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R D Purves

Publications and source records attributed to R D Purves.

At least 19 recordsLinked to original sources
PubMed1996

Electron probe X-ray microanalysis of rabbit ciliary epithelium.

Rabbit iris-ciliary bodies were preincubated in control and experimental Ringer's solutions before quick freezing, cryosectioning, dehydration and electron probe X-ray microanalysis. After preincubation in a baseline bicarbonate-free Cl- Ringer's solution, the ciliary epithelial intracellular Na+, K+ and Cl- concentrations were estimated to be 15 +/- 3, 162 +/- 14 and 46 +/- 5 mmol kg-1 intracellular water, respectively. The water and elemental Na, K, Cl and P contents were similar in the non-pigmented (NPE) and pigmented (PE) ciliary epithelial cells. As expected, inhibition of the Na,K-exchange pump by preincubation with ouabain markedly increased the intracellular Na content, and markedly reduced the intracellular K content, verifying the validity of the experimental analysis. The Cl- channels of the NPE cells likely play a critical role in determining the rate of aqueous humor formation. Therefore, we have examined the effects of altering Cl- transport on the intracellular composition in this initial microprobe study of the ciliary epithelium. As expected, exposure to bicarbonate increased the intracellular Cl and water contents. Replacement of external Cl- by NO3- was twice as effective as replacement by gluconate in leaching Cl- out of the intracellular compartment. An unexpected finding was that NO3- replacement of internal Cl- substantially increased the intracellular Na and decreased the intracellular K content, possibly by stabilizing the Na,K-pump in the E1P form and inhibiting enzyme activity.

Animals↗
PubMed1996

Multiple solutions, illegal parameter values, local minima of the sum of squares, and anomalous parameter estimates in least-squares fitting of the two-compartment pharmacokinetic model with absorption.

When the two-compartment model with absorption is fitted to data by nonlinear least squares, in general six different outcomes can be obtained, arising from permutation of the three exponential rate constants. The existence of multiple solutions in this sense is analogous to the flip-flop phenomenon in the one-compartment model. It is possible for parameter estimates to be inconsistent with the underlying physical model. Methods for recognizing such illegal estimates are described. Other common difficulties are that estimated values for two of the rate constants are almost identical with very large standard deviations, or that the parameter estimation algorithm converges poorly. Such unwanted outcomes usually signal a local (false) minimum of the sum of squares. They can be recognized from the ratio of largest to smallest singular value of the Jacobian matrix, and are, in principle, avoidable by starting the estimation algorithm with different initial values. There also exists a class of data sets for which all outcomes of fitting the usual equations are anomalous. A better fit to these data sets (smaller sum of squares) is obtained if two of the relevant rate constants are allowed to take complex conjugate values. Such data sets have usually been described as having "equal rate constants." A special form of the model equation is available for parameter estimation in this case. Precautions relating to its use are discussed.

Least-Squares Analysis↗
PubMed1995

Accuracy of numerical inversion of Laplace transforms for pharmacokinetic parameter estimation.

Numerical inversion of the Laplace transform is a useful technique for pharmacokinetic modeling and parameter estimation when the model equations can be solved in the Laplace domain but the solutions cannot be inverted back to the time domain. The accuracy of numerical inversion of the Laplace transform using an infinite series approximation due to Hosono was systematically studied by reference to 17 widely differing functions having known inverse transforms. The error of inversion was found to be very sensitive to the details of the computer implementation of the method; for example, double-precision artihmetic is essential. The method used to sum the series in the least-squares program Multi(Filt) was often unable to achieve a relative error of less than 10(-4), and a Monte Carlo simulation showed that this method is insufficiently accurate for reliable least-squares parameter estimation. Improvements to the algorithm are described whereby a better method of applying Euler's transformation is used and the number of terms summed is determined automatically by the rate of convergence of the series. The improved algorithm is more efficient in inverting easy functions and more reliable in inverting difficult functions, especially those involving a time lag. With its use, pharmacokinetic parameter estimation can be performed with essentially the same accuracy as when the function is defined in the time domain.

Algorithms↗
PubMed1995

Effects of voltage clamping on epithelial cell composition in toad urinary bladder studied with x-ray microanalysis.

Toad urinary bladder epithelial cells were incubated in Na Ringer's with the serosal surface of the epithelium clamped at either +50 mV, 0 mV (short-circuited) or -50 mV with respect to the mucosal surface. Following incubation, portions of tissue were coated with an external albumin standard and rapidly frozen. Cryosections were freeze-dried and cell composition determined by x-ray microanalysis. Cell water and ion contents were unaffected when tissues were short-circuited rather than clamped close to their open-circuit potential difference (+50 mV). Incubation with vasopressin at +50 mV, and under short-circuit conditions, caused Na uptake without cell swelling or gain in Cl. Clamping at -50 mV resulted in uptake of water and ions, with considerable variation from cell to cell. These variations in cell composition were exacerbated by vasopressin. The greater the increase in water content, the greater the rise in cell Cl. However, there was no consistent pattern to the associated changes in cation contents. Most cells gained some Na. In some cells, this gain was accompanied by an increase in K. In others, the gain of Na was predominant and cell K content actually fell. At -50 mV with ouabain, many of the cells also gained water. As was found in our earlier study with ouabain under short circuit conditions (Bowler et al., 1991), there was considerable variation in the extent of the Na gain and K loss; some cells were largely depleted of K while in others the K content remained relatively normal. These results indicate differences between granular cells in the availabilities in the plasma membranes of ion pathways, either as a consequence of differences in the numbers of such pathways or in their control.

Animals↗
PubMed1994

Problems in the understanding of cell volume regulation.

The constancy of cell volume under physiological conditions is generally thought to reflect a balance between solute influx and efflux and is therefore critically dependent on the properties of the plasma membrane. Despite a number of unanswered questions, a large amount of experimental data can be accommodated within this pump-leak framework and can by analysed using the simple assumptions of osmotic equality between cells and their surrounding fluid, and fluid electroneutrality. Experimentally, cell volume may be altered in vitro either by changing cell solute content under isosmotic conditions or by changing medium osmolality. Exposure to anisosmotic media may provoke a variety of cell responses that minimise the volume change. However, much of this experimental work has been performed under extreme conditions in vitro that would never be experienced by vertebrate cells in vivo; its relevance to pathophysiological situations is questionable. It is argued that regulation of cell volume should not be seen in isolation but as part of the process, cell homeostasis, by which cells attempt to minimise changes in composition when faced with perturbations in their environment. Given the variety of processes and the large numbers of membrane transporters, an understanding of how cells respond to such perturbations requires a combination of modelling and experimentation. A simple example of this approach is presented.

Animals↗
PubMed1994

Numerical estimation of the noncompartmental pharmacokinetic parameters variance and coefficient of variation of residence times.

Noncompartmental investigation of the distribution of residence times from concentration-time data requires estimation of the second noncentral moment (AUM2C) as well as the area under the curve (AUC) and the area under the moment curve (AUMC). The accuracy and precision of 12 numerical integration methods for AUM2C were tested on simulated noisy data sets representing bolus, oral, and infusion concentration-time profiles. The root-mean-squared errors given by the best methods were only slightly larger than the corresponding errors in the estimation of AUC and AUMC. AUM2C extrapolated "tail" areas as estimated from a log-linear fit are biased, but the bias is minimized by application of a simple correction factor. The precision of estimates of variance of residence times (VRT) can be severely impaired by the variance of the extrapolated tails. VRT is therefore not a useful parameter unless the tail areas are small or can be shown to be estimated with little error. Estimates of the coefficient of variation of residence times (CVRT) and its square (CV2) are robust in the sense of being little affected by errors in the concentration values. The accuracy of estimates of CVRT obtained by optimum numerical methods is equal to or better than that of AUC and mean residence time estimates, even in data sets with large tail areas.

Administration, Oral↗
PubMed1994

Cell Cl and transepithelial na transport in toad urinary bladder.

Relationships between short-circuit current (Isc), cell Cl and the mechanism(s) of Cl accumulation in toad bladder epithelial cells were investigated. In serosal Cl-free gluconate Ringer, 80% of the cell Cl (measured by x-ray microanalysis) was lost over 30-60 min with an associated decrease in cell water content. concomitantly, Isc fell to 20% of its initial value within 10 min but then recovered to 45% of its initial value despite continued Cl loss. With the reintroduction of Cl, cell Cl and Isc both recovered within 10 min. Serosal SITS (4-acetamido-4'-isothiocyano-stilbene-2,2'-disulfonate; 0.5 mM) plus bumetanide (0.1 mM), did not prevent the fall in Isc or the loss of cell Cl in gluconate medium, although they did inhibit subsequent recovery of Isc in this medium. They also prevented the recovery of Isc in Cl medium but not the reaccumulation of Cl by the cells. Although SITS and bumetanide did not prevent the loss or recovery of Cl, they modified the pattern of the ion changes. In their absence, changes in cellular Cl were twice that of the changes in measured cellular cations implicating basolateral Cl/HCO3 exchange in Cl movement. With SITS plus bumetanide present, changes of similar magnitude in Cl were associated with equivalent changes in cation, consistent with the inhibition of Cl/HCO3 exchange.

4-Acetamido-4'-isothiocyanatostilbene-2,2'-disulfo↗
PubMed1993

Anomalous parameter estimates in the one-compartment model with first-order absorption.

A difficulty sometimes encountered in least-squares fitting of a one-compartment model with first-order absorption is that estimated values (ka and ke) of the rate constants of absorption and elimination are almost identical, are highly correlated and have very large standard deviations. This anomaly is explained by the existence of a class of data sets for which least-squares estimates of the rate constants are complex quantities. Such data sets may arise either from an unfortunate combination of random (e.g. assay) errors in the concentration values if ka and ke are sufficiently similar in magnitude, or from delayed absorption.

Algorithms↗
PubMed1992

Bias and variance of extrapolated tails for area-under-the-curve (AUC) and area-under-the-moment-curve (AUMC).

The usual formulas for the extrapolated values of AUC and AUMC from tn to infinity produce estimates that are biased. An empirical correction factor is shown to reduce both bias and variance of estimates. The fitted value Cz at the last time-point tn should normally be used in the formulas, rather than the measured concentration Cn. Nonlinear least squares methods offer no advantage over the fitting of a straight line to ln (C).

Analysis of Variance↗
PubMed1992

Optimum numerical integration methods for estimation of area-under-the-curve (AUC) and area-under-the-moment-curve (AUMC).

Eleven numerical methods for estimation of AUC (including 4 new methods) and 22 methods for AUMC (including 8 new methods) were tested on large simulated noisy datasets representing bolus, oral and infusion concentration-time profiles. Some methods were unacceptable because their mean error was large; these included a commonly recommended form of the linear trapezoidal rule for AUMC. Others, notably Lagrange and cubic spline methods, were unacceptable because the variance of their estimates was large. These methods should be abandoned. A simple and easily programmed new method, parabolas-through-the-origin then log-trapezoidal rule, performed especially well.

Numerical Analysis, Computer-Assisted↗
PubMed1991

Model representation of salicylate pharmacokinetics using unbound plasma salicylate concentrations and metabolite urinary excretion rates following a single oral dose.

The pharmacokinetics of salicylic acid (SA) and its metabolites have been studied in 5 volunteers after administration of 3 g salicylic acid (as sodium salicylate) and collection of serial samples of blood and urine. SA and its metabolites were assayed with a HPLC method specific for each species. The urinary excretion rates of individual metabolites were analyzed using unbound plasma SA concentrations and Lineweaver-Burke plots. The analysis confirmed that the formation of SA urate (SU) and SA phenolic glucuronide (SPG) metabolites are saturable processes, and showed that the Michaelis-Menten values derived are consistent with earlier estimates derived solely from urinary data. The unbound salicylate plasma concentration-time profiles were then analyzed with various models assuming either saturable clearances for metabolite formation and/or saturable protein binding. The data were best described with a model that included both saturable protein binding and saturable metabolism. The model assumed first-order absorption kinetics and instantaneous distribution into extravascular and tissue compartments. The model was validated by comparing predicted relationships between the apparent volume of distribution, clearance, and plasma salicylate concentrations with previous relationships obtained using steady state data.

Administration, Oral↗
PubMed1991

Effects of potassium-free media and ouabain on epithelial cell composition in toad urinary bladder studied with X-ray microanalysis.

The technique of X-ray microanalysis was used to study the composition of toad urinary bladder epithelial cells incubated in Na Ringer's and K-free medium, with and without ouabain. Following incubation under short-circuit conditions, portions of tissue were coated with an external albumin standard and plunge-frozen. Cryosections were freeze-dried and analyzed. In Na Ringer's, granular and basal cells, and also the basal portion of the goblet cells, had similar water and ion compositions. In contrast, mitochondria-rich cells contained less Cl and Na. On average, the granular cells and a subpopulation of the basal cells lost K and gained Na after ouabain and in K-free medium alone. However, there was considerable variation from cell to cell in the responses, indicating differences between cells in the availabilities of ion pathways, either as a consequence of differences in the numbers of such pathways or in their control. In contrast, the compositions of both the low Cl, mitochondria-rich cells and a sub-population of the basal cells were little affected by the different incubation conditions. This is consistent with a comparatively low Na permeability of these cells. The results also indicate that (i) much, if not all, of the K in the dominant cell type, the granular cells, is potentially exchangeable with serosal medium Na, and (ii) Na is accumulated from the serosal medium under K-free conditions. They also provide information about the role of the (Na-K)-ATPase in the maintenance of cellular K in K-free medium, being consistent with other evidence that removal of serosal medium K inhibits transepithelial Na transport by decreasing Na entry to the cells from the mucosal medium, rather than solely by inhibiting the basolateral membrane (Na-K)-ATPase.

Animals↗
PubMed1988

Single-channel recordings from the apical membrane of the toad urinary bladder epithelial cell.

The patch-clamp technique for the recording of single-channel currents was used to investigate the activity of ion channels in the intact epithelium of the toad urinary bladder. High resistance seals were obtained from the apical membrane of tightly stretched tissue. Single-channel recordings revealed the activity of a variety of ion channels that could be classified in 4 groups according to their mean ion conductances, ranging from 5 to 59 pS. In particular, we observed highly selective, amiloride-sensitive Na channels with a mean conductance of 4.8 pS, channels with a similar conductance that were not Na-selective and channels with mean conductance values of 17-58 pS that were mostly seen after stimulation of the tissue with vasopressin or cAMP. When inside-out patches from the apical membrane were exposed to 110 mM fluoride, large conductances (86-490 pS) appeared.

Amiloride↗
PubMed1987

Urinary bladder intramural neurones: an electrophysiological study utilizing a tissue culture preparation.

An enzymic dispersion technique was used to free the intramural ganglia from their usual close association with the other components of the urinary bladder wall. The isolated ganglia obtained were viable and could be kept in culture for several weeks. The development of the cultures was monitored by phase-contrast microscopy and their electrophysiological properties were investigated using intracellular recording techniques. Neurones could be visually identified after 2-3 days in culture; cell groups contained from 2-50 neurones. Three types of spontaneous activity were seen: small changes in membrane potential and action potentials, and slow oscillatory conductance changes. These events were not blocked by hexamethonium but were abolished by hyperpolarizing current. Most neurones spiked without adaptation to direct stimulation; in a few cells the train of spikes was damped out. No neurones generated long afterhyperpolarizations. Indirect stimulation produced responses in the ganglia which are consistent with synaptic activity. Summation of inputs was demonstrated. These results provide evidence for local intraganglionic circuits since the ganglia or neurone groups are unequivocally extrinsically denervated. It was concluded that the intramural ganglia have the capacity to integrate preganglionic input and the question of whether or not they might mediate reflex activity is raised.

Action Potentials↗
PubMed1986

Body sodium in rats: response to DOCA, adrenalectomy, changes in salt intake, and a salt load.

Body Na was studied by an isotope method in rats on Na-free diet plus a choice of H2O and 0.5% or 0.1% NaCl. Two groups (1 on 0.5%, 1 on 0.1% NaCl) had Silastic deoxycorticosterone acetate (DOCA) implants, two similar groups were sham operated, and a fifth group (on 0.5% NaCl) underwent adrenalectomy (ADX). Saline consumption increased in DOCA-treated and ADX rats. Body Na was increased by DOCA and by drinking 0.5% NaCl compared with 0.1% NaCl. Body Na after intraperitoneal NaCl loading (which raised body Na 8-10%) and withdrawal of NaCl drinking fluids was analyzed by use of the model y = Ae-a(t-d) + Be-bt, where y is body Na at time t and d is delay before fast rate constant a is established; d was greater on the lower Na intake. Rate constant a was not reduced by chronic DOCA treatment. Coefficient B of the slow exponential, representing the basal level to which body Na falls on zero Na intake, and equivalent to Hollenberg's "set-point," was higher in DOCA-treated rats. This analysis makes use of Hollenberg's set-point concept, but the findings suggest that the set-point is related to mineralocorticoid activity and is thus presumably variable.

Adrenalectomy↗
PubMed1985

Effects of DOCA and salt intake on body sodium, fluid intake, blood pressure and excretion of a sodium load in rats.

Body sodium was measured repeatedly by a whole-body counting method (22Na) in control and deoxycorticosterone acetate (DOCA)-treated Wistar rats taking a sodium-free pelleted diet and drinking a choice of H2O and either 0.5% NaCl or 0.1% NaCl (n = 11 per group, four groups). Body sodium was higher in DOCA-treated than in control rats and higher in rats on 0.5% NaCl than in those on 0.1% NaCl. These differences persisted even when all sodium intake was stopped. An intraperitoneal NaCl load was excreted at least as rapidly by the DOCA-treated as by the control rats. Commencement of excretion was slower in the rats on 0.1% NaCl than in those on 0.5% NaCl. It is concluded that DOCA raises the basal level of body sodium but does not slow down the excretion of sodium in the body in excess of the basal level.

Animals↗
PubMed1984

Mechanical hypothesis of sperm penetration.

Sperm have generally been supposed to penetrate the zona pellucida surrounding the mammalian egg with the aid of a protease, acrosin. Difficulties associated with this view are discussed and an alternative, mechanical hypothesis introduced. The calculated force exerted by individual sperm is too small to permit the rupture of any but the weakest of secondary chemical bonds. Mechanical progress through the zona must rely on stress relaxation in a viscoelastic medium. The known properties of the zona appear to be consistent with such a mechanism of penetration.

Acrosin↗