Title:

Stochastic models of drugcontrolled ionic channels

We begin this thesis with the study of the stochastic structure of theories of drug action on cells. General expressions for the different characteristics  autocovariance function, relaxation current, mean open lifetime, spectrum, etc.  which determine models built up on the basis of drug action are given. The spectral resolution of the Q matrix in terms of its eigenvalues is derived. Next, we examine the particular solutions of the characteristics which define (i) the classical (MM) model; (ii) KatzMiledi and C.F.Steven's  KM/CFB(l)  model; and (iii) an extension of (ii)  KM/ CFS(2) model in relation to their rote constants. We consider these models under both assumptions of fast binding and fast conformation change. The evaluation of limiting values of the quantities li  eigenvalues;ali  weights corresponding to the respective ai,s, and the spectrum for the KM/CFS(l)model is given. It turns out that expressions derived for the spectrum when limits of quantities are taken are the same as the expressions obtained when states are collapsed under assumptions of fast binding and fast conformation change. This agreement provides a justification for the procedure of collapsing states. The mean open lifetime for KM/CFS(2) model is concentration dependent, and the probability density function for the lifetime of open conformation is mixed exponential with rates equal to the eigenvalues of the QRR matrix formed from transitions between open states. We next proceed to the estimation of parameters in KM/CPS(l) and KM/CF8(2) models. Estimates of the parameters are found via the spectrum which is estimated at various frequency points. Tables of parameter estimates and histograms for the estimates are shown. Finally, we consider a modified KM/CFS(l) model, namely (12 KM/CFS(l)) ; that is, a model which comprises two independent subunits, each of the form KM/CFS(l) model, assuming fast conformation change and fast binding. The shape of the doseresponse, and hence the currentdose curves, is sigmoid in the case of partial agonists for this model. This is important, because one of the inadequacies of the classical model (see Introduction) which necessitates proposals for more complicated models, can be ruled out. Numerical examples with graphs on all models considered are given. It was noticed that in low concentrations the spectrum for these models could be approximated by a single component, given by the fastest eigenvalue.
