Generalized kinetic analysis of ion-driven cotransport systems: II. Random ligand binding as a simple explanation for non-michaelian kinetics

Computation and Functional Studies Provide a Model for the Structure of the Zinc Transporter hZIP4

Members of the Zrt and Irt protein (ZIP) family are a central participant in transition metal homeostasis as they function to increase the cytosolic concentration of zinc and/or iron. However, the lack of a crystal structure hinders elucidation of the molecular mechanism of ZIP proteins. Here, we employed GREMLIN, a co-evolution-based contact prediction approach in conjunction with the Rosetta structure prediction program to construct a structural model of the human (h) ZIP4 transporter. The predicted contact data are best fit by modeling hZIP4 as a dimer. Mutagenesis of residues that comprise a central putative hZIP4 transmembrane transition metal coordination site in the structural model alter the kinetics and specificity of hZIP4. Comparison of the hZIP4 dimer model to all known membrane protein structures identifies the 12-transmembrane monomeric Piriformospora indica phosphate transporter (PiPT), a member of the major facilitator superfamily (MFS), as a likely structural homolog.

A novel delta current method for transport stoichiometry estimation

Background

The ion transport stoichiometry (q) of electrogenic transporters is an important determinant of their function. q can be determined by the reversal potential (E_rev) if the transporter under study is the only electrogenic transport mechanism or a specific inhibitor is available. An alternative approach is to calculate delta reversal potential (ΔE_rev) by altering the concentrations of the transported substrates. This approach is based on the hypothesis that the contributions of other channels and transporters on the membrane to E_rev are additive. However, E_rev is a complicated function of the sum of different conductances rather than being additive.

Results

We propose a new delta current (ΔI) method based on a simplified model for electrogenic secondary active transport by Heinz (Electrical Potentials in Biological Membrane Transport, 1981). ΔI is the difference between two currents obtained from altering the external concentration of a transported substrate thereby eliminating other currents without the need for a specific inhibitor. q is determined by the ratio of ΔI at two different membrane voltages (V₁ and V₂) where q = 2RT/(F(V₂ –V₁))ln(ΔI₂/ΔI₁) + 1. We tested this ΔI methodology in HEK-293 cells expressing the elctrogenic SLC4 sodium bicarbonate cotransporters NBCe2-C and NBCe1-A, the results were consistent with those obtained with the E_rev inhibitor method. Furthermore, using computational simulations, we compared the estimates of q with the ΔE_rev and ΔI methods. The results showed that the ΔE_rev method introduces significant error when other channels or electrogenic transporters are present on the membrane and that the ΔI equation accurately calculates the stoichiometric ratio.

Conclusions

We developed a ΔI method for estimating transport stoichiometry of electrogenic transporters based on the Heinz model. This model reduces to the conventional reversal potential method when the transporter under study is the only electrogenic transport process in the membrane. When there are other electrogenic transport pathways, ΔI method eliminates their contribution in estimating q. Computational simulations demonstrated that the ΔE_rev method introduces significant error when other channels or electrogenic transporters are present and that the ΔI equation accurately calculates the stoichiometric ratio. This new ΔI method can be readily extended to the analysis of other electrogenic transporters in other tissues.

Bacterially produced Pt-GFP as ratiometric dual-excitation sensor for in planta mapping of leaf apoplastic pH in intact Avena sativa and Vicia faba

BACKGROUND

Ratiometric analysis with H(+)-sensitive fluorescent sensors is a suitable approach for monitoring apoplastic pH dynamics. For the acidic range, the acidotropic dual-excitation dye Oregon Green 488 is an excellent pH sensor. Long lasting (hours) recordings of apoplastic pH in the near neutral range, however, are more problematic because suitable pH indicators that combine a good pH responsiveness at a near neutral pH with a high photostability are lacking. The fluorescent pH reporter protein from Ptilosarcus gurneyi (Pt-GFP) comprises both properties. But, as a genetically encoded indicator and expressed by the plant itself, it can be used almost exclusively in readily transformed plants. In this study we present a novel approach and use purified recombinant indicators for measuring ion concentrations in the apoplast of crop plants such as Vicia faba L. and Avena sativa L.

RESULTS

Pt-GFP was purified using a bacterial expression system and subsequently loaded through stomata into the leaf apoplast of intact plants. Imaging verified the apoplastic localization of Pt-GFP and excluded its presence in the symplast. The pH-dependent emission signal stood out clearly from the background. PtGFP is highly photostable, allowing ratiometric measurements over hours. By using this approach, a chloride-induced alkalinizations of the apoplast was demonstrated for the first in oat.

CONCLUSIONS

Pt-GFP appears to be an excellent sensor for the quantification of leaf apoplastic pH in the neutral range. The presented approach encourages to also use other genetically encoded biosensors for spatiotemporal mapping of apoplastic ion dynamics.

Characteristics of glucose uptake by glucose- and NH4-limited grown Penicillium ochrochloron at low, medium and high glucose concentration

Glucose uptake by Penicillium ochrochloron (formerly Penicillium simplicissimum) was studied from 0.01 to 400 mM glucose using chemostat culture and bioreactor batch culture. The characteristics of glucose uptake varied considerably with the conditions of growth, harvest and uptake assay. Glucose-limited grown mycelium showed one saturable transport system [K(S) below 0.01 mM; v(max) 1.1-1.2 mmol (g dry weight)(-1)h(-1)] plus a first order process (permeability P=1.2x10(-7)cm s(-1)). Ammonium-limited grown mycelium showed only one saturable transport system [K(S) 0.3-0.7 mM; v(max) 0.5-0.8 mmol (g dry weight)(-1)h(-1)]. During exponential growth at high glucose concentration (300-400 mM) a first order process was found with a P value of 5.6-9.3x10(-7)cm s(-1). After ammonium exhaustion a second first order phase showed a lower P value (6.1-9.3x10(-8)cm s(-1)). A similar change in permeability was also found after a re-evaluation of published data for Gibberella fujikuroi, Aspergillus niger, Aspergillus awamori and Saccharomycopsis lipolytica. For the first order processes simple diffusion was ruled out as a mechanism for glucose uptake. Glucose uptake by P. ochrochloron was controlled more strongly by metabolism than by transport and was not rate limiting for overflow metabolism.

A high affinity fungal nitrate carrier with two transport mechanisms

We have expressed the CRNA high affinity nitrate transporter from Emericella (Aspergillus) nidulans in Xenopus oocytes and used electrophysiology to study its properties. This method was used because there are no convenient radiolabeled substrates for the transporter. Oocytes injected with crnA mRNA showed nitrate-, nitrite-, and chlorite-dependent currents. Although the gene was originally identified by chlorate selection there was no evidence for transport of this anion. The gene selection is explained by the high affinity of the transporter for chlorite, and the fact that this ion contaminates solutions of chlorate. The pH-dependence of the anion-elicited currents was consistent with H(+)-coupled mechanism of transport. At any given voltage, currents showed hyperbolic kinetics with respect to extracellular H(+), and these data could be fitted with a Michaelis-Menten relationship. But this equation did not adequately describe transport of the anion substrates. At higher concentrations of the anion substrates and more negative membrane voltages, the currents were decreased, but this effect was independent of changes in external pH. These more complicated kinetics could be fit by an equation containing two Michaelis-Menten terms. The substrate inhibition of the currents could be explained by a transport reaction cycle that included two routes for the transfer of nitrate across the membrane, one on the empty carrier and the other proton coupled. The model predicts that the substrate inhibition of transporter current depends on the cytosolic nitrate concentration. This is the first time a high affinity nitrate transport activity has been characterized in a heterologous system and the measurements show how the properties of the CRNA transporter are modified by changes in the membrane potential, external pH, and nitrate concentration. The physiological significance of these observations is discussed.

Plasma membrane transport in context - making sense out of complexity

Major advances in our understanding of the transport of inorganic nutrient ions across plant plasma membranes have emerged from recent studies on the control of the dominant H+-pumping ATPase and from identification of a range of new transporters for divalent cations, potassium, phosphate and nitrate. In many cases, multiple transporter isoforms have been described. An appreciation of the physiological roles of these transporters demands combined genetic and physiological approaches, which, in the case of an outward rectifying K+ channel, have already been used to yield an intriguing insight into root-mediated K+ release into the xylem. In this review we attempt to place some of those developments in a physiological context.

Voltage and cosubstrate dependence of the Na-HCO3 cotransporter kinetics in renal proximal tubule cells

The voltage dependence of the kinetics of the sodium bicarbonate cotransporter was studied in proximal tubule cells. This electrogenic cotransporter transports one Na+, three HCO3-, and two negative charges. Cells were grown to confluence on a permeable support, mounted on a Ussing-type chamber, and permeabilized apically to small monovalent ions with amphotericin B. The steady-state, di-nitro-stilbene-di-sulfonate-sensitive current was shown to be sodium and bicarbonate dependent and therefore was taken as flux through the cotransporter. Voltage-current relations were measured as a function of Na+ and HCO3- concentrations between -160 and +160 mV under zero-trans and symmetrical conditions. The kinetics could be described by a Michaelis-Menten behavior with a Hill coefficient of 3 for HCO3- and 1 for Na+. The data were fitted to six-state ordered binding models without restrictions with respect to the rate-limiting step. All ordered models could quantitatively account for the observed current-voltage relationships and the transinhibition by high bicarbonate concentration. The models indicate that 1) the unloaded transporter carries a positive charge; 2) the binding of cytosolic bicarbonate to the transporter "senses" 12% of the electric field in the membrane, whereas its translocation across the membrane "senses" 88% of the field; 3) the binding of Na+ to the cotransporter is voltage independent.

Transport of small lons and molecules through the plasma membrane of filamentous fungi

Less than 1% of the estimated number of fungal species have been investigated concerning the transport of low-molecular-weight nutrients and metabolites through the plasma membrane. This is surprising if one considers the importance of the processes at the plasma membrane for the cell: this membrane mediates between the cell and its environment. Concentrating on filamentous fungi, in this review emphasis is placed on relating results from biophysical chemistry, membrane transport, fungal physiology, and fungal ecology. Among the treated subjects are the consequences of the small dimension of hyphae, the habitat and membrane transport, the properties of the plasma membrane, the efflux of metabolites, and the regulation of membrane transport. Special attention is given to methodological problems occurring with filamentous fungi. A great part of the presented material relies on work with Neurospora crassa, because for this fungus the most complete picture of plasma membrane transport exists. Following the conviction that we need "concepts instead of experiments", we delineate the lively network of membrane transport systems rather than listing the properties of single transport systems.

Mechanism of high-affinity potassium uptake in roots of Arabidopsis thaliana

Potassium is a major nutrient in higher plants, where it plays a role in turgor regulation, charge balance, leaf movement, and protein synthesis. Terrestrial plants are able to sustain growth at micromolar external K+ concentrations, at which K+ uptake across the plasma membrane of root cells must be energized despite the presence of a highly negative membrane potential. However, the mechanism of energization has long remained obscure. Therefore, whole-cell mode patch clamping has been applied to root protoplasts from Arabidopsis thaliana to characterize membrane currents resulting from the application of micromolar K+. Analysis of whole cell current/voltage relationships in the presence and absence of micromolar K+ enabled direct testing of K+ transport for possible energization by cytoplasmic ATP and the respective trans-membrane gradients of Na+, Ca2+, and H+. Subtracted current/voltage relations for K(+)-dependent membrane currents are independent of ATP and reverse at potentials that imply H(+)-coupled K+ transport with a ratio of 1 H+:K+. Furthermore, the reversal potential of the K+ current shifts negative as external H+ activity is decreased. K(+)-dependent currents saturate in the micromolar concentration range with an apparent Km of 30 microM, a value in close agreement with previously reported Km values for high-affinity K+ uptake. We conclude that our results are consistent with the view that high-affinity K+ uptake in higher plants is mediated by a H+:K+ symport mechanism, competent in driving K+ accumulation to equilibrium ratios in excess of 10(6)-fold.

Ontogeny of Na+/D-glucose cotransport in guinea-pig jejunal vesicles: only one system is involved at both 20 degrees C and 35 degrees C

The kinetic parameters of Na+/D-glucose cotransport were examined in fetal, newborn and adult guinea-pig jejunal brush-border membrane vesicles using a displacement curve and non-linear regression procedure. Our data indicated the presence of a single system with a Km of 0.34 +/- 0.04 mM at both 20 degrees C and 35 degrees C. Vmax was increased by about 4-fold when the kinetic experiments were performed at 35 degrees C. Since our results were not in agreement with the findings of Brot-Laroche et al. (J. Biol. Chem. (1986) 261, 6168-6176) which indicated the existence of a distinct D-glucose transport system in the adult guinea-pig jejunum at 35 degrees C, we verified the influence of their experimental conditions on initial rate uptake measurements. In the presence of D-sorbitol instead of D-mannitol in the transport media, 70% inhibition of D-glucose uptake was observed, an effect which was attributable to contamination of sorbitol preparations by D-glucose. After removal of glucose contamination D-sorbitol did not significantly reduce the initial rate of D-glucose transport. These results led us to conclude the existence of a single D-glucose transport system in the guinea-pig small intestine and to stress the choice of experimental conditions as being crucial for an accurate estimation of kinetic parameters.

Allosterism and Na(+)-D-glucose cotransport kinetics in rabbit jejunal vesicles: compatibility with mixed positive and negative cooperativities in a homo- dimeric or tetrameric structure and experimental evidence for only one transport protein involved

We first present two simple dimeric models of cotransport that may account for all of the kinetics of Na(+)-D-glucose cotransport published so far in the small intestine. Both the sigmoidicity in the Na+ activation of transport (positive cooperativity) and the upward deviations from linearity in the Eadie-Hofstee plots relative to glucose concentrations (negative cooperativity) can be rationalized within the concept of allosteric kinetic mechanisms corresponding to either of two models involving sequential or mixed concerted and sequential conformational changes. Such models also allow for 2 Na+: 1 S and 1 Na+: 1 S stoichiometries of cotransport at low and high substrate concentrations, respectively, and for partial inhibition by inhibitors or substrate analogues. Moreover, it is shown that the dimeric models may present physiological advantages over the seemingly admitted hypothesis of two different cotransporters in that tissue. We next address the reevaluation of Na(+)-D-glucose cotransport kinetics in rabbit intestinal brush border membrane vesicles using stable membrane preparations, a dynamic approach with the Fast Sampling Rapid Filtration Apparatus (FSRFA), and both nonlinear regression and statistical analyses. Under different conditions of temperatures, Na+ concentrations, and membrane potentials clamped using two different techniques, we demonstrate that our data can be fully accounted for by the presence of only one carrier in rabbit jejunal brush border membranes since transport kinetics relative to glucose concentrations satisfy simple Michaelis-Menten kinetics. Although supporting a monomeric structure of the cotransporter, such a conclusion would conflict with previous kinetic data and more recent studies implying a polymeric structure of the carrier protein. We thus consider a number of alternatives trying to reconcile the observation of Michaelis-Menten kinetics with allosteric mechanisms of cotransport associated with both positive and negative cooperativities for Na+ and glucose binding, respectively. Such models, implying energy storage and release steps through conformational changes associated with ligand binding to an allosteric protein, provide a rational hypothesis to understand the long-time debated question of energy transduction from the Na+ electrochemical gradient to the transporter.

Mutual interaction of ion uptake and membrane potential

The concentration dependence of cation uptake by the cell may be considerably complicated when this uptake is accompanied by a depolarization of the cell membrane. In case of carrier-mediated transport deviations from Michaelis-Menten kinetics may come to the fore comparable to those found in a dual mechanism of cation uptake or when substrate inhibition is involved. This remains true when only the maximum rate of uptake and not the Km is dependent upon the membrane potential. We have proven this by means of computer simulation of cation transport mediated by a non-mobile carrier. Under restricted conditions still apparent Michaelis-Menten kinetics may be found despite the fact that the membrane potential varies with increasing substrate cation concentration. But even then there are still differences with 'normal' transport kinetics. A non-competitive inhibitor does not only affect the maximum rate of uptake but also the apparent Km. Depolarization of the cells by a cation which passes the cell membrane by means of diffusion, affects the uptake of the substrate cation almost in the same way as a non-competitive inhibitor does and causes both a decrease in the maximum rate of uptake and an increase in Km. In the case of competitive inhibition the apparent affinity of the inhibitor for the carrier depends upon the rate of transfer of this inhibitor through the cell membrane. The mutual influence of cation uptake and membrane potential is dealt with for uniport of either monovalent or divalent cations and for cotransport of monovalent cation with protons, as well. Possible effects of the surface potential are accounted for.

Reaction kinetic model of a proposed plasma membrane two-cycle H(+)-transport system of Chara corallina

Biophysical and numerical analysis methods were used to characterize and model the transport protein that gives rise to the acid and alkaline regions of Chara. A measuring system that permits the detection of area-specific current-voltage curves was used. These current-voltage curves, obtained from the inward current regions of Chara, underwent a parallel shift when the alkaline region was inverted by means of an acid pH treatment. In this situation the reversal potential of this area shifted from -120 mV to -340 mV. Together with data obtained from experiments using a divided chamber system, these results suggest that a common transport protein generates inward and outward current regions of Chara. On the basis of these experimental findings, a reaction kinetic model is proposed that assigns two operational modes to the proposed transport protein. Switching between these modes generates either acid or alkaline behavior. Since the observed pH dependence of the postulated transporter is rather complex, a reaction kinetic saturation mechanism had to be incorporated into the model. This final 10-state reaction kinetic model provides an appropriate set of mathematical relations to fit the measured current-voltage curves by computer.

Cloning and expression in yeast of a plant potassium ion transport system

A membrane polypeptide involved in K+ transport in a higher plant was cloned by complementation of a yeast mutant defective in K+ uptake with a complementary DNA library from Arabidopsis thaliana. A 2.65-kilobase complementary DNA conferred ability to grow on media with K+ concentration in the micromolar range and to absorb K+ (or 86Rb+) at rates similar to those in wild-type yeast. The predicted amino acid sequence (838 amino acids) has three domains: a channel-forming region homologous to animal K+ channels, a cyclic nucleotide-binding site, and an ankyrin-like region.

Branched reaction mechanism for the Na/K pump as an alternative explanation for a nonmonotonic current vs. membrane potential response

Nonmonotonic velocity vs. membrane potential curves are often taken as evidence that two steps involve charge movement through the electric field. However, a branched reaction scheme in which only one step involves charge movement per cycle can lead to a nonmonotonic response. A similar case occurs in enzyme kinetics: nonmonotonic velocity vs. substrate curves are often taken as evidence for two different substrate-binding sites. However, a branched reaction scheme in which only one substrate binds per complete cycle can lead to a nonmonotonic response (see Segel, I.H. 1975, Enzyme Kinetics, pp. 657-659. John Wiley & Sons, New York). Some analytical constraints on the relative sizes of the rate constants of a branched reaction mechanism that give rise to nonmonotonic responses are derived. There are two necessary conditions. (i) The rate of at least one step in the branched pathway must be less than the rate of the step after the branch. (ii) The rate of the pathway in which S binds first must be slower than the rate of the other pathway. Analogous cases give rise to nonmonotonic current vs. membrane potential curves. A branched mechanism for the Na/K pump provides an alternative explanation for a nonmonotonic pump current vs. membrane potential relationship.

Presteady-state kinetics and carrier-mediated transport: a theoretical analysis

Kinetic studies of cotransport mechanisms have so far been limited to the conventional steady-state approach which does not allow in general to resolve either isomerization or rate-limiting steps and to determine the values of the individual rate constants for the elementary reactions involved along a given transport pathway. Such questions can only be answered using presteady-state or relaxation experiments which, for technical reasons, have not yet been introduced into the field of cotransport kinetics. However, since two recent reports seem compatible with the observation of such transient kinetics, it would appear that theoretical studies are needed to evaluate the validity of such claims and to critically evaluate the expectations from a presteady-state approach. We thus report such a study which was performed on a simple four-state mechanism of carrier-mediated transport. The time-dependent equation for zero-trans substrate uptake was thus derived and then extended to models with p intermediary steps. It is concluded that (p-1) exponential terms will describe the approach to the steady state but that such equations have low analytical value since the parameters of the flux equation cannot be expressed in terms of the individual rate constants of the elementary reactions for models with p greater than 5. We thus propose realistic simplifications based on the time-scale separation hypothesis which allows replacement of the rate constants of the rapid steps by their equilibrium constants, thereby reducing the complexity of the kinetic system. Assuming that only one relaxation can be observed, this treatment generates approximate models for which analytical expressions can easily be derived and simulated through computer modeling. When performed on the four-state mechanism of carrier-mediated transport, the simulations demonstrate the validity of the approximate solutions derived according to this hypothesis. Moreover, our approach clearly shows that presteady-state kinetics, should they become applicable to (co)transport kinetics, could be invaluable in determining more precise transport mechanisms.

Characterization of Cl- transport in vacuolar membrane vesicles using a Cl(-)-sensitive fluorescent probe: reaction kinetic models for voltage- and concentration-dependence of Cl- flux

The effects of Cl- concentration and membrane potential (delta psi) on Cl- influx in isolated vesicles of vacuolar membrane (tonoplast) from red beet (Beta vulgaris L.) storage tissue have been characterized using the Cl(-)-sensitive fluorescent probe, 6-methoxy-1-(3-sulfonatopropyl)quinolinium (SPQ). The initial rate of Cl- transport into the vesicles was enhanced both by the imposition of a positive delta psi and by increases in extravesicular Cl- concentration. The kinetic mechanism underlying these responses was investigated by examining the accuracy with which the data could be described by several transport models. A model based on constant field theory yielded a poor description of the data, but satisfactory fits were generated by pseudo-two-state reaction kinetic models based on classical carrier schemes. Fits were equally good when it was assumed that charge translocation accompanied Cl- entry, or when charge was carried by the unloaded transport system, as long as only a single charge is translocated in each carrier cycle. Expansion of the models to three states enabled description of the Cl- concentration dependence of transport by changes in a single, voltage insensitive rate constant which is tentatively identified with Cl- binding at the external surface of the membrane. The derived value of the dissociation constant between Cl- and the transport system is estimated at between 30 and 52 mM.

Transport of potassium in Chara australis: II. Kinetics of a symport with sodium

An electrogenic K(+)-Na+ symport with a high affinity for K+ has been found in Chara (Smith & Walker, 1989). Under voltage-clamp conditions, the symport shows up as a change in membrane current upon adding either K+ or Na+ to the bathing medium in the presence of the other. Estimation of kinetic parameters for this transport has been difficult when using intact cells, since K(+)-Na+ current changes show a rapid falling off with time at K+ concentrations above 50 microM. Cytoplasm-enriched cell fragments are used to overcome this difficulty, since they do not show the rapid falling off of current change seen with intact cells. Current-voltage curves for the membrane in the absence or presence of either K+ or Na+ are obtained, yielding difference current-voltage curves which isolate the symport currents from other transport processes. The kinetic parameters describing this transport are found to be voltage dependent, with Km for K+ ranging from 30 down to 2 microM as membrane potential varies from -140 to -400 mV, and Km for Na+ ranging between 470 and 700 microM over a membrane potential range of -140 to -310 mV. Two different models for this transport system have been investigated. One of these involves the simultaneous transport of both the driver and substrate ions across the membrane, while the other allows for the possibility of the two ions being transported consecutively in two distinct reaction steps. The experimental results are shown to be consistent with either of these cotransport models, but they do suggest that binding of K+ occurs before that of Na+, and that movement of charge across the membrane (the voltage-dependent step) occurs when the transport protein has neither K+ nor Na+ bound to it.

Separation of two distinct Na+/D-glucose cotransport systems in the human fetal jejunum by means of their differential specificity for 3-O-methylglucose

Based on kinetic arguments, we have recently proposed the existence of two distinct Na+/D-glucose cotransporters in brush-border membrane vesicles isolated from the human fetal jejunum (Biochim. Biophys. Acta 938 (1988) 181-188). In order to further test this hypothesis, inhibition studies of the zero-trans influx of substrate have been performed under Na(+)-gradient and voltage-clamped conditions. Initial rates of D-glucose uptake were totally abolished by D-glucose, D-galactose, alpha-methylglucose and phlorizin while 3-O-methylglucose and phloretin induced only a 65% inhibition even at the highest concentrations used. The residual activity of D-glucose uptake is thus compatible with substrate flux through a low-affinity transport system which is insensitive to phloretin and does not accept 3-O-methylglucose as substrate. This substrate specificity has been used to separate kinetically the two putative pathways for glucose transport. The data obtained are compatible with the existence of the following two systems: (i) a low-affinity, high-capacity system with a Km of 4.7 mM and a Vmax of 22 nmol/min per mg of protein, and; (ii) a high-affinity, low-capacity system with a Km of 0.57 mM and a Vmax of 10.7 nmol/min per mg of protein. These data thus demonstrate clearly the existence of two distinct Na(+)-dependent D-glucose carriers in the human jejunum during the early gestation period since these systems can be differentiated not only by their kinetic properties but also by their differences in both substrate and inhibitor specificities.

Analysis of the H+/sugar symport in yeast under conditions of depolarized plasma membrane

H+/sugar symport in the obligatory aerobic yeast Rhodotorula glutinis was analyzed under conditions where the plasma membrane was selectively depolarized by the lipophilic cation tetraphenylphosphonium (TPP+). Control experiments showed that this treatment did not impair the transmembrane delta pH, the cell energy charge, and the function of plasma membrane H+-ATPase. The kinetic data were fitted to elementary functions derived from a model constructed on the basis of some simplifying premises for ordered (either C + H+ + S or C + S + H+) and random reaction mechanisms. In addition, the comparison of the kinetic parameters in fully energized and depolarized cells provided information about the free carrier charge. It was concluded that the binding sequence of formation of the ternary carrier/H+/substrate complex follows a random mechanism and that the carrier bears a negative charge.

Kinetics of L-valine uptake in tobacco leaf discs. Comparison of wild-type, the digenic mutant Val(r)-2, and its monogenic derivatives

Uptake rates of L-valine in epidermis-free leaf discs of tobacco (Nicotiana tabacum L. cv. Xanthi) were measured over the concentration range 0.1 μM to 50 mM. Wild-type tobacco was compared with the digenic mutant Val(r)-2 (genotype vr2/vr2; vr3/vr3), and with the monogenic mutant strains h9 and h10 (genotype +/+; vr3/vr3) and h17 and h23 (genotype vr2/vr2; +/+). Rate equations consisting of one to three Michaelis-Menten terms, possibly in combination with a linear term were fitted to the kinetic data. These rate equations are equivalent to rational polynomials which may be regarded as the general type of mathematical function describing the kinetics of enzymes and carriers. Kinetic data of the four genotypes conformed to the sum of three Michaelis-Menten terms. Accordingly, three kinetic components could be distinguished. In the wild-type the approximate Kms were 40 μM, 1mM, and 40 mM, respectively. In Val(r)-2 a component with a very low Km (about 4 μM) was found which may represent either the modified low-Km component of the wild-type or a fourth component which is undetectable in the wild-type by kinetic analysis. The Vmax of the low-Km component in Val(r)-2 was at least a 100-fold lower than in the wild-type. In the presence of one of the mutant genes the calculated Vmax of the low-Km component was 48% (strains h9 and h10) or 40% (strains h17 and h23) of the corresponding Vmax in the wild-type. It is reasoned that the mutations have no effect on the activity of the other two kinetic components, though the evidence for this is circumstantial. Autoradiographs of leaf discs showed that in Val(r)-2 the uptake of (14)C-labelled valine in both mesophyll and minor veins was strongly reduced as compared with the wild-type.

Use of progress curves to estimate the co-substrate-to-substrate flow ratio of a symport mechanism. Application to the isoleucine-Na+ symport of mouse ascites-tumour cells and to the lactose-proton symport

The model envisages two components in the process, whereby Ht equivalents of co-substrate and St equivalents of substrate accumulate in the cellular compartment in time t. The first is the flow through the symport, n equivalents of co-substrate entering or leaving with each substrate equivalent. The second is the basal flow of co-substrate outside the symport. In certain specific circumstances n can be derived by plotting Ht/t against St/t. The principal requirement is that, whereas the ratio of the component flows must change in the interval t, the magnitude of the basal flow must either be zero or constant. The procedure is applied to published observations [West & Mitchell (1973) Biochem. J. 132, 587-592] on the lactose-proton symport of Escherichia coli [n = 1.075 +/- 0.064(7)] and to new observations on the isoleucine-Na+ symport of mouse ascites-tumour cells [n = 1.136 +/- 0.120(18)].

Potassium-proton symport in Neurospora: kinetic control by pH and membrane potential

Active transport of potassium in K+-starved Neurospora was previously shown to resemble closely potassium uptake in yeast, Chlorella, and higher plants, for which K+ pumps or K+/H+-ATPases had been proposed. For Neurospora, however, potassium-proton cotransport was demonstrated to operate, with a coupling ratio of 1 H+ to 1 K+ taken inward so that K+, but not H+, moves against its electrochemical gradient (Rodriguez-Navarro et al., J. Gen. Physiol. 87:649-674). In the present experiments, the current-voltage (I-V) characteristic of K+-H+ cotransport in spherical cells of Neurospora has been studied with a voltage-clamp technique, using difference-current methods to dissect it from other ion-transport processes in the Neurospora plasma membrane. Addition of 5-200 microM K+ to the bathing medium causes 10-150 mV depolarization of the unclamped membrane, and yields a sigmoid I-V curve with a steep slope (maximal conductance of 10-30 microS/cm2) for voltages of -300 to -100 mV, i.e., in the normal physiologic range. Outside that range the apparent I-V curve of the K+-H+ symport saturates for both hyperpolarization and depolarization. It fails to cross the voltage axis at its predicted reversal potential, however, an effect which can be attributed to failure of the I-V difference method under reversing conditions. In the absence of voltage clamping, inhibitors-such as cyanide or vanadate-which block the primary proton pump in Neurospora also promptly inhibit K+ transport and K+-H+ currents. But when voltage clamping is used to offset the depolarizing effects of pump blockade, the inhibitors have no immediate effect on K+-H+ currents. Thus, the inhibition of K+ transport usually observed with these agents reflects the kinetic effect of membrane depolarization rather than any direct chemical action or the cotransport system itself. Detailed study of the effects of [K+]o and pHo on the I-V curve for K+-H+ symport has revealed that increasing membrane potential systematically decreases the apparent affinity of the transporter for K+, but increases affinity for protons (Km range: for [K+]o, 15-45 microM; for [H+]o, 10-35 nM). This behavior is consistent with two distinct reaction-kinetic models, in which (i) a neutral carrier binds K+ first and H+ last in the forward direction of transport, or (ii) a negatively charged carrier (-2) binds H+ first and K+ last.

Reaction kinetic parameters for ion transport from steady-state current-voltage curves

This study demonstrates possible ways to estimate the rate constants of reaction kinetic models for ion transport from steady-state current-voltage data as measured at various substrate concentrations. This issue is treated theoretically by algebraic reduction and extension of a reaction kinetic four-state model for uniport. Furthermore, an example for application is given; current-voltage data from an open K+ selective channel (Schroeder, J.I., R. Hedrich, and J.M. Fernandez, 1984, Nature (Lond.), 312:361-362) supplemented by some new data have been evaluated. The analysis yields absolute numerical estimates of the 14 rate constants of a six-state model, which is discussed in a wider context.

THE PHYSIOLOGY OF BASIDIOMYCETE LINEAR ORGANS: I. PHOSPHATE UPTAKE BY CORDS AND MYCELIUM IN THE LABORATORY AND THE FIELD

Phosphate uptake as a function of external medium concentration has been determined for mycelium grown in the laboratory, segments of cords collected from the field and cords in the field for a range of wood-decay basidiomycetes. Hofstee plots in all cases can be interpreted as indicating the presence of two uptake systems. Uptake of phosphate by mycelium is reduced by increasing the concentration of phosphate in the growth medium from 10 μM to 10 mM. The major portion absorbed by cords in the field remains within the segment exposed to radioactive solution, suggesting conversion of the phosphate to an immobile form unavailable for translocation.

Electrogenic properties of the sodium-alanine cotransporter in pancreatic acinar cells: II. Comparison with transport models

In this paper, the results of the preceding electrophysiological study of sodium-alanine cotransport in pancreatic acinar cells are compared with kinetic models. Two different types of transport mechanisms are considered. In the "simultaneous" mechanism the cotransporter C forms a ternary complex NCS with Na+ and the substrate S; coupled transport of Na+ and S involves a conformational transition between states NC'S and NC"S with inward- and outward-facing binding sites. In the "consecutive" (or "ping-pong") mechanism, formation of a ternary complex is not required; coupled transport occurs by an alternating sequence of association-dissociation steps and conformational transitions. It is shown that the experimentally observed alanine- and sodium-concentration dependence of transport rates is consistent with the predictions of the "simultaneous" model, but incompatible with the "consecutive" mechanism. Assuming that the association-dissociation reactions are not rate-limiting, a number of kinetic parameters of the "simultaneous" model can be estimated from the experimental results. The equilibrium dissociation constants of Na+ and alanine at the extracellular side are determined to be K"N less than or equal to 64 mM and K"S less than or equal to 18 mM. Furthermore, the ratio K"N/KS"N of the dissociation constants of Na+ from the binary (NC) and the ternary complex (NCS) at the extracellular side is estimated to be less than or equal to 6. This indicates that the binding sequence of Na+ and S to the transporter is not ordered. The current-voltage behavior of the transporter is analyzed in terms of charge translocations associated with the single-reaction steps. The observed voltage-dependence of the half-saturation concentration of sodium is consistent with the assumption that a Na+ ion that migrates from the extracellular medium to the binding site has to traverse part of the transmembrane voltage.