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If a ligand binds with unequal affinity to two distinct states of a protein, then the equilibrium between the two states becomes a function of the concentration of the ligand. A necessary consequence is that the ligand must also affect the forward and/or reverse rate constants for transition between the two states. For an enzyme or transport protein with such a transition as a slow step in the catalytic cycle, the overall rate also becomes a function of ligand concentration. These conclusions are independent of whether or not the ligand is a direct participant in the reaction. If it is a direct participant, then the kinetic effect arising from the principle of linked functions is distinct from the direct catalytic effect. These principles suffice to account for the biphasic response of the hydrolytic activity of ATP-driven ion pumps to the concentration of ATP, without the need to invoke more than one ATP binding site per catalytic center.

Active ion transport systems with fixed stoichiometry are subject to a thermodynamic limit on the ion concentration gradients that they can generate and maintain, and their net rates of transport must inevitably decrease as this limit is approached. The capability to vary stoichiometry might thus be physiologically advantageous: a shift to lower stoichiometry (fewer ions pumped per reaction cycle) at increasing thermodynamic load could increase the limit on the supportable concentration gradient and could accelerate the rate of transport under high-load conditions. Here we present a theoretical and numerical analysis of this possibility, using the sarcoplasmic reticulum ATP-driven Ca pump as the example. It is easy to introduce alternate pathways into the reaction cycle for this system to shift the stoichiometry (Ca2+/ATP) from the normal value of 2:1 to 1:1, but it cannot be done without simultaneous generation of a pathway for uncoupled leak of Ca2+ across the membrane. This counteracts the advantageous effect of the change in transport stoichiometry and a physiologically useful rate acceleration cannot be obtained. This result is likely to be generally applicable to most active transport systems.

The transport rate of an electrogenic ion pump, and therefore also the current generated by the pump, depends on the potential difference (delta psi) between the two sides of the membrane. This dependence arises from at least three sources: (i) charges carried across the membrane by the transported ions; (ii) protein charges in the ion binding sites that alternate between exposure to (and therefore electrical contact with) the two sides of the membrane; (iii) protein charges or dipoles that move within the domain of the membrane as a result of conformational changes linked to the transport cycle. Quantitative prediction of these separate effects requires presently unavailable molecular information, so that there is great freedom in assigning voltage dependence to individual steps of a transport cycle when one attempts to make theoretical calculations of physiological behavior for an ion pump for which biochemical data (mechanism, rate constants, etc.) are already established. The need to make kinetic behavior consistent with thermodynamic laws, however, limits this freedom, and in most cases two points on a curve of rate versus delta psi will be fixed points independent of how voltage dependence is assigned. Theoretical discussion of these principles is illustrated by reference to ATP-driven Na,K pumps. Physiological data for this system suggest that all three of the possible mechanisms for generating voltage dependence do in fact make significant contributions.

The sarcoplasmic reticulum Ca-pump protein can be solubilized in monomeric form in nonionic detergents with full retention of ATPase activity. It is impossible to prove directly that coupling between ATP hydrolysis and Ca2+ transport is maintained in the soluble state, because separate compartments for Ca2+ uptake and Ca2+ discharge are required to demonstrate this, but here we provide strong indirect evidence that coupling in fact persists, in both the forward and reverse directions of the normal pump cycle. Demonstration of coupling in the forward direction makes use of the fact that the solubilized protein is structurally labile in the absence of bound Ca2+. Loss of activity accompanying ATP hydrolysis in solution is quantitatively consistent with sequential Ca2+ binding and dissociation during the hydrolysis cycle. Coupling in the reverse direction is demonstrated by the dependence of ATP synthesis on Ca2+ concentration. Although substantial differences between solubilized (monomeric) and membrane-bound protein are shown to exist, as previously reported, they do not affect the main conclusion from this work, which is that the molecular machinery for free-energy coupling in active Ca2+ transport is an inherent property of each individual catalytic polypeptide chain of the pump protein.

Sedimentation equilibrium measurements can be used to determine the molecular weight of the protein moiety of a protein-detergent complex without prior knowledge of detergent binding. The procedure is to adjust the solvent density by addition of D2O so as to blank out the contribution of bound detergent to the sedimentation potential. An approximate measure of detergent binding can be obtained from the effect of solvent density on the sedimentation result. The procedure is also applicable to protein-lipid complexes. It can be used for complexes containing both lipid and detergent if the lipid content is known. The use of the method is demonstrated by experimental data for the AI polypeptide of serum high density lipoprotein, in separate complexes with nonionic detergents and with a phospholipid.

The conventional alternating access model for Ca2+ transport by the sarcoplasmic reticulum Ca2+ pump is modified, partly on the basis of the proposed MacLennan-Green domain structure for the Ca2+-pump protein. The present model divides the uptake state (E1) of the protein into three substates, differing in the condition of the Ca2+-binding domain. The domain is an open cavity in the first substate and can bind only a single Ca2+ ion. A fast "jaw-closing" (or "hinge-bending") step then partially closes the cavity to generate the second substate that has a second Ca2+-binding site. Occupation of this site is followed by another jaw-closing step that closes the binding cavity and occludes the bound ions. The subsequent translocation step (to form E2) remains unchanged from previous models. The modified model predicts a constant transport stoichiometry of two Ca2+ per pump reaction cycle. It suggests a plausible mechanism for coupling between Ca2+ binding and ATP utilization: the model predicts (in agreement with experiment) that Ca2+ binding should be a mandatory requirement for phosphorylation of the pump protein, though ATP binding per se does not require Ca2+. The model is consistent with high cooperativity in equilibrium binding of Ca2+, both in the absence and presence of ATP.

Possible pathways for translocation across the membrane in active transport processes are examined theoretically. Thermodynamic and kinetic requirements are readily satisfied by an alternating-access mechanism of the kind that has been proposed in the past by several investigators. The essential features of this mechanism (for transport of a single species) are shown to be defined by four explicit conditions. (i) The transport protein must have at least two distinct conformational states, each accessible from only one side of the membrane. (ii) Binding affinity for the transported species is high in the state accessible from the uptake side of the membrane and much lower in the state accessible from the discharge side. (iii) The change from one conformation to the other involves movement of the binding site itself (with the transported species remaining attached) or rearrangement within the site that is topologically equivalent to such movement. (iv) Return to the original conformation occurs with unoccupied binding sites. The analysis demonstrates that a passage through the membrane that is simultaneously accessible from both sides cannot be used for active transport regardless of what the energetics of opening or closing of the passage may be. Even movement from one fixed site to another within the protein, without access to the outside, is virtually excluded as a possible element of the central mechanism. A ligand conduction mechanism for ATP-linked ion transport is in principle conceivable but is subject to restrictions that make it improbable.

Cooperative interaction of L-alpha-didecanoyl phosphatidylcholine with the AI polypeptide from human serum high density lipoprotein results in a complex particle containing 2 molecules of AI and 190 molecules of the lipid. Binding occurs two orders of magnitude above the critical micelle concentration of the lipid and requires the simultaneous presence of low levels of single-chain amphiphiles. The present investigation and previous studies from this laboratory suggest that AI contains "pockets" capable of interacting with a fixed hydrophobic volume and that amphiphilic head groups do not affect the binding capacity.

The apparent permeability of H+ through phospholipid bilayers was determined by measuring H+ efflux from large unilamellar phospholipid vesicles with internal space buffered at pH 4. The value obtained is about 10(-9) cm/sec at room temperature, five orders of magnitude lower than was recently reported for the combined permeability for H+ and OH- [Nichols, J. W. & Deamer, D. W. (1980) Proc. Natl. Acad. Sci. USA, 77, 2038-2042]. The apparent permeability measured in this way is the sum of contributions from the movement of H+ and of uncharged species (HCl or HNO3) in equilibrium with anions in the solution. There is evidence that the uncharged species make the dominant contribution and that the permeability coefficient for H+ per se is no larger than 5 X 10(-12) cm/sec. An attempt to measure OH- permeability by use of vesicles buffered at pH 10 did not give a conclusive result because the vesicle walls appeared to be damaged by exposure to this pH. An apparent permeability coefficient of about 10(-7) cm/sec was estimated for undamaged membranes.

Contrary to common belief, theoretical analysis does not predict any necessary relationship between cooperativity in the equilibrium binding of an ion to multiple binding sites on a protein and cooperativity in the kinetic activation of a reaction for which such binding is prerequisite. The sarcoplasmic reticulum Ca pump protein, for example, has two high-affinity binding sites for Ca2+, here considered to be nearly identical and independent. Equilibrium binding to these sites can be highly cooperative in spite of site-independence, as demonstrated by the well-known allosteric mechanism based on Wyman's principle of linked functions. We show in this paper that kinetic activation of the pump reaction cycle by binding of Ca2+ to these same sites can likewise be a cooperative function of Ca2+ concentration but that the criteria that determine cooperativity in the two situations are different. It is possible to observe kinetic cooperativity without concomitant cooperativity in equilibrium binding and vice versa. Application of these theoretical considerations to experimental data for the pump protein raises questions about the Ca2+ binding mechanism.

The thermodynamic pathway for "chemiosmotic" free energy transduction in active transport is discussed with an ATP-driven Ca2+ pump as an illustrative example. Two innovations are made in the analysis. (i) Free energy dissipated as heat is rigorously excluded from overall free energy bookkeeping by focusing on the dynamic equilibrium state of the chemiosmotic process. (ii) Separate chemical potential terms for free energy donor and transported ions are used to keep track of the thermodynamic state of each substrate through the reaction cycle. These procedures clarify the mechanism of free energy transduction, even without step-by-step analysis. The results show that free energy exchange must occur in its entirety among protein-bound species. Imposition of conditions for an adequate rate of physiological function further indicates (i) that the standard free energy of hydrolysis of protein-bound ATP (to yield protein-bound products) needs to differ substantially from the standard free energy of hydrolysis in solution and (ii) that binding sites for the transported ions must have different affinities when facing opposite sides of the membrane. The results also demonstrate that step-by-step "basic" free energy changes (often used in the form of free energy level diagrams) are inherently unsuited for analysis of the mechanism of free energy transduction.

A numerical analysis was carried out to explore limitations on kinetic and thermodynamic parameters for an ATP-driven Ca pump. A conventional pump reaction cycle was employed, with a transport stoichiometry of two Ca ions per cycle. Rigid requirements were imposed to represent the needs of physiological function, defined as the ability to maintain the cytoplasmic Ca concentration below 10(-7) M against a 3 mM concentration on the opposite side of the membrane. Realistic physical limits were placed on the magnitudes of rate constants for individual reaction steps. Reversibility under laboratory conditions was assumed. The results show that these requirements can be satisfied simultaneously only if the equilibrium constant for binding Ca from the cytoplasmic (uptake) side of the membrane is much larger than the binding constant on the discharge side. More generally, the results demonstrate that limitations on rate constants make it possible for the pump to maintain an adequate rate only if steady-state levels of kinetically important (slowly reacting) reaction intermediates do not become too disparate. Experimental data for the sarcoplasmic reticulum calcium pump support these theoretical conclusions.