A mathematical model of the crustacean stretch receptor neuron.
Biomechanics of the receptor muscle, mechanosensitive ion channels and
SWERUP, C. and RYDQVIST, B.
Department of Physiology and Pharmacology, Karolinska Institutet, S-171 77
APStracts 3:0081N, 1996.
SUMMARY AND CONCLUSIONS
1. A mathematical model of the primary transduction process in a
mechanoreceptor, the slowly adapting stretch receptor organ of the crayfish,
has been developed taking into account the viscoelastic properties of the
accessory structures of the receptor, i.e. the receptor muscle, the
biophysical properties of the mechanosensitive channels (MSC's) and the
passive electrical properties of the neuronal membrane (leak conductance and
capacitative properties). The work is part of an effort to identify and
characterize the mechanical and ionic mechanisms in a complex mechanoreceptor.
The parameters of the model are mainly based on results of our own experiments
and to some extent on results from other studies. The performance of the model
has been compared with the performance of the slowly adapting receptor. 2. The
model resulted in nonlinear differential equations which were solved by an
iterative, fourth order Runge-Kutta method. For the calculations of potential
the cell was treated as an idealized spherical body. The extension of the
receptor muscle was 0-30% which is within the physiological limits for this
receptor. 3. The mechanical properties of the receptor muscle were modelled by
a simple Voigt element (a spring in parallel with a dashpot) in series with a
nonlinear spring. This element can resonably well describe the tension
development in the receptor muscle at least for large extensions (>12%).
However, for small extensions (<12%) the muscle seems to be more stiff than
for large extensions. 4. The receptor current at different extensions of the
receptor was computed using typical viscoelastic parameters for a receptor
muscle together with a transformation of muscle tension to tension in the
neuronal dendrites and finally the properties of the mechanosensitive
channels. The model fit was satisfactory in the high extension range whereas
in the low extension range the deviation from the experimental results could
partly be explained by insufficient modelling of the nonlinear viscoelastic
properties. The voltage dependence of the receptor current was also well
predicted by the model. 5. If the parameters of the viscoelastic model were
adjusted for each extension so that each tension response closely resembled
the experimental values, the fit of the current responses was improved but
still deviated from the experimental currents. One factor that might explain
the difference is the possibility that the MSC's in the stretch receptor
neuron might have intrinsic adaptive properties. Introducing an exponential
adaptive behaviour of individual MSC's increased the ability of the model to
predict the receptor current. 6. The receptor potential was calculated by
modelling the neuronal membrane by a lumped leak conductance and capacitance.
The calculated receptor potential was higher than the experimental receptor
potential. However the fit of the receptor potential was substantially
improved by introducing an adaptation of the MSC's as outlined in the
preceding paragraph. The remaining discrepancy might be explained by
insufficient blocking of K+ channels in the experiment. 7. The model can
predict a wide range of experimental data from the slowly adapting stretch
receptor neuron including the mechanical response of the receptor muscle, the
receptor current and its voltage dependence and the receptor potential. It
also describes accurately the passive electrical properties of the neuronal
Received 3 January 1996; accepted in final form 17 April 17 1996.
APS Manuscript Number J6-6.
Article publication pending J. Neurophysiol.
ISSN 1080-4757 Copyright 1996 The American Physiological Society.
Published in APStracts on 8 May 96