A theory of dynamic and steady responses in chemoreception

Abstract

A theoretical model which can account for both the dynamic and steady responses is proposed based on the occupation theory. The reaction scheme used is; ▪ Here, S and A are stimulus chemicals and receptor sites unbound, respectively. The binding of S to A leads to an active complex ( SA) active, which is successively transformed into an inactive complex ( SA) active. The response is assumed to be proportional to number of ( SA) active. When a stimulating solution is applied instantaneously at t = 0, the solution to the set of differential equations based on the above scheme is obtained as follows; p=α 1 e −ω 1t +α 2 −ω 2t + C k −1 k 1 +(1+ k 2 k −2 )C where p and C stand for the fraction of ( SA) active to the total number of receptor sites and stimulus concentration, respectively, and α i , and ω i ( i = 1, 2) are numerical parameters depending on the rate constants and on C. The steady response is expressed as the third term in the above equation, which indicates that the response accords with the Beidler taste equation. Mathematical analysis of the above scheme shows that the dynamic response appears when k 1 C > k −2, and the calculated results for the dynamic response agree approximately with the Hill equation. The Hill coefficient lays within 1·00 and 0·79 and reaches unity with increasing k −1 k 2 , which implies that the dynamic response under this condition satisfies the Beidler taste equation. For the case of gradual application of stimuli, i.e. the experimental condition, the time course of p is simulated with use of an analogue computer rather than with a numerical solution to the above equation. The results indicate that the dynamic response diminishes with decreasing the application speed of stimulus solution. The present theory accounts consistently for various experimental data observed in the chemoreceptor systems.