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.     

Ionic and osmotic regulation of the haemolymph of the dragonfly, Libellula quadrimaculata (Odonata : Libellulidae)

Larvae of the widespread dragonfly, Libellula quadrimaculata, were adapted to a series of salt solutions, and the osmotic pressure, and sodium, potassium and chloride concentrations in the haemolymph measured. The regulation of potassium is extremely efficient over the range 0–50 m-mole/l. external concentration. Above this, larvae die. Sodium and chloride are regulated to a lesser extent, the larvae being able to withstand considerable changes in the concentration of these ions in the haemolymph. However, at higher external concentrations, the haemolymph concentration of these ions is maintained below that of the external medium. The osmotic pressure is regulated in parallel with sodium concentration over most of the range tested. However, in higher salinities, the osmotic pressure of the haemolymph does not fall below that of the external medium. This is seen as a strategy to limit the amount of drinking in saline media. Overall, the osmoregulatory system of L. quadrimaculata resembles that of brackish-water insects, rather than that of the more strictly freshwater dragonflies that have been studied.     

DONNAN EQUILIBRIUM AND THE PHYSICAL PROPERTIES OF PROTEINS : I. MEMBRANE POTENTIALS.

1. It is shown that a neutral salt depresses the potential difference which exists at the point of equilibrium between a gelatin chloride solution contained in a collodion bag and an outside aqueous solution (without gelatin). The depressing effect of a neutral salt on the P.D. is similar to the depression of the osmotic pressure of the gelatin chloride solution by the same salt. 2. It is shown that this depression of the P.D. by the salt can be calculated with a fair degree of accuracy on the basis of Nernst''s logarithmic formula on the assumption that the P.D. which exists at the point of equilibrium is due to the difference of the hydrogen ion concentration on the opposite sides of the membrane. 3. Since this difference of hydrogen ion concentration on both sides of the membrane is due to Donnan''s membrane equilibrium this latter equilibrium must be the cause of the P.D. 4. A definite P.D. exists also between a solid block of gelatin chloride and the surrounding aqueous solution at the point of equilibrium and this P.D. is depressed in a similar way as the swelling of the gelatin chloride by the addition of neutral salts. It is shown that the P.D. can be calculated from the difference in the hydrogen ion concentration inside and outside the block of gelatin at equilibrium. 5. The influence of the hydrogen ion concentration on the P.D. of a gelatin chloride solution is similar to that of the hydrogen ion concentration on the osmotic pressure, swelling, and viscosity of gelatin solutions, and the same is true for the influence of the valency of the anion with which the gelatin is in combination. It is shown that in all these cases the P.D. which exists at equilibrium can be calculated with a fair degree of accuracy from the difference of the pH inside and outside the gelatin solution on the basis of Nernst''s logarithmic formula by assuming that the difference in the concentration of hydrogen ions on both sides of the membrane determines the P.D. 6. The P.D. which exists at the boundary of a gelatin chloride solution and water at the point of equilibrium can also be calculated with a fair degree of accuracy by Nernst''s logarithmic formula from the value pCl outside minus pCl inside. This proves that the equation x² = y ( y + z) is the correct expression for the Donnan membrane equilibrium when solutions of protein-acid salts with monovalent anion are separated by a collodion membrane from water. In this equation x is the concentration of the H ion (and the monovalent anion) in the water, y the concentration of the H ion and the monovalent anion of the free acid in the gelatin solution, and z the concentration of the anion in combination with the protein. 7. The similarity between the variation of P.D. and the variation of the osmotic pressure, swelling, and viscosity of gelatin, and the fact that the Donnan equilibrium determines the variation in P.D. raise the question whether or not the variations of the osmotic pressure, swelling, and viscosity are also determined by the Donnan equilibrium.     

Interactions of highly charged colloidal cylinders with applications to double-stranded DNA

This paper presents new applications of the McMillan-Mayer solution theory to dispersions of highly charged colloidal cylinders in monovalent salt solutions. The thermodynamic solution properties are given in terms of the virial expansions relating to a Donnan membrane equilibrium. General expressions are derived for the second Donnan pressure virial coefficient B₂ and for the first two salt distribution coefficients A₁ and A₂. The effect of electric interactions is represented as an increased effective diameter d_B or d_A of the colloidal cylinder. This yields the simple excluded volume expressions B₂ = πd_BL²/4 and A₁ = πd_A²L/4 for hard cylinders of length L and diameter d_B and d_A, respectively. The coefficient A₂ is derived from the dependence of B₂ on the salt concentration. Computations are made for double-stranded DNA in sodium chloride solutions with the DNA model developed in the preceding paper: a uniformly charged cylinder, with size and charge consistent with transport experiments, and surrounded by a Gouy double layer. In 1–0.005M sodium chloride solutions d_B is found to vary from 29 Å to about 220 Å, and d_A from 30 Å to about 170 Å, with little sensitivity to the uncertainties in the kinetic diameter d ≈ 24 Å and the experimental ζ potentials of DNA. Corresponding results predicted by the classical Donnan theory are 6–167 times too high for B₂. Values of A₂ are relatively small, in line with the expected rapid convergence of the virial expansion for the salt distribution. This is consistent with a phase transition from random to parallel orientation of the cylinders predicted first by Onsager for hard cylinders on the basis of B₂, but not yet observed for DNA in simple salt solutions.     

THE KINETICS OF EXOSMOSIS OF WATER FROM LIVING CELLS

1. The rate of exosmosis of water was studied in unfertilized Arbacia eggs, in order to bring out possible differences between the kinetics of exosmosis and endosmosis. 2. Exosmosis, like endosmosis, is found to follow the equation See PDF for Equation, in which a is the total volume of water that will leave the cell before osmotic equilibrium is attained, x is the volume that has already left the cell at time t, and k is the velocity constant. 3. The velocity constants of the two processes are equal, provided the salt concentration of the medium is the same. 4. The temperature characteristic of exosmosis, as of endomosis, is high. 5. It is concluded that the kinetics of exosmosis and endosmosis of water in these cells are identical, the only difference in the processes being in the direction of the driving force of osmotic pressure.     

ELECTRICAL CHARGES OF COLLOIDAL PARTICLES AND ANOMALOUS OSMOSIS

1. It has been shown in previous publications that when solutions of different concentrations of salts are separated by collodion-gelatin membranes from water, electrical forces participate in addition to osmotic forces in the transport of water from the side of the water to that of the solution. When the hydrogen ion concentration of the salt solution and of the water on the other side of the membrane is the same and if both are on the acid side of the isoelectric point of gelatin (e.g. pH 3.0), the electrical transport of water increases with the valency of the cation and inversely with the valency of the anion of the salt in solution. Moreover, the electrical transport of water increases at first with increasing concentration of the solution until a maximum is reached at a concentration of about M/32, when upon further increase of the concentration of the salt solution the transport diminishes until a concentration of about M/4 is reached, when a second rise begins, which is exclusively or preeminently the expression of osmotic forces and therefore needs no further discussion. 2. It is shown that the increase in the height of the transport curves with increase in the valency of the cation and inversely with the increase in the valency of the anion is due to the influence of the salt on the P.D. (E) across the membrane, the positive charge of the solution increasing in the same way with the valency of the ions mentioned. This effect on the P.D. increases with increasing concentration of the solution and is partly, if not essentially, the result of diffusion potentials. 3. The drop in the transport curves is, however, due to the influence of the salts on the P.D. (ε) between the liquid inside the pores of the gelatin membrane and the gelatin walls of the pores. According to the Donnan equilibrium the liquid inside the pores must be negatively charged at pH 3.0 and this charge is diminished the higher the concentration of the salt. Since the electrical transport is in proportion to the product of E x ε and since the augmenting action of the salt on E begins at lower concentrations than the depressing action on ε, it follows that the electrical transport of water must at first rise with increasing concentration of the salt and then drop. 4. If the Donnan equilibrium is the sole cause for the P.D. (ε) between solid gelatin and watery solution the transport of water through collodion-gelatin membranes from water to salt solution should be determined purely by osmotic forces when water, gelatin, and salt solution have the hydrogen ion concentration of the isoelectric point of gelatin (pH = 4.7). It is shown that this is practically the case when solutions of LiCl, NaCl, KCl, MgCl₂, CaCl₂, BaCl₂, Na₂SO₄, MgSO₄ are separated by collodion-gelatin membranes from water; that, however, when the salt has a trivalent (or tetravalent?) cation or a tetravalent anion a P.D. between solid isoelectric gelatin and water is produced in which the wall assumes the sign of charge of the polyvalent ion. 5. It is suggested that the salts with trivalent cation, e.g. Ce(NO₃)₃, form loose compounds with isoelectric gelatin which dissociate electrolytically into positively charged complex gelatin-Ce ions and negatively charged NO₃ ions, and that the salts of Na₄Fe(CN)₆ form loose compounds with isoelectric gelatin which dissociate electrolytically into negatively charged complex gelatin-Fe(CN)₆ ions and positively charged Na ions. The Donnan equilibrium resulting from this ionization would in that case be the cause of the charge of the membrane.     

High osmotic stress behavior of hyaluronate and heparin.

Using polyethylene glycol and dextran as osmotic stressing agents, the concentrations of hyaluronate and heparin were measured as a function of osmotic pressure II over the range of 0.03 to nearly 50 atmospheres. The experimental results were analyzed in terms of the Donnan osmotic pressure, the virial expansion, and Flory's first neighbor interaction parameter. In addition, II was looked at as a function of the reciprocal cube root of the concentration, which represents an average intermonomer spacing at high concentrations. The decay lengths in the so-called hydration region were found to be around 2.6 A and negligibly salt dependent. In the electrostatically dominated region the decay lengths were found to be dependent on the ionic strength, but not simply so. The osmotic compressibilities were also calculated, and were compared to compressibility data of corneal stroma and articular cartilage. These latter compressibilities were close to those for the pure hyaluronate and heparin, strengthening the evidence that glycosaminoglycans (GAGs) are largely responsible for connective tissue compressibility. Higher compressibilities for previously reported GAG data is thought to be related to the protein content of those samples.     

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.     

THE INFLUENCE OF ELECTROLYTES ON THE SOLUTION AND PRECIPITATION OF CASEIN AND GELATIN

1. Colloids have been divided into two groups according to the ease with which their solutions or suspensions are precipitated by electrolytes. One group (hydrophilic colloids), e.g., solutions of gelatin or crystalline egg albumin in water, requires high concentrations of electrolytes for this purpose, while the other group (hydrophobic colloids) requires low concentrations. In the latter group the precipitating ion of the salt has the opposite sign of charge as the colloidal particle (Hardy''s rule), while no such relation exists in the precipitation of colloids of the first group. 2. The influence of electrolytes on the solubility of solid Na caseinate, which belongs to the first group (hydrophilic colloids), and of solid casein chloride which belongs to the second group (hydrophobic colloids), was investigated and it was found that the forces determining the solution are entirely different in the two cases. The forces which cause the hydrophobic casein chloride to go into solution are forces regulated by the Donnan equilibrium; namely, the swelling of particles. As soon as the swelling of a solid particle of casein chloride exceeds a certain limit it is dissolved. The forces which cause the hydrophilic Na caseinate to go into solution are of a different character and may be those of residual valency. Swelling plays no rôle in this case, and the solubility of Na caseinate is not regulated by the Donnan equilibrium. 3. The stability of solutions of casein chloride (requiring low concentrations of electrolytes for precipitation) is due, first, to the osmotic pressure generated through the Donnan equilibrium between the casein ions tending to form an aggregate, whereby the protein ions of the nascent micellum are forced apart again; and second, to the potential difference between the surface of a micellum and the surrounding solution (also regulated by the Donnan equilibrium) which prevents the further coalescence of micella already formed. This latter consequence of the Donnan effect had already been suggested by J. A. Wilson. 4. The precipitation of this group of hydrophobic colloids by salts is due to the diminution or annihilation of the osmotic pressure and the P.D. just discussed. Since low concentrations of electrolytes suffice for the depression of the swelling and P.D. of the micella, it is clear why low concentrations of electrolytes suffice for the precipitation of hydrophobic colloids, such as casein chloride. 5. This also explains why only that ion of the precipitating salt is active in the precipitation of hydrophobic colloids which has the opposite sign of charge as the colloidal ion, since this is always the case in the Donnan effect. Hardy''s rule is, therefore, at least in the precipitation of casein chloride, only a consequence of the Donnan effect. 6. For the salting out of hydrophilic colloids, like gelatin, from watery solution, sulfates are more efficient than chlorides regardless of the pH of the gelatin solution. Solution experiments lead to the result that while CaCl₂ or NaCl increase the solubility of isoelectric gelatin in water, and the more, the higher the concentration of the salt, Na₂SO₄ increases the solubility of isoelectric gelatin in low concentrations, but when the concentration of Na₂SO₄ exceeds M/32 it diminishes the solubility of isoelectric gelatin the more, the higher the concentration. The reason for this difference in the action of the two salts is not yet clear. 7. There is neither any necessity nor any room for the assumption that the precipitation of proteins is due to the adsorption of the ions of the precipitating salt by the colloid.     

Ionic and osmotic equilibria of human red blood cells treated with nystatin

Human red blood cells have been incubated in the presence of nystatin, which allows Na and K, as well as Cl and pH to equilibrate rapidly when cell volume is set with external impermeant sucrose. The intracellular mean ionic activity coefficients, relative to values in the extracellular solution, for KCl and NaCl are 1.01 +/- 0.02 and 0.99 +/- 0.02 (SD, n = 10), respectively, and are independent of external pH, pH o, and of [sucrose]o. With nystatin the dependence of red cell volume on [sucrose]o deviates from ideal osmotic behavior by as much as a factor of three. A virial equation for the osmotic coefficient, phi, of human hemoglobin, Hb, accounts for the cell volumes, and is the same as that which describes Adair's measurements of phi Hb for Hb isolated from sheep and ox bloods. In the presence of nystatin the slope of the acid-base titration curve of the cells is independent of cell volume, implying that the charge on impermeant cellular solutes is independent of Hb concentration at constant pH. By modifying the Jacobs-stewart equations (1947. J. Cell. Comp. Physiol. 30: 79--103) with the osmotic coefficients of Hb and of salts, a nonideal thermodynamic model has been devised which predicts equilibrium Donnan ratios and red cell volume from the composition of the extracellular solution and from certain parameters of the cells. In addition to accounting for the dependence of cell volume on osmotic pressure, the model also describes accurately the dependence of Donnan ratios and cell volumes on pHo either in the presence or absence of nystatin.     

Osmotic Pressure of DNA Solutions and Effective Diameter of the Double Helix

Abstract

A simple osmometer with nuclear filters (polymer films with pores of a preset diameter) were used to measure the osmotic pressure of Col El plasmid DNA solutions in the concentration range of 1–4 mg/ml DNA. Linear and open circular DNA forms proved to have the same osmotic pressure within the experimental accuracy. The results of the measurements were used for calculating the second virial coefficient A ₂ of the solution of DNA segments and the effective chain diameter d _eff in the ionic strength range of 10^?2-0.1 M, As the ionic strength is lowered from 0.1 to 10^?2 M the effective diameter of DNA increases from 80 to 220 A. The results are in rather good agreement with theory and with other experimental data.     

Physiological Control of Chloride Transport in Chara corallina: II. THE ROLE OF CHLORIDE AS A VACUOLAR OSMOTICUM

The extent to which Cl⁻ is replaceable as the major anionic constituent of the vacuole of Chara corallina was investigated. It was found that external Cl⁻ is not essential in order for nongrowing cells to increase internal osmotic pressure. After growth of cells in low (9 micromolar) Cl⁻, the vacuolar Cl⁻ concentration is one-half that of cells grown at normal external Cl⁻ concentration (850 micromolar). In contrast, both internal osmotic pressure and total concentration of the major cations, K⁺ and Na⁺, in the same cells were found to be only slightly sensitive to the external Cl⁻ concentration. Thus, it is proposed that, at limiting external Cl⁻ concentration, the cell is able to transport or synthesize another anion for vacuolar use rather than utilize a neutral solute.     

The Donnan Equilibrium: A Theoretical Study of the Effects of Interionic Forces

We investigate the conditions under which nonideality in solution influences the Donnan equilibrium. Of the various parameters that characterize this equilibrium, the osmotic pressure established across the Donnan membrane is found to be particularly sensitive to intermolecular interactions between the diffusible and nondiffusible ionic species. Under physiologically appropriate conditions, we find that it is almost never valid to use Debye-Hückel theory to calculate ionic activities: it is important to take proper account of ion size. When the diffusible species is a 1-1 electrolyte, this can be done using the mean spherical approximation (MSA) for a mixture of ions of different diameters. For 2-2, or higher-valent, electrolytes one should also include the effects of the second ionic virial coefficient, which the MSA omits.     

Measurement of grouped intracellular solute osmotic virial coefficients

Models of cellular osmotic behaviour depend on thermodynamic solution theories to calculate chemical potentials in the solutions inside and outside the cell. These solutions are generally thermodynamically non-ideal under cryobiological conditions. The molality-based Elliott et al. form of the multi-solute osmotic virial equation is a solution theory which has been demonstrated to provide accurate predictions in cryobiological solutions, accounting for the non-ideality of these solutions using solute-specific thermodynamic parameters called osmotic virial coefficients. However, this solution theory requires as inputs the exact concentration of every solute in the solution being modeled, which poses a problem for the cytoplasm, where such detailed information is rarely available. This problem can be overcome by using a grouped solute approach for modeling the cytoplasm, where all the non-permeating intracellular solutes are treated as a single non-permeating “grouped” intracellular solute. We have recently shown (Zielinski et al., J Physical Chemistry B, 2017) that such a grouped solute approach is theoretically valid when used with the Elliott et al. model, and Ross-Rodriguez et al. (Biopreservation and Biobanking, 2012) have previously developed a method for measuring the cell type-specific osmotic virial coefficients of the grouped intracellular solute. However, the Ross-Rodriguez et al. method suffers from a lack of precision, which—as we demonstrate in this work—can severely impact the accuracy of osmotic model predictions under certain conditions. Thus, we herein develop a novel method for measuring grouped intracellular solute osmotic virial coefficients which yields more precise values than the existing method and then apply this new method to measure these coefficients for human umbilical vein endothelial cells.     

Water balance and the mantle cavity fluid of Nucella lapillus(L.) (Mollusca: Prosobranchia)

When uncovered by the tide Nucella lapillus (L.) retains fluid in the mantle cavity which accounts for ≈ 39% of the total water content of the attached animal. This extra-corporeal fluid reservoir retained in the mantle cavity has been investigated in relation to desiccation. Volume changes of mantle cavity fluid (m.c.f.) and concentration changes in Cl^?, Na⁺ and total osmotic pressure of m.c.f. and blood, suggest that the m.c.f. reduces the full effects of desiccation on the animal by restricting those effects to the external compartment. The blood of Nucella living in normal sea water was found to be hypo-osmotic and an hypothesis is presented which links this to the rôle of the m.c.f. during desiccation.     

The Effect of Inorganic Salts on the Senescence of Dianthus caryophyllus Flowers

Certain inorganic salts like KNO₃, KCl, K₂SO₄, Ca(NO₃)₂ and NH₄NO₃ extend longevity of cut carnation flowers. The effect of KNO₃ was studied in some detail. There is an osmotic adjustment in response to KNO₃ treatment. The osmotic concentration change occurred in the external as well as in the internal compartments. The osmotic concentration change in the external compartment is well correlated with extension of longevity. The effect of KNO₃ on the sensitivity to ethylene, and its significance in delaying senescence is discussed.     

The Role of Glycerol in the Osmotic Regulation of the Halophilic Alga Dunaliella parva

Dunaliella parva, a green halophilic alga, was found to accumulate very large amounts of intracellular glycerol. Through measurements of the intracellular volume the internal concentration of glycerol was calculated and found to be around 2.1 m in cells cultured in 1.5 m NaCl. When the extracellular salt concentration of an algal suspension was increased or decreased, the intracellular glycerol varied accordingly, reaching its new osmotic equilibrium after about 90 minutes. Since no leakage of intracellular glycerol was observed above 0.6 m NaCl, these alterations in glycerol content are interpreted as due to metabolic formation and degradation of intracellular glycerol. The above results indicate the existence of a new type of algal osmoregulation, in which the osmotic balance depends on the synthesis or degradation of intracellular glycerol in response to the external salt concentration.     

DONNAN EQUILIBRIUM AND THE PHYSICAL PROPERTIES OF PROTEINS : II. OSMOTIC PRESSURE.

1. It had been shown in previous publications that the osmotic pressure of a 1 per cent solution of a protein-acid salt varies in a characteristic way with the hydrogen ion concentration of the solution, the osmotic pressure having a minimum at the isoelectric point, rising steeply with a decrease in pH until a maximum is reached at pH of 3.4 or 3.5 (in the case of gelatin and crystalline egg albumin), this maximum being followed by a steep drop in the osmotic pressure with a further decrease in the pH of the gelatin or albumin solution. In this paper it is shown that (aside from two minor discrepancies) we can calculate this effect of the pH on the osmotic pressure of a protein-acid salt by assuming that the pH effect is due to that unequal distribution of crystalloidal ions (in particular free acid) on both sides of the membrane which Donnan''s theory of membrane equilibrium demands. 2. It had been shown in preceding papers that only the valency but not the nature of the ion (aside from its valency) with which a protein is in combination has any effect upon the osmotic pressure of the solution of the protein; and that the osmotic pressure of a gelatin-acid salt with a monovalent anion (e.g. Cl, NO₃, acetate, H₂PO₄, HC₂O₄, etc.) is about twice or perhaps a trifle more than twice as high as the osmotic pressure of gelatin sulfate where the anion is bivalent; assuming that the pH and gelatin concentrations of all the solutions are the same. It is shown in this paper that we can calculate with a fair degree of accuracy this valency effect on the assumption that it is due to the influence of the valency of the anion of a gelatin-acid salt on that relative distribution of the free acid on both sides of the membrane which Donnan''s theory of membrane equilibrium demands. 3. The curves of the observed values of the osmotic pressure show two constant minor deviations from the curves of the calculated osmotic pressure. One of these deviations consists in the fact that the values of the ascending branch of the calculated curves are lower than the corresponding values in the curves for the observed osmotic pressure, and the other deviation consists in the fact that the drop in the curves of calculated values occurs at a lower pH than the drop in the curves of the observed values.     

Evaluation of second osmotic virial coefficients from molecular simulation following scaled-particle theory

ABSTRACT

We report a scaled particle theory-based method for evaluation of second osmotic virial coefficients from molecular simulations of dilute species in solution. In this method, we evaluate the work associated with growing a cavity in solution that is perfectly permeable to the solvent but is completely impermeable to the solutes, thereby establishing an osmotic stress between the cavity interior and exterior. Extrapolating our results to determine the solute concentration in contact with a cavity with an infinite radius, we are able to evaluate the solute osmotic pressure and second osmotic virial coefficient. A finite size correction is introduced to account for the impact of effectively concentrating the solutes in the periphery of the simulation box with increasing cavity size. We demonstrate the utility of the proposed method by evaluating second osmotic virial coefficients for methane in water as a function of temperature. The approach proposed here provides a physically transparent route for calculation of second osmotic virial coefficients by direct interrogation of simulation configurations without having to explicitly evaluate the long-range integral over solute-solute correlations required following McMillan-Mayer theory.     

A fixed charge model of the transverse tubular system of frog sartorius

Volume changes of the transverse tubular system (T system) of frog sartorius in different solutions can be explained by a model which assumes fixed negative charges in the T system lumen, an open T system mouth, and a Donnan equilibrium between the T system and external solution. The T system volume is regulated by the osmotic pressure difference between the lumen and external solution, as well as by constraining forces whose nature is as yet unclear. The decreased swelling tendency produced by hypotonic solutions and increased tendency produced by some hypertonic solutions are ascribed to changes in the pressure constraint from the sarcoplasm. Fixed charge concentration was estimated tentatively from swelling and resistivity data to be between 0.1 and 0.4 M.