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F G Ball

Publications and source records attributed to F G Ball.

15 recordsLinked to original sources
PubMed2000

Stochastic models for systems of interacting ion channels.

We consider a variety of Markov based models for systems of ion channels exhibiting dependence between channels. It is shown how many useful properties which may be calculated for an aggregated single-channel model, or a system of independent channels, can be extended to various types of interacting channel systems. Key structure and results from the theory of aggregated Markov processes are summarized in a convenient matrix form. These are then applied to the superposition of independent and dependent channels, including a patch of channels in a random environment, and a system of channels with spatial interactions. Calculations based on the resultant matrix expressions and intensity arguments can be implemented straightforwardly in a matrix-oriented package such as Matlab. The role of reversibility is also studied. A number of examples illustrate the strengths of the methods and enable numerical comparisons between the different types of systems.

Computer Simulation↗
PubMed1994

Ion channel gating and time interval omission: statistical inference for a two-state Markov model.

Statistical inference is considered for a two-state Markov model of a single ion channel, when time interval omission is incorporated. A simple method of obtaining confidence sets for the mean open and closed sojourn times for the underlying single channel, based on the method-of-moments estimators, is presented. Time interval omission induces non-identifiability, in that the method-of-moments usually leads to two distinct estimates of the mean open and closed sojourn times, one corresponding to the true values and the other being an artefact of time interval omission. A new method of overcoming such non-identifiability on the basis of one single channel record is described. The methodology is illustrated by a numerical example.

Animals↗
PubMed1994

Model properties underlying non-identifiability in single channel inference.

Models of ion channel kinetics subserve inferential methods applied to patch clamp data. For Markov models the density function of a sojourn time in a class of states is a mixture of exponentials. Determination of kinetic parameters from density functions may be complicated by non-uniqueness of solutions. This non-identifiability is investigated analytically for a class of two states, assuming detailed balance; relations between model properties, observable density parameters, and non-uniqueness are presented. The results are further developed in terms of similarity transform methods. Additional information provided by joint distributions is discussed. An example is given where identifiability of a model can be demonstrated explicitly. Attention is drawn to instances where the number of components in a density function may be misleading when used to infer the number of underlying states.

Ion Channels↗
PubMed1993

Single ion channel models incorporating aggregation and time interval omission.

We present a general theoretical framework, incorporating both aggregation of states into classes and time interval omission, for stochastic modeling of the dynamic aspects of single channel behavior. Our semi-Markov models subsume the standard continuous-time Markov models, diffusion models and fractal models. In particular our models allow for quite general distributions of state sojourn times and arbitrary correlations between successive sojourn times. Another key feature is the invariance of our framework with respect to time interval omission: that is, properties of the aggregated process incorporating time interval omission can be derived directly from corresponding properties of the process without it. Even in the special case when the underlying process is Markov, this leads to considerable clarification of the effects of time interval omission. Among the properties considered are equilibrium behavior, sojourn time distributions and their moments, and auto-correlation and cross-correlation functions. The theory is motivated by ion channel mechanisms drawn from the literature, and illustrated by numerical examples based on these.

Biophysical Phenomena↗
PubMed1992

Poisson sampling-based inference for single ion channel data with time interval omission.

Patch-clamp recording allows investigations of the gating kinetics of single ion channels. Statistical analysis of kinetic data can enhance our understanding of channel gating at a molecular level. Experimental channel records suffer from time interval omission, i.e. failure to detect brief channel openings and closings. It is important to incorporate this phenomenon into statistical analyses of ion channel data. When time interval omission is ignored, the method of maximum likelihood can usually be used to estimate gating parameters from a single channel record. However, it is far more difficult to apply this method when time interval omission is incorporated. We present an alternative approach to parameter estimation based on Poisson sampling. A simulated homogeneous Poisson process is superimposed onto the channel record and inference is based on the numbers of points in successive open and closed sojourns, rather than on the sojourn times themselves. We describe the method for the two-state Markov model C<-->O, although it is applicable to more general models. Computer-simulated data are used to demonstrate the efficacy of the method. Modifications of the method are discussed briefly.

Animals↗
PubMed1991

Dynamic population epidemic models.

Most multipopulation epidemic models are of the contact distribution type, in which the locations of successive contacts are chosen independently from appropriate contact distributions. This paper is concerned with an alternative class of models, termed dynamic population epidemic models, in which infectives move among the populations and can infect only within their current population. Both the stochastic and deterministic versions of such models are considered. Their threshold behavior is analyzed in some depth, as are their final outcomes. Velocities of spread of infection are considered when the populations have a spatial structure. A criterion for finding the equivalent contact distribution epidemic for any given dynamic population epidemic is provided, enabling comparisons to be made for the velocities and final outcomes displayed by the two classes of models. The relationship between deterministic and stochastic epidemic models is also discussed briefly.

Disease Outbreaks↗
PubMed1990

Single-channel data and missed events: analysis of a two-state Markov model.

Patch-clamp recording permits investigation of the gating kinetics of single ion channels. Careful statistical analysis of kinetic data can yield clues as to the molecular events underlying channel gating. However, it is important that such analysis should take full account of the limitations that arise from the finite time resolution of patch-clamp recording techniques. Single-ion-channel data are generally interpreted in terms of Markov process models of channel gating mechanisms. Experimental channel records suffer from time interval omission, i.e. failure to detect brief channel openings and closings. This leads to an identifiability problem when analysing single-channel data, i.e. different gating mechanisms provide equally convincing descriptions of the same experimental data. We consider a two-state Markov model of receptor-channel gating in which the channel opening rate is proportional to the agonist concentration, C in equilibrium with OA. By using computer-simulated data, the approximate likelihood of the data is maximized to yield parameter estimates for the model. At a single agonist concentration there is an identifiability problem in that two pairs of parameter estimates are obtained. The 'true' parameter estimates cannot be distinguished from the 'false' ones. By considering data corresponding to a range of agonist concentrations one may identify the 'true' parameter estimates as those that do not change as the agonist concentration is increased. Alternatively, one may identify the 'true' parameter estimates directly by maximizing a global likelihood, the latter being obtained by simultaneous consideration of data obtained at several different agonist concentrations.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMed1990

Glutamate receptor-channel gating. Maximum likelihood analysis of gigaohm seal recordings from locust muscle.

Gigaohm recordings have been made from glutamate receptor channels in excised, outside-out patches of collagenase-treated locust muscle membrane. The channels in the excised patches exhibit the kinetic state switching first seen in megaohm recordings from intact muscle fibers. Analysis of channel dwell time distributions reveals that the gating mechanism contains at least four open states and at least four closed states. Dwell time autocorrelation function analysis shows that there are at least three gateways linking the open states of the channel with the closed states. A maximum likelihood procedure has been used to fit six different gating models to the single channel data. Of these models, a cooperative model yields the best fit, and accurately predicts most features of the observed channel gating kinetics.

Animals↗
PubMed1989

Ion-channel gating mechanisms: model identification and parameter estimation from single channel recordings.

Patch-clamp data may be analysed in terms of Markov process models of channel gating mechanisms. We present a maximum likelihood algorithm for estimation of gating parameters from records where only a single channel is present. Computer simulated data for three different models of agonist receptor gated channels are used to demonstrate the performance of the procedure. Full details of the implementation of the algorithm are given for an example gating mechanism. The effects of omission of brief openings and closings from the single-channel data on parameter estimation are explored. A strategy for discriminating between alternative possible gating models, based upon use of the Schwarz criterion, is described. Omission of brief events is shown not to lead to incorrect model identification, except in extreme circumstances. Finally, the algorithm is extended to include channel gating models exhibiting multiple conductance levels.

Animals↗
PubMed1989

Analysis of post-perturbation gating kinetics of single ion channels.

Analysis of mean dwell-times as a function of the number of channel openings elapsed since a stepwise perturbation in ion-channel kinetics is shown to provide information concerning the topology of the underlying gating mechanism. The difference between the post-perturbation mean dwell-time and the corresponding equilibrium mean is shown to decay as the sum of Ng-1 geometric terms in k, the number of openings since the perturbation, where Ng is the minimum number of gateway states in the channel gating mechanism. The method is illustrated by consideration of various simple gating schemes. A modification of the method accommodating the presence of channel inactivation or desensitization is described. Application of the method to a delayed-rectifier type K+ channel of NG108-15 cells reveals that Ng greater than or equal to 2, consistent with a branched gating mechanism.

Ion Channels↗
PubMed1989

A note on single-channel autocorrelation functions.

It is shown for time-reversible ion channel gating mechanisms that the sojourn time autocorrelation functions are necessarily nonnegative, decreasing, and convex. It is also shown, again for time-reversible mechanisms, that the lagged moments of all orders are determined by the first three moments. The application of these results to the statistical analysis of single-channel kinetics is briefly discussed.

Ion Channel Gating↗
PubMed1989

Markov, fractal, diffusion, and related models of ion channel gating. A comparison with experimental data from two ion channels.

The gating kinetics of single-ion channels are generally modeled in terms of Markov processes with relatively small numbers of channel states. More recently, fractal (Liebovitch et al. 1987. Math. Biosci. 84:37-68) and diffusion (Millhauser et al. 1988. Proc. Natl. Acad. Sci. USA. 85:1502-1507) models of channel gating have been proposed. These models propose the existence of many similar conformational substrates of the channel protein, all of which contribute to the observed gating kinetics. It is important to determine whether or not Markov models provide the most accurate description of channel kinetics if progress is to be made in understanding the molecular events of channel gating. In this study six alternative classes of gating model are tested against experimental single-channel data. The single-channel data employed are from (a) delayed rectifier K+ channels of NG 108-15 cells and (b) locust muscle glutamate receptor channels. The models tested are (a) Markov, (b) fractal, (c) one-dimensional diffusion, (d) three-dimensional diffusion, (e) stretched exponential, and (f) expo-exponential. The models are compared by fitting the predicted distributions of channel open and closed times to those observed experimentally. The models are ranked in order of goodness-of-fit using a boot-strap resampling procedure. The results suggest that Markov models provide a markedly better description of the observed open and closed time distributions for both types of channel. This provides justification for the continued use of Markov models to explore channel gating mechanisms.

Animals↗
PubMed1988

The use of dwell time cross-correlation functions to study single-ion channel gating kinetics.

The derivation of cross-correlation functions from single-channel dwell (open and closed) times is described. Simulation of single-channel data for simple gating models, alongside theoretical treatment, is used to demonstrate the relationship of cross-correlation functions to underlying gating mechanisms. It is shown that time irreversibility of gating kinetics may be revealed in cross-correlation functions. Application of cross-correlation function analysis to data derived from the locust muscle glutamate receptor-channel provides evidence for multiple gateway states and time reversibility of gating. A model for the gating of this channel is used to show the effect of omission of brief channel events on cross-correlation functions.

Ion Channels↗
PubMed1988

Single-channel autocorrelation functions: the effects of time interval omission.

We present a general mathematical framework for analyzing the dynamic aspects of single channel kinetics incorporating time interval omission. An algorithm for computing model autocorrelation functions, incorporating time interval omission, is described. We show, under quite general conditions, that the form of these autocorrelations is identical to that which would be obtained if time interval omission was absent. We also show, again under quite general conditions, that zero correlations are necessarily a consequence of the underlying gating mechanism and not an artefact of time interval omission. The theory is illustrated by a numerical study of an allosteric model for the gating mechanism of the locust muscle glutamate receptor-channel.

Computer Simulation↗