Generalized concentration dependence of globular protein self-diffusion coefficients in aqueous solutions.

The self-diffusion coefficients of globular proteins (myoglobin, bovine serum albumin, barstar, lysozyme) in aqueous solutions at different temperatures and pH values are obtained by pulsed-gradient spin-echo NMR, and their concentration dependence is analyzed. The generalized concentration dependence of globular protein self-diffusion coefficients is empirically established, and compared to the concentration dependence of diffusion coefficients of flexible polymers and rigid Brownian particles.     

Diffucison of OXYGEN, Nitrogen and water in hyluronate solutions.

A method is reported for the measurement of the diffusion coefficients in water of some sparingly soluble gases. The results obtained for the diffusion coefficients of oxygen and nitrogen gas through water at 25 degrees C are 2.12. 10-5 and 2.61 . 10-5 cm-2 . s-1, respectively. A check on the accuracy of the teachnique using tritiated water as the diffusing substance gave a value of 2.15 . 10-5 cm-2 . s-1 which agrees within 3% with recent values from the literature. The method was applied to the measurement of oxygen, nitrogen, and tritiated water diffusion coefficients through agarose gels and through agarose gels containing hyluronate. The results indicate that the hyaluronate had only a small effect as a barrier to the diffusion of such low molecular weight substance.     

Activity coefficients of salts in highly concentrated protein solutions. II. Potassium salts in isoionic bovine serum albumin solutions

Mean activity coefficients of different potassium salts KX (X = F-, Cl-, Br-, I-, NO3-, SCN-) have been measured in concentrated isoionic bovine serum albumin (BSA) solutions, by use of the EMF method with ion-exchange membrane electrodes. These solutions may be regarded as simple model systems for the cytoplasm of living cells as far as the influence of the macromolecular component on the activity coefficients of the salts is concerned. Two series of measurements have been carried out: (a) varying the amount of salt from 0.01 to 0.5 molal and maintaining the BSA concentration constant at 20 wt% and (b) varying the protein concentration up to 25 wt% and keeping the salt concentration constant at 0.1 molal. For all salts studied, the mean activity coefficients in the protein-salt solutions increase as the salt concentration rises, when the protein concentration is maintained constant. In the series of measurements (b) the activity coefficients of all salts change linearly with the protein concentration. Marked qualitative differences, however, were observed depending on the anion species, which could be interpreted in terms of specific ion binding of X- to the protein molecule. By taking into account BSA-bound 'non-solvent' water, the results were analyzed in terms of numbers of anions bound per BSA molecule. Comparison with the results of Scatchard, obtained at low protein concentrations, showed only a very small electrostatic effect of the BSA-(X-)v polyions on the activity coefficient of the salts at higher protein and salt concentrations.     

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.     

Biological ion exchanger resins. VII. Counter-ion activity coefficients in solutions of biological polyelectrolytes.

The single ion activity coefficients of K+ and Cl- counter-ions were determined in concentrated polyelectrolyte solutions. The polyelectrolytes investigated included DNA and several proteins. Results indicate that ion gradients of up to 40:1 do not lower the counter-ion activity coefficient below 0.5. Thus, published values of the intracellular activity coefficient of K+ are not incompatible with cellular models utilizing cytoplasmic ion exchange.     

Virial coefficients of protein solutions

An osmometer capable of measuring protein osmotic pressures up to 100 cms. of mercury pressure has been described. The principle of the osmometer is to set a given pressure and to permit the protein concentration to equilibrate with the pressure. The higher virial osmotic coefficients of egg albumin in various electrolytes and in 1 m urea as well as a function of NaCl concentration are reported. The virial coefficients of bovine serum albumin and of bovine methemoglobin in 1 m NaCl are also given. It appears that the primary cause for the departure of the osmotic pressure from ideality is due to the covolumes of the proteins.     

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.     

Hyaluronate diffusion in semidilute solutions

Analysis of the mutual diffusion coefficient of hyaluronate reveals that it rapidly increases with increasing concentration or decreasing ionic strength. The mutual diffusion coefficients analyzed by boundary relaxation in the analytical ultracentrifuge by either Raleigh interference optics or absorption optics (through the use of fluorescein-labeled hyaluronate) yielded similar values. The theoretical treatment of the mutual diffusion coefficient has been analyzed in terms of experimentally measured intradiffusion coefficients and thermodynamic virial coefficients. Only approximate agreement between theory and experiment was found. The concept of formation of transient statistical network structures in semidilute solutions of hyaluronate was applied to evaluate a critical concentration at which network formation occurs. This has been discussed in relation to the marked decrease in the intradiffusion coefficient of hyaluronate with concentration. The formation of network structures in hyaluronate was found not to preclude the hyaluronate undergoing extremely rapid rates of mutual diffusion (with diffusion coefficients ～30 × 10^?11 m² s¹) under conditions of relatively large initial chemical potential gradients. Measurements of the unidirectional flux of hyaluronate for nonzero gradients demonstrated their marked sensitivity to the magnitude of the concentration difference across the boundary. An experimental feature of the unidrectional diffusion coefficients of hyaluronate is that they may be analyzed purely in terms of mutual and intradiffusion processes. The backflux diffusion coefficient (describing the flux against the imposed concentration gradient) appeared identical with the intradiffusion coefficient. The analysis of the various sources of errors made in this study suggests that the magnitude of the diffusion coefficients measured may be regarded only as approximate.     

The anomaly of oxygen diffusion in aqueous xanthan solutions

A membrane-covered polarographic oxygen electrode was used to measure oxygen diffusion coefficients in aqueous polyelectrolyte solutions of xanthan gum, sodium alginate, and sodium carboxymethylcellulose (CMC). In sodium alginate solutions, dilute xanthan solutions, and solutions containing more than 0.3 wt % CMC, oxygen diffusion coefficients decrease with increasing polymer concentrations. Interestingly, in dilute CMC solutions and concentrate xanthan solutions containing more than 0.5 wt % xanthan gum, oxygen diffusion coefficients increase with increasing polymer concentrations, and values exceeding that in pure water are generally observed.     

Activity coefficients of salts in highly concentrated protein solutions: I. Alkali chlorides in isoionic bovine serum albumin solutions

In order to understand the thermodynamic state of simple salts in living cells, the mean activity coefficients of LiCl, NaCl, KC1, RbCl, CsCl were determined in concentrated isoionic bovine serum albumin (BSA) solutions by use of the EMF method with ion exchange membrane electrodes. The protein concentration range extended up to 22 wt %, whereas the salt concentration was kept constant at 0.1 mole per kilogram water. These solutions may be regarded as crude but appropriate model systems for the cytoplasm of cells as far as type and magnitude of the macromolecular component influence on the chemical potential of the salts is concerned. The mean stoichiometric activity coefficients of the alkali chlorides in the isoionic BSA solutions decreased linearly with the protein molality; this decrease, however, did not exceed ca. 10% compared with the pure 0.1 molal salt solutions. Only very small differences in the behaviour of the different alkali chlorides were observed. The results may be interpreted by the superposition of the effects of specific Cl^? ion binding to BSA and BSA bound “non-solvent” water with probably electrostatic long range interactions of the BSA(Cl^?)_v polyions with the salt ions in solution. The resulting mean activity coefficients, corrected for ion binding and non-solvent water, showed a very slight linear dependence on the protein concentration. The departure from the value in the pure 0.1 molal salt solutions did not exceed ± 2%.     

Bifurcation diagram of a model chemical reaction—I. Stability changes of time-periodic solutions

The stability properties of the first two time-periodic solutions bifurcating from an unstable uniform steady-state are analyzed for a model chemical system subject to zero fluxes at the boundaries. The existence of new (secondary) bifurcation points is investigated on the small amplitude solutions and calculated analytically in the limit of small diffusion coefficients.     

Parametrization of direct and soft steric-undulatory forces between DNA double helical polyelectrolytes in solutions of several different anions and cations.

Directly measured forces between DNA helices in ordered arrays have been reduced to simple force coefficients and mathematical expressions for the interactions between pairs of molecules. The tabulated force parameters and mathematical expressions can be applied to parallel molecules or, by transformation, to skewed molecules of variable separation and mutual angle. This "toolbox" of intermolecular forces is intended for use in modelling molecular interactions, assembly, and conformation. The coefficients characterizing both the exponential hydration and the electrostatic interactions depend strongly on the univalent counterion species in solution, but are only weakly sensitive to anion type and temperature (from 5 to 50 degrees C). Interaction coefficients for the exponentially varying hydration force seen at spacings less than 10 to 15 A between surfaces are extracted directly from pressure versus interaxial distance curves. Electrostatic interactions are only observed at larger spacings and are always coupled with configurational fluctuation forces that result in observed exponential decay lengths that are twice the expected Debye-Huckel length. The extraction of electrostatic force parameters relies on a theoretical expression describing steric forces of molecules "colliding" through soft exponentially varying direct interactions.     

Activity coefficients of antibiotics in aqueous NaCl solutions at 298.2 K

Data at 298.2 K for aqueous NaCl solutions containing either D-phenylglycin, D-(p-hydroxy)phenylglycine, 6-amino penicillanic acid (6-APA), amoxicillin or ampicillin, are reported. The mean ionic activity coefficients of NaCl were determined from measurements of the responses of a sodium and a chloride ion-selective electrode. The activity coefficients of the precursors or the antibiotics were calculated from the values of the mean ionic activity coefficients using the exact cross differential relation between them. The correlation of solubility data using the activity coefficients measured in this work shows the same puzzling results previously observed in systems containing amino acids.     

Molecular basis of the apparent near ideality of urea solutions

Activity coefficients of urea solutions are calculated to explore the mechanism of its solution properties, which form the basis for its well-known use as a strong protein denaturant. We perform free energy simulations of urea solutions in different urea concentrations using two urea models (OPLS and KBFF models) to calculate and decompose the activity coefficients. For the case of urea, we clarify the concept of the ideal solution in different concentration scales and standard states and its effect on our subsequent analysis. The analytical form of activity coefficients depends on the concentration units and standard states. For both models studied, urea displays a weak concentration dependence for excess chemical potential. However, for the OPLS force-field model, this results from contributions that are independent of concentration to the van der Waals and electrostatic components whereas for the KBFF model those components are nontrivial but oppose each other. The strong ideality of urea solutions in some concentration scales (incidentally implying a lack of water perturbation) is discussed in terms of recent data and ideas on the mechanism of urea denaturation of proteins.     

Exact fundamental solutions of linear parabolic equations with spatially varying coefficients

The exact general solution is obtained to a linear second order ordinary differential equation which has quite general coefficients depending on an arbitrary function of the independent variable. From this, the exact fundamental solution is derived for the corresponding linear parabolic partial differential equation with coefficients depending on the single space coordinate. In a special case this latter equation reduces to one of the Fokker-Planck type. These coefficients are then generalised and the appropriate fundamental solution is obtained. Extensions are given to linear parabolic equations in two andn space dimensions. The paper provides a collection of basic examples which illustrate and develop the theory for the generation of the exact fundamental solutions. Reduction to, and the corresponding fundamental solutions of the Fokker-Planck equations is presented, where appropriate.     

Gibbs free energy of transfer of glycine and diglycine from water to alkylurea solutions. Measured vs. calculated values

Ternary systems comprising water (1), glycine (diglycine) (2) and alkylurea (3) have been investigated using vapor pressure osmometry. Equations were obtained in terms of the molalities of the solutes for the activity coefficients of glycine and diglycine in these systems. The alkylureas used were methyl-, ethyl- and N, N'-dimethylurea. Using the activity coefficients the Gibbs free energy of transfer at infinite dilution of component 2 from water to alkylurea solutions was determined. Since the enthalpies of transfer are known, the corresponding entropies could also be obtained. Calculation of the Gibbs free energy of transfer at infinite dilution of component 2 rests on the assumption that it can be divided into two parts: the difference between the Gibbs free energy of cavity formation and that of interaction in the alkylurea solution and water, respectively. The first part was calculated by scaled particle theory using experimental density and surface tension data. The second part was taken to be due mainly to the change in dipole-dipole interactions.     

Aqueous solutions containing amino acids and peptides. Part 20. Volumetric behavior of some terminally substituted amino acids and peptides at 298.15 K

The densities at 298.15 K of aqueous solutions containing some terminally substituted amino acids and peptides containing the glycyl, L -and D -alanyl, L -leucyl, sarcosyl, and L -prolyl residues have been dertermined and standard state partial molar volumes and volumetric pairwise virial coefficients obtained. It is shown that the partial molar volumes can be represented using group volume contributions, but this approach is only approximate, and significant effects of N-terminal substitution and sequence dependence are observed. The volumetric virial coefficients for the amino acid amides have been expressed using a group-additivity approach, and the results obtained indicate that the dominant contributions come from peptide group interactions with other peptide groups and with hydrophobic groups. There is also some evidence of both sequence and chiral effects on the volumetric virial coefficients for proline-containing dipeptides.     

Activity coefficients of counterions in solutions of diethylaminoethyl dextran hydrochloride

Activity coefficients of counterions in solutions of diethylaminoethyl dextran hydrochloride have been determined. It has been observed that they increase with decreasing concentration of the polyelectrolyte. The experimental values have been compared with those calculated using Oosawa's theory of activity coefficients. The calculated values are higher than those observed, which suggests that the rodlike model on which Oosawa's theory is based is inadequate for the present case. Activity coefficients of counterions of some solutions containing NaCl and KC1, respectively, have also been determined. It has been found that the additivity rule for activity of counterions applies for these solutions.     

Interpretation of osmotic pressure in solutions of one and two nondiffusible components.

Osmotic pressure data from aqueous solutions of nondiffusible serum albumin (BSA), chondroitin sulfate (CHS), and dextran T110 (D110), taken singly and in binary combinations, were interpreted in terms of excluded volume. The principal solvent was phosphate-buffered saline, pH 7.2, at 23 degrees C. Osmotic pressures were measured with a membrane osmometer fitted with Amicon PM-10 membranes. Data from each solution were fit by stepwise regression with a three- or four-term polynomial in integral powers of total nondiffusible solute concentration in accordance with the general solution theory of McMillan and Mayer (1945, J. Chem. Phys. 13:276) as extended by Yamakawa (1971, Modern Theory of Polymer Solutions, Harper & Row, New York). The date display a high internal consistency, and the results correlate well with published molecular weights and exclusion data where available. Number average molecular weights calculated from the "first virial coefficients" are: BSA, 67,000 +/- 11%; D110, 76,000 +/- 11%, CHS, 39,000 +/- 6%. Excluded volumes (in cubic centimeters per molecule) calculated from the "second virial coefficients" are: BSA, 0.97 X 10(-18); D110, 3.04 X 10(-18); CHS, 14.3 X 10(-18); BSA-D110, 6.8 X 10(-18); BSA-CHS, 7.8 X 10(-18). Uncertainty is about 30%. An empirical model for interpretation of calculated excluded volumes is proposed. It appears that CHS has the "largest" exclusion effect of the three molecules.