THE ROLE OF N-METHYL-D-ASPARTATE (NMDA) RECEPTORS IN WIND-UP - A MATHEMATICAL-MODEL

We present a mathematical model for the phenomenon of wind-up (Mendell , 1966, Exper. Neur. 16, 316-22) which occurs in many neurons. We conc entrate on its occurrence in the substantia 'gelatinosa of the dorsal horns of the spinal cord, where it is connected with certain pathologi cal and nonpathological pain states. The model is a development of the model by Britton & Skevington (1989, J. Theor. Biol. 137, 91-105) for Melzack & Wall's gate control theory of pain (1965, Science, New York , 150, 971-9; 1982, The Challenge of Pain, Penguin: Harmondsworth), mo dified to take account of more recent information. Its variables are t he electric potentials of various cells in the midbrain and the spinal cord. Britton & Skevington's original model simulated many of the phe nomena observed in acute pain in humans, but not the wind-up mechanism . This is not surprising, since this model did not include the N-methy l-D-aspartate (NMDA) receptors that are now recognized as being crucia l to the phenomenon. Here we rectify this omission, and obtain good ag reement between the model and experimental data on wind-up. The positi ve feedback that NMDA receptors exhibit is shown to be the essential f eature in producing wind-up. As an independent test of the model we si mulate a completely different experimental set-up, and obtain good qua litative agreement with data there. Finally, we present a prediction o f the model that has yet to be tested experimentally.