{'fraction_non_alphanumeric': 0.03435602428891019, 'fraction_numerical': 0.021640871113546088, 'mean_word_length': 4.61772249294691, 'pattern_counts': {'":': 0, '<': 2, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Kinetics of activation and inactivation of swelling-stimulated K+/Cl- transport. The volume-sensitive parameter is the rate constant for inactivation

Red blood cells of several species are known to exhibit a ouabain- insensitive, anion-dependent K+ (Rb+) flux that is stimulated by cell swelling. We have used rabbit red cells to study the kinetics of activation and inactivation of the flux upon step changes in tonicity. Sudden hypotonic swelling (210 mosmol) activates the flux after a lag period of 10 min at 37 degrees C and 30-50 min at 25 degrees C. In cells that were preswollen to activate the transporter, sudden shrinkage (by addition of hypertonic NaCl) causes a rapid inactivation of the flux; the time lag for inactivation is less than 2 min at 37 degrees C. A minimal model of the volume-sensitive KCl transport system requires two states of the transporter. The activated (A) state catalyzes transport at some finite rate (turnover number unknown because the number of transporters is unknown). The resting (R) state has a much lower or possibly zero transport rate. The interconversion between the states is characterized by unimolecular rate constants R k12 in equilibrium with k21 A. The rate of relaxation to any new steady state is equal to the sum of the rate constants k12 + k21. Because the rate of transport activation in a hypotonic medium is lower than the rate of inactivation in an isotonic medium, we conclude that the volume- sensitive rate process is inactivation (the A to R transition); that is, cell swelling activates transport by lowering k21. Three phosphatase inhibitors (fluoride, orthovanadate, and inorganic phosphate) all inhibit the swelling-activated flux and also slow down the rate of approach to the swollen steady state. This finding suggests that a net dephosphorylation is necessary for activation of the flux and that the net dephosphorylation takes place as a result of swelling- induced inhibition of a kinase rather than stimulation of a phosphatase.


INTRODUCTION
Many cells exhibit solute transport systems that are influenced by changes in cell volume. In general, the volume-sensitive fluxes cause cell volume to return toward normal after an acute swelling or shrinkage. Several different volume-sensitive transport processes have been identified in nature, and there seems to be no general single mechanism for cell volume regulation (Kregenow, 1981;Pierce, 1982;Parker, 1983;Cala, 1980Cala, , 1983Grinstein et al., 1984).
Little is known about the mechanisms by which a change in cell volume activates or inactivates transport. The main information available on this issue comes from studies in which transport is activated in the absence of a volume change. For example, Na-K-C1 cotransport in avian red cells can be activated either by cell shrinkage or by catecholamines (see McManus et al., 1985). Amiloride-sensitive Na+-H + exchange is activated either by cell shrinkage or by low intracellular pH, growth factors, or, in some cells, elevation of intracellular Ca + + (see Grinstein et al., 1989). Hypoxia can activate the same process in fish red cells (see Mahe et al., 1985). Naindependent KC1 cotransport is activated by cell swelling or by slight intracellular acidification (Brugnara et al., 1985), N-ethylmaleimide (NEM) treatment (Lauf, 1985), or high hydrostatic pressure (Hall and Ellory, 1986a).
In addition to interventions that activate transport in the absence of volume change, there are also interventions that prevent cell volume from affecting transport. For example, glutaraldehyde treatment can "fix" the dog red cell Na+-H + exchanger in a volume-insensitive state (Parker, 1984). Norepinephrine treatment prevents cell swelling from activating KCI cotransport in duck red cells (Haas and McManus, 1985). All these studies provide interesting information about possible mediators of volume effects on transport, but the level of understanding of the signaling mechanisms is still very primitive and certainly no general principles have emerged.
The present study concerns the swelling-activated, anion-dependent K + transport system of mammalian red cells (see Dunham, 1990, for recent review). The transport is Na-independent, and recent work by Brugnara et al. (1989) indicates that a CI-gradient can drive an uphill K + flux; accordingly, we will refer to the swellingstimulated K + (Rb +) flux as "KCI cotransport." The swelling-stimulated KCI cotransport flux is detectable in unfractionated human red cells (Kaji, 1986), but the effect of cell volume is much more pronounced in the younger cells (Canessa et al., 1987;Brugnara and Tosteson, 1987;Hall and Ellory, 1986b;O'Neill, 1987O'Neill, , 1989. The KC1 cotransport flux is much larger in human SS and CC cells than in AA cells (Brugnara et al., 1985(Brugnara et al., , 1986Canessa et al., 1986;Berkowitz and Orringer, 1987). In the LK sheep red cell, and presumably in other species, the swelling-stimulated and NEM-stimulated fluxes are very likely catalyzed by the same transport protein (Lauf, 1984). In rabbit, LK sheep, and human SS cells, NEM treatment removes most of the volume sensitivity of KCI cotransport. Human red cell KCI cotransport, however, is still sensitive to cell volume after NEM treatment (Dunham and Benjamin, 1985;Lauf et al., 1985). Raising the intracellular [Mg ++] inhibits KC1 cotransport in human and LK sheep red cells (Brugnara and Tosteson, 1987;Lauf, 1985;Lauf et al., 1985;Sachs, 1988).
Although there have been many dozen studies of the effects of cell volume on various transport processes, there have been very few studies of the rates of change of transport after step changes in cell volume. Sarkadi et al. (1984) showed that volume-sensitive conductances in lymphocytes have complex time dependences, with a rapid, time-dependent inactivation under some conditions. Kim et al. (1989) recently demonstrated that swelling-activated KCI cotransport in pig red cells requires a time lag of several minutes. Kregenow (1971) had originally observed a slight time lag in the activation of the same process in duck red cells. Dunham (1989), Lauf (personal communication) and McManus (personal communication) have also observed a time lag for activation of the flux in LK sheep and duck red cells, respectively.
The work described below is a study of the rates of activation (by cell swelling) and inactivation (by an imposed cell shrinkage) of KCI cotransport in young rabbit red cells. These cells have the advantage that the swelling-stimulated fluxes are large enough to measure accurately (AI-Rohil and Jennings, 1989) but still slow enough that the cell does not shrink back down to normal volume before a steady-state KC1 cotransport flux can be measured. We find that the time lag for activation of KC1 cotransport by swelling is much longer than that for inactivation of transport by sudden shrinkage of preswollen cells. Analysis of a simple kinetic model of the system indicates that cell swelling stimulates transport by decreasing the rate constant for inactivation. The effects of three inhibitors of phosphatases indicate that the activation of transport by cell swelling involves a net dephosphorylation caused by the inhibition of a kinase rather than the activation of a phosphatase. This is to our knowledge the first published analysis of the rates of activation and inactivation of a volume-sensitive transport system. A preliminary report of this work has been presented (Jennings and AI-Rohil, 1989).

Rabbit Red Blood Cells
Blood was drawn by cardiac puncture from New Zealand white rabbits immediately after a lethal injection of pentobarbital sodium through a marginal ear vein. (The rabbits were killed to obtain not only the blood, but also the intestine, urinary bladder, skeletal muscle, and brain for studies in other laboratories; the animals were killed in accordance with National Institutes of Health guidelines.) The anticoagulant was ethylenediaminetetraacetate (EDTA).
Cells were usually used on the same day or after at most 2 d of storage as whole blood at 4~ To maximize the swelling-stimulated flux, the least dense one-third of the cells were isolated on a Percoll-Renografin gradient (Speiser and Etlinger, 1982). In previous work (A1-Rohil and , we had discarded reticulocytes, but in the present study reticulocytes were included in the "light" cell fraction. The rabbits had not been previously bled, and the reticulocyte count in the "light" fraction was generally 2-3%. After density gradient centrifugation, cells from the top third of the gradient were washed twice and suspended in 10 vol of N-2-hydroxyethylpiperazine-N'-ethanesulfonic acid (HEPES)-buffered physiological saline (HPS): 150 mM NaC1, 5 mM KC1, 1 mM MgCI 2, 1 mM CaCI~, 1 mM NaH~PO4, 10 mM glucose, 10 mM HEPES, pH 7.5 (measured at 23~ The suspension was incubated 1 h at 37~ in order to attempt to establish a reproducible physiological steady state.

Other Materials
Salts and buffers were from either Sigma Chemical Co., St. Louis, MO or Fisher Scientific Co., Pittsburgh, PA. a6RbC1 was purchased from DuPont-New England Nuclear, Boston, MA. Sodium orthovanadate (NasVO4) was from Fisher Scientific Co.; a stock solution of 100 mM was prepared and titrated to pH 7.4 with morpholine propane sulfonic acid (MOPS).

Influx Measurements
Influx of S6Rb+ was measured essentially as described previously (AI-Rohil and Jennings, 1989), but with different flux media. The standard starting medium in these experiments was HEPES-buffered saline with ouabain (HBSO): 160 mM NaCI, 5 mM KC1, 10 mM HEPES, pH 7.4, at 37~ 10 -4 M ouabain. In early experiments the NaC1 concentration was 150 mM; the concentration was 160 mM in later experiments because the basal flux is smaller in the slightly hypertonic solution and the relative effect of cell swelling is larger. The protocols for altering the tonicities of the suspensions during flux measurements are given in the figure legends. Bumetanide was not included in the flux media; rabbit red cells appear to lack the Na-K-C1 cotransporter (A1-Rohil and . Unidirectional influx was calculated assuming that S6Rb+ is an ideal tracer for K +. In the plots of intracellular S6Rb+ vs. time, 1 ml of cells refers to the number of cells that would occupy 1 ml in an isotonic medium.

Data Analysis
Influx time courses were fit to the two-state model (see below) using a nonlinear least squares iteration according to the Marquardt algorithm (Bevington, 1969). The computation was performed on a personal computer with "NFIT" (Island Products, Galveston, TX). The program was written by Bruce Simon and Bill Little of this department. The parameters derived from the curve-fitting are indicated in the text and figure legends. For some experiments, not enough data points were taken after cell swelling for a quantitative analysis.

Time Course of Shifts from One Steady-State Flux to Another
The purpose of the studies in this paper is to test a simple theoretical model for the activation and inactivation of anion-dependent K + transport by cell swelling and shrinkage. The experiments are not concerned with the kinetics of transport itself; all measurements were performed at a single extracellular K + concentration. At this single K + concentration, the ouabain-insensitive unidirectional K+/S6Rb+ flux is assumed to be a measure of the number of functioning KCI cotransporters. The rate of change of this flux thus reflects the rate of activation or inactivation of transporters.
A minimal model of the swelling-activated transport system requires two states of the transporter: resting (R) and activated (A). These states do not refer to intermediates in the catalytic cycle for transport itself, but rather are regulatory states. The R state catalyzes transport slowly or not at all, and the A state catalyzes transport at some appreciable rate. According to the minimal model, the transitions between these two states are characterized by unimolecular rate constants, which in general are affected by cell volume through unknown signaling mechanisms:

R. "A.
Cell swelling induces a net conversion of R states to A states; according to the model, this increase in A states must be caused by an increase in k12 and/or a decrease in k~x. It can be shown very easily that in two-state systems the rate of approach to any new steady state is given by the sum of the forward and reverse rate constants, evaluated at the new steady state. The following derivation is essentially identical to that for the relaxation kinetics of any two-state system (see Czerlinski, 1966).
Start by assuming that each cell contains an ensemble of independently functioning KCI cotransporters, each of which can be in either of the two states. For any given steady state the actual proportions of the A and R states are not known, but it is still possible to write an expression for the time course of the transition from one steady state to another after an abrupt change in cell volume. Begin at a steady state with initial flux J0. In this steady state there is some fraction A0 of transporters in the A state. The remainder (1 -A 0) are in the R state. Suddenly the cell volume is changed by adding water or hypertonic NaC1. The change in cell volume alters one or both the rate constants kx2 and k2~, and the system relaxes to a new steady state, in which a new fraction A~ of the transporters is in the A state. In the new steady state, the fraction AI is related to the rate constants as follows: kl2(1 -A1) = k~lAl 9 (1) At any time during the approach to the new steady state, let A = Aa + x, where x represents the departure from the final new steady state. From the definition of the forward and reverse rate constants.
In this equation the rate constants k~2 and k2~ have the magnitudes that apply to the new conditions (i.e., after the sudden swelling or shrinkage). Substituting Eq. 1 into Eq. 2 gives a very simple differential equation with the following solution: So the time course of the fraction of transporters in the activated state is Thus, the relaxation to any new steady state, after a sudden swelling or shrinkage of the cells, proceeds at a rate given by the sum of the forward and reverse rate constants.
It is now possible to express the unidirectional S6Rb+ flux (at a given K/Rb concentration) as a function of the proportions of R and A states. Let JR be the total KC1 cotransport flux if all copies of the system were in the R state; this flux could be zero but need not be. Let JA be the flux that would be mediated by the system if all copies were in the A state. The actual flux, then, for any given steady state, is Eqs. 4 and 5 can be combined and rearranged to the following: where J0 is the flux before the step change and J, is the final steady state flux. The accumulated S6Rb+ (under conditions of zero back flux) is given by the time integral of the unidirectional influx: Eq. 7 describes the time course of the 86Rb+ accumulation after any abrupt change (increase or decrease) in cell volume at t = 0. There are in general three unknowns: the initial steady-state flux, the final steady-state flux, and the relaxation time (k~ + k~t) -~. A three-parameter fit of the data is possible, but in most experiments we have independent estimates of the initial flux. Therefore, most of the curve-fits were with two adjustable parameters: the final steady-state flux and the relaxation time.

Stability of Cell Volume
The experiments were designed to measure the rates of transition from one steadystate flux to another. That is, cell volume is viewed as the independent variable, to Young rabbit red cells were prepared as described in Materials and Methods and preincubated 1 h at 37~ in HPS plus glucose. The cells were centrifuged and resuspended in HBSO (160 mM NaCI, 5 KCI, 10 mM HEPES, pH 7.5, at 23~ 10 -4 M ouabain. The suspension was diluted with distilled water to a final osmolality of 210 mosmol, and the cells were incubated further at 37*C. At the indicated times, aliquots were removed and centrifuged, and the cell water was determined from the wet weight, dry weight, and hematocrit of an 80-90% suspension. The different symbols refer to two different preparations of cells. Cell water is expressed relative to that of cells in 300 mosmol medium. be stepped to various values. The experiments would be very difficult to interpret if the cell volume itself were not stable over the times needed for the flux to reach a new steady state. Fortunately, rabbit red cell volume is relatively stable for time periods of up to 1 h under the conditions of the transport experiments. Fig. 1 shows the time course of cell water for cells suspended in a hypotonic medium under the same conditions as were used to measure aSRb+ influx. The bypotonicity causes the expected 25% increase in cell volume, and, after 1 h in the hypotonic medium, the cells are still 20% larger than normal. These cells do of course have a substantial swelling-stimulated net KC1 effiux (Davson, 1937;A1-Rohil and Jennings, 1989). The rate constant for 86Rb+ effiux under these conditions is ~0.2/h in swollen ceils. On the basis of the 86Rb+ effiux, a somewhat more rapid volume regulatory decrease would be expected. However, ouabain is included in the flux medium, and the net NaCI influx partially offsets the swelling-induced KCI effiux. We have not made a systematic study of the rate of net water loss compared with the 86Rb+ efflux in the same cells. The important point for the present purposes is that, after acute cell swelling in the presence of ouabain, cell volume is reasonably stable at 37~ for at least 60 min.

Possible Effects of Heterogeneous Cell Population
It is well established that, in both human and rabbit red cells, the least dense cells have the highest swelling-sensitive fluxes (e.g., Canessa et al., 1987;Brugnara and Tosteson, 1987;O'Neill, 1989;A1-Rohil and Jennings, 1989). Our experiments were all performed on a cell preparation in which the densest two-thirds of the cells were discarded so as to eliminate the cells that have only small swelling-stimulated fluxes. In our cell preparations, most of the cells undergo a slow regulatory volume decrease, as demonstrated by the time course of the water content ( Fig. 1) and by osmotic fragility measurements after incubation in hypotonic medium (AI-Rohil, 1988). Thus, although there are undoubtedly variations in the flux among cells of different ages even within a density-separated fraction, these variations are much less pronounced than in unfractionated human AA cells (O'Neill, 1989).

Time Lag for Activation of Transport
It is difficult to use efflux measurements in a study of the time course of activation of the swelling-stimulated transport. In the first few minutes after cell swelling, 2% of the intracellular radioactivity has left the cells, and even a trace of lysis in the hypotonic medium could cause a significant overestimate of the initial effiux. Slight errors in the early time points after cell swelling make it difficult to detect possible time lags in the onset of the swelling-stimulated effiux. In contrast, the same degree of lysis causes only a trivial error in the influx determination. For this reason, all the results presented here were obtained from tracer (86Rb+) influx measurements. The influx is measured over times in which there is negligible backflux (the intracellular specific activity is <5% of the extracellular specific activity). Fig. 2 shows the time course of entry of SrRb+ into young rabbit red cells from a medium containing 5 mM K + and 10 -4 M ouabain. Initially the medium is isotonic and the influx is relatively slow. At the arrow, the tonicity of the suspension is lowered from 310 to 215 mosmol. The flux begins to increase until a new steady state is reached after about 25 min. (The time course of the influx for longer incubations is more complicated because the cells do shrink slowly and the flux declines.) The time course of activation of transport after sudden hypotonic swelling clearly displays a lag that can be estimated visually from the point of intersection of the lines representing the initial and final steady-state fluxes. The lag can be estimated more objectively by fitting the data to the two-state model. Curve-fitting gives a slightly larger time lag than would be estimated graphically, probably because the eye tends to underestimate the final steady-state flux. In 14 separate preparations of cells, we have found that the time lag for approach to the swollen steady state is 10 _+ 4 min (mean _+ SD) under these conditions (37"C, 210 _+ 5 mosmol). In Br-medium, in which the flux itself is more rapid than in CI-(AI-Rohil and , the ~6Rb+ in l-ml aliquots of the suspension was measured at the indicated times. At t = 22 min, 5 mM KC1 plus ~RbCI was added to lower the osmolality from 300 to 215 mosmol while keeping the extracellular concentration of K + and 86Rb+ constant. The curve through the data is fit to the equivalent of Eq. 7 (with axes offset because the swelling is not at t = 0). The fitting procedure fixed the initial flux at the value measured over the first 20 min. The derived time lag [(k~2 = k21) -I] is 10.5 min. A single time course is shown, typical of at least 15 others. FIGURE 2. Time course of ouabain-insensitive 86Rb+ influx before and after a sudden increase in cell volume. Cells were preincubated in HPS plus glucose for 1 h, then centrifuged, and resuspended at 37~ 2.5% Hct, in HBSO (150 mM NaC1, 5 mM KCI, 10 mM HEPES, pH 7.5, at 23"C), 10 -4 M ouabain. At t = 0, 86RB+ was added, and the intracellular time lag for activation is indistinguishable from that in C1-(two experiments; data not shown).

Effect of Degree of Cell Swelling
In three experiments the extent of cell swelling was varied to determine the effect of final cell volume on the rate of approach to the new steady state (Fig. 3). The final steady-state flux is of course larger in cells that are more swollen, and the time lag appears to be larger for higher degrees of swelling. The longer time lag for the higher final flux is consistent with the idea that cell swelling causes a decrease in k21 , the rate constant for the transition from the A state to the R state (see below).   Fig. 4 depicts the time course of SrRb+ influx into cells that were swollen hypotonically (210 mosmol) 20 min before the addition of tracer. The 20-min preincubation is sufficiently time to activate the anion-dependent transport to roughly 90% of the steady-state value, and the initial tracer influx, as expected, is large. At the indicated time, the cells were shrunk back to normal volume by the addition of hypertonic NaCI, which raised the osmolality from 210 to 310 mosmol. The flux abruptly returned to a low level, with a time lag not exceeding 2 min. In six cell preparations, the time lag for inactivation of the flux after shrinkage was 1.4 _+ 0.4 min at 37~ The large uncertainty in the delay time reflects the difficulty of the measurements; on the time scale of the inactivation of the transport, there is little change in the intracellular radioactivity and it is therefore hard to obtain an exact time course of the change in flux. Although the precise time lag for inactivation of transport is uncertain, we are confident that the relaxation time for inactivation in an isotonic or hypertonic medium is shorter than that for activation in a hypotonic medium. of tracer influx measured as usual. At the arrow, NaCI was added from a 1.5 M stock to raise the osmolality to 310 mostool. The curve through the data, starting at the NaC1 addition, is derived from Eq. 7 with a time lag of 1.0 min. A single time course is shown, representative of six others. Ellory et al. (1985) have shown that the swelling-stimulated KCI flux is very temperature-dependent: lowering the temperature from 40~ to 30~ causes a 10-fold reduction of the maximum flux. The large temperature effect could have at least three origins. The transport process itself (i.e., the number of ions transported per second by a single activated transporter) would be expected to have a finite temperature dependence. In addition, both the rate and the extent of activation at a given cell volume could depend on temperature. Fig. 5 depicts the time course of SnRb+ influx into cells suspended in the same hypotonic medium at two different temperatures. Cell volume is approximately the same at each temperature. (The Donnan ratio for CI-will not change much with temperature under these conditions because the extracellular and intracellular hydrogen ion buffers have similar temperature dependences.) At 37~ in this experiment, the influx activated with a delay time of about 11 min. At 25~ the steady-state flux was about threefold lower than at 37~ and the approach to the new steady state was also about threefold slower. In five separate preparations of cells the delay time for activation of the flux in a 210 msmol medium averaged 55 min at 25~ (range 23-101 min). Although there is large uncertainty in the activation rate at 25~ it is clear that lowering the temperature from 37~ to 25~ has a sizable effect on the rate; the apparent E a (activation energy) of the activation process is 20-25 kcal/mol.

Effect of Temperature
As mentioned above, the temperature dependence of the steady-state flux in a hypotonic medium might not reflect the temperature dependence of the flux through an activated transporter, because the number of A states in a given medium could depend on temperature. That is, the forward and reverse rate constants kl~ and k2~ could have different temperature dependences. We attempted to measure the effect of temperature on the transport process itself, independent of the effects of cell volume, by activating the transport with NEM (see Lauf, 1985). With maximal treatment with NEM, the anion-dependent flux in rabbit red cells is not Temperature dependence of the rate of activation of swelling-stimulated a6Rb + influx. Cells were prepared as in Figs. 1-3 and suspended in 6 ml of HBSO plus 3 ml of 5 mM KC1 (210 mosmol). Cell swelling and 86Rb addition were both at t = 0. One pair of fluxes was performed at 37~ another (same cells, same medium) was performed at 25~ The time lag at 370C in this experiment is ~11 rain; that at 25~ is ~35 min.
affected by cell swelling, presumably because NEM has locked the system into a swelling-independent, activated state (Al-Rohil and . The temperature dependence of the NEM-stimulated flux is shown in Fig. 6. The flux is only slightly affected by temperature between 25"C and 37"C; the apparent activation energy of the flux is ~9 kcal/mol. The small temperature dependence of the NEMactivated flux suggests that the transport process itself has a low activation energy. The higher temperature dependence of the swelling-activated flux could be explained by a temperature dependent shift in the proportion of active and inactive transporters at a given cell volume.

Time Course of Shrinkage-induced Inactivation of 25~
Although the time course of the activation of transport after hypotonic swelling is considerably slower at 25~ than at 37~ the time course of inactivation after sudden shrinkage is still quite rapid at 25~ (Fig. 7). The flux was activated for 60 min . Temperature dependence of NEM-stimulated H~Rb+ influx. Cells were incubated in HBS, then split in half, and one half was exposed to 2 mM NEM, 15 min, 37"C. Both halves were washed and then resuspended in HBSO at either 37"C or 25"C, and the influx of 86Rb+ was measured over a 20-min interval (during which the time course is linear). The data shown are from a single experiment (mean and range of duplicate determinations). The identical effect of temperature was observed in a separate experiment.
at 25~ in a 205 mosmol medium before the addition of hypertonic NaCI to inactivate the transport. The lag time for inactivation at 25~ is 2.8-3.5 rain (range, two experiments).

Approach to the Same Steady State from Two Different Directions
To test further the two-state model of transport regulation, we attempted experiments in which the cells approach the same steady-state flux from two different directions. If the transport regulation can be modeled as a two-state process, then the rate of approach to any new steady state should depend only on the final conditions, and not on the direction of the approach.

Time (rain)
In two of the suspensions, concentrated NaCI was also added at t = 0 to raise the osmolality to 315 mosmol. In the cells that continued to be swollen, the influx was reasonably linear, but in the cells that were returned to normal volume, the influx was inactivated rapidly. Indistinguishable results were obtained in two other experiments at this temperature.
in Eq. 2 can be either positive or negative, and the rate of decay of x is independent of the sign.) The steady state in this case is the following: swollen cells (210 mosmol), pH 7.4, 25~ One set of cells was initially at 25~ in isotonic medium and then swollen (with S6Rb+ added simultaneously) to measure the time lag for activation of transport as in Figs. 2 and 5. Another aliquot of the same cells in the same hypotonic medium was preincubated 20 min at 37~ to activate a larger proportion of the transporters, and then the temperature was quickly shifted (within 2 min) to 25 _+ 1 ~ immediately before adding S6Rb+. In the cells that had been at 37~ the initial flux is rapid and then decays to a lower value with a time lag of -30 min. In the cells that were simply exposed to a hypotonic medium at 25~ the flux starts out small and increases to a new steady state, with a similar time lag (Fig. 8). To a first approximation, therefore, the rate of approach to the 25~ steady state in

Time (min)
in hypotonic medium without 86Rb+ and incubated 20 min at 37"C to activate the swelling-stimulated transport. Then the cells were chilled to 25~ over a time period of <2 min, and 86Rb+ was added at t = 0 (e). The initial flux was more rapid in the warm preincubated cells; a finite amount of time was needed for the system to return to the 25"C steady state. The curves through the data represent Eq. 7, with the final steady-state flux equal to 0.20 t~mol/ml cells per hour for both sets of data. The time lag for the flux increase was 39.8 min (A); the time lag for the flux decrease was 34.0 min (O). Essentially identical results were obtained in two other experiments. swollen cells is the same from either direction, in keeping with a simple two-state model.

Effects of Phosphatase Inhibitors
Given the sizable literature on the regulation of various transport processes by phosphorylation/dephosphorylation cycles (e.g., Beam et al., 1979;Grinstein et al., 1986Grinstein et al., , 1989Altamirano et al., 1988), we tested the effect of three known phosphatase inhibitors: fluoride, vanadate, and inorganic phosphate (Li, 1982). All three inhibit the swelling-stimulated flux (Fig. 9). Cells were preincubated with vanadate or inorganic phosphate to allow entry into the cells. No preincubation was necessary for F-, because it is rapidly permeant (Tosteson, 1959). The phosphatase inhibitors lowered the basal flux very slightly, but in the 310 mosmol medium in which the basal flux was measured, the KC1 cotransporter is activated only to a very small extent, and inhibition of this flux is hard to detect.
The inhibitory effect of the above agents on the swelling-stimulated flux appears to be caused by a decrease in kl~, as indicated by the time course of activation of the flux in the presence of low concentrations of the phosphatase inhibitors (Fig. 9, lower panels). In four experiments with 2 mM F-and two experiments with 10 mM phosphate, the inhibitors decreased the rate of activation of the flux. Moreover, in swollen cells, the continued presence of 8 mM F-(added after transport was activated) causes a slow decline in the flux (Fig. 10). These findings are consistent with At the arrow, the osmolality was lowered to 210 mosmol. Triangles represent the suspensions with vanadate. The intracellular vanadate concentration is unknown but is less than the extracellular concentration, because the Donnan ratio is less than unity and because of reduction of vanadate (Macara et al., 1980). Data shown are mean and range of duplicate determinations. Upper right: Same as upper left, except that 55 mM of the NaC1 was replaced with either 40 mM NaeSO 4 or 40 mM Na~HPO4/NaH2PO 4. The comparison of sulfate with phosphate was performed to ensure that the phosphate inhibition is not caused by removal of some of the chloride. Single experiment representative of three. Lower left: Cells were swollen simultaneously with 86Rb+ addition 9 The triangles represent suspensions in which 10 mM NaC1 was replaced by 8 mM Na~HPO4/2 mM NaH2PO 4 40 min before the beginning of the influx measurement. Lower right: Same as lower left, except 2 mM NaF replaced 2 mM NaC1 1 min before the influx began. Similar results were obtained in three other experiments.
the idea that fluoride inhibits swelling-activated transport by way of a decrease in k]~ rather than an increase in k~]. Thus, cell volurrie appears to affect k2~ whereas phosphatase inhibitors affect kl~ (see below).

DISCUSSION
The goal of this study was to derive information from the rates of activation and inactivation of the volume-dependent KC1 cotransport flux in rabbit red cells.
According to a very simple two-state model, the rate of relaxation to any new steady state is equal to the sum of the unimolecular rate constants for activation and inactivation of the transport system. We find that the rate of transport activation in swollen cells is much slower than that for inactivation of the flux by shrinking preswollen cells. Cell swelling must cause an increase in the ratio kl2/k21 , because swelling increases the proportion of activated states. But the rate of approach to the swollen steady state (kl~ + k2]) is smaller than the rate of approach to the steady state in cells of normal volume. The only way that cell swelling can cause an increase in kl~/k2] and a decrease in (kx2 + k~]) is if cell swelling causes a decrease in k~] rather than an increase in k]~. Moreover, the time lag for activation is largest at high cell volumes (Fig. 3). At high cell volume the ratio k12/k21 is largest, and the rate of approach to the steady state is the slowest, as expected if k2] becomes progressively smaller at higher degrees of swelling. . Progressive inhibition of 86Rb+ influx by fluoride in preswollen cells. Cells were prepared as usual, suspended in 105 mM NaCl, 7 mM HEPES, pH 7.5, 10 -4 M ouabain, and incubated 20 min at 37~ to activate the swelling-stimulated transport system. To one suspension, NaF was added from a 100 mM stock solution to a final concentration of 8 mM. 1 min later, 86RbC1/5 mM KC1 was added and the time course of influx was measured as usual. Similar results, but with less inhibition, were obtained in a separate experiment with 2 mM NaF.
Rate analysis provides insight into the effects of phosphatase inhibitors. Three inhibitors (fluoride, vanadate, and inorganic phosphate) all lower the swelling-stimulated flux. The effects are not likely caused by metabolic depletion, because the exposures were short, and inorganic phosphate would not be expected to cause ATP depletion. The effects are also not likely to be caused by changes in intracellular [Mg++], because a decrease in [Mg ++] would be expected to stimulate the flux, not inhibit it (Brugnara and Tosteson, 1987;Sachs, 1988). Although fluoride, vanadate, and phosphate are certainly not pharmacologically specific, we believe that the most reasonable interpretation of the effect of all three is that they act by inhibiting a phosphatase. Several phosphatases are known to be in red cells (Usui et al., 1983;Clari et al., 1986;Boivin and Galand, 1986;Cooke et al., 1989), but it is not yet clear which of these is the most likely candidate for the phosphatase of interest here. The phosphatase need not be a protein phosphatase.
The fact that low concentrations of phoshpatase inhibitors slow down the rate of swelling activation of transport (Fig. 9) indicates that the agents cause a decrease in k]2 rather than an increase in k21. This conclusion, though simple, is an illustration of the power of knowing the rates of change of transport. Fluoride lowers the steady-state flux and also lowers the rate of approach to the steady state. The only way (within the two-state model) that this could happen is if phosphatase inhibition lowers the forward rate constant k]~.

Swelling-inhibited Kinase Can Explain the Data
A very simple hypothesis that can explain our data is that cell swelling inhibits a kinase and has little or no effect on the conjugate phosphatase (Fig. 11). The kinase inhibition would cause a net dephosphorylation over time, and this would cause transport activation. In normal cells the system is poised such that in the steady state most of the crucial sites are phosphorylated. It is only when the kinase is inhibited Because kl2 appears to be linked to a phosphatase activity, it is likely that k~ is associated with a kinase.
by cell swelling that the dephosphorylation rate becomes comparable to th e phosphorylation rate. If cells are swollen in the presence of a phosphatase inhibitor, then the net dephosphorylation is slower, and both the rate and extent of transport activation are smaller, as observed.

Magnesium Effects
The notion of a phosphorylation-dephosphorylation cycle regulating KC1 cotransport is consistent with the known inhibitory effect of high [Mg ++] on KC1 cotransport (Sachs, 1988;Brugnara et al., 1988). The inhibitory effect of Mg + § could be explained if high [Mg § ] either inhibited the phosphatase or activated the kinase. Dunham (1989) has recently shown that Mg ++ depletion activates the KCI flux and also eliminates the time lag; these effects are consistent with Mg ++ inhibition of a phosphatase. Removal of that inhibition would increase k12 and thereby activate the flux and shorten the relaxation time.

Relation to Studies on Red Cell Ghosts
In the context of discussing kinases and phosphatases that may regulate KC1 cotransport, it is relevant to mention studies in red cell ghosts. Anion-dependent K + (Rb +) transport has been demonstrated in human red cell ghosts (Dunham and Logue, 1986;Brugnara et al., 1988;Sachs, 1988). In ghosts prepared by batch hemolysis/reversal, Dunham and Logue (1986) found that the furosemide-inhibitable K + influx is doubled by a 20% cell swelling. Ghosts prepared by this method retain nearly 10% of the original cytoplasm. Sachs (1988) used ghosts prepared by the gel filtration method; these ghosts retain only a very small fraction of cytoplasm. In these ghosts the K + influx is volume-dependent, but somewhat less so than those in the Dunham/Logue study. The influx is roughly doubled by a doubling of ghost volume. The observation of a volume-sensitive influx in these ghosts indicates that at least some elements of the volume sensing/signal transduction apparatus are preserved in the absence of cytoplasm. However, a separate study using the same kind of ghosts showed that the K + effiux, though anion-dependent, is not affected by cell volume (Brugnara et al., 1988); the reasons for the differences between the two studies are not clear. Sachs (1988) showed that there is no detectable time lag for either activation or inactivation of the swelling-stimulated KCI flux in human red cell ghosts. This finding is in marked contrast with the present study and those in five other laboratories using intact red cells of pig (Kim et al., 1989), duck (Kregenow, 1971;McManus, personal communication), and LK sheep (Dunham, 1989;Lauf, personal communication). The lack of time lag may be caused by a low Mg ++ concentration in the ghosts (Dunham, 1989). In any case, the regulation of KC1 cotransport is significantly different in intact cells and resealed ghosts.

Relationship to Work Showing A TP Requirement
The suggestion that a net dephosphorylation may activate KCI cotransport seems at odds with the clearly demonstrated requirement of the system for low concentrations of ATP (Dunham and Logue, 1986;Sachs, 1988;Brugnara et al., 1988). However, there are protein phosphatases known that require ATP (Li, 1982;Clari et al., 1986). Complete removal of ATP could inactivate both the kinase and phosphatase associated with transport regulation. With both enzymes inactive, the transport could be frozen in the phosphorylated, inactive state. Therefore, the ATP requirement does not rule out the possibility that kinase inhibition is involved with swelling activation of transport.

Relation to NEM-activated Transport
It is well known that pretreatment of several species of red cells with NEM causes activation of KC1 cotransport (see Lauf, 1985); in rabbit red cells the flux appears to be locked by NEM into a volume-independent state (A1- Rohil and Jennings, 1989). In the context of the present data, the stimulatory effect of NEM in principle could be explained by either a strong, irreversible inhibition of the putative swelling-inhibited kinase or an acceleration of the phosphatase. If the latter were true, then phosphatase inhibition should still inhibit the flux following NEM activation. However, 20 mM fluoride does not inhibit the flux in NEM-pretreated cells (AI-Rohil, 1988). This finding is consistent with a direct effect of NEM on the transporter, but given the multiplicity of sulfhydryl groups related to KC1 cotransport (see Lauf, 1987), it is not possible at present to distinguish between a direct action of NEM on the transporter and an action on the regulatory machinery. Conversely, though, it is worth pointing out that the lack of effect of fluoride on the NEM-stimulated flux suggests that fluoride does not act directly on the transporter itself, but rather affects regulation.

Temperature Dependence
The temperature dependence of NEM-activated S6Rb+ influx is remarkably low: ~9 kcal/mol. (The temperature of the flux measurement, not the NEM pretreatment, is varied.) The only other measurement of temperature dependence of NEM-activated transport is that by Lauf (1983), who found an apparent activation energy of 15 kcal/mol for NEM-stimulated effiux from LK sheep red cells. The E a of 9 kcal/mol measured here is an underestimate of the E a of the translocation event for KCI cotransport, because all our measurements were at a single extracellular K + concentration. The affinity for extracellular K + rises as the temperature drops (see Dunham, 1989). Therefore, the effect of temperature on the influx is not as large as it would be at higher substrate concentration. Similarly, the temperature dependence of the swelling-stimulated influx measured here at 5 mM extracellular K + is smaller than that measured by Ellory et al. (1985) at higher concentrations.
The point of our temperature study was not to estimate a true activation energy of a well-defined kinetic event, but rather to learn how temperature affects the relative numbers of transporters in the resting vs. activated state in swollen cells. The most important result is that the steady-state KCI cotransport flux in swollen cells is more temperature-dependent than that of NEM-treated cells. The former changes by a factor of about 3.5 between 370C and 25~ and the latter changes by a factor of 1.6 between the same two temperatures. The simplest interpretation of this finding is that, at a given cell volume, there are more transporters in the activated state at 37~ than at 25~ even if enough time is allowed at each temperature for a steady state to be reached.