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B W Madsen

Publications and source records attributed to B W Madsen.

At least 37 records · Page 2Linked to original sources
PubMed1988

Statistical inference from single channel records: two-state Markov model with limited time resolution.

Though stochastic models are widely used to describe single ion channel behaviour, statistical inference based on them has received little consideration. This paper describes techniques of statistical inference, in particular likelihood methods, suitable for Markov models incorporating limited time resolution by means of a discrete detection limit. To simplify the analysis, attention is restricted to two-state models, although the methods have more general applicability. Non-uniqueness of the mean open-time and mean closed-time estimators obtained by moment methods based on single exponential approximations to the apparent open-time and apparent closed-time distributions has been reported. The present study clarifies and extends this previous work by proving that, for such approximations, the likelihood equations as well as the moment equations (usually) have multiple solutions. Such non-uniqueness corresponds to non-identifiability of the statistical model for the apparent quantities. By contrast, higher-order approximations yield theoretically identifiable models. Likelihood-based estimation procedures are developed for both single exponential and bi-exponential approximations. The methods and results are illustrated by numerical examples based on literature and simulated data, with consideration given to empirical distributions and model control, likelihood plots, and point estimation and confidence regions.

Ion Channels↗
PubMed1988

Verapamil, neuromuscular transmission and the nicotinic receptor.

The effect of verapamil on neuromuscular transmission was studied in the frog by analysing ionophoretic endplate current (iEPC) trains and the growth and decay phases of miniature endplate currents (mepcs). In addition, single channel data on the interaction of verapamil with the nicotinic acetylcholine receptor were obtained from cultured embryonic chick skeletal muscle cells. Verapamil caused both open and closed channel blockade in the iEPC trains. Mepc amplitude was decreased at low micromolar concentrations, and at higher concentrations there was also accelerated mepc decay indicating open channel blockade. The latter effect could not be explained by a sequential channel occlusion mechanism. Analysis of the mepc rising phase showed that low micromolar concentrations of the drug decreased the pool of receptors which could be activated. Single channel data confirmed the specific interaction of verapamil with the nicotinic receptor, showing closed channel blockade at low concentrations, and at higher levels the shortening of open channel lifetime. It is suggested that both forms of blockade may involve desensitization processes.

Animals↗
PubMed1988

Stochastic modelling of a single ion channel: an alternating renewal approach with application to limited time resolution.

Stochastic models of ion channels have been based largely on Markov theory where individual states and transition rates must be specified, and sojourn-time densities for each state are constrained to be exponential. This study presents an approach based on random-sum methods and alternating-renewal theory, allowing individual states to be grouped into classes provided the successive sojourn times in a given class are independent and identically distributed. Under these conditions Markov models form a special case. The utility of the approach is illustrated by considering the effects of limited time resolution (modelled by using a discrete detection limit, xi) on the properties of observable events, with emphasis on the observed open-time (xi-open-time). The cumulants and Laplace transform for a xi-open-time are derived for a range of Markov and non-Markov models; several useful approximations to the xi-open-time density function are presented. Numerical studies show that the effects of limited time resolution can be extreme, and also highlight the relative importance of the various model parameters. The theory could form a basis for future inferential studies in which parameter estimation takes account of limited time resolution in single channel records. Appendixes include relevant results concerning random sums and a discussion of the role of exponential distributions in Markov models.

Ion Channels↗
PubMed1987

Interaction of narcotic antagonist naltrexone with nicotinic acetylcholine receptor.

The interactions of naltrexone with the nicotinic acetylcholine receptor were studied electrophysiologically using the frog sciatic nerve-sartorius muscle and biochemically using membranes from the electric organ of Torpedo ocellata. At nanomolar concentrations naltrexone increased the peak amplitude of endplate currents with little change in the decay time constant. At micromolar concentrations there was a concentration-dependent depression of endplate current and miniature endplate current amplitudes and decay time constants. Decay time constant depression was enhanced with hyperpolarization. Only marginal curvature was induced in peak endplate current amplitude versus membrane voltage plots by naltrexone. Naltrexone had no effect on single channel conductance but decreased open channel lifetime, according to fluctuation analysis. Naltrexone alone (less than or equal to 3 microM) did not impair binding of [125I]alpha-bungarotoxin to the receptor in a fast pre-equilibration assay, but increased the ability of acetylcholine to displace [125I]alpha-bungarotoxin. The drug displaced the agonist-stimulated binding of [3H]perhydrohistrionicotoxin to the channel site. Biphasic functional changes in neuromuscular transmission can be attributed to an allosteric mechanism with increased agonist binding to the nicotinic receptor at nanomolar concentrations and caused a non-competitive blockade of the ionic channel at micromolar concentrations.

Amphibian Venoms↗
PubMed1987

Neurotransmission parameters estimated from miniature endplate current growth phase.

A numerical model of miniature endplate current (mepc) generation was fitted to the rising phase of individual mepcs recorded at the frog neuromuscular junction, and estimates of 6 transmission parameters were obtained. Model fitting was enabled by assuming literature values for geometric parameters and determining single channel current by noise analysis, the channel closing rate constant from the mepc decay, and acetylcholine hydrolysis parameters from mepcs recorded in esterase-blocked endplates. Under control conditions, mean estimates were: number of molecules in a quantum = 29,000, diffusion coefficient = 2.8 X 10(-6) cm2s-1, endplate receptor density = 8500 micron-2, forward binding rate constant = 7.6 X 10(8) M-1s-1, equilibrium dissociation constant = 58 microM and channel opening rate constant = 8100 s-1.

Animals↗
PubMed1986

Stochastic modelling of a single ion channel: interdependence of burst length and number of openings per burst.

Previous modelling of single channel behaviour based on Markov processes has been concerned mainly with means and marginal distributions of particular quantities. The present study derives the joint distribution, conditional distributions, and associated mean values for the burst length (T) and the number (N) of openings per burst in two simple three-state models in which bursting is possible, one for an agonist-only and one for a channel blocking mechanism. In both models the conditional mean burst length (E(T/N = r)) increases linearly as a function of the number of openings per burst, while the conditional mean number of openings per burst (E(N/T = x)) is a nonlinear strictly increasing function of burst length, which is asymptotically linear for large burst length. The asymptotic intercept for each model is shown to be less than, equal to, or greater than unity according as mean channel closed-time is less than, equal to, or greater than mean open-time. For parameter values typical of the nicotinic receptor, this intercept is less than unity for the agonist-only model and greater than unity for the blocking model. As a result of the dependence between the number of openings per burst and burst length, it is shown that experimental estimates of the unconditional mean number of openings per burst may be biased if bursts of only short duration are collected.

Animals↗
PubMed1985

Distribution of exponentiality in miniature endplate current decay.

Exponential functions are commonly used to describe miniature endplate current (MEPC) decay; under control conditions a monoexponential is usually regarded as sufficient, whereas in the presence of some drugs a biexponential may be necessary. Using an automated fitting procedure which estimated exponential parameters and the period of decay from peak to baseline, a unimodal distribution of curvature was found for control MEPCs recorded in frog sartorius muscle. The majority of MEPCs were of monoexponential form, while the remainder were biexponential with either less or greater curvature than expected for a simple exponential (hypoexponential or hyperexponential, respectively). The proportion of MEPCs in each of the 3 groups was constant for a given endplate but varied between endplates. A possible explanation for this phenomenon could be differences in synaptic geometry within and between endplates. The increased curvature of individual MEPCs in the hyperexponential group was analyzed by assuming a sequential model for agonist blockade or desensitization, and calculating closing and reopening rate constants. These rate constants were altered by procaine and verapamil (100 microM) in a manner consistent with blockade of the acetylcholine receptor by enhancement of agonist-induced desensitization.

Animals↗
PubMed1985

The narcotic antagonist naltrexone has a biphasic effect on the nicotinic acetylcholine receptor.

It is known that narcotic antagonists interact with many cholinergic pathways but less in known about specific mechanisms. Using neonatal rat myoballs to study single channel behaviour of the acetylcholinegated nicotinic receptor, it was found that micromolar concentrations of naltrexone had no effect on channel conductance but caused open channel blockade by increasing the flickering from the open to the closed state in a concentration-dependent manner. At micromolar concentrations of naltrexone, the frequency of channel opening was decreased and bursts were grouped in clusters, whereas at nanomolar levels the frequency of opening was increased. The sequential model for ion-channel blockade cannot explain these effects, and an alternative allosteric mechanism of action is proposed.

Acetylcholine↗
PubMed1985

Verapamil alters the amplitude and time course of miniature endplate current.

The effect of verapamil on neuromuscular transmission was examined by recording miniature endplate currents (mepcs) in voltage-clamped frog sartorius muscle fibres. In the presence of 100 microM verapamil, the amplitude and time constant of decay of the mepcs (tau D) were reduced to 68% and 55% of control respectively, and the normal voltage dependency of tau D was decreased. Part of the decrease in amplitude of the mepc was independent of changes in tau D because, on washout, recovery of tau D was more rapid than that of amplitude, and in some cells smaller concentrations of verapamil (1 and 10 microM) decreased amplitude without affecting tau D. Evidence of open and closed channel blockade by verapamil (5-20 microM) was obtained from ionophoretic end-plate current trains and it is proposed that these effects are mediated via an allosteric mechanism.

Animals↗
PubMed1984

Numerical simulation of miniature endplate currents.

A FORTRAN computer program is described which enables solution of a set of partial differential equations describing synaptic transmission, including neurotransmitter diffusion, binding to receptors on the postsynaptic membrane with subsequent formation of open ion-conducting channels, and hydrolysis. Integration is performed with a widely available package (PDETWO), and flexibility is achieved through use of 6 user-specified routines. The reliability of solution was checked by comparison with an analytic solution for a diffusion-only model. Application of the program is illustrated with an analysis of miniature endplate current rise times.

Acetylcholine↗
PubMed1981

A compartmental model for the uptake of chlorphentermine in isolated perfused rat lung.

Equilibrium binding studies in vitro have established that chlorphentermine (CP) can be accumulated in rat lung by both binding and partitioning. Kinetic analysis of CP uptake in the isolated organ assuming an exponential process also suggests two separate mechanisms, one being saturable binding or transport, and the other, non-saturable partitioning. The present study was concerned with an alternative compartmental representation of the uptake process, and the validity of conclusions based on an exponential model. A three compartment model was finally selected which explain ed the observed uptake over a wide range of CP perfusate concentrations (2.5 x 10(-7) - 2.5 x 10(-5) mol/L) to within experimental error; it consisted of a binding and partitioning compartment in addition to one associated with the vascular bed. At low perfusate concentrations (2.5 x 10(-7) mol/L) uptake was essentially due to binding, while at higher perfusate concentrations (2.5 x 10(-5) mol/L) most uptake was due to partitioning. The total number of kinetically estimated binding sites (0.109 mumol/g) was less than that found by equilibrium dialysis for lung homogenates in vitro (8.3 mumol/g), suggesting an accessibility limitation for binding sites in the isolated preparation receiving a brief (10 min) perfusion. The data also indicate that there are probably two classes of binding sites or regional concentration of CP in the lung. It is proposed that interpretation of exponential model parameters may be problematical.

Animals↗
PubMed1981

Plasma theophylline assay service for outpatients.

It is generally agreed that the bronchodilator response to theophylline can be directly related to plasma concentration and that the efficacy of theophylline therapy can be improved if plasma concentrations are monitored. However, it is not known whether this improvement is realised in routine clinical practice. In this study, theophylline plasma concentrations were measured in 359 outpatients attending a teaching hospital respiratory medicine clinic. In nearly three-quarters of these patients (73.2%), the plasma concentration of theophylline was below the recommended therapeutic range of 55-110 mumoles/liter (10-20 mg/liter). These results were made available to the medical staff at the patient consultation. One hundred and seventy-seven patients reattended for a second visit and their plasma concentrations remeasured. At this visit, 63.2% of plasma levels were below the therapeutic range of 55-110 mumoles/liter; the percentage of patients in this therapeutic range had risen from 25.6% at the first visit to 33.9% at the second. Concentrations in excess of 110 mumoles/liter were rare and accounted for only 1.1-2.8% of sample assayed. The increase in the percentage of patients whose plasma concentration was in the therapeutic range may have been due to a better patient compliance resulting from provision of the "on-line" plasma monitoring service. The data suggest that physicians are conservative in their use of theophylline and may be maintaining the patients at a therapeutic range of 28-55 mumoles/liter, particularly when the drug is given with other therapeutic agents such as the beta 2-adrenoceptor agonists.

Adolescent↗