Thermodynamics of Symport and Antiport Catalyzed by Cloned or Native Transporters

Physical and kinetic models of symport or antiport are often developed in conjunction with thermodynamic arguments that support the concept of secondary active transport. In this review, we discuss the energetics of ion-coupled solute active transport catalyzed by native transport systems or by membrane proteins encoded by cDNAs associated with transport. We show that secondary active transport models can be supported by experimentally measuring accumulation gradients of solute and activator ion, transmembrane electrical potentials and rates of flux or charge transfer. Finally, an invertebrate cell model is used to examine the energetic adequacy of the separate electrical and chemical components of a Na⁺ gradient in maintaining high cellular accumulation gradients of amino acids or sugars.

The current literature regarding cloned transporter proteins and native transport systems vindicates the pioneering transport concepts of Christensen, Crane, Kaback, Mitchell and others. Christensen (1990) and colleagues (Christensen and Riggs, 1952; Riggs et al. 1958) initially proposed that ion gradients across plasma membranes could energize organic solute transport and accumulation in eukaryotic cells. They initially postulated that a physical mechanism might exist in the membrane to catalyze the energetic coupling of neutral amino acid influx to K⁺ efflux. A few years later, Crane proposed a model that described Na⁺-activated glucose uptake in the small intestine (Crane et al. 1961). The Crane model was further developed for sugars and amino acids by Curran, Schultz and others (see reviews by Crane, 1977; Schultz, 1980; Kimmich, 1990; Kessler and Semenza, 1983; Schultz and Curran, 1970; Stevens, 1992a,b; Stevens et al. 1984; Wright, 1993; Kilberg et al. 1993). Kaback developed the model of prokaryotic β-galactoside/H⁺ symport (e.g. Escherichia coli lactose permease) as a similar paradigm associated with the chemiosmotic concept of Mitchell (Mitchell, 1961, 1991; Kaback et al. 1993). Several sources contribute to our current understanding of ion-activated transport: Crane’s sodium-coupled sugar or amino acid symport was confirmed in epithelial membranes of intestine and renal proximal tubule (cloned proteins typified by the eukaryote SGLT1 family); the β-galactoside/H⁺ symport mechanism in E. coli has been examined using cloned proteins typified by the lactose permease of bacteria; and the emergence of a superfamily of neurotransmitter transport systems that are energized by Na⁺, K⁺ and/or Cl⁻ (typified by the GAT isoforms and the GLAST-1 and EAAC1 expression clones). The extensive molecular characterization of β-galactoside/H⁺ symport perhaps gives this system the edge as the archetypal symporter. The following discussion concerning ion-coupled organic solute transport is applicable to virtually any secondary active transport system selective for such substrates as neurotransmitters, dipeptides, drugs, antibiotics, nucleotides, phosphate, sulfate, chloride and bicarbonate.

For passive diffusion, the rate of solute influx or efflux is proportional to the substrate’s electrochemical potential difference across the membrane; at equilibrium the net flux (J) is zero and the electrochemical gradient collapses (i.e. and J=0). Fig. 1 shows an example of simple passive diffusion of a solute transported across the membrane, following Fick’s law, with the flux curve passing through the origin at ⁠. This example involves the simplest case of a non-charged solute S, so that electrical potentials do not play a role and ⁠. If energy can be coupled to the transport process, then ‘active transport’ could occur, and this would be operationally defined at equilibrium as a shift in the curve of Fig. 1 such that J>0 when or, alternatively, when J=0.

The direct coupling of energy to a solute flux, usually by dephosphorylation of ATP, is called primary active transport. This mode of transport is largely responsible for generating the asymmetric distribution of Na⁺, K⁺, H⁺ and other ions across cell membranes. The electrochemical gradients generated by primary active transport can be coupled to the flux of other solute species; the subsequent uphill transport of a given solute at the energetic expense of the other solute’s electrochemical potential is called secondary active transport. Ion-coupled organic solute symport represents an example of secondary active transport. Alternatively, in bacterial or mitochondrial membranes, generation of ⁠, which arises by respiration, can be used to couple solute symport or antiport of other ions and organic solutes.

The coupling of energy can be described in terms of both equilibrium and non-equilibrium themodynamics (Heinz et al. 1972; Kedem, 1978; Stein, 1986; Schultz, 1980; Onsager, 1931; Katchalsky, 1960). First, we provide a brief phenomenological description of energy coupling of an uncharged solute (S) with an activator cation that is independent of the actual transport mechanism. Following this, we present an example of a physical mechanism that can catalyze energy coupling in a membrane. The discussion is focused on simple ion-energized symport, but the arguments are applicable to virtually any system of symport or antiport, or to a combination of the two.

It is well established that Na⁺, K⁺, H⁺, Cl⁻ and even lanthanide-series trivalent cations (Stevens and Kneer, 1988) can drive symport or antiport of a variety of solutes in many cell types of different species. Accumulation can be enhanced by additional coupling to ΔΨ. Although the above example is given for the case of cation-coupled symport with an uncharged solute, similar arguments hold whether the membrane involves complex systems of symport plus antiport, symport only or antiport only. This includes virtually all known ion-coupled transport systems that can be classified into various families and superfamilies in prokaryotes and eukaryotes (Kilberg et al. 1993; Maillard et al. 1994; Stevens, 1992a,b; Marger and Saier, 1993).

Equations 9 and 10 predict that the solute concentrating ability of a system can involve both the chemical and electrical components of ⁠. Indeed, a computer-generated surface plot of equation 10 is shown in Fig. 2 to emphasize visually that the concentrating ability of a symport system is greatly enhanced when the coupling coefficient and are compounded. Fig. 2 was generated by varying Na⁺ concentrations in equation 10, with the condition that ΔΨ remains fixed at –60 mV at 20°C, and assuming that contributes to ΔΨ. The generalization of Fig. 2 holds true for virtually any real ΔΨ. Note, for example, that the organic solute concentrating ability is about 100:1 for the condition of coupling coefficient ⁠, and that by merely increasing the coupling coefficient L_S,Na to 3, the system can sustain a solute gradient greater than 10⁶, as predicted by equation 10.

The model of Fig. 2 graphically demonstrates how many membrane systems – ranging from sugars in bacteria, to neurotransmitters in glia, neurons or synaptosomes, to amino acids in marine invertebrate epithelia – can support experimentally measured hundred-fold to million-fold steady-state concentration gradients of solutes (Clark and Amara, 1993; Preston and Stevens, 1982; Stephens, 1988; Stevens and Preston, 1980; Wright and Stephens, 1985; Ahearn and Behnke, 1991). Such membrane systems possess ion coupling coefficients of 2 or 3, with additional coupling to the electrical component (Manahan et al. 1983; Preston and Stevens, 1982; Schultz, 1980; Stephens, 1988; Wright et al. 1983; Wright and Stephens, 1985; Wright, 1987; Kaback et al. 1993; Clark and Amara, 1993). In the case of marine invertebrates, the measured high flux rates and free amino acid intracellular:extracellular steady-state concentration ratios of 10⁶:1 to 10⁷:1 arise from coupling uptake of 1 S to 3 Na⁺ plus ΔΨ (Preston and Stevens, 1982; Manahan et al. 1983). In the case of humans and other vertebrates, neurotransmitters such as glutamate, glycine and GABA are accumulated against steep gradients in neurons and glia coupled to Na⁺, K⁺ and/or Cl⁻ chemical and electrical potentials (Hempling, 1993). Intracellular:extracellular measured concentration gradients of neurotransmitters in synaptosomes can exceed several thousand-fold in membrane systems known to couple neurotransmitter uptake to chemical and electrical gradients of multiple ion species (Hempling, 1993). In oocytes injected with GLAST-1 cRNA, glutamate transport is energized with a symport stoichiometry of 3Na⁺: 1 glutamate in exchange for 1K⁺ antiport (Klockner et al. 1993). Several other high-affinity proteins associated with neurotransmitter uptake or re-uptake have been cloned (e.g. the GAT series, BGT-1, GLT-1, PROT-1, EAAC1), and some of these can be energized with multiple ion coupling stoichiometries of Na⁺, K⁺ and/or Cl⁻.

The stoichiometry of ion coupling can be experimentally measured by several techniques. The most straightforward techniques are based on equation 4, involving simultaneous measurement of S-dependent J_ion together with ion-dependent J_S using radiotracers.

Measuring the ion activation of symport gives only the stoichiometry of activation and does not itself prove that the ion is cotransported with the other substrate. Furthermore, the Hill number may not be an exact integer, but may represent an estimate of the coupling coefficient, as is the case for Na⁺/proline symport, where the Hill number is 1.9 (Stevens and Wright, 1987), or Na⁺/glucose transport, where the Hill number is 1.6 (Wright, 1993). This disparity is due to theoretical limitations of the Hill equation which flaw the analysis (Segal, 1975) and to the fact that the actual coupling mechanism may not be energetically tight (i.e. there may be inefficiency or ‘slippage’ in the system, as discussed above).

Another way to estimate experimentally the coupling coefficient in a tightly coupled cotransporting system is the ‘static head’ application of equation 6. Using this technique, various net J_S values are measured in membrane vesicles or reconstituted proteoliposomes under solute-dissipating (non-equilibrium) conditions with variously imposed ΔΨ. In contrast to the activation method described above, the number of ion charges moved per mole of organic solute is measured under conditions of variously imposed and ΔμS, and the condition is sought whereby J_S=0. Turner (1985) has promoted static head experimental methods, whereby gradients are established by pre-loading membrane vesicles with sodium gluconate or SO₄^2- (final gradient [Na⁺]°/[Na⁺]ⁱ=1), radiolabeled S (at various gradients of [S]ⁱ/[S]°) and potassium gluconate or SO₄^2- {to clamp ΔΨ in the presence of valinomycin according to the Nernst equation ΔΨ=(RT/F)ln([K⁺]ⁱ/[K⁺]°)}. The impermeant anions gluconate or SO₄^2- are used to reduce short-circuiting of ΔΨ. The J_S is subsequently measured by radiotracer efflux at various clamped ΔΨ. Under these conditions, the charge stoichiometry, q, approximately equals the coupling coefficient L_S,Na, and is thus computed directly from the condition [S]ⁱ/[S]°=([K⁺]ⁱ/[K⁺]°)^q. A control measurement made in the absence of Na⁺ (substituting mannitol, choline or N-methyl-D-glucamine) measures the total Na⁺-independent J_S efflux. The actual static head condition occurs at the ΔΨ that exactly counteracts the charges carried by Na⁺ cotransported with the organic solute. That is, the imposed [K⁺]ⁱ/[K⁺]° is sought which experimentally results in net J_S=0 (i.e. control). For example, in kidney brush-border membranes (Turner, 1985; Fukuhara and Turner, 1984), a 2:1 K⁺ gradient is required to balance a 4:1 glucose gradient with a 1:1 Na⁺ gradient, so that the coupling ratio is 2Na⁺:1 glucose.

Mechanistic models of symport/antiport are derived from both energetic and kinetic measurements. Fig. 4 describes a model of -activated solute binding and translocation in intestinal apical membranes. Considerable experimental evidence specifically supports the model for Na⁺/glucose symport, but it is recognized that a similar mechanism is likely to operate for other members of the SGLT-1 family of transporters (Stevens and Wright, 1985, 1987; Stevens, 1992a,b; Loo et al. 1993; Wright, 1993; Kimmich, 1990; Kessler and Semenza, 1983). The Cleland diagram of Na⁺/solute symport (Fig. 4) shows the dominant symport pathway and does not consider leak or slip paths for solute and Na⁺. This simplified model assumes net vectorial influx of one solute molecule activated with a 2Na⁺:1 solute coupling stoichiometry, assuming and ΔΨ<0. The unloaded carrier valence is –2, and membrane voltage influences the binding of Na⁺ to the carrier molecule as well as translocation rates of the loaded carrier. The binding of both sodium ions occurs before binding of S, and this is grouped as a single event in the simplified model. Binding sites for the membrane’s extracellular side symporter C′ combine with Na⁺ and solute S to form the loaded complex SC′Na₂. This complex undergoes a conformational change that translocates S and Na⁺ to the cytoplasmic side of the membrane SC′Na₂. The unloaded cytoplasmic conformation of the carrier site facing the cytoplasm C′ then reverts to the extracellular binding conformation C′, which can accept new substrates at the membrane’s extracellular surface. Internal slippage and substrate leakage across the membrane (not shown in Fig. 4) would reduce the efficiency of coupling and could reduce the steady-state intracellular accumulation of solute. Additional details of this model are described in the legend of Fig. 4.

Some evidence suggests that polypeptides associated with transport may behave in situ in the membrane as a ‘functional unit’. Polypeptide multimeric interactions may occur for intestinal or renal Na⁺/glucose symport, or for transport of substrates by the structurally homologous transport systems of the SGLT-1 family (systems serving nucleotides, myo-inositol or neutral amino acids in eukayotes, and proline or pantothenic acid in bacteria).

Evidence for the functional multimer arrangement of the Na⁺/glucose symport system comes from several independent techniques. Keopsell’s group (Veyhl et al. 1993) used antibodies raised against the cloned SGLT-1 protein (approximately 70 kDa monomer) and against a cloned putative regulatory subunit of Na⁺/glucose symport (denoted RS1, approximately 70 kDa monomer) to identify a 300 kDa multimer by non-denaturing Western analysis (Veyhl et al. 1993). Stevens et al. (1990) had previously shown, using Western analysis and transport activity in conjunction with radiation inactivation analysis, that the functional unit of the symporter in situ in the apical membrane is a composite of 70 kDa monomers giving a 290 kDa functional multimer. Stoichiometric co-injection of RS1 cRNA with SGLT-1 cRNA into an oocyte expression system indicated that both of these proteins were required for full expression of transport function that possessed physiological properties similar to those of the native intestinal membrane protein (Veyhl et al. 1993). Fig. 5 shows the in situ membrane-bound arrangement of the functional Na⁺/glucose symport system. The 290 kDa functional unit is a tetramer made up of four independent 70 kDa monomer subunits associated non-covalently. The stated evidence suggests that this is may be a heterotetramer, although alternative associations cannot be ruled out (e.g. dimer of RS1 and SGLT-1 homodimers). Koepsell’s group showed that the maximal oocyte expression of glucose transport activity occurred when the cRNA molar ratio of RS1:SGLT-1 was 2; however, the stoichiometric distribution of these subunits within the 290 kDa transporting functional unit is unknown.

According to the kinetic model discussed in Fig. 4, two sodium ions bind and activate the transport functional unit shown in Fig. 5. After sodium and glucose or proline have bound, the functional unit undergoes a conformational shift that relocates the substrates to the cytoplasmic side. After Na⁺ and solute have been released, the symporter shifts back to a conformation that again favors binding of extracellular Na⁺ and solute. Ugolev and Metel’skii (1990) have suggested that, for Na⁺/glucose symport, the physical arrangement of the subunits may form individual conduits for Na⁺ and glucose.

In this section, we examine the individual roles of the chemical (Δμ_Na= RTln[Na⁺]°/[Na⁺]ⁱ) and electrical (zFΔΨ) components of in order to assess their energetic adequacy relative to the reversible work required to maintain neutral amino acids and sugars at cellular accumulation ratios greater than one. Sodium-activated solute transport in the foregut absorptive epithelial cells of Aplysia californica will serve as an example.

Although it is clear that the Na⁺ chemical gradient contributes significantly to the overall energy required for accumulative sugar and amino acid transport in Aplysia gut and other epithelia, the adequacy of Δμ_Na as the sole energy source for this purpose was questioned by Gerencser (1981a, 1983a, 1984). In the 1960s and 1970s, it had been demonstrated that, in the absence of mucosally applied organic solutes, small transepithelial potential differences (Ψ_ms, serosa positive) were normally observed across invertebrate gut wall (Gerencser, 1981a). The short-circuit current (I_sc) across animal gut preparations was accounted for either by a purely active absorptive Na⁺ current or by mixed active absorptive Na⁺ and Cl⁻ currents (Gerencser, 1981a). Subsequent addition of an accumulated sugar or amino acid to the mucosal aspect of animal gut preparations instantaneously enhance both Ψ_ms and I_sc (Schultz and Curran, 1970). In most cases, these observed electrical changes were accounted for by enhanced Na⁺ absorption (Gerencser, 1981b).

Studies involving the effects of sugars (Gerencser, 1978) or amino acids (Gerencser, 1981b) on Na⁺ absorption across the isolated gut of Aplysia californica revealed that mucosally applied organic solutes transported by secondary active transport (D-glucose, D-galactose, D-3-O-methylglucose, glycine, L-alanine and L-aminoisobutyric acid, AIB) instantaneously increased Ψ_ms and I_sc. These electrical effects were accounted for, in part, by means of an increase in the unidirectional mucosal-to-serosal (ms) flux of Na⁺ (Gerencser, 1978, 1981b). The addition of these same sugars or amino acids to the serosal aspect of the gut, at the same concentration, had virtually no effect on the transmural electrical characteristics, Ψ_ms and I_sc, nor on the unidirectional ms or sm fluxes of Na⁺ (Gerencser, 1978, 11981a,b). These results, coupled with the observation of the rapid nature of the organic solute-induced mucosal response (Gerencser, 1978), suggest interaction of these solutes with specific components of the mucosal membrane. In addition, D-galactose (Table 3), glycine, AIB or L-alanine accumulation in the Aplysia gut tissue was shown to be absolutely dependent upon the presence of Na⁺ in the seawater bathing medium, suggesting a reciprocal relationship between Na⁺ and organic solute transport (Gerencser, 1978, 1981a), as predicted by the Na⁺ gradient hypothesis and observed in vertebrate gut (Schultz and Curran, 1970).

The net ms Na⁺ transport by isolated Aplysia gut, in the absence of an electrochemical potential gradient, indicates that there is primary active transport of Na⁺ in this preparation (Gerencser, 1983a,b). This observation confirms a similar observation of net ms transfer of Na⁺ across short-circuited Aplysia gut (Gerencser, 1978). The observation that serosally applied ouabain inhibits the net absorptive flux of Na⁺, Ψ_ms and I_sc (Gerencser, 1983a) strongly suggests that the endogenous electrical characteristics are dependent upon cellular ATP and its consequent hydrolysis by a ouabain-sensitive Na⁺/K⁺-ATPase. These observations are consistent with the hypothesis that there is a Na⁺/K⁺ pump located within the basolateral membrane, which is responsible for uphill K⁺ and Na⁺ transport through this membrane and therefore for the maintenance of Ψ_ms and I_sc. This hypothesis has been directly confirmed with the demonstration that Na⁺/K⁺-ATPase activity is exclusively localized to the basolateral membrane in Aplysia foregut absorptive cells (Gerencser and Lee, 1985).

Inasmuch as the Na⁺ intracellular activity coefficient is considerably less than one in cells of Aplysia and other animals (Gerencser, 1983a,b, Walker and Brown, 1977), the energetic formalism presented above holds true, but the ion concentrations ([Na⁺]) should be modified to and . To determine accurately by liquid ion-exchange microelectrode measurements, it is necessary to have a previous estimate of . Therefore, K⁺-specific microelectrodes were advanced across the mucosal membrane of Aplysia foregut absorptive cells (Gerencser, 1983a,b). The calculated these impalements averaged 383±15 mmol l⁻¹ (Table 1). Unlike the obtained from measurements, Na⁺-specific microelectrodes advanced across the mucosal membrane of Aplysia foregut absorptive cells recorded negative potentials relative to the mucosal medium in every impalement; these changes in ΔΨ are consistent with Na⁺ existing below electrochemical equilibrium in the Aplysia cellular cytosol (Gerencser, 1983a,b). The calculated averaged 17.2±2.5 mmol l⁻¹ (Table 1). Also given in Table 1 are values for and ⁠, which clearly indicate that intracellular K⁺ and Na⁺ are far from electrochemical equilibrium across the Aplysia absorptive cell mucosal membrane. Thus, there is an electrochemical force of approximately 43 mV driving K⁺ out of the cells and of 129 mV moving Na⁺ into the cells, consistent with the operation of a basolaterally located Na⁺/K⁺ pump proposed in other epithelia (Schultz and Curran, 1970).

Intracellular concentrations of sodium ([Na⁺]ⁱ), and potassium ([K⁺]ⁱ), D-galactose, L-alanine, AIB and glycine, were obtained from the villous foregut absorptive cells of Aplysia gut (Gerencser, 1983a,b, 1984), as were the and measurements. These measurements ensure reasonably valid activity coefficients for both Na⁺ and K⁺ when considering the structural and functional heterogeneity of the gut relative to villous, intervillous and crypt cell regions. As can be seen in Table 2, the experimental is much lower than that predicted for all cellular Na⁺ being in free solution in the Aplysia absorptive cells. Approximately 30% of the intracellular Na⁺ was bound or sequestered within the absorptive cells.

Table 3 shows that there was a significant steady-state intracellular accumulation of all of the electroneutral organic solutes: D-galactose, L-alanine, AIB and glycine. Translating these data into transapical chemical potential differences for these organic solutes, Δμ_Gal (D-galactose), Δμ_Ala (L-alanine), Δμ_AIB (AIB) and Δμ_Gly (glycine), and transposing the previously derived Δμ_Na and into a composite table (Table 4), one can compare the reversible work, in J mol⁻¹, required to transfer one equivalent of Na⁺ or organic solute across the mucosal membrane of an Aplysia villous absorptive cell. As can be seen in Table 4, Δμ_Na is energetically adequate to drive the intracellular accumulation of all the organic solutes except glycine. However, the energy implicit within is thermodynamically adequate for the steady-state accumulation of glycine and the other organic solutes into the Aplysia foregut absorptive cell. Therefore, the glycine case exemplifies and highlights the situation in which ΔΨ can be (and sometimes has to be) utilized as an energy source, in addition to Δμ_Na, for the accumulation of organic solute relative to this and other cellular membrane systems.

Relative to other studies (Armstrong et al. 1979) regarding energetic adequacy of active organic solute accumulation in epithelia, the Aplysia gut demonstrates that Δμ_Na is energetically sufficient to drive uphill movement of sugar and amino acid into absorptive cells (Table 4), whereas in bullfrog gut Δμ_Na alone is not energetically sufficient to drive sugar uphill into the enterocyte. This physiological difference derives from the fact that there is a large disparity in Δμ_Na of the respective species. for both bullfrog and Aplysia gut cells are approximately the same; however, for Aplysia gut (sea water) approximates 306 mmol l⁻¹, whereas for bullfrog gut extracellular fluid approximates 76 mmol l⁻¹. Hence, the huge difference in Δμ_Na across the mucosal membranes of the two species is reflected in their different energetic requirements for driving organic solute uphill. It is worth adding that across the mucosal membrane of gut cells in both species is sufficient for their respective organic solute accumulation.

As referred to above, one major difficulty residing in the conclusive evaluation of the Na⁺ gradient hypothesis as a mechanism for Na⁺-dependent solute transport is the uncertainty about the activity of intracellular Na⁺ and its distribution in the cytoplasm. Some studies (Schultz and Curran, 1970) have equated the Na⁺ gradient across the mucosal membrane to the ratio between mucosal bathing solution Na⁺ concentration and the intracellular Na⁺ concentration. This approach contains the following uncertainties. (1) Chemical determinations of intracellular Na⁺ concentrations in tissues bathed in media with high Na⁺ concentrations are affected drastically by relatively small errors in extracellular space measurement. This problem is seen in the wide variance of values for intracellular Na⁺ concentrations reported in the literature from the 1960s and 1970s. (2) The assumption that all cellular water can be utilized as solvent water is questionable in several cell types. (3) In several cell types it is reasonably well established that intracellular Na⁺ concentration does not reflect the true (Armstrong and Lee, 1971; Gerencser, 1983a,b). Most of these difficulties can be circumvented by the use of ion-selective microelectrodes, which would directly determine ⁠, and therefore ⁠, across the biomembrane, and this could then be applied to ascertain the true energetic adequacy to the active uptake of solutes as stated in the Na⁺ gradient hypothesis.