Contributions to the theory of active transport

A system consisting of two solutions separated by a membrane may be in one of four possible states: (1) transient, (2) steady, (3) equilibrium, or (4) pseudo-equilibrium. The latter state denotes that in the solutions the net flow of all components is zero but at least one of the components is not in thermodynamic equilibrium. Transient and steady-state systems may or may not have active transport. Thus only systems in either equilibrium or pseudo-equilibrium are considered in this paper, since the former indicates that there is no active transport, whereas in the latter case there always is active transport. This simplifies the problem of finding whether a system does or does not have an active transport mechanism, since it is frequently fairly easy to determine experimentally whether a system is in equilibrium or pseudo-equilibrium. The assumption that electric neutrality exists within very thin membranes is shown not to be valid. However, electric neutrality does exist in the solutions in a system in a pseudo-equilibrium state with fixed charges and impermeative ions. It is then shown how the presence and sign of an electric potential may be found by use of electroneutrality. The mechanism of active transport may be due to a general force acting on all particles of a particular component or to an individual force acting on the individual particles of a particular component. A general solvent flow or a diffusion drag force illustrates the first mechanism while the second is accomplished by either a carrier or a Maxwell Demon. The general type of active transport has been extensively treated in the literature, while the individual type has not been treated in a generalized form. Therefore, the individual type of active transport is discussed at length, and a simple illustrative model is intensively analyzed. Following this, there is a discossion of the Maxwell Demon and some models of it are presented. This research was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command under contract No. AF 18(600) 1454.     

Energetics of active transport processes.

Active sodium transport across epithelial membranes has been analyzed by means of linear nonequilibirium thermodynamics. In this formulation the rates of active sodium transport JNa and the associated metabolic reaction Jr are postulated to be linear functions of both the electrochemical potential difference of sodium--XNa and the affinity A (negative free energy) of the metabolic reaction of driving transport. Experimental studies in various epithelia demonstrate that both JNa and Jr (oxygen consumption) are indeed linear functions of XNa. Theoretical considerations and experimental studies in other systems suggest that likelihood of linearity in A as well. If so, A may be evaluated. Several observations indicate that the quantity A evaluated from the thermodynamic formalism does in fact reflect the substrate-product ratio of the metabolic reaction which supports transport. This is in contrast to measurements of mean cellular concentrations, which may not reflect conditions at the site of transport. Associated studies of isotope kinetics permit the distinction between effects on the permeability of the active and passive transport pathways. With these combined approaches, it may prove possible to characterize both the energetic and permeability factors which regulate transport. The formulation has been applied to an analysis of the mechanism of action of the hormone aldosterone.     

Secondary active transport

Secondary active transport is defined as the transport of a solute in the direction of its increasing electrochemical potential coupled to the facilitated diffusion of a second solute (usually an ion) in the direction of its decreasing electrochemical potential. The coupling agents are membrane proteins (carriers), each of which catalyzes simultaneously the facilitated diffusion of the driving ion and the active transport of a given solute. The review starts with some considerations on the energetics followed by a presentation of the kinetics of secondary active transport. Examples of information which may be gained by such studies are discussed. In the second part, some examples of secondary transport are given; we also describe the characteristics of the corresponding carriers. The various transport systems presented are: the D-glucose/Na+ symport in brush-border membranes, the lactose/H+ symport in E. coli, the Na+/H+ antiport, the different transport systems in the inner mitochondrial membrane.     

On the definition of active transport

A reappraisal of recently proposed definitions and criteria of active transport in terms of experimentally accessible parameters leads to the conclusion that it is in principle impossible to give a rigorous quantitative defintion of the active component of the flux of a specific molecular species across a membrane without prior knowledge of the mechanism. The attempted distinctions between various types of “non-passive” transport (coupled, forced, facilitated, etc.) are thus of necessity operationally ambiguous. The essential equivalence of formulations based on classical thermodynamics and on thermodynamics of irreversible processes is pointed out, and the significance of Curie’s theorem to any theoretical formulation is discussed.     

Dynamic loading of deformable porous media can induce active solute transport

Active solute transport mediated by molecular motors across porous membranes is a well-recognized mechanism for transport across the cell membrane. In contrast, active transport mediated by mechanical loading of porous media is a non-intuitive mechanism that has only been predicted recently from theory, but not yet observed experimentally. This study uses agarose hydrogel and dextran molecules as a model experimental system to explore this mechanism. Results show that dynamic loading can enhance the uptake of dextran by a factor greater than 15 over passive diffusion, for certain combinations of gel concentration and dextran molecular weight. Upon cessation of loading, the concentration reverts back to that achieved under passive diffusion. Thus, active solute transport in porous media can indeed be mediated by cyclical mechanical loading.     

A kinetic model for determining the consequences of electrogenic active transport in cardiac muscle

When active transport is electrogenic in a tissue that is continuously active, such as cardiac muscle, the active transport current is as important in the generation of the action potential as are the passive currents. A thermodynamically constrained kinetic model of electrogenic active transport of sodium and potassium ions has been developed in which the influences of voltage and chemical composition are explicitly defined. This model is coupled to a system of passive permeabilities, of the minimum degree of complexity, to simulate the integrated activity of active and passive ion transport in the generation of the cardiac action potential. Results of preliminary simulations indicate that electrogenic active transport provides a mechanism for slowly changing currents both within the time scale of an action potential as well as of many action potentials. The presence of active transport also complicates the interpretation of isotopic flux measurements and the separation of currents.     

Thermal events associated with active membrane transport in Escherichia coli

Active transport of non-metabolizable compounds by $\text{Escherichia coli}$ resulted in thermogenesis. With substrates of the lactose permease (thiomethyl galactoside, lactose) and of the glucose transport system (α-methylglucoside) the rate of heat production was largest on initial addition, but then decreased. The kinetics of heat production varied with the transport system. For the lactose transport system, more than turnover of the permease was required since heat was not produced in azide treated cells, where facilitated diffusion is known to take place. The lactose permease thermal effects are suggested to reflect operation of the energy coupling system. The thermal effects are considered to represent a useful approach in studying transport energetics and mechanisms.     

The flux-force relations across complex membranes with active transport

Equations are derived for the total material flux, and the total electric current flux, across a complex membrane system with active transport. The equations describe the fluxes as linear functions of forces across the system, and specifically of electrical potential, hydrostatic pressure, chemical potentials, and active transport rates. The equations can be simplified for experimental studies by making one or more of the forces equal to zero. The osmotic pressure difference across a membrane system is shown to be a function of the electrical potential and chemical potential differences and of the active transport rates. The transmembrane potential is shown to be the sum of a diffusion potential and an active transport potential. A simple equation is derived describing the current across a membrane as a linear function of the electrical potential and the active transport rate. Specific examples of the application of the equations to nerve membrane potentials are considered.     

Autocatalytic cooperativity and self-regulation of ATPase pumps in membrane active transport

We investigate the effect of autocatalysis on the conformational changes of membrane pumps during active transport driven by ATP. The translocation process is described by means of an alternating access model. The usual kinetic scheme is extended by introducing autocatalytic steps and allowing for dynamic formation of enzyme complexes. The usual features of cooperative models are recovered, i.e., sigmoid shapes of flux versus concentration curves. We show also that two autocatalytic steps lead to a mechanism of inhibition by the substrate as experimentally observed for some ATPase pumps. In addition, when the formation of enzyme complexes is allowed, the model exhibits a multiple stationary states regime, which can be related to a self-regulation mechanism of the active transport in biological systems. Correspondence to: G. Weissmüller     

Phenomenological description of active transport of salt and water

The phenomenological definition of active transport by Kedem and the methods of Kedem and Katchalsky have been used to obtain practical equations describing active transport in the single salt and bi-ionic systems. Procedures were devised to evaluate the required set of 10 coefficients for the single salt case and 15 for the bi-ionic. Three of these coefficients are unusual. They express the effects of active transport, i.e. of entrainment between metabolism and the conventional transport flows: active salt transport coefficient, a volume pump coefficient, and an electrogenicity coefficient. In the bi-ionic case a new passive coefficient, lambda, was used to express the linkage between the fluxes of the two salts. However, if primary active transport involves only one ion, for example in the bi-ionic case, 12 coefficients suffice and certain relations can be predicted between the practical coefficients. Particular types of primary active transport could be identified by this means. The relation of active transport to membrane electrogenesis was also examined and the flux ratio equation was rederived in terms of the practical coefficients. Applications to specific parallel and series membrane systems have been analyzed.     

The reversibility of active sulphate transport in membrane vesicles of Paracoccus denitrificans.

An uncoupler-sensitive active transport of sulphate into membrane vesicles prepared from the plasma membrane of Paracoccus denitrificans (previously Micrococcus denitrificans) can be driven by respiration or by a trans-membrane pH gradient (alkaline inside) generated by the addition either of KCL ( in the presence of nigericin) or of NH4CL. Valinomycin does not substitute for nigericin. Respiration-driven transport is observed in right-side-out vesicles but not in inside-out vesicles, whereas transport driven by the addition of KCL (in the presence of nigericin) or of NH4CL is observed in both types of membrane vesicle. The active transport of sulphate into these vesicles is shown to be carrier-mediated by its sensitivity to thiol-group reagents. It is proposed that the sulphate carrier in the plasma membrane of P. denitrificans operates by a mechanism of electroneutral proton symport, and is capable of actively transporting sulphate in either direction across the plasma membrane, but that in whole cells respiration-driven proton expulsion drives the accumulative uptake of sulphate.     

Ion Transport in Isolated Rabbit Ileum : II. The interaction between active sodium and active sugar transport

The addition of actively transported sugars to the solution bathing the mucosal surface of an in vitro preparation of distal rabbit ileum results in a rapid increase in the transmural potential difference, the short-circuit current, and the rate of active Na transport from mucosa to serosa. These effects are dependent upon the active transport of the sugar per se and are independent of the metabolic fate of the transported sugar. Furthermore, they are inhibited both by low concentrations of phlorizin in the mucosal solution and by low concentrations of ouabain in the serosal solution. The increase in the short-circuit current, ΔI_sc, requires the presence of Na in the perfusion medium and its magnitude is a linear function of the Na concentration. On the other hand, ΔI_sc is a saturable function of the mucosal sugar concentration which is consistent with Michaelis-Menten kinetics suggesting that the increase in active Na transport is stoichiometrically related to the rate of active sugar transport. An interpretation of these findings in terms of a hypothetical model for intestinal Na and sugar transport is presented.     

Ca2+ transport in human platelet membranes. Kinetics of active transport and passive release

Active Ca2+ transport and passive release were characterized in crude and purified human platelet membranes to facilitate comparison with skeletal muscle sarcoplasmic reticulum. Endoplasmic reticulum markers were enriched from 3- to 14-fold in the purified membranes, while surface membrane antigens were reduced 4-fold and mitochondrial contamination was completely eliminated. The pH optimum for active Ca2+ transport in platelet membranes was 7.6, and the optimum for Ca2+-ATPase activity ranged from 7.6 to 8.0. Upon addition of MgATP there was a burst in active Ca2+ transport activity. In the absence of phosphate, steady state was reached within 20 s; added phosphate promoted continued uptake for greater than 1 h. The maximum pump stoichiometry was 2.0 Ca2+/ATP. The Ca2+ ionophore A23187 caused rapid release of 90% of the sequestered Ca2+ in the presence of phosphate. The dependence of Ca2+ transport on MgATP was biphasic with apparent Km values of 0.6 mM and 9.5 microM. Kinetic measurements with varied external Ca2+ yielded a single Km of 0.1 microM. Mg2+ stimulated Ca2+ transport and Ca2+-ATPase activities. Results with crude and purified membranes were similar, and comparison with the Ca2+ pump from sarcoplasmic reticulum revealed nearly identical enzymatic properties. In contrast to the results of comparing active Ca2+ transport, the characteristics of Ca2+ release from platelet membranes were quite different from those of sarcoplasmic reticulum. External Ca2+ did not promote release of sequestered Ca2+ from platelet membranes in contrast to sarcoplasmic reticulum. In addition, spontaneous release of Ca2+ from platelet membranes did not occur after ATP depletion. Inositol trisphosphate induced rapid partial release of Ca2+ from platelet membranes but had no effect on sarcoplasmic reticulum under identical conditions. Thus active Ca2+ transport is quite similar in internal membranes of platelet and skeletal muscle, but the mechanism of Ca2+ release appears to be entirely different.     

K-Na transport: the Brewer model replaces the active transport model

In the 1940's several experimental observations were made regarding the K+ and Na+ content of chilled and restored red blood cells. As a consequence, the concept of active transport was developed. Brewer, a physicist, developed a model for membrane transport based on the electrical properties of double bonds in the ground and excited states. Of particular importance is the membrane double bond P = O. This model was largely formulated from isotope concentration studies using mass spectroscopy, photospectrometry and the nature of malignant cells. In this study, it is shown that the Brewer model completely explains the experimental results which led to the concept of active transport. In addition, it also explains the results of some adjunct experiments.     

Ordered binding model as a general mechanistic mechanism for secondary active transport systems.

The mechanistic mechanism of secondary active transport processes has not been fully elucidated. Based on substrate binding studies dependent on coupling cation concentrations of the glutamate, melibiose, lactose and proline transport carriers in Escherichia coli, the ordered binding mechanism was proposed as the energy coupling mechanism of the transport systems. This ordered binding mechanism satisfactorily explained the properties of the secondary active transport systems. Thus, this mechanism as the general energy coupling mechanism for the transport systems is discussed.     

Permease on parade: application of site-directed mutagenesis to ion-gradient driven active transport

Oligonucleotide-directed, site-specific mutagenesis is being applied to the problem of ion-gradient driven active transport with the lac permease as a model system. It has been shown that Arg-302, His-322 and Glu-325, neighboring residues in putative transmembrane helices IX and X, play an important role in lactose-coupled H⁺ translocation, possibly as components of a catalytic triad similar to that found in the serine proteases. In addition, Cys residues, long thought to be involved in the mechanism of the permease, are not directly involved in either substrate binding or H⁺ translocation. Finally, a variety of mutations have no effect on permease activity indicating that single amino acid changes do not lead indiscriminately to long-range conformational alterations.     

The mechanism of arsenate inhibition of the glucose active transport system in Neurospora crassa.

The mechanism of arsenate inhibition of the glucose active transport system in wild-type cells of Neurospora crassa has been examined. Arsenate treatment results in approximately 65% inhibition of the glucose active transport system with only a small depression of cellular ATP levels. The transport system is not inhibited in cells treated with sodium arsenate in the presence of sodium azide. The transport inhibition is suppressed when orthophosphate is present during arsenate treatment, but is not reversed by orthophosphate when added after the arsenate treatment. The transport inhibition is completely reversed by treatment of the cells with mercaptoethanol. Gel chromatography of sonicates of intact cells which had been treated with [⁷⁴As]arsenate reveals three radioactive peaks, one with the elution volume of arsenate, one with the elution volume of arsenite, and a high molecular-weight radioactive fraction. Treatment of the high molecular-weight radioactive fraction with mercaptoethanol results in the production of radioactive arsenite. In view of these findings, it is proposed that arsenate inhibition of the glucose active transport system in Neurospora involves transport of arsenate into the cells, probably via the orthophosphate transport system, reduction of the transported arsenate to arsenite, and interaction of arsenite with some component of the glucose active transport system, presumably via covalent binding with vicinal thiol groups.     

Action of steroidal diamines on active transport and permeability properties of Escherichia coli

The steroidal diamine irehdiamine A (IDA) is a potent inhibitor of bacteriophage growth and macromolecular synthesis in Escherichia coli. By using radioactive (42)K and (14)C-thiomethylgalactoside (TMG), rapid effects of IDA and related steroids, both on the influx of potassium and TMG via their respective transport systems and on the efflux (leakage) of radioactivity from the treated cells, have been measured. IDA affects both the influx and efflux of (42)K at concentrations of steroid as low as 2 x 10(-5)m. Because of the increased leakage, it is not possible to tell whether there is a direct effect reducing the rate of active transport of potassium. The primary diamine, IDA, and its bis-secondary, bis-tertiary, and bis-quaternary diamine analogues are decreasingly effective in altering cell permeability properties in the order 1 degrees > 2 degrees > 3 degrees > 4 degrees . The effects of IDA on potassium transport are mirrored by similar effects on the transport of TMG. Therefore, the action of IDA is on the cell membrane and not directly on one or another transport system. The effects of IDA on cell permeability can reasonably explain the inhibitory actions of the drugs on bacteriophage growth and cellular metabolism.     

Calcium-stimulated respiration and active calcium transport in the isolated chick chorioallantoic membrane

Summary Calcium markedly stimulates the respiration of the isolated chick chorioallantoic membrane. This stimulation of oxygen uptake appears to be closely associated with the membrane's active transcellular calcium transport mechanism. In the presence of 1mm Ca⁺⁺ the rate of uptake increases from 9.3±0.15 to 13.0±0.2 liters O₂/cm²/hr, an increase of about 40%. The calcium-stimulated respiration is specific for the ectodermal layer of cells, the known location of the calcium transport mechanism, and only occurs when the calcium transport mechanism is operative. Sr⁺⁺ and Mn⁺⁺ are transported by the tissue at a lower rate than Ca⁺⁺ and cause a smaller stimulation of oxygen consumption. Mg⁺⁺ and La³⁺ have no effect on tissue respiration. In the presence of Ca⁺⁺, the organic mercurialp-chloromercuribenzene sulfonate (PCMBS) inhibits calcium transport and specifically decreases the oxygen uptake of the ectoderm to a rate identical to that obtained in a calcium-free medium. Stripping the inner shell membrane away from the chorioallantoic membrane mimics these effects. The specificity and locus of action of these two inhibitors suggest that a vital component of the active transcellular calcium transport mechanism resides on or near the outer surface of the plasma membrane of the ectodermal cells and that sulfhydryl groups are important to the normal function of this component.     

Mathematical theory of biological periodicities II. Effect of active transport

A previous study (Bull. Math. Biophysics,30, 735–749) is generalized to the case of active transport, which acts together in general with ordinary diffusion. The basic results obtained are the same except for an additional important conclusion. In principle it is possible to obtain sustained oscillations even when the secretions of the different glands do not affect the rates of formation or decay of each other at all, but affect the “molecular pumps,” which are responsible for the active transports in various parts of the system. Thus no biochemical interactions need necessarily take place between then-metabolites to make sustained oscillations possible in principle. This is an addition to a previous finding (Bull. Math. Biophysics,30, 751–760) that due to effects of the secreted hormones on target organs, non-linearity of biochemical interactions is not needed for production of sustained oscillations.