The quality of maximum likelihood estimates of ion channel rate constants

Abstract

Properties of maximum likelihood estimators of rate constants for channel mechanisms are investigated, to see what can and cannot be inferred from experimental results. The implementation of the HJCFIT method is described; it maximises the likelihood of an entire sequence of apparent open and shut times, with the rate constants in a specified reaction mechanism as free parameters. The exact method for missed brief events is used. Several methods for testing the quality of the fit are described. The distributions of rate constants, and correlations between them, are investigated by doing sets of 1000 fits to simulated experiments. In a standard nicotinic receptor mechanism, all nine free rate constants can be estimated even from one single channel recording, as long as the two binding sites are independent, even when the number of channels in the patch is not known. The estimates of rate constants that apply to diliganded channels are robust; good estimates can be obtained even with erroneous assumptions (e.g. about the value of a fixed rate constant or the independence of sites). Rate constants that require distinction between the two sites are less robust, and require that an EC50 be specified, or that records at two concentrations be fitted simultaneously. Despite the complexity of the problem, it appears that there exist two solutions with very similar likelihoods, as in the simplest case. The hazards that result from this, and from the strong positive correlation between estimates of opening and shutting rates, are discussed.

One-channel Cell-attached Patch-clamp Recording

“…Fitting of these data to kinetic models may be performed in order to gain further insight into the behaviors of the ion channel. Maximum likelihood fitting can be performed with software such as QuB or HJCFIT 18 , in which the algorithms implemented by each program have their own benefits. While the idealization demonstrated in Figure 5 Figure 5C) 19 , in which these gating characteristics are crucial for determining the shape of the NMDA receptor mediated synaptic signal 20,21 .…”

Nicotinic Acetylcholine Receptors

“…This method has the drawback that the extrapolation has to be done with the wrong equation (the Hill equation), and that it is often hard to get close to saturation. It is not, in any case, necessary, because β 2 is easy to estimate directly, simultaneously with the other parameters, by the maximum likelihood method Colquhoun et al 2003). In practice, however, there is not much disagreement about the value of β 2 .…”

“…The principles of the methods currently in use have been described by Hawkes et al, (1990), Hawkes et al (1992), Colquhoun et al (1996), Qin et al (1996); (see also Colquhoun & Hawkes, 1995). The HJCFIT approach has been tested by Colquhoun et al (2003), and used by Hatton et al 2003 and by Beato et al (2002). The MIL program has been used in many publications from the Auerbach and Sine labs.…”

“…In other words, they are sufficient to determine the characteristics of the predominant doubly-liganded bursts of openings (channel 'activations') that are responsible for neuromuscular transmission. These three rates are, fortunately, the easiest to determine (see Colquhoun et al, 2003).…”

ASIC1a activation by amitriptyline and FMRF-amide is removed by serine proteases

“…Electrophysiology experiments were performed using standard patch-clamp procedures and equipment, in the classical (ruptured) and amphotericin-perforated whole-cell configuration, as well as on excised outside-out patches. Pipettes were prepared from glass capillaries (GC150F-10, Harvard Apparatus Ltd., Edenbridge, UK) pulled using 4-step protocols with a microprocessor-controlled rate refinement for a complex gating model using hidden Markov model (HMM) algorithms with the Hawkes-Jalali-Colquhoun module (HJCFIT) provided in the DCPROGS package (http:// www.ucl.ac.uk/Pharmacology/dc.html); [41][42][43][44][45][46] (2) Idealization using segmental k-means analysis and a simplified three-state (COC) gating model, followed by model search and rate refinement for a multistate gating model using maximum interval likelihood criteria, with the modules SKM, MSEARCH and MIL of the QuB package v1.4.0.50 (http://www.qub.buffalo. edu/).…”