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Importance: Recurrent urinary tract infection (UTI) is a common debilitating condition in women, with limited prophylactic options. d-Mannose has shown promise in trials based in secondary care, but effectiveness in placebo-controlled studies and community settings has not been established., Objective: To determine whether d-mannose taken for 6 months reduces the proportion of women with recurrent UTI experiencing a medically attended UTI., Design, Setting, and Participants: This 2-group, double-blind randomized placebo-controlled trial took place across 99 primary care centers in the UK. Participants were recruited between March 28, 2019, and January 31, 2020, with 6 months of follow-up. Participants were female, 18 years or older, living in the community, and had evidence in their primary care record of consultations for at least 2 UTIs in the preceding 6 months or 3 UTIs in 12 months. Invitation to participate was made by their primary care center. A total of 7591 participants were approached, 830 responded, and 232 were ineligible or did not proceed to randomization. Statistical analysis was reported in December 2022., Intervention: Two grams daily of d-mannose powder or matched volume of placebo powder., Main Outcomes and Measures: The primary outcome measure was the proportion of women experiencing at least 1 further episode of clinically suspected UTI for which they contacted ambulatory care within 6 months of study entry. Secondary outcomes included symptom duration, antibiotic use, time to next medically attended UTI, number of suspected UTIs, and UTI-related hospital admissions., Results: Of 598 women eligible (mean [range] age, 58 [18-93] years), 303 were randomized to d-mannose (50.7%) and 295 to placebo (49.3%). Primary outcome data were available for 583 participants (97.5%). The proportion contacting ambulatory care with a clinically suspected UTI was 150 of 294 (51.0%) in the d-mannose group and 161 of 289 (55.7%) in the placebo group (risk difference, -5%; 95% CI, -13% to 3%; P = .26). Estimates were similar in per protocol analyses, imputation analyses, and preplanned subgroups. There were no statistically significant differences in any secondary outcome measures., Conclusions and Relevance: In this randomized clinical trial, daily d-mannose did not reduce the proportion of women with recurrent UTI in primary care who experienced a subsequent clinically suspected UTI. d-Mannose should not be recommended for prophylaxis in this patient group., Trial Registration: isrctn.org Identifier: ISRCTN13283516.

It is often assumed that ion channels in cell membrane patches gate independently. However, in the present study nicotinic receptor patch clamp data obtained in cell-attached mode from embryonic chick myotubes suggest that the distribution of steady-state probabilities for conductance multiples arising from concurrent channel openings may not be binomial. In patches where up to four active channels were observed, the probabilities of two or more concurrent openings were greater than expected, suggesting positive cooperativity. For the case of two active channels, we extended the analysis by assuming that 1) individual receptors (not necessarily identical) could be modeled by a five-state (three closed and two open) continuous-time Markov process with equal agonist binding affinity at two recognition sites, and 2) cooperativity between channels could occur through instantaneous changes in specific transition rates in one channel following a change in conductance state of the neighboring channel. This allowed calculation of open and closed sojourn time density functions for either channel conditional on the neighboring channel being open or closed. Simulation studies of two channel systems, with channels being either independent or cooperative, nonidentical or identical, supported the discriminatory power of the optimization algorithm. The experimental results suggested that individual acetylcholine receptors were kinetically identical and that the open state of one channel increased the probability of opening of its neighbor.

Quantitative analysis of patch clamp data is widely based on stochastic models of single-channel kinetics. Membrane patches often contain more than one active channel of a given type, and it is usually assumed that these behave independently in order to interpret the record and infer individual channel properties. However, recent studies suggest there are significant channel interactions in some systems. We examine a model of dependence in a system of two identical channels, each modeled by a continuous-time Markov chain in which specified transition rates are dependent on the conductance state of the other channel, changing instantaneously when the other channel opens or closes. Each channel then has, e.g., a closed time density that is conditional on the other channel being open or closed, these being identical under independence. We relate the two densities by a convolution function that embodies information about, and serves to quantify, dependence in the closed class. Distributions of observable (superposition) sojourn times are given in terms of these conditional densities. The behavior of two channel systems based on two- and three-state Markov models is examined by simulation. Optimized fitting of simulated data using reasonable parameters values and sample size indicates that both positive and negative cooperativity can be distinguished from independence.

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.

1. Although (+)-tubocurarine (Tc) is classically considered to be a competitive antagonist at the neuromuscular junction, kinetic details of the interaction remain unclear. 2. We studied the competitive action of Tc on the nicotinic receptor at the frog neuromuscular junction using a quantitative analysis of the generation phase of miniature endplate currents (m.e.p.cs) recorded in Ringer solution (20 degrees C) under voltage clamp (-90 mV) in the absence or presence of 1-5 microM Tc. Under control conditions four neurotransmission parameters were estimated by non-linear regression using a mathematical model of synaptic transmission incorporating transmitter release, diffusion, hydrolysis, receptor binding and channel gating. These parameters were then used in a further regression to estimate binding rate constants for Tc at the same endplate. Allowance was made for open channel block by Tc, which under the conditions of this study was only a small component of total blockade. 3. The results suggest that Tc binds to the two agonist recognition sites on the nicotinic receptor with equal affinity (stoichiometric KDs of 2.2 and 8.8 microM), and that most of the functional blockade at concentrations up to 5 microM is due to occupancy of only one site. 4. The association rate constant for Tc binding to sites on the nicotinic acetylcholine receptor appears to be very fast (k+D = 8.9 x 10(8) M-1 s-1) and comparable to that for acetylcholine (ACh). 5. In the brief time during which an m.e.p.c. is generated (approximately 200 microseconds, reversal of Tc blockade by transiently high concentrations of ACh seems to be kinetically limited.

This paper considers the distribution of a sojourn time in a class of states of a stochastic process having finite discrete state space where sojourn times in any individual state are independent and identically distributed, and transitions between states follow a Markov chain. The state space and possible transitions of the process are represented by a graph. Class sojourn time distributions are derived by modifying this graph using 'composition' of states, defining a new Markov chain on the modified graph, and expressing the sojourn time in a composition state as a random sum. Appropriate compositions are chosen according to the possible "cores" of sojourns in the particular class, where a core describes the structure of a sojourn in terms of a single state or a chain in the original graph. Graph methods provide an algorithmic basis for the derivation, which can be simplified by using symmetry results. Models of ion-channel kinetics are used throughout for illustration; class sojourn time distributions are important in such models because individual states are often indistinguishable experimentally. Markov processes are the special case where sojourn times in individual states are exponentially distributed. In this case kinetic parameter estimation based on the observed class sojourn time distribution is briefly discussed; explicit estimating equations applicable to sequential models of nicotinic receptor kinetics are given.

The effects of ethanol (5-50 mM) on cell F1 in the right parietal ganglion of Helix aspersa were studied electrophysiologically. In normal physiological solution ethanol depressed both spontaneous action potential duration and frequency by enhancement of the repolarization and after-hyperpolarization phases respectively. Depolarization under voltage-clamp in Na-free solution produced an outward current which peaked at about 100 ms and decayed to 75% of peak by 250 ms. Variation of external K+ and Ca2+ concentrations and blockade of Ca current with Co2+ suggests that this current, which is increased by more than 50% with 5 mM ethanol, is a Ca-activated K current. These results add to evidence that a variety of ion channels, depending on cell type and conditions, are affected by pharmacologically relevant concentrations of ethanol.

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.

Inhibition descending the spinal cord from the medullary brainstem was systematically mapped in two dimensions in anaesthetized cats. Fifty-four ipsi- and contralateral sites and 27 ipsilateral sites were electrically stimulated with concentric bipolar or with monopolar electrodes, respectively, whilst extracellularly recording firing of dorsal horn neurones to noxious heat. Effective bipolar stimulation, but not monopolar stimulation caused gross lesions at the stimulated sites. There were 3 ipsilateral sites at which descending inhibition was evoked with the smallest stimuli. These areas corresponded to nucleus raphe magnus, nucleus reticularis magnocellularis and the lateral tegmental field. Contralateral stimulation was as effective or more effective than ipsilateral stimulation. The inhibition of dorsal horn neurones was not due to the cardiovascular changes which sometimes accompanied stimulation of the brainstem. The data are discussed in relation to the analgesia which results from stimulating these areas of the brainstem.

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.

Large quantities of morphine injected directly into the brainstem of spinal anaesthetized cats inhibited the noxious heat-evoked excitation of dorsal horn neurones. The amounts required were similar to those that were required intravenously in cats with the spinal cord intact or transected. When the spinal cord was intact the amount of morphine microinjected into the brainstem required to inhibit the excitation of dorsal horn neurones was about ten fold less than it was in spinal animals. It is concluded that large, but not small doses of morphine microinjected into the brainstem can exert effects on the spinal cord after first entering the circulation. The effects of small doses are attributed to a local action in the brainstem which causes inhibition of spinal neurones either by activating descending inhibitory neuronal systems or by liberating endogenous substances which reach the spinal cord via the cerebro-spinal fluid. The concentrations of morphine achieved at various distances from the site of injection by the microinjection of microgram quantities and the time courses of the concentration changes were calculated from diffusion equations, assuming diffusion coefficients of 3 or 5 X 10(6) cm2 s-1. The curves obtained closely approximated those obtained experimentally. The concentrations achieved at distances up to 2 mm from the site of injection of 10 micrograms of morphine were calculated to exceed 10(-4)M and the time-courses of these concentration changes were compatible with the time course of inhibition of spinal neurones, or the production of analgesia after microinjection. Such concentrations are vastly in excess of those achieved in the brain after the systemic administration of morphine in analgesic doses. It is concluded that the local effects in the brainstem produced by the microinjection of microgram quantities of morphine have no relevance to the mechanism of analgesia produced by systemic administration.

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.

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.

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.

The limited responsiveness of single-channel recording systems results in some brief events not being detected, and if this is ignored parameter estimation from the observed data will be biased. Statistical methods of correcting for this limited time resolution in a two-state Markov model have been proposed by Neher (1983. J. Physiol. (Lond.). 339:663-678) and by Colquhoun and Sigworth (1983. Single Channel Recording. 191-263). However, a numerical study by Blatz and Magleby (1986. Biophys. J. 49:967-980) indicated differences of 3-40% in the corrected values given by the two techniques. Here we explain why Neher's method produces biased results and the Colquhoun and Sigworth approach, which is no more difficult, provides reasonably accurate estimates.