Single-channel data and missed events

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Abstract
Interval omission was done as described in our earlier publications (Ball et al. 1988). For the mono-exponential approximations, (f(1)) and f(2))), the maxima of the log-likelihood (equation (6)) occur at the moment estimators of (μ0,μc) obtained by setting α and β to the appropriate sample means and solving the pair of equations defined by equations (2 b) and (3 b)for (μ0,μc). For the bi-exponential approximation, (f(3)), and for the global likelihood (equation (7)) maximization of log-likelihoods was performed by NAG subroutine E04CCF, which uses a simplex algorithm (Nelder & Mead 1965), and maxima were checked by using NAG subroutine C05NCF to solve the equations formed by setting the first derivatives of the log-likelihoods to zero. 3. RESULTS (a) Computer-simulated data Our strategy has been to simulate ion-channel data according to equation (1) for a range of agonist concentrations, and then to use the maximum likelihood procedure to examine the behaviour of the parameter estimates generated by the two approximations. In selecting model parameter values for the simulations, we have made two assumptions. First, we have assumed that association of the agonist molecule with the receptor is diffusion limited, yielding μc = 10-4M ms. Secondly, the dissociation constant for the receptor-agonist complex has been assumed to be 10-4 M, yielding μo = 1 ms. These values yield agonist-concentration-dependent channel kinetics comparable to those used in our earlier studies on inference (Ball & Sansom 1989), and fall within physiologically reasonable limits.

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