Estimating kinetic constants from single channel data

Abstract

The process underlying the opening and closing of ionic channels in biological or artificial lipid membranes can be modeled kinetically as a time-homogeneous Markov chain. The elements of the chain are kinetic states that can be either open or closed. A maximum likelihood procedure is described for estimating the transition rates between these states from single channel data. The method has been implemented for linear kinetic schemes of fewer than six states, and is suitable for nonstationary data in which one or more independent channels are functioning simultaneously. It also provides standard errors for all estimates of rate constants and permits testing of smoothly parameterized subhypotheses of a general model. We have illustrated our approach by analysis of single channel data simulated on a computer and have described a procedure for analysis of experimental data.

Linking Exponential Components to Kinetic States in Markov Models for Single-Channel Gating

“…E 2 is comprised of any leftover intervals from { C 1 C 2 } plus intervals from { C 1 } as needed to complete the E 2 exponential, and E 1 is comprised of any leftover intervals from { C 1 } . Hawkes, 1982Hawkes, , 1995b, nor is the question the detection of components in histograms, as kinetic mechanisms are typically determined by maximum likelihood fi tting of rate constants to data, with the numbers of components implicit in the mechanism being fi tted ( Horn and Lange, 1983 ;McManus and Magleby, 1991 ;Colquhoun et al, 1996). Rather, the question is the physical basis for the exponential components, e.g., what is the state contribution to each component?…”

“…Normalizing the area of the distribution to 1.0 by dividing by the number of intervals in the distribution gives a probability density function, where the area under the curve between any two time values gives the probability of observing an interval with a lifetime (dwell time) between those values Hawkes, 1994, 1995b ). methods used in the calculations ( Horn and Lange, 1983 ;Colquhoun and Hawkes, 1995a ;Colquhoun et al, 1996;Qin et al, 1997 ).…”

Nicotinic Acetylcholine Receptors

“…obtaining the time constants by fitting each distribution separately) does not make the best use of the information in the record because the lengths of openings and shuttings are correlated in just about every sort of ion channel in which the question has been examined, and use of bivariate distributions is necessary to extract all the information (Fredkin et al, 1985). A method that extracts all of the information in the record was first proposed by Horn & Lange (1983), but it could not be used in practice because of the missed event problem.…”

Statistical properties of ion channel records. Part I: Relationship to the macroscopic current

“…Different calibration procedures (mostly numerical) have been developed to find the transition rates between kinetic states of a particular Markov structure to optimally replicate a set of single channel records. These procedures are based on maximum likelihood techniques [6] for matching the statistical properties of the model to the single channel records [7] or the macroscopic current [8,9] (The macroscopic current is the summation current through a large ensemble of ion channels). There are in theory infinite number of stochastic models (including many Markov structures) that can be calibrated to a set of single channel records to replicate certain statistical properties of the records and/or the resultant macroscopic current.…”