Association effect of the phytocannabinoid beta-caryophyllene and indomethacin carried in topical nanoemulgels: an evaluation by in vivo anti-inflammatory model

The sesquiterpene β-caryophyllene, classified as a phytocannabinoid compound, has been widely studied owing to its multi-target action. In addition, this compound has demonstrated application as a skin permeation promoter. In this context, this study aimed to evaluate the feasibility of associating β-caryophyllene and indomethacin in the oily core of hydrogel thickened nanoemulsions, as well as, to evaluate the in vivo anti-inflammatory effect of this association by croton oil ear edoema induced model. After topical application, the nanoemulgels resulted in increased edoema mass when compared to the substances in their free form. Overall, the results differed from expected, and the data found may be owing to the specificities of the in vivo model applied, as well as the tested ratio between β-caryophyllene and indomethacin (200:1). New perspectives arise from the data found regarding the evaluation of the association of terpenic compounds with indomethacin in nanoemulsified systems.

Co-delivery of beta-caryophyllene and indomethacin in the oily core of nanoemulsions potentiates the anti-inflammatory effect in LPS-stimulated macrophage model

The potentiation of pharmacological effects can be achieved through several strategies, such as the association of substances and delivery in nanostructured systems. In practice, potentiation can be measured by the law of mass action and joint evaluation of the combination index (CI) and dose-response curves. In this context, this study aimed to evaluate the anti-inflammatory effect of the association of β-caryophyllene and indomethacin in the free form and delivered in nanoemulsions using the in vitro model of LPS-stimulated murine macrophage. The results indicated potentiation of the anti-inflammatory effect of nanoemulsified substances compared to free substances, as well as synergistic action between the sesquiterpene and the selected NSAID. In comparison, the association of β-caryophyllene and indomethacin in the free form inhibited the production of nitric oxide by 50% at 48.60 µg/mL (CI = 0.21), while the nanoemulsified association of these substances resulted in an IC50 of 1.45 µg/mL (CI = 0.14). In parallel, cytotoxicity assays on HaCaT and MRC-5 cell lines demonstrated the safety of IC50-equivalent concentrations of the anti-inflammatory action, and no irritating effects on the chorioallantoic membrane of embryonated eggs were observed (HET-CAM assay). The results suggest that β-caryophyllene may be an alternative to replace an inert oily core in nanoemulsion systems when anti-inflammatory effects are desirable.

Dissolving Microneedles Developed in Association with Nanosystems: A Scoping Review on the Quality Parameters of These Emerging Systems for Drug or Protein Transdermal Delivery

The largest organ of the body provides the main challenge for the transdermal delivery of lipophilic or high molecular weight drugs. To cross the main barrier of the skin, the stratum corneum, many techniques have been developed and improved. In the last 20 years, the association of microneedles with nanostructured systems has gained prominence for its versatility and for enabling targeted drug delivery. Currently, the combination of these mechanisms is pointed to as an emerging technology; however, some gaps need to be answered to transcend the development of these devices from the laboratory scale to the pharmaceutical market. It is known that the lack of regulatory guidelines for quality control is a hindrance to market conquest. In this context, this study undertakes a scoping review of original papers concerning methods applied to evaluate both the quality and drug/protein delivery of dissolving and hydrogel-forming microneedles developed in association with nanostructured systems.

A New, Rapid and Simple RP-HPLC Method for Stability Quantification of a Protease Inhibitor in Tablets

Fosamprenavir calcium is a protease inhibitor widely used in the treatment and prevention of human immunodeficiency virus and acquired immunodeficiency syndrome. This protease inhibitor serves as a prodrug of amprenavir, offering better oral bioavailability. Although this drug was approved by the FDA in 2003, there are few methods established for quantifying the stability for quality control analysis of fosamprenavir-coated tablets. The purpose of the study was to develop and validate a method for determining the stability of fosamprenavir-coated tablets (Telzir®) that may be applied by any quality control laboratory. Chromatographic separation was performed using a Vertical RP-18 column programmed to run a gradient elution with sodium acetate buffer and acetonitrile. Flow rate was 1.2 mL min-1 for a total run time of 15 min. Ultraviolet detection was set at 264 nm and the use of a photodiode array detector in scan mode allowed selectivity confirmation by peak purity evaluation. The analyte peak was found to be adequately separated from degradation products generated during forced degradation studies. Thus, the proposed method was found to accurately indicate stability and was sufficient for routine quantitative analysis of fosamprenavir in coated tablets without interference from major degradation products and excipients.

Anti-inflammatory activity of Brunfelsia uniflora root extract: phytochemical characterization and pharmacologic potential of this under-investigated species

Brunfelsia uniflora (Pohl) D. Don roots have been widely used in folk medicine for treating inflammatory conditions. However, few studies have elucidated compounds that justify their traditional use. This study was conducted to characterize the phytochemical profile and evaluate the in vitro antioxidant capacity, and in vivo anti-inflammatory activity of extracts obtained from B. uniflora roots by comparing an herbal remedy (HR) with the crude hydroalcoholic extract (CHE). In the phytochemical analysis, scopoletin was identified as the marker compound. In quantitative analyses, CHE showed better results than HR. Furthermore, CHE had an effective anti-inflammatory activity. Animals treated with CHE (200 mg/kg) showed an 89.1% and a 73.8% reduction in edema volume after 1 hour of edema induction compared with those treated with negative control and positive control (indomethacin), respectively. These results show that B. uniflora root extracts have promising antioxidant and anti-inflammatory activities, thus corroborating their application in ethnomedicine.

The interaction of Na+, K+, and phosphate with the gastric H,K-ATPase. Kinetics of E1-E2 conformational changes assessed by eosin fluorescence measurements

H,K-ATPase and Na,K-ATPase show the highest degree of sequence similarity among all other members of the P-type ATPases family. To explore their common features in terms of ligand binding, we evaluated conformational transitions due to the binding of Na⁺, K⁺ and Pi in the H,K-ATPase, and compared the results with those obtained for the Na,K-ATPase. This work shows that eosin fluorescence time courses provide a reasonably precise method to study the kinetics of the E1-E2 conformational changes in the H,K-ATPase. We found that, although Na⁺ shifts the equilibrium toward the E1 conformation and seems to compete with H⁺ in ATPase activity assays, it was neither possible to isolate a Na⁺-occluded state, nor to reveal an influx of Na⁺ related to H,K-ATPase activity. The high rate of the E2K → E1 transition found for the H,K-ATPase, which is not compatible with the presence of a K⁺-occluded form, agrees with the negligible level of occluded Rb⁺ (used as a K⁺ congener) found in the absence of added ligands. The use of vanadate and fluorinated metals to induce E2P-like states increased the level of occluded Rb⁺ and suggests that-during dephosphorylation-the probability of K⁺ to remain occluded increases from the E2P-ground to the E2P-product state. From kinetic experiments we found an unexpected increase in the values of k_obs for E2P formation with [Pi]; consequently, to obey the Albers-Post model, the binding of Pi to the E2 state cannot be a rapid-equilibrium reaction.

Impact of roasting conditions on the quality and acceptance of the peanut paste

Roasting is the main processing step performed to improve sensory and conservative properties of peanuts. The objective of this study was to evaluate changes in peanut oil and paste during roasting at different temperatures in a conventional oven (80, 110, 140, 170, and 200°C) and microwave. The increase in roasting temperature promoted reduction of L* value, b* value, and increases of a*, K₂₃₂ , K_270, and acidity. For alpha (α), gamma (γ), and delta (δ) tocopherols, as well as fatty acids, less degradation were observed at the roasting temperature of 140°C. Paste acceptability greater than 70% was achieved with roasting at 140°C. Based on the results, 140°C was the optimal roasting temperature that achieved the best paste acceptance rates with the smallest changes in oil and tocopherol quality parameters.

The impact of CUP1 gene copy-number and XVI-VIII/XV-XVI translocations on copper and sulfite tolerance in vineyard Saccharomyces cerevisiae strain populations

In wine production, sulfites are widely used as antimicrobials and antioxidants, whereas copper is associated with fungicides and wine fining treatments. Therefore, wine yeasts are constantly exposed to these agents. Copper tolerance is related to the copy number of the CUP1 gene, encoding for a metallothionein involved in copper detoxification. In wine yeasts, sulfite resistance mainly depends on the presence of the translocation t(XVI;VIII) in the promoter region of the SSU1 gene. This gene encodes for a plasma membrane sulfite pump involved in sulfite metabolism and detoxification. Recently, a new translocation, t(XVI;VIII), was identified. In this work, 253 Saccharomyces cerevisiae strains, representing three vineyard populations from two different continents, were analyzed, along with 20 industrial starters. Copper and sulfites tolerance as well as distribution of CUP1 gene copy-number, t(XVI;VIII)and t(XVI;XV) of SSU1 gene were studied to evaluate the impact of these genomic variations on population phenotypes. The CUP1 gene copy-number was found to be highly variable, ranging from zero to 79 per strain. Moreover it differently impacted the copper tolerance in the populations of the two continents. The diffusion of t(XVI;VIII) and, for the first time, t(XVI;XV) was determined in the three vineyard populations. The correlation between the presence of the translocation and strain sulfite tolerance levels was significant only for the t(XVI;VIII).

In vitro Probiotic Potential and Anti-cancer Activity of Newly Isolated Folate-Producing Streptococcus thermophilus Strains

Most probiotic strains commercially available today are lactic acid bacteria. Within this functional group, Streptococcus thermophilus is a thermophilic species widely used as starter culture for a huge number of dairy products. Besides being rapid acidifiers, many S. thermophilus strains are able to produce and release folate during growth but, unfortunately, they are seriously impaired during passage through the human gastrointestinal tract. In this work, we studied eight S. thermophilus strains isolated from dairy environments in Italy, which already had shown good technological properties, to evaluate their possible probiotic potential and cytotoxicity against cancer cells in vitro. All strains were also evaluated for some health-related properties such as susceptibility to most common antibiotics, hemolytic activity, resistance to simulated gastrointestinal conditions, bile salts hydrolytic activity, production of folate, adhesion to HT-29 human colorectal adenocarcinoma cells and cytotoxic activity against cancer cells and production of biogenic amines. Results revealed that two fast acidifying S. thermophilus strains were found to possess in vitro probiotic properties along with anticancer activity and production of folate. These properties resulted similar and, in some cases, superior to those of Lactobacillus rhamnosus GG, a well-known commercial probiotic strain. These findings encourage further in vivo studies to evaluate the actual health benefits of these strains on the human host.

Development and validation of a discriminating in vitro dissolution method for a poorly soluble drug, olmesartan medoxomil: comparison between commercial tablets

A dissolution test for tablets containing 40 mg of olmesartan medoxomil (OLM) was developed and validated using both LC-UV and UV methods. After evaluation of the sink condition, dissolution medium, and stability of the drug, the method was validated using USP apparatus 2, 50 rpm rotation speed, and 900 ml of deaerated H(2)O + 0.5% sodium lauryl sulfate (w/v) at pH 6.8 (adjusted with 18% phosphoric acid) as the dissolution medium. The model-independent method using difference factor (f(1)) and similarity factor (f(2)), model-dependent method, and dissolution efficiency were employed to compare dissolution profiles. The kinetic parameters of drug release were also investigated. The obtained results provided adequate dissolution profiles. The developed dissolution test was validated according to international guidelines. Since there is no monograph for this drug in tablets, the dissolution method presented here can be used as a quality control test for OLM in this dosage form, especially in a batch to batch evaluation.

Steady-state kinetic analysis of the Na+/K+-ATPase. The activation of ATP hydrolysis by cations

We studied the interactions between pairs of cations during activation of the steady-state hydrolysis of ATP of the Na+/K+-ATPase. Non-linear regression was used to obtain empirical equations that describe quantitatively the behaviour of the system. The curve relating activity to Na+ concentration was describable by a Hill equation with nH = 2 and not by the more frequently used expression based on rapid-equilibrium binding of Na+ to three identical and non-interacting sites. At non-limiting concentrations of the other ligands, changes in the concentration of Na+ or of Mg2+ modified in the same proportion the maximum effects and the apparent affinities of K+, revealing the operation of either ping-pong or of ordered sequential mechanisms with irreversible steps separating the additions of each ligand. In contrast with this, changes in the concentration of Mg2+ altered only the maximum effect of Na+, indicating that a ternary complex between the cations and the enzyme has to be formed and that certain particular relations have to hold among the rate constants of the system. The interactions described in this paper, together with those previously reported, allowed us to derive a general equation that adequately predicted the response of the Na+/K+-ATPase to the concentration of any pair of ligands at non-limiting concentrations of the rest. Confrontation of this equation with computer simulations of the behaviour of the Albers-Post model shows that this model predicts the interactions in which K+ participates and perhaps also the interaction between Mg2+ and Na+, but seems unable to predict the interactions between pairs of ligands that do not include K+.

Volumetric response of vertebrate hepatocytes challenged by osmotic gradients: a theoretical approach

In this study we use a theoretical approach to study the volumetric response of goldfish hepatocytes challenged by osmotic gradients and compared it with that of hepatocytes from another teleost (the trout) and a mammal (the rat). Particular focus was given to the multiple non-linear interactions of transport systems enabling hypotonically challenged cells to trigger a compensatory response known as volume regulatory decrease or RVD. For this purpose we employed a mathematical model which describes the rates of change of the intracellular concentrations of main diffusible ions, of the cell volume, and of the membrane potential. The model was fitted to experimental data on the kinetics of volume change of hepatocytes challenged by anisotonic media. In trout and rat hepatocytes, experimental results had shown that hypotonic cell swelling was followed by RVD, whereas goldfish cells swelled with no concomitant RVD (M.V. Espelt et al., 2003, J. Exp. Biol. 206, 513-522). A comparison between data predicted by the model and that obtained experimentally suggests that in trout and rat hepatocytes hypotonicity activates a sensor element and this, in turn, activates an otherwise silent efflux of KCl - whose kinetics could be successfully predicted - thereby leading to volume down-regulation. In contrast, with regard to the absence of RVD in goldfish hepatocytes the model proposed suggests that either a sensor element triggering RVD is absent or that the effector mechanism (the loss of KCl) remains inactive under the conditions employed. In line with this, we recently found that extracellular nucleotides may be required to induce RVD in these cells, indicating that our model could indeed lead to useful predictions.

Synthesis and human leukocyte elastase inhibitory evaluation of phosphate triesters and acyl phosphates of penam sulfides and sulfones

The synthesis of 6,6-dibromo-3alpha-(diphenylphosphate)oxymethyl-2,2-dimethyl penam sulfone (3a), 6alpha-chloro-3alpha-(diphenylphosphate)oxymethyl-2,2-dimethyl penam sulfone (3b), benzyl 6alpha-(diphenyl-phosphate)oxypenicillanate sulfone (4) and 6,6-dibromo-3alpha-(methylphosphate)carbonyl-2,2-dimethylpenam sulfone (12) are reported. When tested as inhibitors of human leukocyte elastase, the compound 4 proved to be the most active.

Quantitation of plasma membrane calcium pump phosphorylated intermediates by electrophoresis

P-ATPases are characterized by the formation of acid-stable phosphorylated intermediates (EP) during their reaction cycle. We have developed a microscale method to determine EP that involves the phosphorylation of the enzyme using [gamma-(32)P]ATP and precipitation with TCA; separation of the sample by SDS-PAGE, and measurement of the enzyme protein and (32)P-labeled EP by digital analysis of both the stained gel and its autoradiogram, respectively. The principal advantages of this method over typical procedures (filtration and centrifugation) are the low amount of enzyme required and the substantial decrease in the blank values and data scattering produced by unspecific phosphorylation and nonquantitative recovering of the enzyme. Application of this new method to a purified preparation of the plasma membrane calcium ATPase (PMCA) results in overcoming the difficulties of measuring EP at high ATP concentrations. A biphasic behavior of the substrate curve for EP was observed when the study was extended to ATP levels within the physiological range. Since, in principle, the method does not require the use of highly purified preparations, it could be helpful for the study of phosphorylated intermediates especially under conditions in which small amounts of protein are available, e.g., mutated variants of P-ATPases.

Are the states that occlude rubidium obligatory intermediates of the Na(+)/K(+)-ATPase reaction?

In the Albers-Post model, occlusion of K(+) in the E(2) conformer of the enzyme (E) is an obligatory step of Na(+)/K(+)-ATPase reaction. If this were so the ratio (Na(+)/K(+)-ATPase activity)/(concentration of occluded species) should be equal to the rate constant for deocclusion. We tested this prediction in a partially purified Na(+)/K(+)-ATPase from pig kidney by means of rapid filtration to measure the occlusion using the K(+) congener Rb(+). Assuming that always two Rb(+) are occluded per enzyme, the steady-state levels of occluded forms and the kinetics of deocclusion were adequately described by the Albers-Post model over a very wide range of [ATP] and [Rb(+)]. The same happened with the kinetics of ATP hydrolysis. However, the value of the parameters that gave best fit differed from those for occlusion in such a way that the ratio (Na(+)/K(+)-ATPase activity)/(concentration of occluded species) became much larger than the rate constant for deocclusion when [Rb(+)] <10 mM. This points to the presence of an extra ATP hydrolysis that is not Na(+)-ATPase activity and that does not involve occlusion. A possible way of explaining this is to posit that the binding of a single Rb(+) increases ATP hydrolysis without occlusion.

An attachment for nondestructive, fast quenching of samples in rapid-mixing experiments

The present paper describes a quenching-and-washing chamber (QWC) to be used with a rapid-mixing apparatus (RMA) for the study of processes in the millisecond time scale. The QWC enables fast, nondestructive quenching by cooling and dilution of reactants in particulate systems that can be trapped on a filter. The reaction mixture (e.g., at 25 degrees C) is injected from the RMA into the QWC where it is immediately mixed with a stream of ice-cold solution flowing at a rate of 15-40 ml s-1. Quenching requires that the process studied is slowed considerably by cooling to 0-2 degrees C and/or by removal of reactants by dilution. The equipment was characterized through a study of the tight binding (occlusion) of 86Rb+ to purified, membrane-bound Na+/K+-ATPase. Millipore filters of 0.22-0.80 microm pore size trapped close to 100% of the enzyme protein. Enzyme with occluded 86Rb+ was formed in the RMA under conditions where the rate constant for release of Rb+ at 25 degrees C is up to 25 s-1 and then injected into the QWC. The high off-rate constant is due to the presence of 2.5 mM ATP, which accelerates release of Rb+. The recovery of occluded 86Rb+ on the filter was at least 90%, indicating that both cooling of the reactants and dilution of ATP are fast enough to stop the reaction. The quenching time was 3-4 ms.

Functional role of ecto-ATPase activity in goldfish hepatocytes

Extracellular [gamma-32P]ATP added to a suspension of goldfish hepatocytes can be hydrolyzed to ADP plus gamma-32Pi due to the presence of an ecto-ATPase located in the plasma membrane. Ecto-ATPase activity was a hyperbolic function of ATP concentration ([ATP]), with apparent maximal activity of 8.3 +/- 0.4 nmol P(i).(10(6) cells)-1.min-1 and substrate concentration at which a half-maximal hydrolysis rate is obtained of 667 +/- 123 microM. Ecto-ATPase activity was inhibited 70% by suramin but was insensitive to inhibitors of transport ATPases. Addition of 5 microM [alpha-32P]ATP to the hepatocyte suspension induced the extracellular release of alpha-32P(i) [8.2 pmol.(10(6) cells)-1.min-1] and adenosine, suggesting the presence of other ectonucleotidase(s). Exposure of cell suspensions to 5 microM [2,8-3H]ATP resulted in uptake of [2,8-3H]adenosine at 7.9 pmol.(10(6) cells)-1.min-1. Addition of low micromolar [ATP] strongly increased cytosolic free Ca2+ (Ca2+i). This effect could be partially mimicked by adenosine 5'-O-(3-thiotriphosphate), a nonhydrolyzable analog of ATP. The blockage of both glycolysis and oxidative phosphorylation led to a sixfold increase of Ca2+i and an 80% decrease of intracellular ATP, but ecto-ATPase activity was insensitive to these metabolic changes. Ecto-ATPase activity represents the first step leading to the complete hydrolysis of extracellular ATP, which allows 1) termination of the action of ATP on specific purinoceptors and 2) the resulting adenosine to be taken up by the cells.

An unexpected effect of ATP on the ratio between activity and phosphoenzyme level of Na+/K(+)-ATPase in steady state

According to the Albers-Post model the hydrolysis of ATP catalyzed by the Na+/K(+)-ATPase requires the sequential formation of at least two conformers of a phosphoenzyme (E1P and E2P), followed by the K(+)-stimulated hydrolysis of E2P. In this paper we show that this model is a particular case of a more general class of models in all of which the ratio between ATPase activity (v) and total phosphoenzyme level (EP) in steady state is determined solely by the rate constants of interconversion between phosphoconformers and of dephosphorylation. Since these are thought to be unaffected by ATP, the substrate curves for ATPase activity and EP should be identical in shape so that the ratio v/EP ought to be independent of the concentration of ATP. We tested this prediction by parallel measurements of v and EP as a function of [ATP] in the absence or presence of non-limiting concentrations of K+, Rb+ or NH+4. In the absence of K+ or its congeners, both curves followed Michaelis-Menten kinetics, with almost identical Km values (0.16 microM) so that v/EP remained independent of [ATP]. In the presence of either K+, Rb+ or NH+4, v and EP increased with [ATP] along the sum of two Michaelis-Menten equations. The biphasic response of v is well known but, to the best of our knowledge, our results are the first demonstration that the response of EP to [ATP] is also biphasic. Under these conditions, the ratio v/EP increased with [ATP] from 19.8 to 40.1 s-1 along a hyperbola that was half-maximal at 9.5 microM. To preserve the validity of the current model it seems necessary to assume that ATP acts on the E1P <--> E2P transition and/or on the rate of hydrolysis of E2P. The latter possibility was ruled out. We also found that to fit the Albers-Post model to our data, the rate constant for K+ deocclussion from E2 has to be about 10-times higher than that reported from measurements of partial reactions. The results indicate that the Albers-Post model quantitatively predicts the experimental behavior of the Na(+)-ATPase activity but is unable to do this for the Na+/K(+)-ATPase activity, unless additional and yet unproved hypothesis are included.

Low affinity acceleration of the phosphorylation reaction of the Na,K-ATPase by ATP

The maximum rate of phosphorylation (rm) of a highly purified Na,K-ATPase from red outer medulla of pig kidney was measured at 25 degrees C as a function of ATP concentration in media with Mg2+, Na+, and no K+. When rm was plotted as a function of the concentration of ATP a biphasic response was observed with a hyperbolic component of high affinity (Km = 15.7 +/- 2.6 microM) and low velocity ((rm)max = 460 +/- 40 nmol of Pi/(mg of protein.s)) plus a parabolic component which showed no saturation up to 1000 microM ATP, concentration at which rm was 1768.1 +/- 429.6 nmol Pi/(mg protein.s) (mean +/- S.E.; n = 3). This low affinity effect of ATP on the rate of phosphorylation disappeared when the Na,K-ATPase underwent turnover in medium without K+ suggesting that, like superphosphorylation (Peluffo, R. D., Garrahan, P. J., and Rega, A. F. (1992) J. Biol. Chem. 267, 6596-6601), it required the enzyme to be at rest. This property of the Na,K-ATPase was not predicted by the Albers-Post reaction scheme. The observed behavior of the enzyme could be simulated by a scheme that involves a resting enzyme (Er) functionally different from E1 or E2, which is able to bind three molecules of ATP, one with high and two with low affinity, and that after phosphorylation is converted into the phosphointermediates that are generally considered to participate in the reaction cycle described by Albers and Post.

Kinetics of K(+)-stimulated dephosphorylation and simultaneous K+ occlusion by Na,K-ATPase, studied with the K+ congener Tl+. The possibility of differences between the first turnover and steady state

Using the K+ congener Tl+ and rapid mixing combined with special quench techniques, we have investigated (at 20 degrees C) what is usually assumed to be the enzymatic correlate of active transport of K+ by Na,K-ATPase: the Tl(+)-catalyzed dephosphorylation of the K(+)-sensitive phosphointermediate(s), EP, and the resulting occlusion of Tl+ in the enzyme protein. We measured [EP] and [occluded Tl] as a function of time in phosphorylation, as well as dephosphorylation experiments with the following results. First, we found that with 150 mM Na+ and 600 mM Na(+)--NO3- was the anion--[Tl+] = 0.1-1 mM was without influence on the phosphorylation rate. Tl(+)-catalyzed dephosphorylation and Tl+ occlusion appeared to be simultaneous, and the stoichiometry was always 2 Tl+ occluded/EP dephosphorylated. Second, we tried computer simulations of the transient kinetic experiments, using an Albers-Post-type reaction scheme. This produced satisfactory curve-fits only in the case of 150 mM Na+, and although we could arrange that calculated [EP]steady-state was equal to that measured, the calculated steady-state Na,Tl-ATPase hydrolysis rates were always two to four times the rates measured directly. Third, we propose, as one (possibly of several) solution to these discrepancies between model and data, an expanded kinetic model consisting of an initiation reaction sequence followed by a propagation (or steady-state) reaction cycle. In this alternative model the first turnover of the enzyme is kinetically different from subsequent reaction cycles, and this allowed us to obtain both satisfactory curve-fits and accordance between calculated and measured values of hydrolysis-rate and [EP]steady-state.