The rate of convergence of a generalized stable population

In an age-structured population that grows exponentially, each age groupP _i(t) at periodt is asymptotically equivalent tox ₀ ^t for some positive number x₀. In this paper we show that the speed at which the ith age group reaches its exponential state of equilibrium can be measured by the rate at which the ratio v_i(t)=P_i(t)/p_i(t–1) converges tox ₀. The age specific rate of convergence is determined by considering a quantityr satisfyingv _i(t)-x ₀ ¦ r ^t whent is large;R _i=Infr (over all initial populations,r satisfying the above inequality) is the R-factor used in numerical analysis to measure the rate at which the sequencev _i (t) converges tox ₀;S _i =- In R_i is then defined as the rate of convergence to stability of the ith age group. The case of constant net maternity rates is studied in detail; in this contextS ₀ is compared to the population entropyH, which was proposed by Tuljapurkar (1982) as a measure of the rate of convergence to stability.     

Phosphate concentration and transport in Ehrlich ascites tumor cells: Effect of sodium

The effects of extracellular P_i and Na⁺ on cellular P_i concentration and transport were studied. Steady-state P_i exchange flux was measured by ³²P uptake in the presence and absence of Na⁺. Model experiments were also conducted to assess the possibility that hydrolysis of organic phosphate esters contributes to the chemically measured intracellular P_i concentration of Ehrlich ascites tumor cells. The results of these experiments indicate that hydroloysis of labile organic phosphate esters does not contribute to the measured intracellular pool of P_i. The P_i transport system exhibits an apparent K_s of 0.115 mM P_i and a maximal flux of 1.73 mmole min^?1 (kg dry wt)^?1. When incubated in a phosphate-buffered choline chloride medium (5 mM P_i) the intracellular P_i and the P_i influx fall by 65 and 88%, respectively. At 5 mM extracellular P_i, the Na⁺-dependent component of P_i transport fits Michaelis-Menten kinetics with the maximal flux equal to 2.46 mmole min^?1 (kg dry wt)^?1 and an apparent K_s of 35.4 mM Na⁺. In addition, a Na⁺-independent component of P_i transport, comprising about 12% of the total P_i flux, was identified. The data support the hypothesis that a P_i transport system, dependent on Na⁺, plays a principal role in the maintenance of intracellular P_i concentration.     

Various X2-Tests of Homogeneity: Some Comments

Methodological issues in the analysis of incidence rates or prevalence proportions for count data, presented in a form of a sequence of 2×2 tables, corresponding to levels (strata) of a specified variable (risk factor) X, are discussed. Suppose λ_1i and λ_2i are the incidence rates of an event D in the ith stratum for populations 1 and 2, respectively. The homogeneity (null) hypothesis is formulated in the form: H_0:λ1i=λ_2i for all i (i = 1, 2, …, I). Three X²-tests for H₀ and their theoretical bases are discussed: X_Total² which is sensitive to alternatives HA :λ1i± λ2i for at least some i; X_Comb² which is sensitive to alternatives H A : λ1iλ2i² or < λ_2i but not both for all i; and X_Diff² which is sensitive to alternatives H_A:λ1i>λ2i³ for some i and λ_1i′ < λ_2i′ for some i′ (i≠i′). These statistics satisfy the relation X_Total² = X_Comb² + X_Diff². Also, X′²-statistic for pooled data is calculated, which in conjunction with X_Comb² can serve for detecting confounding. Although most of these techniques are known, they are rather scattered in the literature, and not always considered jointly, as it is emphasized in the present paper. It is hoped that these comments will be helpful to biostatisticians as well as to epidemiologists and medical researchers in the analysis of mortality and morbidity data. For illustration, two examples with large sets of epidemiological data are given.     

Dynamics and management of the white potato cyst nematode Globodera pallida in commercial potato crops

Eight trials were conducted in commercial potato fields infested with the white potato cyst nematode (wPCN, Globodera pallida) and one in a field infested with the yellow PCN (yPCN, Globodera rostochiensis). Our aims were to produce data to validate and refine a computer‐based program (The Model) for the long‐term management of PCN, to determine nematicide effectiveness and to assess rates of PCN population decline between potato crops. Prior to planting, each farmer applied an overall nematicide treatment to his field, except for ten untreated plots that were widely spaced to encompass a range of PCN population densities. Each untreated plot was paired with a similar plot in the adjacent treated area and all plots were intensively sampled for PCN population densities at planting (P_i) and again at harvest (P_f) when tuber yields were determined. Four trials were re‐sampled 2–4 years later to determine PCN population decline rates. Regressions that form the basis of ‘The Model’ and described the relationship between P_i and tuber yield and PCN population density at harvest were fitted to the results from both the untreated and nematicide treated plots. These regressions also enabled us to estimate the yield potential at each site in the absence of PCN and showed that nematicide treatment generally did not increase yield potential and that both tuber yield and PCN multiplication decreased with increasing P_i. However, there were major differences between sites and cultivars. When untreated, the yield of cv. Maris Piper was hardly affected in a highly organic soil with P_i > 200 eggs g^?1 whereas the yield of partially resistant cv. Santé was decreased from a potential of c. 60 t ha^?1 to c. 20 t ha^?1 in a light silt with P_i = 20 egg g^?1 soil. Similarly, untreated wPCN multiplication rates at a low P_i ranged from 46‐fold to >100‐fold. Nematicide effectiveness was estimated from the regressions and, at several sites, yield was decreased despite nematicide treatment. Control of wPCN multiplication was even poorer. In only two of seven trials planted with susceptible cultivars was more than 50% control achieved – maximum populations in treated plots usually exceeded 250 eggs g^?1. Partially resistant Santé decreased the multiplication rate of wPCN in the two trials where it was planted. An alternative analysis using Genstat indicated that The Model tended to underestimate the maximum multiplication rate and overestimate the maximum population density. When four sites were re‐sampled 2–4 years after harvest the populations of wPCN had declined by between 15% and 33.5% per annum with a mean of 26% per annum. Modelling indicated that rotations longer than 8 years were required to control wPCN unless other effective control measures, such as growing a partially resistant cultivar, were used.     

The impact of bleaching on the metabolic contribution of dinoflagellate symbionts to their giant clam host

Bleaching (loss of symbiotic dinoflagellates) is known to significantly decrease the fitness of symbiotic marine invertebrates resulting in reduced growth, fecundity and survival. This report is the first to quantify the effects of bleaching on inorganic carbon (C_i) and ammonium flux, fixation and export of photosynthate to the host, in this case the giant clam Tridacna gigas. The 1998 bleaching event was found to decrease the zooxanthellae population 30‐fold when comparing bleached to non‐bleached clams. This resulted in significant increases in haemolymph C_i and decreases in haemolymph pH and glucose concentration, the predominant photosynthate exported from zooxanthellae in this symbiosis. There was also a decrease in the expression levels of host carbonic anhydrase, an enzyme involved in C_i transport to the zooxanthellae, and although host glutamine synthase levels were unaffected, the clams ability to assimilate ammonium was eliminated in bleached individuals, suggesting that photosynthate from the zooxanthellae is required for ammonium assimilation. In an artificial bleaching experiment haemolymph C_i (r² = 0.97), pH (r² = 0.94) and glucose levels (r² = 0.95) were correlated to zooxanthellae numbers during both bleaching and recovery. Recovery of the zooxanthellae population, was enhanced four‐fold by the addition of organic and inorganic nutrients, as were related haemolymph characteristics. These results highlight the profound physiological changes that occur in symbiotic organisms during and after a bleaching event.     

Interactions of intracellular pH and intracellular calcium in primary cultures of rabbit corneal epithelial cells

Summary Homeostasis of intracellular calcium ([Ca⁺⁺]_i) and pH (pH_i) is important in the cell's ability to respond to growth factors, to initiate differentiation and proliferation, and to maintain normal metabolic pathways. Because of the importance of these ions to cellular functions, we investigated the effects of changes of [Ca⁺⁺]_i and pH_i on each other in primary cultures of rabbit corneal epithelial cells. Digitized fluorescence imaging was used to measure [Ca⁺⁺]_i with fura-2 and pH_i with 2′,7′-bis(2-carboxyethyl)-5(6)-carboxyfluorescein (BCECF). Resting pH_i in these cells was 7.37±0.05 (n=20 cells) and resting [Ca⁺⁺]_i was 129±10 nM (n=35 cells) using a nominally bicarbonate-free Krebs Ringer HEPES buffer (KRHB), pH 7.4. On exposure to 20 mM NH₄Cl, which rapidly alkalinized cells by 0.45 pH units, an increase in [Ca⁺⁺]_i to 215±14 nM occurred. Pretreatment of the cells with 100 μM verapamil or exposure to 1 mM ethylene bis-(oxyethylenenitrilo)-tetraacetic acid (EGTA) without extracellular calcium before addition of 20 mM NH₄Cl did not abolish the calcium increase, suggesting that the source of the calcium transient was from intracellular calcium stores. On removal of NH₄Cl or addition of 20 mM sodium lactate, there were minimal changes in calcium even though pH_i decreased. Treatment of CE cells with the calcium ionophores, ionomycin and 4-bromo A23187, increased [Ca⁺⁺]_i, but produced a biphasic change in pH_i. Initially, there was an acidification of the cytosol, and then an alkalinization of 0.10 to 0.11 pH units above initial values. When [Ca⁺⁺]_i was decreased by treating the cells with 5 mM EGTA and 20 μM ionomycin, pH_i decreased by 0.35±0.02 units. We conclude that an increase in pH_i leads to an increase in [Ca⁺⁺]_i in rabbit corneal epithelial cells; however, a decrease in pH_i leads to minor changes in [Ca⁺⁺]_i. The ability of CE cells to maintain proper calcium homeostasis when pH_i is decreased may represent an adaptive mechanism to maintain physiological calcium levels during periods of acidification, which occur during prolonged eye closure.     

Spatial and temporal patterns of intracellular calcium in colonic smooth muscle

Summary Intracellular calcium [Ca²⁺] _i measurements in cell suspension of gastrointestinal myocytes have suggested a single [Ca²⁺] _i transient followed by a steady-state increase as the characteristic [Ca²⁺] _i response of these cells. In the present study, we used digital video imaging techniques in freshly dispersed myocytes from the rabbit colon, to characterize the spatiotemporal pattern of the [Ca²⁺] _i signal in single cells. The distribution of [Ca²⁺] _i in resting and stimulated cells was nonhomogeneous, with gradients of high [Ca²⁺] _i present in the subplasmalemmal space and in one cell pole. [Ca²⁺] _i gradients within these regions were not constant but showed temporal changes in the form of [Ca²⁺] _i oscillations and spatial changes in the form of [Ca²⁺] _i waves. [Ca²⁺] _i oscillations in unstimulated cells (n = 60) were independent of extracellular [Ca²⁺] and had a mean frequency of 12.6 +1.1 oscillations per min. The baseline [Ca²⁺], was 171 ± 13 nm and the mean oscillation amplitude was 194 ± 12 nm. Generation of [Ca²⁺] _i waves was also independent of influx of extracellular Ca²⁺. [Ca²⁺] _i waves originated in one cell pole and were visualized as propagation mostly along the subplasmalemmal space or occasionally throughout the cytoplasm. The mean velocity was 23 +3 m per sec (n = 6). Increases of [Ca²⁺] _i induced by different agonists were encoded into changes of baseline [Ca²⁺] _i and the amplitude of oscillations, but not into their frequency. The observed spatiotemporal pattern of [Ca²⁺] _i regulation may be the underlying mechanism for slow wave generation and propagation in this tissue. These findings are consistent with a [Ca²⁺] _i regulation whereby cell regulators modulate the spatiotemporal pattern of intracellularly generated [Ca²⁺] _i oscillations.The authors thank Debbie Anderson for excellent technical assistance with the electron microscopy and Dr. M. Regoli for providing the NK-1 agonist [Sar⁹,Met(O₂)¹¹]-SP. This work was supported by National Institutes of Health Grants DK 40919 and DK 40675 and Veterans Administration Grant SMI.     

Photosynthesis of ground vegetation in different aged pine forests: Effect of environmental factors predicted with a process‐based model

Question: How do stand age and environmental factors affect the species‐specific photosynthesis of ground vegetation? Location: Five different aged pine forests in Southern Finland. Methods: We measured photosynthesis of common species of ground vegetation during the growing season of 2006. Results: The measured vascular species, especially those with annual leaves, had a clear seasonal cycle in their measured photosynthetic activity (P_maxⁱ). A simple model that uses site‐specific temperature history, soil moisture and recent frost as input data was able to predict the changes in photosynthetic activity in dwarf shrubs with perennial leaves. The P_maxⁱ values of mosses did not have a clear seasonal cycle, but low values occurred after rain‐free periods and high values after precipitation. We modified the model for mosses and included temporary rain events. The model was able to predict most of the large changes in P_maxⁱ of mosses resulting from varying weather events but there was still some uncertainty, which was probably due to difficulties in measuring fluxes over a moss population. Conclusions: Temperature history, recent frosts and soil moisture determine the changes in P_maxⁱ of dwarf shrubs with perennial leaves. The P_maxⁱ of mosses depends mostly on recent precipitation.     

Role of ionization of the phosphate cosubstrate on phosphorolysis by purine nucleoside phosphorylase (PNP) of bacterial (<Emphasis Type="Italic">E. coli</Emphasis>) and mammalian (human) origin

Kinetics of the reactions of purine nucleoside phosphorylases (PNP) from E. coli (PNP-I, the product of the deoD gene) and human erythrocytes with their natural substrates guanosine (Guo), inosine (Ino), a substrate analogue N(7)-methylguanosine (m⁷Guo), and orthophosphate (P_i, natural cosubstrate) and its thiophosphate analogue (SP_i), found to be a weak cosubstrate, have been studied in the pH range 5–8. In this pH range Guo and Ino exist predominantly in the neutral forms (pK_a 9.2 and 8.8); m⁷Guo consists of an equilibrium mixture of the cationic and zwitterionic forms (pK_a 7.0); and P_i and SP_i exhibit equilibria between monoanionic and dianionic forms (pK_a 6.7 and 5.4, respectively). The phosphorolysis of m⁷Guo (at saturated concentration) with both enzymes exhibits Michaelis kinetics with SP_i, independently of pH. With P_i, the human enzyme shows Michaelis kinetics only at pH ∼5. However, in the pH range 5–8 for the bacterial enzyme, and 6–8 for the human enzyme, enzyme kinetics with P_i are best described by a model with high- and low-affinity states of the enzymes, denoted as enzyme-substrate complexes with one or two active sites occupied by P_i, characterized by two sets of enzyme-substrate dissociation constants (apparent Michaelis constants, K _m1 and K _m2) and apparent maximal velocities (V _max1 and V _max2). Their values, obtained from non-linear least-squares fittings of the Adair equation, were typical for negative cooperativity of both substrate binding (K _m1 < K _m2) and enzyme kinetics (V _max1/K _m1 > V _max2/K _m2). Comparison of the pH-dependence of the substrate properties of P_i versus SP_i points to both monoanionic and dianionic forms of P_i as substrates, with a marked preference for the dianionic species in the pH range 5–8, where the population of the P_i dianion varies from 2 to 95%, reflected by enzyme efficiency three orders of magnitude higher at pH 8 than that at pH 5. This is accompanied by an increase in negative cooperativity, characterized by a decrease in the Hill coefficient from n _H ∼1 to n _H ∼0.7 for Guo with the human enzyme, and to n _H ∼0.7 and 0.5 for m⁷Guo with the E. coli and human enzymes, respectively. Possible mechanisms of cooperativity are proposed. Attention is drawn to the substrate properties of SP_i in relation to its structure.     

Intracellular pH,intracellular free Ca,and junctional cell-cell coupling

Summary Intracellular pH (pH _i ) and intracellular Ca²⁺ ([Ca²⁺] _i ) were determined inChironomus salivary gland cells under various conditions of induced uncoupling. pH _i was measured with aThomas-type microelectrode, changes in [Ca²⁺] _i and their spatial distribution inside the cell were determined with the aid of intracellularly injected aequorin and an image intensifier-TV system, and cell-to-cell coupling was measured electrically. Treatments with NaCN (5mm), DNP (1.2mm), or ionophore A23187 (2m) caused fall in junctional conductance (uncoupling) that was correlated with [Ca²⁺] _i elevation, as was shown before (Rose & Loewenstein, 1976,J. Membrane Biol. 28:87) but not with changes in pH _i : during the uncoupling induced by CN, the pH _i (normally 7.5) decreased at most by 0.2 units; during the uncoupling induced by the ionophore, pH _i fell by 0.13 or rose by 0.3; and in any one of these three agents' uncouplings, the onset of uncoupling and recovery of coupling were out of phase with the changes in pH _i . Intracellular injection of Ca-citrate or Ca-EGTA solutions buffered to pH 7.2 or 7.5 produced uncoupling with little or no pH _i change when their free [Ca²⁺] _i was >10^–5 m. On the other hand, such a solution at pH 4, buffered to [Ca²⁺]<10^–6 m, lowered pH _i to 6.8 but produced no uncoupling. Thus, a decrease in pH _i is not necessary for uncoupling in any of these conditions. In fact, uncoupling ensued also during increase in pH _i : exposure to NH₄HCO₃ or withdrawal of propionate following exposure to a propionate-containing medium caused pH _i to rise to 8.74, accompanied by [Ca²⁺] _i elevation and uncoupling at pH _i >7.8.Cell acidification itself can cause elevation of [Ca²⁺] _i : injection (iontophoresis) of H⁺ invariably caused [Ca²⁺] _i elevation and uncoupling. These effects were produced also by an application of H⁺-transporting ionophore Nigericin at extracellular pH 6.5 which caused pH _i to fall to 6.8. Exposure to 100% CO₂ produced a fall in pH _i , associated in 10 out of 25 cases with [Ca²⁺] _i elevation and, invariably, with uncoupling. The absence of a demonstrable [Ca²⁺] _i elevation in a proportion of these trials is attributable to depression in Ca²⁺-measuring sensitivity; inin vivo tests, detection sensitivity for [Ca²⁺] _i by aequorin was found to be depressed by the CO₂ treatment. Upon CO₂ washout, pH _i and coupling recovered, but onset of recoupling set in at pH _i as low as 6.32–6.88, generally lower than at the pH _i at which uncoupling had set in. Exposure to 5% CO₂ lowered pH _i on the average by 0.3 and depressed coupling (in initially poorly coupled cells). After CO₂-washout, pH _i and coupling recovered. During the recovery phase [Ca²⁺] _i was elevated, an elevation associated with renewed uncoupling or decrease in rate of recoupling. The results are discussed in connection with possible regulatory mechanisms of junctional permeability.     

Fluctuations of an alpha-helix.

Fluctuations in backbone dihedral angles in the α-helical conformation of homopolypeptides are studied based on an assumption that the conformational energy function of a polypeptide consisting of n amino-acid residues can be approximated by a 2n-dimensional parabola around the minimum point in the range of fluctuations. A formula is derived that relates 〈Δθ_iΔθ_j〉, the mean value of the product of deviations of dihedral angles ?_i and ψ_i (collectively designated by θ_i) from their energy minimum values, with a matrix inverse to the second derivative matrix F ,_n of the conformational energy function at the minimum point. A method of calculating the inverse matrix F _n^?1 explicitly is given. The method is applied to calculating 〈Δθ_iΔθ_j〉 for the α-helices of poly(L -alanine) and polyglycine. The autocorrelations 〈(Δ?_i)²〉 and 〈(Δψ_i)²〉 at 300°K are found to be about 66 deg² and 49 deg², respectively, for poly(L -alanine), and 84 deg² and 116 deg², respectively, for polyglycine. The length of correlations of fluctuations along the chain is found for both polypeptides to be about eight residues long.     

Characterization of Na+-Dependent Phosphate Uptake in Cultured Fetal Rat Cortical Neurons

Abstract: Our laboratory has recently cloned and expressed a brain- and neuron-specific Na⁺-dependent inorganic phosphate (P_i) cotransporter that is constitutively expressed in neurons of the rat cerebral cortex, hippocampus, and cerebellum. We have now characterized Na⁺-dependent ³²P_i cotransport in cultured fetal rat cortical neurons, where >90% of saturable P_i uptake is Na⁺-dependent. Saturable, Na⁺-dependent ³²P_i uptake was first observed in primary cultures of cortical neurons at 7 days in vitro (DIV) and was maximal at 12 DIV. Na⁺-dependent P_i transport was optimal at physiological temperature (37°C) and pH (7.0–7.5), with apparent K_m values for P_i and Na⁺ of 54 ± 12.7 µM and 35 ± 4.2 mM, respectively. A reduction in extracellular Ca²⁺ markedly reduced (>60%) Na⁺-dependent P_i uptake, with a threshold for maximal P_i import of 1–2.5 mM CaCl₂. Primary cultures of fetal cortical neurons incubated in medium where equimolar concentrations of choline were substituted for Na⁺ had lower levels of ATP and ADP and higher levels of AMP than did those incubated in the presence of Na⁺. Furthermore, a substantial fraction of the ³²P_i cotransported with Na⁺ was concentrated in the adenine nucleotides. Inhibitors of oxidative metabolism, such as rotenone, oligomycin, or dinitrophenol, dramatically decreased Na⁺-dependent P_i import rates. These data establish the presence of a Na⁺-dependent P_i cotransport system in neurons of the CNS, demonstrate the Ca²⁺-dependent nature of ³²P_i uptake, and suggest that the neuronal Na⁺-dependent P_i cotransporter may import P_i required for the production of high-energy compounds vital to neuronal metabolism.     

Chloride Conductance and P i Transport are Separate Functions Induced by the Expression of NaPi-1 in Xenopus Oocytes

Expression of the protein NaPi-1 in Xenopus oocytes has previously been shown to induce an outwardly rectifying Cl⁻ conductance (G_Cl), organic anion transport and Na⁺-dependent P _i -uptake. In the present study we investigated the relation between the NaPi-1 induced G_Cl and P _i -induced currents and transport. NaPi-1 expression induced P _i -transport, which was not different at 1–20 ng/oocyte NaPi-1 cRNA injection and was already maximal at 1–2 days after cRNA injection. In contrast, G_Cl was augmented at increased amounts of cRNA injection (1–20 ng/oocyte) and over a five day expression period. Subsequently all experiments were performed on oocytes injected with 20 ng/oocytes cRNA. P _i -induced currents (Ip) could be observed in NaPi-1 expressing oocytes at high concentrations of P _i (≥ 1 mm P _i ). The amplitudes of Ip correlated well with G_Cl. Ip was blocked by the Cl⁻ channel blocker NPPB, partially Na⁺-dependent and completely abolished in Cl⁻ free solution. In contrast, P _i -transport in NaPi-1 expressing oocytes was not NPPB sensitive, stronger depending on extracellular Na⁺ and weakly affected by Cl⁻ substitution. Endogenous P _i -uptake in water-injected oocytes amounted in all experiments to 30–50% of the Na⁺-dependent P _i -transport observed in NaPi-1 expressing oocytes. The properties of the endogenous P _i -uptake system (K _m for P _i > 1 mm; partial Na⁺- and Cl⁻-dependence; lack of NPPB block) were similar to the NaPi-1 induced P _i -uptake, but no Ip could be recorded at P _i -concentrations ≤3 mm. In summary, the present data suggest that Ip does not reflect charge transfer related to P _i -uptake, but a P _i -mediated modulation of G_Cl. Received: 22 October 1997/Revised: 24 March 1998     

Apical and basolateral Na+/H+ exchange in the rabbit outer medullary thin descending limb of henle: Role in intracellular pH regulation

Summary The present study was designed to investigate the apical and basolateral transport processes responsible for intracellular pH regulation in the thin descending limb of Henle. Rabbit thin descending limbs of long-loop nephrons were perfused in vitro and intracellular pH (pH _i ) was measured using BCECF. Steady-state pH _i in HEPES buffered solutions (pH 7.4) was 7.18±0.03. Following the removal of luminal Na⁺, pH _i decreased at a rate of 1.96±0.37 pH/min. In the presence of luminal amiloride (1mm), the rate of decrease of pH _i was significantly less, 0.73±0.18 pH/min. Steady-state pH _i decreased 0.18 pH units following the addition of amiloride (1mm) to the lumen (Na⁺ 140mm lumen and bath). When Na⁺ was removed from the basolateral side of the tubule, pH _i decreased at a rate of 0.49±0.05 pH/min. The rate of decrease of pH _i was significantly less in the presence of 1mm basolateral amiloride, 0.29±0.04 pH/min. Addition of 1mm amiloride to the basolateral side (Na⁺ 140mm lumen and bath) caused steady-state pH _i to decrease significantly by 0.06 pH units. When pH _i was acutely decreased to 5.87±0.02 following NH₄Cl removal (lumen, bath), pH _i failed to recover in the absence of Na⁺ (lumen, bath). Addition of 140mm Na⁺ to the lumen caused pH _i to recover at a rate of 2.17±0.59 pH/min. The rate of pH _i recovery was inhibited 93% by 1mm luminal amiloride. When 140mm Na⁺ was added to the basolateral side, pH _i recovered only partially at 0.38±0.07 pH/min. Addition of 1mm basolateral amiloride inhibited the recovery of pH _i , by 97%. The results demonstrate that the rabbit thin descending limb of long-loop nephrons possesses apical and basolateral Na⁺/N⁺ antiporters. In the steady state, the rate of Na⁺-dependent H⁺ flux across the apical antiporter exceeds the rate of Na⁺-dependent H⁺ flux via the basolateral antiporter. Recovery of pH _i following acute intracellular acidification is Na⁺ dependent and mediated primarily by the luminal antiporter.     

Interactions of external and internal H+ and Na+ with Na+/Na+ and Na+/H+ exchange of rabbit red cells: Evidence for a common pathway

Summary We have studied the kinetic properties of rabbit red cell (RRBC) Na⁺/Na⁺ and Na⁺/H⁺ exchanges (EXC) in order to define whether or not both transport functions are conducted by the same molecule. The strategy has been to determine the interactions of Na⁺ and H⁺ at the internal (i) and external (o) sites for both exchanges modes. RRBC containing varying Na _i and H _l were prepared by nystatin and DIDS treatment of acid-loaded cells. Na⁺/Na⁺ EXC was measured as Na _o -stimulated Na⁺ efflux and Na⁺/H⁺ EXC as Na _o -stimulated H⁺ efflux and pH _o -stimulated Na⁺ influx into acid-loaded cells.The activation of Na⁺/Na⁺ EXC by Na _o at pH _i 7.4 did not follow simple hyperbolic kinetics. Testing of different kinetic models to obtain the best fit for the experimental data indicated the presence of high (K _m 2.2 mM) and low affinity (K _m 108 mM) sites for a single- or two-carrier system. The activation of Na⁺/H⁺ EXC by Na _o (pH _i 6.6, Na _i <1 mM) also showed high (K _m 11 mM) and low (K _m 248 mM) affinity sites. External H⁺ competitively inhibited Na⁺/Na⁺ EXC at the low affinity Na _o site (K _H 52 nM) while internally H⁺ were competitive inhibitors (pK 6.7) at low Na _i and allosteric activators (pK 7.0) at high Na _i .Na⁺/H₊ EXC was also inhibited by acid pH _o and allosterically activated by H _i (pK 6.4). We also established the presence of a Na _i regulatory site which activates Na⁺/H⁺ and Na⁺/Na⁺ EXC modifying the affinity for Na _o of both pathways. At low Na _i , Na⁺/Na⁺ EXC was inhibited by acid pH _i and Na⁺/H⁺ stimulated but at high Na _i , Na⁺/Na⁺ EXC was stimulated and Na⁺/H⁺ inhibited being the sum of both pathways kept constant. Both exchange modes were activated by two classes of Na _o sites,cis-inhibited by external H _o , allosterically modified by the binding of H⁺ to a H _i regulatory site and regulated by Na _i . These findings are consistent with Na⁺/Na⁺ EXC being a mode of operation of the Na⁺/H⁺ exchanger.Na⁺/H⁺ EXC was partially inhibited (80–100%) by dimethyl-amiloride (DMA) but basal or pH _i -stimulated Na⁺/Na⁺ EXC (pH _i 6.5, Na _i 80 mM) was completely insensitive indicating that Na⁺/Na⁺ EXC is an amiloride-insensitive component of Na⁺/H⁺ EXC. However, Na⁺ and H⁺ efflux into Na-free media were stimulated by cell acidification and also partially (10 to 40%) inhibited by DMA: this also indicates that the Na⁺/H⁺ EXC might operate in reverse or uncoupled modes in the absence of Na⁺/Na⁺ EXC.In summary, the observed kinetic properties can be explained by a model of Na⁺/H⁺ EXC with several conformational states, H _i and Na _i regulatory sites and loaded/unloaded internal and external transport sites at which Na⁺ and H⁺ can compete. The occupancy of the H⁺ regulatory site induces a conformational change and the occupancy of the Na _i regulatory site modulates the flow through both pathways so that it will conduct Na⁺/H⁺ and/or Na⁺/Na⁺ EXC depending on the ratio of internal Na⁺:H⁺.     

Effects of potassium on the anion and cation contents of primary cultures of mouse astrocytes and neurons

Inastrocytes, as [K⁺]_o was increased from 1.2 to 10 mM, [K⁺]_i and [Cl^–]_i were increased, whereas [Na⁺]_i was decreased. As [K⁺]_o was increased from 10 to 60 mM, intracellular concentration of these three ions showed no significant change. When [K⁺]_o was increased from 60 to 122 mM, an increase in [K⁺]_i and [Cl^–]_i and a decrease in [Na⁺]_i were observed.Inneurons, as [K⁺]_o was increased from 1.2 to 2.8 mM, [Na⁺]_i and [Cl^–]_i were decreased, whereas [K⁺]_i was increased. As [K⁺]_o was increased from 2.8 to 30 mM, [K⁺]_i, [Na⁺]_i and [Cl^–]_i showed no significant change. When [K⁺]_o was increased from 30 to 122 mM, [K⁺]_i and [Cl^–]_i were increased, whereas [Na⁺]_i was decreased. Inastrocytes, pH_i increased when [K⁺]_o was increased. Inneurons, there was a biphasic change in pH_i. In lower [K⁺]_o (1.2–2.8 mM) pH_i decreased as [K⁺]_o increased, whereas in higher [K⁺]_o (2.8–122 mM) pH_i was directly related to [K⁺]_o. In bothastrocytes andneurons, changes in [K⁺]_o did not affect the extracellular water content, whereas the intracellular water content increased as the [K⁺]_o increased. Transmembrane potential (E_m) as measured with Tl-204 was inversely related to [K⁺]_o between 1.2 and 90 mM, a ten-fold increase in [K⁺]_o depolarized the astrocytes by about 56 mV and the neurons about 52 mV. The E_m values measured with Tl-204 were close to the potassium equilibrium potential (E_k) except those in neurons at lower [K⁺]_o. However, they were not equal to the chloride equilibrium potential (E_Cl) at [K⁺]_o lower than 30 mM in both astrocytes and neurons. Results of this study demonstrate that alteration of [K⁺]_o produced different changes in [K⁺]_i, [Na⁺]_i, [Cl^–]_i, and pH_i in astrocytes and neurons. The data show that astrocytes can adapt to alterations in [K⁺]_o, in such a way to maintain a more suitable environment for neurons.     

Dynamic regulation of guard cell anion channels by cytosolic free Ca2+ concentration and protein phosphorylation

In guard cells, activation of anion channels (I_anion) is an early event leading to stomatal closure. Activation of I_anion has been associated with abscisic acid (ABA) and its elevation of the cytosolic free Ca²⁺ concentration ([Ca²⁺]_i). However, the dynamics of the action of [Ca²⁺]_i on I_anion has never been established, despite its importance for understanding the mechanics of stomatal adaptation to stress. We have quantified the [Ca²⁺]_i dynamics of I_anion in Vicia faba guard cells, measuring channel current under a voltage clamp while manipulating and recording [Ca²⁺]_i using Fura‐2 fluorescence imaging. We found that I_anion rises with [Ca²⁺]_i only at concentrations substantially above the mean resting value of 125 ± 13 nm , yielding an apparent K_d of 720 ± 65 nm and a Hill coefficient consistent with the binding of three to four Ca²⁺ ions to activate the channels. Approximately 30% of guard cells exhibited a baseline of I_anion activity, but without a dependence of the current on [Ca²⁺]_i. The protein phosphatase antagonist okadaic acid increased this current baseline over twofold. Additionally, okadaic acid altered the [Ca²⁺]_i sensitivity of I_anion, displacing the apparent K_d for [Ca²⁺]_i to 573 ± 38 nm . These findings support previous evidence for different modes of regulation for I_anion, only one of which depends on [Ca²⁺]_i, and they underscore an independence of [Ca²⁺]_i from protein (de‐)phosphorylation in controlling I_anion. Most importantly, our results demonstrate a significant displacement of I_anion sensitivity to higher [Ca²⁺]_i compared with that of the guard cell K⁺ channels, implying a capacity for variable dynamics between net osmotic solute uptake and loss.     

Mechanism and role of furosemide-sensitive K+ transport in L cells: A genetic approach

Summary As part of a genetic study of the mechanisms for cation transport in cultured mammalian cells, two mouse fibroblastic cell lines have been compared with respect to unidirectional⁴²K⁺ influx. The cell lines areLM(TK ^–) andLTK-5, a mutant selected fromLM(TK ^–) by the ability to grow in medium containing 0.2mm K⁺. In both cell lines, the overall influx can be resolved into three components: (i) a ouabain- and vanadate-sensitive component ( ⁱ M_K ^f), presumably the Na/K pump, which is a saturable function of extracellular K⁺ with aK _1/2 of 1.3mm; (ii) a furosemide-sensitive component ( ⁱ M_k ^fx), also a saturable function of extracellular K⁺, with aK _1/2 of 6mm; and (iii) a diffusional component ( ⁱ M_k ^d); which is a linear function of extracellular K⁺.By several independent criteria, ⁱ M_k ^o and ⁱ M_k ^f appear to be distinct transport processes. First, as indicated above, they can be separated with the use of inhibitors. In addition, they can be separated genetically, since theLTK-5 mutant shows a threefold elevation in ⁱ M_k ^f with no change in ⁱ M_k ^o. And finally, extracellular Na⁺ has no effect on ⁱ M_k ^o, but stimulates ⁱ M_k ^f, a result consistent with the notion that ⁱ M_k ^f influx occurs by Na–K cotransport.Further experiments were directed towards understanding the nature of theLTK-5 mutation and the physiological role of ⁱ M_k ^f. LTK-5 differs from the parental cell line, not only in having an increased ⁱ M_k ^f, but also in having a large cell volume, a slow maximal growth rate, and an ability to grow at 0.2mm K⁺. The most straightforward interpretation — that the increased ⁱ M_k ^f is itself responsible—is unlikely since the addition of furosemide to the growth medium had no effect upon the growth rate or cell volume of the mutant at either normal or low extracellular K⁺ concentrations. It did, however, render the parent capable of growth at 0.2mm K⁺. Possible interpretations are discussed.     

Syntheses of 1-[2-(Phosphonomethoxy)Alkyl]Thymine Monophosphates and an Evaluation of their Inhibitory Activity Toward Human Thymidine Phosphorylase

A series of new monophosphates of 1-[2-(phosphonomethoxy)alkyl]thymines, such as PMPTp_, 3-MeO-PMPTp, HPMPTp, and FPMPTp, were synthesized and tested for their ability to inhibit human thymidine phosphorylase. Kinetic measurements of enzyme activity were performed using thymidine and inorganic phosphate as the substrates. The data show that some monophosphates provide a considerable increase of the multisubstrate inhibitory effect. The highest inhibitory potency was found with (R)-FPMPTp 4c (K _i ^dT = 4.09 ± 0.47 μM, K _i(P_i) = 2.13 ± 0.29 μM) and (R) 3-MeO-PMPTp 4d (K _i ^dT = 5.78 ± 0.71 μM, K _i(P_i) = 2.71 ± 0.37 μM).     

Conformational interconversions in peptide β-turns: Discrimination between enantiomeric conformations by chiral perturbation

The crystal structure of the model tripeptide Boc-Aib-Gly-Leu-OMe ( 1 ) reveals two independent molecules in the asymmetric unit that adopt “enantiomeric” type I and type I′ β-turn conformations with the Aib and Gly residues occupying the corner (i + 1 and i + 2) positions. ¹³C cross polarization and magic angle sample spinning spectra in the solid state also support the coexistence of two conformational species. ¹³C-nmr in CDCl₃ establishes the presence of a single species or rapid exchange between conformations. 400 MHz ¹H-nmr provides evidence for conformational exchange involving a major and minor species, with β-turn conformations supported by the low solvent exposure of Leu(3) NH and the observation of N_iH ↔ N_i+1H nuclear Overhauser effects. CD bands in the region 190–230 nm are positive, supporting a major population of type I′ β-turns. The isomeric peptide, Boc-Gly-Leu-Aib-OMe ( 2 ), adopts an “open” type II′ β-turn conformation in crystals. Solid state and solution nmr support population of a single conformational species. Chiral perturbation introduced outside the folded region of peptides may provide a means of modulating screw sense in achiral sequences. © 1998 John Wiley & Sons, Inc. Biopoly 45: 191–202, 1998