The overshoot phenomenon in cotransport

Based on simplified equations, the overshoot curve experimentally observed with Na⁺-linked cotransport of neutral substrate (sugars or amino acids) has been simulated by computer. The approach is in principle similar to that of previous approaches (Weiss, S.D., McNamara, P.D. and Segal, S. (1981) J. Theor. Biol. 91, 597–608), but more general; in particular, it includes the effect of electrical membrane potential difference, and the quantitative relationship between height of peak and certain transport parameters, such as maximum rate, dissociation constant of ternary complex, electric charge of translocator, respectively. In addition, it tests two alternative models with respect to the rate-determining step: the translocation, on the one hand, and the association/dissociation of the ligands at the translocator site, on the other. The major findings are the following: (1) An overshoot can be obtained similar to that usually found experimentally, provided that maximum rate and affinity between translocator and transport of solute exceed certain minimum values. (2) The overshoot effect with Na-linked cotransport is enhanced by a negative membrane potential (inside relative to outside) and decreased by a positive potential. In the first case, the peak is higher and occurs faster. In the latter case, the peak is lower and delayed. (3) The effect of an electric potential difference on the overshoot curve does not depend appreciably on the charge of the empty translocator, except if the translocation of the latter is strongly rate-limiting. (4) To obtain an overshoot curve, it is not necessary that the translocation step be rate-limiting, contrary to what has been postulated previously (Läuger, P. (1980) J. Membrane Biol. 57, 163–178).     

The thermodynamics of general anesthesia

It is known that the action of general anesthetics is proportional to their partition coefficient in lipid membranes (Meyer-Overton rule). This solubility is, however, directly related to the depression of the temperature of the melting transition found close to body temperature in biomembranes. We propose a thermodynamic extension of the Meyer-Overton rule, which is based on free energy changes in the system and thus automatically incorporates the effects of melting point depression. This model accounts for the pressure reversal of anesthesia in a quantitative manner. Further, it explains why inflammation and the addition of divalent cations reduce the effectiveness of anesthesia.     

The thermodynamics of thiol sulfenylation

Protein sulfenic acids are essential cysteine oxidations in cellular signaling pathways. The thermodynamics that drive protein sulfenylation are not entirely clear. Experimentally, sulfenic acid reduction potentials are hard to measure, because of their highly reactive nature. We designed a calculation method, the reduction potentials from electronic energies (REE) method, to give for the first time insight into the thermodynamic aspects of protein sulfenylation. The REE method is based on the correlation between reaction path-independent reaction energies and free energies of a series of analogous reactions. For human peroxiredoxin (Tpx-B), an antioxidant enzyme that forms a sulfenic acid on one of its active-site cysteines during reactive oxygen scavenging, we found that the reduction potential depends on the composition of the active site and on the protonation state of the cysteine. Interaction with polar residues directs the RSO(-)/RS(-) reduction to a lower potential than the RSOH/RSH reduction. A conserved arginine that thermodynamically favors the sulfenylation reaction might be a good candidate to favor the reaction kinetics. The REE method is not limited to thiol sulfenylation, but can be broadly applied to understand protein redox biology in general.     

The thermodynamics of water-protein interactions

Information about the effects of water on protein structure and function can be obtained from studies on freeze dried protein powders of varying water content. Sorption isotherms of water on proteins can be used to obtain thermodynamic quantities for water-protein interactions. Since such isotherms show hysteresis, there is doubt in regard to their interpretation.General expressions for the thermodynamic quantities of sorption are derived. If isotherms represent data at equilibrium, it is possible to calculate these thermodynamic quantities.There are two types of hysteresis, non-equilibrium hysteresis and equilibrium hysteresis. Absorption and desorption isotherms can show equilibrium hysteresis if different protein conformations, which are only slowly interconvertible, can be present. In this case valid thermodynamic quantities can be obtained. Experimental tests for equilibrium hysteresis are presented. More experiments are needed before definite conclusions can be drawn in regard to isotherms in the literature.If the protein conformation in a protein powder is similar to the protein conformation in aqueous solution, equilibrium data obtained from sorption isotherms can be used to approximate thermodynamic quantities for the interaction of water with proteins in aqueous solution. Examination of what experimental evidence is available indicates that the protein in powders prepared by desorption of water should have a conformation similar to that in solution. Further study of such samples will help to clarify the thermodynamics of water-protein interactions in aqueous solution.     

The thermodynamics of solvent exchange

A model for solvation in mixed solvents, which was developed for the free energy and preferential interaction [J. A. Schellman (1987), Biopolymers, Vol. 26, pp. 549–559; (1990), Biophysical Chemistry, Vol. 37, pp. 121–140; (1993), Biophysical Chemistry, Vol. 45, pp. 273–279], is extended in this paper to cover the thermal properties: enthalpy, entropy, and heat capacity. An important result is that the enthalpy of solvation H? responds directly to the fraction of site occupation. This differs from the free energy ? and preferential interaction Γ₃₂, which are measures of the excess binding above a random distribution of solvent molecules. In other words, the enthalpy is governed by K while ? and Γ₃₂ are governed by (K ? 1) where K is the equilibrium constant on a mole fraction scale [Schellman (1987)]. The solvation heat capacity C?p consists of two term: (1) the intrinsic heat capacity of species in solution with no change in composition, and (2) a term that accounts for the change in composition that accompanies solvent exchange. Binding to biological macromolecules is heterogeneous but experiementalists must use binding isotherms that assume the homogeneity of sites. Equations are developed for the interpretation of the experimental parameters (number of sites n_exp, equilibrium constant K_exp, and enthalpy, Δh_exp), when homogeneous formulas are applied to the heterogeneous case. It is shown that the experimental parameters for the occupation and enthalpy are simple functions of the moments of the distribution of equilibrium constants over the sites. In general, n_exp is greater than the true number of sites and K_exp is greater than the average of the equilibrium constants. The free energy and preferential interaction can be fit to a homogenious formula, but the parameters of the curve are not easily represented in terms of the moments of distributions over the sites. The strengths and deficiencies of this type of thermodynamic model are discussed. © 1994 John Wiley & Sons, Inc.     

Sodium cotransport proteins.

Significant advances have been made in elucidating the structure of Na+ cotransport proteins. Some fifteen of these low-abundance proteins have been cloned, sequenced and functionally expressed. They are members of the 12 membrane-spanning superfamily and they segregate into two groups, the Na+/glucose (SGLT1) and Na+/Cl-/GABA (GAT-1) families. SGLT1 transporters are expressed in bacteria and animal cells, while GAT-1 transporters are mostly expressed in the brain. None have yet been found in plants.     

Sodium-substrate cotransport in bacteria

A variety of sodium-substrate cotransport systems are known in bacteria. Sodium enters the cell down an electrochemical concentration gradient. There is obligatory coupling between the entry of the ion and the entry of substrate with a stoichiometry (in the cases studied) of 1:1. Thus, the downhill movement of sodium ion into the cell leads to the accumulation of substrate within the cell. The melibiose carrier of Escherichia coli is perhaps the most carefully studied of the sodium cotransport systems in bacteria. This carrier is of special interest because it can also use protons or lithium ions for cotransport. Other sodium cotransport carriers that have been studied recently are for proline, glutamate, serine-threonine, citrate and branched chain amino acids.     

Energetic coupling of Na-glucose cotransport

(1) Energetic coupling in Na-linked glucose transport in renal brush border membrane vesicles has been studied in terms of various carrier models differing with respect to reaction order (random vs. ordered), and to rate limitation of steps within the routes of carrier-mediated solute transfer (translation across the membrane barrier vs. binding/release between carrier and bulk solution). (2) By computer simulation it was found that effective energetic coupling requires the leakage routes to be significantly, if not predominantly, rate-limited by their (barrier-crossing) translatory steps. This does not apply to the transfer route of the ternary complex, as coupling is possible whether or not this route is rate-limited by the translatory step. (3) The system transports glucose in the absence of Na+ (uniport) and the unidirectional flux is stimulated by unlabeled glucose on the trans side (negative tracer coupling). It is concluded that glucose binds to the carrier on either side without Na, as would be consistent with either a random system or one mode of ordered system with mirror symmetry (glucose binds before Na) but inconsistent with either mode of glide symmetry. The tracer coupling appears to indicate that the rate coefficient of carrier-mediated glucose transfer exceeds that of the empty carrier. (4) The Na-linked zero-trans flow of glucose in either direction is strongly trans-inhibited by Na. This consistent with a random system in which Na blocks or retards the translocation of the glucose-free carrier, thereby reducing 'slipping' through an internal leakage route. It is also consistent with the above mentioned ordered system, (i.e., in the absence of Na-transport without D-glucose) if it is assumed that trans Na interferes with the dissociation of the ternary complex, thereby slowing the release of glucose. (5) Minimum equilibrium exchange of glucose is stimulated in the presence of Na. This appears to indicate that Na expands the flow density of carrier-mediated glucose transfer. This expansion does not result from a 'velocity effect' (the ternary complex moving faster than the binary glucose carrier complex), as Na fails to stimulate maximum equilibrium exchange. It can instead be accounted for by an 'affinity effect' (the affinity of the carrier for glucose being increased by Na) as Na depresses the Michaelis constant of equilibrium exchange.(ABSTRACT TRUNCATED AT 400 WORDS)     

The effect of vanadate on proton-sucrose cotransport in ricinus cotyledons

The effects of orthovanadate on the uptake of sucrose by Ricinus cotyledons and on sucrose-coupled proton influx were measured in order to gain insight into the relationship to the plasma membrane proton pump. Vanadate had no effect on short-term sucrose uptake. In longterm experiments (>30 min) sucrose uptake was progressively inhibited, but only at high external sucrose concentrations. Vanadate did not affect proton efflux pumping in the absence of sucrose and neither did it change the initial rate of sucrose-coupled proton influx. However, it enhanced the maximal level of sucrose-induced alkalinization of the medium at all sucrose concentrations tested. This is interpreted as an inhibiting effect of vanadate on the proton pump that recycles protons during sucrose-proton cotransport. The sensitivity towards vanadate indicates that this proton pump is an ATPase. A second proton-translocating system, that is insensitive to vanadate, is postulated to function in the absence of sucrose.     

Sucrose and proton cotransport in Ricinus cotyledons

In Ricinus cotyledons, evidence for proton extrusion came from observation of direct acidification of the medium in the presence of potassium salts. Increasing K⁺ influx with increasing pH suggested a link between K⁺ influx and H⁺ efflux by an H⁺ pump. The kinetics of K⁺ influx and H⁺ efflux were consistent with a 1:1 stoichiometry K⁺:H⁺, which may indicate either electrical coupling or carrier mediated exchange. The results were consistent with an H⁺ pump setting up an electrochemical potential gradient which provides the driving force for an H⁺-sucrose cotransport and the movement of K⁺. With reference to this, a model for phloem loading is suggested.     

Computational analysis of models for cotransport

A well-characterized crude peroxisomal fraction from brown adipose tissue was used to compare peroxisomal beta-oxidation with beta-oxidation in isolated mitochondria. The apparent Km and chain-length specificity for peroxisomal (acyl-CoA) and mitochondrial (acyl-carnitine) beta-oxidation were determined with saturated C4-C22 fatty acyls and some unsaturated fatty acyls. Peroxisomes showed the lowest Km for medium-chain (9:0-10:0) and mono-unsaturated long-chain (16:1-22:1) fatty acids, and highest oxidation rates with lauroyl-CoA (12:0). Mitochondria showed the lowest Km for long-chain fatty acids (16:0-18:0) and highest oxidation rates with 12:0-16:0 and with 18:2. These in vitro results offer an explanation of previous results obtained in situ by Foerster et al. (Foerster, E.-C., F?hrenkemper, T., Rabo, U., Graf, P. and Sies, H. (1981) Biochem. J. 196, 705-712) and indicate a role for peroxisomes in degradation of medium-chain and mono-unsaturated long-chain fatty acids. It is concluded that no mechanism, other than relative preferences, needs to be suggested for channelling of fatty acids between the two subcellular organelles.     

From irreversible thermodynamics to network thermodynamics

Whenever the subject of the thermodynamics of irreversible processes TIP is brought up among biologists, there seems to be a very polarized reaction: some have found it a useful tool, others reject it utterly, and for some reason which I do not understand, even fervently. For the present school, Professor Aharon Katchalsky had suggested that we try together to point out some ways in which TIP has been useful, to discuss limitations and shortcomings, and, finally, to show the direction and first results of present efforts, mainly in network thermodynamics¹. It would have been my task to show you the darker side of the coin, but now Aharon is not with us to show you the shining side in his unique way, to carry you along with his enthusiasm. I believe it is in Aharon's spirit that I do not attempt to evaluate or commemorate his contributions and achievements, but just talk science and try to convey a little of what was at the center of his interest during the last years.     

The self-association of ATP: thermodynamics and geometry.

The concentration and temperature dependence of the self-association of ademosin-5'-triphosphate (ATP) in aqueous solution was studied by means of ultraviolet absorption spectroscopy and circular dichroism (CD). Of several possible models, a model was indefinite linear self-association, in which each step has the same equilibrium constant, describes the data best. The two different methods lead within experimental error to the same thermodynamic parameters. At pH 8.7, IN 1 M Tris and 0.5 M 7gCl-2, we find deltaH-0 equals -5.1 kcal/mole and deltaS-0 equals -13.0 e.u. These values do not differ much from those found for the self-association of uncharged bases and nucleosides in aqueous solution. The CD spectrum that results from the self-association is conservative and quite similar in shape to that observed for some stacked dinucleotides: it is interpreted as a first approximation within the framework of the exciton model.     

The thermodynamics of interaction between Sephadex and penetrating solutes

1. We have measured the partition coefficients of bovine serum albumin with Sephadex grades G-100, G-150 and G-200, and of a dextran ([unk]_n 19700) and a polyethylene glycol ([unk]_n 8000) with Sephadex G-200. We have also measured the effects of these solutes on the inner volumes of the grades of Sephadex. 2. The results can be described with fair consistency by means of a simple thermodynamic treatment that makes use of the virial coefficients of Sephadex and of the solute, and of a coefficient that expresses their interaction. This coefficient is related to the `exclusion volume' of Sephadex for the solutes. 3. The Sephadex G-200–polyethylene glycol system shows anomalies of behaviour that are ascribed to the occurrence of `incompatible' phase separation within the Sephadex beads.     

The osteoblast mechano-receptor, microgravity perception and thermodynamics

Mechano-sensing in cells is tightly obliged with changes in intracellular free calcium (IFC), regulation of specific genes and activation of specific second messenger systems. To investigate whether single non-professional cells like osteoblasts can detect microgravity through the mechano-sensor, measurements on a sub-orbital rocket and parabolic flights observing the IFC and gene expression were performed. We find that microgravity did neither effect IFC nor gene expression. Thermal and mechanical noise within cells is too high in relation to the change of force due to the change from gravity to microgravity. Complementary force measurements have shown that cells exert high forces on the substrate and that these high forces have to be applied for activation.