Modification of the Kedem-Katchalsky equations

The presented modification of the transport equations of Kedem-Katchalsky resulted in the introduction of (omega s/omega) and omega/(omega-Lp sigma[(1-sigma)C1-(1-sigma s)C2]) factors into the Kedem-Katchalsky equations. The above factors determine the influence of boundary layers on transport across the membrane. The modified Kedem-Katchalsky equations were verified for synthetic membranes and it was shown that the value of the (omega s/omega) factor depended on the type of membrane and the membrane configuration system. This modification facilitated a wider range of application of the Kedem-Katchalsky equations to systems in which the solutions were stirred or unstirred.     

Generalization of the Spiegler-Kedem-Katchalsky frictional model equations of the transmembrane transport for multicomponent non-electrolyte solutions.

The Spiegler-Kedem-Katchalsky frictional model equations of the transmembrane transport for systems containing n-component, non-ionic solutions is presented. The frictional interpretation of the phenomenological coefficients of membrane and the expressions connecting the practical coefficients (Lp, sigma i, omega ij) with frictional coefficients (fij) are presented.     

Permeation of glycerol and propane-1,2-diol into human platelets

The permeability of human platelets to glycerol (GLY) and propane-1,2-diol (propylene glycol, PG) has been determined by measuring the time course of their change in volume following abrupt immersion in solutions of these solutes. A simple light-scattering method, and its calibration to measure mean platelet volume is described. The data are analyzed by means of the Kedem-Katchalsky (K-K) equations, modified to take into account the nonideal behavior of both intracellular and extracellular solutes. The values of the K-K parameters at 2, 21, and 37 degrees C, respectively, were as follows: the hydraulic conductivities (Lp) were 1 x 10(-7), 7 x 10(-7) and 3 x 10(-6) cm.sec-1.atm-1; the solute permeabilities for PG (omega RTPG) were 1.9 x 10(-6), 2.8 x 10(-5), and 1.3 x 10(-4) cm.sec-1; the solute permeabilities for GLY (omega RTGLY), at 21 and 37 degrees C only, were 2.6 x 10(-7) and 1.4 x 10(-6) cm.sec-1. The reflection coefficient (sigma) was 1 throughout. The relevant activation energies were -Lp, 16.5 kcal.mol-1; omega RTPG, 20.5 kcal.mol-1; and omega RTGLY, 17.9 kcal.mol-1. The use of these data is illustrated by computing schedules for the addition and removal of GLY and PG so that the amplitudes of changes in platelet volume are held within predetermined limits.     

A Biomechanical Triphasic Approach to the Transport of Nondilute Solutions in Articular Cartilage

Biomechanical models for biological tissues such as articular cartilage generally contain an ideal, dilute solution assumption. In this article, a biomechanical triphasic model of cartilage is described that includes nondilute treatment of concentrated solutions such as those applied in vitrification of biological tissues. The chemical potential equations of the triphasic model are modified and the transport equations are adjusted for the volume fraction and frictional coefficients of the solutes that are not negligible in such solutions. Four transport parameters, i.e., water permeability, solute permeability, diffusion coefficient of solute in solvent within the cartilage, and the cartilage stiffness modulus, are defined as four degrees of freedom for the model. Water and solute transport in cartilage were simulated using the model and predictions of average concentration increase and cartilage weight were fit to experimental data to obtain the values of the four transport parameters. As far as we know, this is the first study to formulate the solvent and solute transport equations of nondilute solutions in the cartilage matrix. It is shown that the values obtained for the transport parameters are within the ranges reported in the available literature, which confirms the proposed model approach.     

General continuum analysis of transport through pores. I. Proof of Onsager's reciprocity postulate for uniform pore.

The nonelectrolyte (Js) and volume (Jv) flux across a membrane is usually described in terms of two equations derived from the theory of irreversible thermodynamics: (see article) where delta c and delta P are the concentration and pressure difference; omega and Lp are the diffuse and hydraulic permeability; and sigma s and sigma v are the reflection coefficients. If Onsager's reciprocity postulate is assumed, it can be shown that signa s and sigma v are equal. This is an important assumption because it allows one to apply the continuum theory relationship between sigma s and the pore radius to experimental measurements of sigma v. In this paper, general continuum expressions for both the Jv (a new result) and Js equation will be derived and the equality of sigma s and sigma v proved. The proof uses only general hydrodynamic results and does not require explicit solutions for the drag coefficients or, for example, the assumption that the solute is in the center of the pore. The proof applys to arbitrarily shaped solutes and any pore whose shape is independent of axial position (uniform). In addition, new expressions for the functional dependence of omega and sigma on the pore radius are derived (including the effect of the particle lying off the pore axis). These expressions differ slightly from earlier results and are probably more accurate.     

Temperature dependence of blood surface tension

Whole blood surface tension of 15 healthy subjects recorded by the ring method was investigated in the temperature range from 20 to 40 degrees C. The surface tension omega as a function of temperature t ( degrees C) is described by an equation of linear regression as omega(t) = (-0.473 t + 70.105) x 10(-3) N/m. Blood serum surface tension in the range from 20 to 40 degrees C is described by linear regression equation omega(t) = (-0.368 t + 66.072) x 10(-3) N/m and linear regression function of blood sediment surface tension is omega(t) = (-0.423 t + 67.223) x10(-3) N/m.     

Transport across homoporous and heteroporous membranes in nonideal, nondilute solutions. II. Inequality of phenomenological and tracer solute permeabilities.

The phenomenological solute permeability (omega p) of a membrane measures the flux of solute across it when the concentrations of the solutions on the two sides of the membrane differ. The relationship between omega p and the the conventionally measured tracer permeability (omega T) is examined for homoporous and heteroporous (parallel path) membranes in nonideal, nondilute solutions and in the presence of boundary layers. In general, omega p and omega T are not equal; therefore, predictions of transmembrane solute flux based on omega T are always subject to error. For a homoporous membrane, the two permeabilities become equal as the solutions become ideal and dilute. For heteroporous membranes, omega p is always greater than omega T. An upper bound on omega p- omega T is derived to provide an estimate of the maximum error in predicted solute flux. This bound is also used to show that the difference between omega P and omega T demonstrated earlier for the sucrose-Cuprophan system can be explained if the membrane is heteroporous. The expressions for omega P developed here support the use of a modified osmotic driving force to describe membrane transport in nonideal, nondilute solutions.     

Deuterium isotope effects and product studies for the oxidation of N(omega)-allyl-L-arginine and N(omega)-allyl-N(omega)-hydroxy-L-arginine by neuronal nitric oxide synthase

The nitric oxide synthases (NOS), which require heme, tetrahydrobiopterin, FMN, FAD, and NADPH, catalyze the O2-dependent conversion of L-arginine to L-citrulline and nitric oxide. N(omega)-Allyl-L-arginine, a mechanism-based inactivator of neuronal NOS, also is a substrate, producing L-arginine, acrolein, and H2O (Zhang, H. Q.; Dixon, R. P., Marletta, M. A.; Nikolic, D.; Van Breemen, R.; Silverman, R. B. J. Am. Chem. Soc. 1997, 119, 10888). Two possible mechanisms for this turnover are proposed, one initiated by allyl C-H bond cleavage and the other by guanidino N H cleavage, and these mechanisms are investigated with the use of N(omega)-allyl-L-arginine (1), N(omega)-[1,1-(2)H2]allyl-L-arginine (7), N(omega)-allyl-N(omega)-hydroxy-L-arginine (2) and N(omega)-[1,1-(2)H2]allyl-N(omega)-hydroxy-L-arginine (8) as substrates. Significant isotope effects on the two kinetic parameters, kcat and kcat/Km, are observed in case of 1 and 7 during turnover, but not with 2 and 8. No kinetic isotope effects are observed for either compound in their role as inactivators. These results support a mechanism involving initial C-H bond cleavage of N(omega)-allyl-L-arginine followed by hydroxylation and breakdown to products.     

Transport across homoporous and heteroporous membranes in nonideal, nondilute solutions. I. Inequality of reflection coefficients for volume flow and solute flow.

The Kirkwood formulation of the Stefan-Maxwell equations is used to develop the transport equations for a membrane bounded by nonideal, nondilute solutions. The reflection coefficients for volume flow and solute flow are not equal but are related by a simple expression that depends on the concentration of the bounding solutions. The ratio of the two coefficients is independent of heteroporous membrane structure and the thickness of adjacent boundary layers. Experimental measurements of these reflection coefficients for sucrose transport across Cuprophan verify this relationship; this indicates that the Onsager reciprocal relation, which is assumed by the theory, holds for nonideal, nondilute solutions. The two reflection coefficients may be made operationally identical by a simple redefination of the osmotic driving force.     

Existence and uniqueness of solutions in general multisolute renal flow problems

This paper considers systems of differential equations that describe flows in renal networks. The flow geometry is of the type that occurs in modelling the renal medulla. The unknowns in the system include the flow rate, the hydrostatic pressure, and the concentrations of the various solutes. Existence and uniqueness of solutions of the appropriate boundary value problems are established, in the case of small permeability coefficients and transport rates, or large diffusion coefficients and small resistance to flow constants.Work supported in part by NIH Grants 5-R01-AM28617 and 7-R01-DK38817Work supported in part by NIH Grant 5-R01-AM20373     

Sorption and desorption studies on chitin gels

The aim of this work was to study various transport phenomena in chitin gels obtained by N-acetylation of chitosan in a water-alcohol mixture. Three kinds of transport were investigated: the sorption of solutes interacting with chitin, the desorption of solutes without significant interaction with the polymer, and osmosis phenomena. In the case of interactive sorption, dyes having different chemical structures such as C.I. Acid Blue 74, C.I. Reactive Violet 5 or C.I. Direct Red 28 were tested. Sorptions of C.I. Acid Blue 74 and C.I. Reactive Violet 5 depend on the charge density of the polymer network and, as a consequence, on DA, pH and the dielectric constant of the media. This result reveals the importance of electrostatic interactions. On the other hand, the sorption of C.I. Direct Red 28 is mainly due to hydrophobic interactions and H-bonding, it is limited to the extreme surface of the gel. Concerning the non-interactive desorption, solutes of different steric hindrance such as PP vitamin, B1 vitamin and caffeine exhibit similar diffusion coefficients located within 3.7-5.6x10(-6) cm(2) s(-1). Finally, the osmotic behaviour of the gel immersed in a concentrated solution of gelatin allows us to multiply by 25 the concentration of chitin in the gel without any penetration of gelatin.     

Phosphatidylinositol glycan (PI-G) anchored membrane proteins. Amino acid requirements adjacent to the site of cleavage and PI-G attachment in the COOH-terminal signal peptide.

Secreted proteins are processed from a nascent form that contains an NH2-terminal signal peptide. During processing, the latter is cleaved by a specific NH2-terminal signal peptidase. The nascent form of phosphatidylinositol glycan (PI-G) tailed proteins contain both an NH2- and a COOH-terminal signal peptide. The two signal peptides have much in common, such as size and hydrophobicity. The COOH-terminal peptide is also cleaved during processing. We propose that the amino acid in a nascent protein that ultimately combines with the PI-G moiety be designated the omega site. Amino acids adjacent and COOH-terminal to the omega site would then be omega + 1, omega + 2, etc. In previous studies, we showed that allowable substitutions at the omega site of an engineered form of placental alkaline phosphatase (miniPLAP) are limited to 6 small amino acids. In the present study, mutations were made at the omega + 1 and omega + 2 sites. At the omega + 1 site, processing to varying degrees was observed with 8 of the 9 amino acids substituted for alanine, the normal constituent. Only the proline mutant showed no processing. By contrast, the only substituents permitted at the omega + 2 site were glycine and alanine, with only trace activity observed with serine and cysteine. Thus, just as there is a -1, -3 rule for predicting cleavage by NH2-terminal signal peptidase, there appears to be a comparable omega, omega + 2 rule for predicting cleavage/PI-G addition by COOH-terminal signal transamidase.     

Cryomicroscopic determination of the membrane osmotic properties of human monocytes at subfreezing temperatures

Monocytes were isolated from fresh whole human blood and resuspended in Hanks balanced salt solution; a portion of the cells was mixed with an equal volume of 2M dimethyl sulfoxide (DMSO) to form a 1 M solution. Microliter volumes of cell suspension were placed directly onto a computer-controlled cryostage and cooled to a predetermined subzero temperature. Ice was nucleated in the extracellular medium and a continuous video record was made of the subsequent osmotically induced volume changes of individual cells owing to exposure to the concentrated extracellular solutes. Selected micrographs emphasizing the initial transient data were digitized for computer analysis with an interactive boundary tracing algorithm to determine metric parameters of specific cells, and apparent volume changes were measured as a function of elapsed time after nucleation. The Kedem-Katchalsky-coupled transport equations were fit to the data using a network thermodynamic model implemented on a microcomputer to determine values for the permeability properties Lp, omega, and sigma. Experiments were performed over the temperature range from -7 degrees to -10 degrees C. Cells pre-equilibrated with DMSO had a lower Lp and a higher activation energy, delta E, than without additive, although the statistical significance of the difference could not be substantiated. It was found that the movement of DMSO across the plasma membrane in response to extracellular freezing was apparently so much smaller than the water flux that values for omega and sigma could not be determined from the data base.     

Helix-forming tendencies of amino acids depend on the restrictions of side-chain rotamer conformations: crystal structure of the tripeptide GAI in two crystalline forms.

In our attempts to design crystalline alpha-helical peptides, we synthesized and crystallized GAI (C11H21N3O4) in two crystal forms, GAI1 and GAI2. Form 1 (GAI1) Gly-L-Ala-L-Ile (C11H21N3O4.3H2O) crystals are monoclinic, space group P2(1) with a = 8.171(2), b = 6.072(4), c = 16.443(4) A, beta = 101.24(2) degrees, V = 800 A3, Dc = 1.300 g cm-3 and Z = 2, R = 0.081 for 482 reflections. Form 2 (GAI2) Gly-L-Ala-L-Ile (C11H21N3O4.1/2H2O) is triclinic, space group P1 with a = 5.830(1), b = 8.832(2), c = 15.008(2) A, alpha = 102.88(1), beta = 101.16(2), gamma = 70.72(2) degrees, V = 705 A3, Z = 2, Dc = 1.264 g cm-3, R = 0.04 for 2582 reflections. GAI1 is isomorphous with GAV and forms a helix, whereas GAI2 does not. In GAI1, the tripeptide molecule is held in a near helical conformation by a water molecule that bridges the NH3+ and COO- groups, and acts as the fourth residue needed to complete the turn by forming two hydrogen bonds. Two other water molecules form intermolecular hydrogen bonds in stabilizing the helical structure so that the end result is a column of molecules that looks like an incipient alpha-helix. GAI2 imitates a cyclic peptide and traps a water molecule. The conformation angles chi 11 and chi 12 for the side chain are (-63.7 degrees, 171.1 degrees) for the helical GAI1, and (-65.1 degrees, 58.6 degrees) and (-65.0 degrees, 58.9 degrees) for the two independent nonhelical molecules in GAI2; in GAI1, both the C gamma atoms point away from the helix, whereas in GAI2 the C gamma atom with the g+ conformation points inward to the helix and causes sterical interaction with atoms in the adjacent peptide plane. From these results, it is clear that the helix-forming tendencies of amino acids correlate with the restrictions of side-chain rotamer conformations. Both the peptide units in GAI1 are trans and show significant deviation from planarity [omega 1 = -168(1) degrees; omega 2 = -171(1) degrees] whereas both the peptide units in both the molecules A and B in GAI2 do not show significant deviation from planarity [omega 1 = 179.3(3) degrees; omega 2 = -179.3(3) degrees for molecule A and omega 1 = 179.5(3) degrees; omega 2 = -179.4(3) degrees for molecule B], indicating that the peptide planes in these incipient alpha-helical peptides are considerably bent.     

Predicted permeability parameters of human ovarian tissue cells to various cryoprotectants and water

This study presents a generic numerical model to simulate the coupled solute and solvent transport in human ovarian tissue sections during addition and removal of chemical additives or cryoprotective agents (CPA). The model accounts for the axial and radial diffusion of the solute (CPA) as well as axial convection of the CPA, and a variable vascular surface area (A) during the transport process. In addition, the model also accounts for the radial movement of the solvent (water) into and out of the vascular spaces. Osmotic responses of various cells within an human ovarian tissue section are predicted by the numerical model with three model parameters: permeability of the tissue cell membrane to water (L(p)), permeability of the tissue cell membrane to the solute or CPA (omega) and the diffusion coefficient of the solute or CPA in the vascular space (D). By fitting the model results with published experimental data on solute/water concentrations within an human ovarian tissue section, I was able to determine the permeability parameters of ovarian tissue cells in the presence of 1.5M solutions of each of the following: dimethyl sulphoxide (DMSO), propylene glycol (PROH), ethylene glycol (EG), and glycerol (GLY), at two temperatures (4 degrees C and 27 degrees C). Modeling Approach 1: Assuming a constant value of solute diffusivity (D = 1.0 x 10(-9) m(2)/sec), the best fit values of L(p) ranged from 0.35 x 10(-14) to 1.43 x 10(-14) m(3)/N-sec while omega ranged from 2.57 x 10(-14) to 70.5 x 10(-14) mol/N-sec. Based on these values of L(p) and omega, the solute reflection coefficient, sigma defined as sigma = 1-omega v(CPA)/L(P) ranged from 0.9961 to 0.9996. Modeling Approach 2: The relative values of omega and sigma from our initial modeling suggest that the embedded ovarian tissue cells are relatively impermeable to all the CPAs investigated (or omega approximately 0 and sigma approximately 1.0). Consequently the model was modified and used to predict the values of L(p) and D assuming omega = 0 and sigma = 1.0. The best fit values of L(p) ranged from 0.44 x 10(-14) to 1.2 x 10(-14) m(3)/N-sec while D ranged from 0.85 x 10(-9) to 2.08 x 10(-9) m(2)/sec. Modeling Approach 3: Finally, the best fit values of D from modeling approach 2 were incorporated into model 1 to re-predict the values of L(p) and omega. It is hoped that the ovarian tissue cell parameters reported here will help to optimize chemical loading and unloading procedures for whole ovarian tissue sections and consequently, tissue cryopreservation procedures.     

Mapping of the spectral densities of N-H bond motions in eglin c using heteronuclear relaxation experiments.

A new strategy is used for studying the internal motions of proteins based on measurements of NMR relaxation parameters. The strategy yields values of the so-called spectral density functions J(omega) for N-H bond vectors. The spectral density functions are related to the distribution of frequencies contained in the rotational (overall and internal) motions of these NH bond vectors. No a priori model assumptions about the dynamics are required in this approach. The method involves measurements of six relaxation parameters consisting of 15N longitudinal relaxation rates, transverse relaxation rates of in-phase and antiphase coherence, the relaxation rates of heteronuclear 1H-15N two-spin order, the heteronuclear 1H-15N nuclear Overhauser effects, and longitudinal relaxation rates of the amide protons. The values of the spectral density functions at the five frequencies 0, omega N, omega H + omega N, omega H, and omega H - omega N are determined from the relaxation parameters using analytical relations derived previously [Peng & Wagner (1992) J. Magn. Reson. 98, 308-332]. Here, the method is applied to characterize the backbone dynamics of the 15N-enriched proteinase inhibitor eglin c, a protein of 70 residues. The values for J(0) and J(omega N = 50 MHz) vary significantly with the amino acid sequence, whereas the spectral densities at higher frequencies, J(450 MHz), J(500 MHz), and J(550 MHz), are typically much smaller and show no significant variation with the sequence. The collective behavior of the J(omega) values indicate greater internal motion for the proteinase binding loop residues and the first eight N-terminal residues. The additional internal motion in these regions is in the rate range below 450 MHz. The values of J(omega) are also compared with root mean square deviations (rmsds) of backbone atoms as obtained in NMR structure determinations. Low values of J(0) and J(omega N) are correlated with high rmsds. Spectral densities at higher frequencies, J(450 MHz), J(500 MHz), and J(550 MHz), are small and show no correlation with rmsds. A comparison with the spectral density functions obtained by fitting the experimental data to the functional dependence of the Lipari and Szabo formalism [Lipari & Szabo (1982a) J. Am. Chem. Soc. 104, 4546-4559] is made.     

Osmotic Biosensors. How to Use a Characean Internode for Measuring the Alcohol Content of Beer

Isolated internodes of Chara corallina and Nitella flexilis have been used to determine the concentration of one passively permeating solute in the presence of non-permeating solutes. The technique was based on the fact that the shape of the peaks of the biphasic responses of cell turgor (as measured in a conventional way using the cell pressure probe) depended on the concentration and composition of the solution and on the permeability and reflection coefficients of the solutes. Peak sizes were proportional to the concentration of the permeating solute applied to the cell. Thus, using the selective properties of the cell membrane as the sensing element and changes of turgor pressure as the physical signal, plant cells have been used as a new type of biosensor based on osmotic principles. Upon applying osmotic solutions, the responses of cell turgor (P) exactly followed the P(t) curves predicted from the theory based on the linear force/flow relations of irreversible thermodynamics. The complete agreement between theory and experiment was demonstrated by comparing measured curves with those obtained by either numerically solving the differential equations for volume (water) and solute flow or by using an explicit solution of the equations. The explicit solution neglected the solvent drag which was shown to be negligible to a very good approximation. Different kinds of local beers (regular and de-alcoholized) were used as test solutions to apply the system for measuring concentrations of ethanol. The results showed a very good agreement between alcohol concentrations measured by the sensor technique and those obtained from conventional techniques (enzymatic determination using alcohol dehydrogenase or from measurement of the density and refraction index of beer). However, with beer as the test solution, the characean internodes did show irreversible changes of the transport properties of the membranes leading to a shift in the responses when cells were treated for longer than 1 h with diluted beer. The accuracy and sensitivity of the osmotic biosensor technique as well as its possible applications are discussed.     

Membrane transport of electrolyte ions and time-dependent membrane potential

Equations are derived for the transport of a symmetrical electrolyte, consisting of cations and anions of equal valency, through a neutral membrane that separates two solutions of finite volume under quasi-steady-state conditions. The time-dependent membrane potential produced by the flow of ions is taken into account. Deviation of the time course of the solute concentrations from that of neutral solutes is found to be determined by the permeability ratio of cations and anions (when this ratio equals unity, the derived membrane transport equations reduce to those for neutral substances). Simple approximate expressions for the solute concentrations and of the membrane potential as functions of time are proposed, which are in excellent agreement with the exact numerical results.