CHEMICAL AND PHYSICAL CHANGES IN GELATIN SOLUTIONS DURING HYDROLYSIS

1. The change in viscosity and the corresponding increase in the carboxyl groups, as determined by the formol titration, has been determined in gelatin solutions during the progress of hydrolysis by pepsin. 2. Very marked changes in viscosity are found to result from very slight chemical changes. If the viscosity is increased by the addition of acid a greater change in viscosity (volume of solute) is caused by the same percentage change in the number of carboxyl groups. The percentage change in the volume of solute, caused by the same percentage increase in the number of carboxyl groups, is independent of the concentration of gelatin. 3. These results are in agreement with the idea that the high viscosity of gelatin solutions is due to the presence of swollen micells, since a slight chemical hydrolysis may be sufficient to rupture a micella and so cause a very large change in viscosity.     

MOLECULAR WEIGHT,MOLECULAR VOLUME,AND HYDRATION OF PROTEINS IN SOLUTION

1. The gram molecular weight of a substance may be calculated from the osmotic pressure of its solution. 2. The radius of the hydrated molecule and, hence, the gram molecular volume of the hydrated solute may be determined from diffusion measurements. The hydration of the molecules may, therefore, be calculated from osmotic pressure and diffusion measurements. 3. Hydration may also be determined by viscosity measurements. Hydration of crystalline hemoglobin, crystalline trypsin, and gelatin have been determined by these methods and found to be as follows: See PDF for Structure     

DONNAN EQUILIBRIUM AND THE PHYSICAL PROPERTIES OF PROTEINS : III. VISCOSITY.

1. Gelatin solutions have a high viscosity which in the case of freshly prepared solutions varies under the influence of the hydrogen ion concentration in a similar way as the swelling, the osmotic pressure, and the electromotive forces. Solutions of crystalline egg albumin have under the same conditions a comparatively low viscosity which is practically independent of the pH (above 1.0). This difference in the viscosities of solutions of the two proteins seems to be connected with the fact that solutions of gelatin have a tendency to set to a Jelly while solutions of crystalline egg albumin show no such tendency at low temperature and pH above 1.0. 2. The formulæ for viscosity demand that the difference in the order of magnitude of the viscosity of the two proteins should correspond to a difference in the relative volume occupied by equal masses of the two proteins in the same volume of solution. It is generally assumed that these variations of volume of dissolved proteins are due to the hydration of the isolated protein ions, but if this view were correct the influence of pH on viscosity should be the same in the case of solutions of gelatin, of amino-acids, and of crystalline egg albumin, which, however, is not true. 3. Suspensions of powdered gelatin in water were prepared and it was found, first, that the viscosity of these suspensions is a little higher than that of gelatin solutions of the same concentration, second, that the pH influences the viscosity of these suspensions similarly as the viscosity of freshly prepared gelatin solutions, and third, that the volume occupied by the gelatin in the suspension varies similarly as the viscosity which agrees with the theories of viscosity. It is shown that this influence of the pH on the volume occupied by the gelatin granules in suspension is due to the existence of a Donnan equilibrium between the granules and the surrounding solution.     

A METHOD FOR THE DETERMINATION OF DIFFUSION CONSTANTS AND THE CALCULATION OF THE RADIUS AND WEIGHT OF THE HEMOGLOBIN MOLECULE

A method is described for determining the diffusion coefficient of solutes by determining the rate of passage of the solute through a thin porous membrane between two solutions of different concentration. The method has been used to determine the diffusion coefficient of carbon monoxide hemoglobin. This was found to be 0.0420 ± 0.0005 cm.² per day at 5°C. The molecular weight of carbon monoxide hemoglobin calculated by means of Einstein''s equation from this quantity is 68,600 ± 1,000.     

Viscosity of concentrated solutions and of human erythrocyte cytoplasm determined from NMR measurement of molecular correlation times. The dependence of viscosity on cell volume

Metabolically active human erythrocytes were incubated with [alpha-13C]glycine which led to the specific enrichment of intracellular glutathione. The cells were then studied using 13C-NMR in which the longitudinal relaxation times (T1) and nuclear Overhauser enhancements of the free glycine and glutathione were measured. The T1 values of labelled glycine were also determined in various-concentration solutions of bovine serum albumin and glycerol and also of the natural abundance 13C of glycerol in glycerol solutions. From the T1 estimates the rotational correlation time (tau r) was calculated using a formula based on a model of an isotropic spherical rotor or that of a symmetrical ellipsoidal rotor; for glycine the differences in estimates of tau r obtained using the two models were not significant. From the correlation times and by use of the Stokes-Einstein equations viscosity and translational diffusion coefficients were calculated; thus comment can be made on the likelihood of diffusion control of certain enzyme-catalysed reactions in the erythrocyte. Bulk viscosities of the erythrocyte cytoplasm and the above-mentioned solutions were measured using Ostwald capillary viscometry. Large differences existed between the latter viscosity estimates and those based upon NMR-T1 measurements. We derived an equation from the theory of the viscosity of concentrated solutions which contains two phenomenological interaction parameters, a 'shape' factor and a 'volume' factor; it was fitted to data relating to the concentration dependence of viscosity measured by both methods. We showed, by using the equation and interaction-parameter estimates for a particular probe molecule in a particular solution, that it was possible to correlate NMR viscosity and bulk viscosity; in other words, given an estimate of the bulk viscosity, it was possible to calculate the NMR 'micro' viscosity or vice versa. However, the values of the interaction parameters depend upon the relative sizes of the probe and solute molecules and must be separately determined for each probe-solute-solvent system. Under various conditions of extracellular osmotic pressure, erythrocytes change volume and thus the viscosity of the intracellular milieu is altered. The volume changes resulted in changes in the T1 of [alpha-13C]glycine. Conversely, we showed that alterations in T1, when appropriately calibrated, could be used for monitoring changes in volume of metabolically active cells.     

Rotational diffusion of TEMPONE in the cytoplasm of Chinese hamster lung cells.

The correlation time for rotational diffusion (tau R) of 2,2,6,6-tetramethyl-4-piperidone-N-oxide (TEMPONE) in Chinese hamster lung (V79) cells has been measured. For these cells in an isosmotic solution at 20 degrees C, tau R = 4.18 X 10(-11) s, approximately 3.6 times greater than tau R = 1.17 X 10(-11) s in water. The relationship between tau R and viscosity was investigated in a number of glycerol-water (0-50%) and sucrose-water (20-40%) solutions and a constant Stokes-Einstein volume of 44 A3 was found for TEMPONE in solutions of less than 20% glycerol and sucrose. This gives an average shear viscosity (for rotation of a small molecule) of 0.038 poise for the cytoplasm. When nonsecular terms were used in the calculation of tau R, the activation energies for rotation of TEMPONE in the above solutions correlated well with the activation energies for shear viscosity. The viscosity increases as the cell is shrunk in hypertonic solutions. It also increases with decreasing temperature with an activation energy of 3.7 kcal/mol, about the same as the activation energy for the viscosity of pure water. The rotational correlation times were carefully calculated considering inhomogeneous line broadening, non-Lorentzian line shapes, the need for accurate tensor values and nonsecular terms.     

Apparent specific volumes of some dipeptides (containing L-valine and L-leucine in aqueous alkylurea solutions).

The apparent molal volumes of nine dipeptides containing glycine, L-valine, and L-leucine have been determined in methyl, N,N'-dimethyl and ethylurea solutions from precise density measurements. Limiting partial molal volumes. V2(0), at various solute concentrations have also been calculated. The experimental values of V2(0) in water agree reasonably well with those calculated as the sum of V2(0) of both acids after accounting for the electrostrictive effect and loss of water. There is no correlation between the values of V2(0) of individual dipeptides in alkylureas which means that the intrinsic volume and the electrostrictive effect make the largest contribution to V2(0). The contribution from other effects is within the limit of experimental error. The volumes of transfer from water to alkylurea solutions are all positive and reflect by and large the electrostrictive effect.     

Osmotic Flow of Water across Permeable Cellulose Membranes

Direct measurements have been made of the net volume flow through cellulose membranes, due to a difference in concentration of solute across the membrane. The aqueous solutions used included solutes ranging in size from deuterated water to bovine serum albumin. For the semipermeable membrane (impermeable to the solute) the volume flow produced by the osmotic gradient is equal to the flow produced by the hydrostatic pressure RT ΔC, as given by the van't Hoff relationship. In the case in which the membrane is permeable to the solute, the net volume flow is reduced, as predicted by the theory of Staverman, based on the thermodynamics of the steady state. A means of establishing the amount of this reduction is given, depending on the size of the solute molecule and the effective pore radius of the membrane. With the help of these results, a hypothetical biological membrane moving water by osmotic and hydrostatic pressure gradients is discussed.     

Description of hydration free energy density as a function of molecular physical properties

A method to calculate the solvation free energy density (SFED) at any point in the cavity surface or solvent volume surrounding a solute is proposed. In the special case in which the solvent is water, the SFED is referred to as the hydration free energy density (HFED). The HFED is described as a function of some physical properties of the molecules. These properties are represented by simple basis functions. The hydration free energy of a solute was obtained by integrating the HFED over the solvent volume surrounding the solute, using a grid model. Of 34 basis functions that were introduced to describe the HFED, only six contribute significantly to the HFED. These functions are representations of the surface area and volume of the solute, of the polarization and dispersion of the solute, and of two types of electrostatic interactions between the solute and its environment. The HFED is described as a linear combination of these basis functions, evaluated by summing the interaction energy between each atom of the solute with a grid point in the solvent, where each grid point is a representation of a finite volume of the solvent. The linear combination coefficients were determined by minimizing the error between the calculated and experimental hydration free energies of 81 neutral organic molecules that have a variety of functional groups. The calculated hydration free energies agree well with the experimental results. The hydration free energy of any other solute molecule can then be calculated by summing the product of the linear combination coefficients and the basis functions for the solute.     

THE SWELLING AND OSMOTIC PRESSURE OF GELATIN IN SALT SOLUTIONS

1. The swelling and the osmotic pressure of gelatin at pH 4.7 have been measured in the presence of a number of salts. 2. The effect of the salts on the swelling is closely paralleled by the effect on the osmotic pressure, and the bulk modulus of the gelatin particles calculated from these figures is constant up to an increase in volume of about 800 per cent. As soon as any of the salts increase the swelling beyond this point, the bulk. modulus decreases. This is interpreted as showing that the elastic limit has been exceeded. 3. Gelatin swollen in acid returns to its original volume after removal of the acid, while gelatin swollen in salt solution does not do so. This is the expected result if, as stated above, the elastic limit had been exceeded in the salt solution. 4. The modulus of elasticity of gelatin swollen in salt solutions varies in the same way as the bulk modulus calculated from the osmotic pressure and the swelling. 5. The increase in osmotic pressure caused by the salt is reversible on removal of the salt. 6. The observed osmotic pressure is much greater than the osmotic pressure calculated from the Donnan equilibrium except in the case of AlCl₃, where the calculated and observed pressures agree quite closely. 7. The increase in swelling in salt solutions is due to an increase in osmotic pressure. This increase is probably due to a change in the osmotic pressure of the gelatin itself rather than to a difference in ion concentration.     

Systemic and renal hemodynamics after moderate hemodilution with HbOCs in anesthetized rabbits

Hb-based O(2)-carrying solutions (HbOCs) have been developed as red blood cell substitutes for use in patients undergoing hemodilution. Variously modified Hb with diverse solution properties have been shown to produce variable hemodynamic responses. We examined, through pulsed-Doppler velocimetry, the systemic and renal hemodynamic effects of dextran-benzene-tetracarboxylate-conjugated (Hb-Dex-BTC), bis(3,5-dibromosalicyl)fumarate cross-linked (alphaalpha-Hb), and o-raffinose-polymerized (o-raffinose-Hb) Hb perfused in rabbits after moderate hemodilution (30% hematocrit), and we compared the effects of these Hb solutions with the effects elicited by plasma volume expanders. In addition, vascular hindrance (resistance/blood viscosity at 128.5 s(-1)) was calculated to determine whether a moderate decrease in the viscosity of blood mixed with HbOCs may impair vasoconstriction as a result of autoregulation after infusion of cell-free Hb. No changes were observed in renal hemodynamics after hemodilution with reference or Hb solutions. Increase in blood pressure and vascular resistance was found with Hb-Dex-BTC and alphaalpha-Hb (for 180 min) and, to a lesser extent, with o-raffinose-Hb (for 120 min). Furthermore, Hb-Dex-BTC (high viscosity) and o-raffinose-Hb (medium viscosity) induced comparable increases in vascular hindrance (from 0.091 to 0. 159 and from 0.092 to 0.162 cm(-1), respectively) but far less than that produced by alphaalpha-Hb (low viscosity, from 0.092 to 0.200 cm(-1)). These results suggest that maintaining the viscosity of blood by infusing solutions with high viscosity makes it possible to limit vasoconstriction due to autoregulation mechanisms and mainly caused by hemodilution per se.     

Determinants of the translational mobility of a small solute in cell cytoplasm

The purposes of this study were: (a) to measure the translational mobility of a small solute in cell cytoplasm; (b) to define quantitatively the factors that determine solute translation; and (c) to compare and contrast solute rotation and translation. A small fluorescent probe, 2,7-bis-(2-carboxyethyl)-5-(and 6-)- carboxyfluorescein (BCECF), was introduced into the cytoplasm of Swiss 3T3 fibroblasts. BCECF translation was measured by fluorescence recovery after photo-bleaching; rotation was measured by Fourier transform polarization microscopy. Diffusion coefficients relative to those in water (D/D0) were determined by comparing mobility in cytoplasm with mobility in standard solutions of known viscosity. At isosmotic cell volume, the relative diffusion coefficients for BCECF translation and rotation in cytoplasm were 0.27 +/- 0.01 (SEM, n = 24, 23 degrees C) and 0.78 +/- 0.03 (n = 4), respectively. As cell volume increased from 0.33 to 2 times isosmotic volume, the relative translational diffusion coefficient increased from 0.047 to 0.32, while the relative rotational diffusion coefficient remained constant. The factors determining BCECF translation were evaluated by comparing rotation and translation in cytoplasm, and in artificial solutions containing dextrans (mobile barriers) and agarose gels (immobile barriers). It was concluded that the hindrance of BCECF translation in cytoplasm could be quantitatively attributed to three independent factors: (a) fluid-phase cytoplasmic viscosity is 28% greater than the viscosity of water (factor 1 = 0.78); (b) 19% of BCECF is transiently bound to intracellular components of low mobility (factor 2 = 0.81); and most importantly, (c) translation of unbound BCECF is hindered 2.5- fold by collisions with cell solids comprising 13% of isosmotic cell volume (factor 3 = 0.40). The product of the 3 factors is 0.25 +/- 0.03, in good agreement with the measured D/D0 of 0.27 +/- 0.01. These results provide the first measurement of the translational mobility of a small solute in cell cytoplasm and define quantitatively the factors that slow solute translation.     

The osmotic behavior of corn mitochondria

The volume changes undergone by corn (Zea mays L.) mitochondria suspended in solutions of constant or varying osmolarity were studied. Within the range of osmotic pressure from 1.8 to 8.4 atmospheres, corn mitochondria behave as osmometers, if allowance is made for an osmotic “dead space” of about 6.9 μl/mg protein. The final equilibrium volume of mitochondria swollen in solutions containing both ribose and sucrose were shown to depend upon the concentration of impermeable solute (sucrose) present and not upon the concentration of ribose present. Osmotic reversibility was found for mitochondria swollen in isotonic solutions of KCI or ribose. The passive swelling of corn mitochondria may be due to the osmotic flow of water coupled to the diffusion of a permeable solute.     

A Numerical Study of the Hydrodynamic Stable Concentration Boundary Layers in a Membrane System Under Microgravitational Conditions

On the basis of the classic formula of the concentration Rayleigh number and the Kedem–Katchalsky equation for diffusive membrane transport, we derived the equations of sixteenth order which show the dependence of the thicknesses of the concentration boundary layers on the difference of the solution concentrations, the concentration Rayleigh number, the solute permeability coefficient of the membrane and the diffusion coefficients in the solution, the kinematic viscosity of the solution, the density of solutions, the temperature and gravitational acceleration. The obtained equation has numerical solutions in the first, third and fourth quadrant of a co-ordinate system. However, only two solutions from the first quadrant of the co-ordinate system have physical meaning. Confining ourselves to the set of solutions with physical meaning only, the thicknesses of concentration boundary layers for different parameters occurring in the obtained equation were calculated numerically.     

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.     

Viscosity of supercooled aqueous glycerol solutions, validity of the Stokes-Einstein relationship, and implications for cryopreservation

The viscosity of supercooled glycerol aqueous solutions, with glycerol mass fractions between 0.70 and 0.90, have been determined to confirm that the Avramov-Milchev equation describes very well the temperature dependence of the viscosity of the binary mixtures including the supercooled regime. On the contrary, it is shown that the free volume model of viscosity, with the parameters proposed in a recent work (He, Fowler, Toner, J. Appl. Phys. 100 (2006) 074702), overestimates the viscosity of the glycerol-rich mixtures at low temperatures by several orders of magnitude. Moreover, the free volume model for the water diffusion leads to predictions of the Stokes-Einstein product, which are incompatible with the experimental findings. We conclude that the use of these free volume models, with parameters obtained by fitting experimental data far from the supercooled and glassy regions, lead to incorrect predictions of the deterioration rates of biomolecules, overestimating their life times in these cryopreservation media.     

Loss of translational entropy in molecular associations

Molecular associations in solution are opposed by the loss of entropy (DeltaS) that results from the restriction of motion of each component in the complex. Theoretical estimates of DeltaS are essential for rationalizing binding affinities, as well as for calculating entropic contribution to enzyme catalysis. Recently a statistical-mechanical framework has been proposed for estimating efficiently the translational entropy loss (DeltaS(trsl)), while taking explicitly into account the complex intermolecular interactions between the solute and the solvent. This framework relates the translational entropy of a solute in solution to its "free volume," defined as the volume accessible to the center of mass of the solute in the presence of the solvent and calculated by using an extension of the cell model (CM) for condensed phases. The translational entropy of pure water, estimated with the CM algorithm, shows good agreement with the experimental information. The free volume of various solutes in water, calculated within the CM by using molecular dynamics simulations with explicit solvent, displays a strong correlation with the solutes' polar and total surface areas. This correlation is used to propose a parameterization that can be used to calculate routinely the translational entropy of a solute in water. We also applied the CM formalism to calculate the free volume and translational entropy loss (DeltaS(trsl)) on binding of benzene to a cavity in a mutant T4-lysozyme. Our results agree with previously published estimates of the binding of benzene to this mutant T4-lysozyme. These and other considerations suggest that the cell model is a simple yet efficient theoretical framework to evaluate the translational entropy loss on molecular association in solution.     

A novel thermodynamic relationship based on Kramers Theory for studying enzyme kinetics under high viscosity

In most studies of enzyme kinetics it has been found sufficient to use the classical Transition State Theory (TST) of Eyring and others. This theory was based on the solvent being an ideal dilute substance treated as a heat bath. However, enzymes found in organisms adapted to very low (psychrophiles) and very high (thermophiles) temperatures are also subjected to variable solute concentrations and viscosities. Therefore, the TST may not always be applicable to enzyme reactions carried out in various solvents with viscosities ranging from moderate to very high. There have been numerous advances in the theory of chemical reactions in realistic non-ideal solvents such as Kramers Theory. In this paper we wish to propose a modified thermodynamic equation, which have contributions from kcat, Km and the viscosity of the medium in which the enzyme reaction is occurring. These could be very useful for determining the thermodynamics of enzymes catalyzing reactions at temperature extremes in the presence of substrate solutions of different compositions and viscosities.     

Fractionation of a hyaluronic acid preparation in a density gradient. Some properties of the hyaluronic acid

1. Hyaluronic acid was isolated from ox synovial fluid by sedimentation equilibrium in a caesium chloride density gradient (Silpananta, Dunstone & Ogston, 1967). The product was almost free from chondroitin sulphate and from protein. 2. Its composition did not differ significantly from that of the carbohydrate part of the protein-containing material isolated by filtration. Its physicochemical properties and molecular configuration were similar, except for its viscosity, which showed markedly reduced concentration-dependence and shear-dependence. This suggests that the associated protein tends to form links between molecules of hyaluronic acid. 3. The accurate measurement of viscosity at very low velocity gradient, by use of the damping of oscillations in a Couette viscometer, is described. 4. A method is described for measuring, approximately, the thermodynamic non-ideality of a solute from the shape of its schlieren curve at sedimentation equilibrium in a density gradient. 5. A value for the partial specific volume of hyaluronic acid in dilute salt solution was calculated from its isopycnic density in a caesium chloride gradient.     

Determination of Some Hydrodynamic Parameters of Ovine Serum Albumin Solutions Using Viscometric Measurements

The influence of protein concentration and temperature on the viscosity of ovine serum albumin (OSA) solutions was studied. The Mooney equation and a modified Arrhenius formula were used to described the viscosity-concentration and viscosity-temperature dependence of the solutions, respectively. The effective specific volume, the activation energy and entropy of viscous flow for hydrated OSA were calculated. The axial ratio and the dimensions of the main semi-axes of hydrated OSA were established. At low concentration limit, the temperature dependence of the intrinsic viscosity and Huggins coefficient is presented. Comparison of some hydrodynamic parameters obtained for different proteins has been made.