model of nictitating membrane control. Biol Cybern 96, 39–57 (2007). https://doi.org/10.1007/s00422-006-0105-5

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  • DOI: https://doi.org/10.1007/s00422-006-0105-5

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