Diffusion in colloidal media

When the molecules of a solute diffuse through a medium containing large colloidal particles, which absorb the diffusing molecules, the latter are transported in the diffusion flow not as free molecules, but as absorbtion compounds: solute+colloid. When the colloidal particle is much larger than the molecule of the solute, and has therefore a much smaller mobility, this results in a reduction of the apparent diffusion coefficient for the solute. The biological implications of this are discussed.     

The physical origin of the low solubility of nonpolar solutes in water

Elementary but general statistical-mechanical relations are derived that relate the thermodynamic properties of the dissolution process to those of the pure solvent. A number of conclusions are drawn from qualitative arguments that these relations suggest. These include the following: (1) The low solubility of nonpolar solutes in water arises not from the fact that water molecules can form hydrogen bonds, but rather from the fact that they are small in size. (2) The large entropy decrease attending the transfer of an inert solute from a nonaqueous solvent to water is largely due to the decrease in entropy of the nonaqueous solvent as the solvent–solvent interaction is restored on removal of the solute from it. (3) It is improper to use values of thermodynamic quantities obtained from small-molecule transfer studies for those that involve macromolecular folding and interaction.     

Does Flory–Huggins theory help in interpreting solute partitioning experiments?

The development of Flory–Huggins (FH) theory is reviewed, particularly with regard to the molecular significance of the interaction parameter that scales the contact interaction of solute and solvent. The chemical potential given by FH theory for an “idealute” solute is then compared with that provided by a more general, statistical thermodynamic approach. It is found that the FH contact term does not directly correspond to the solvation free energy. The significance of this result for the interpretation of free energies of transfer of a solute from one solvent to another is examined. It is shown that neither the earlier recommended standard free energy change for the process (using the infinitely dilute reference state, mole fraction units) nor the recently recommended FH-corrected standard free energy change provides the solvation energy desired. Instead, the standard free energy using the infinitely dilute reference state and molarity units, as long advocated by Ben-Naim, provides the desired solvation free energy. Correction of extant values, based on mole fraction units, is easily made. However, application of such results to problems of protein folding is not straightforward. © 1994 John Wiley & Sons, Inc.     

A molecular dynamics simulation study of the effect of water–graphene interaction on the properties of confined water

The role of water in determining the structure and stability of biomacromolecules has been well studied. In this work, molecular dynamics simulations have been applied to investigate the effect of surface hydrophobicity on the structure and dynamics of water confined between graphene surfaces. In order to evaluate this effect, we apply various attractive/repulsive water–graphene interaction potentials (hydrophobicity). The properties of confined water are studied by applying a purely repulsive interaction potential between water–graphene (modelled as a repulsive r^?12 potential) and repulsive–attractive forces (modelled as an LJ(12-6) potential). Compared to the case of a purely repulsive graphene–water potential, the inclusion of repulsive–attractive forces leads to formation of sharp peaks for density and the number of hydrogen bonds. Also, it was found that repulsive–attractive graphene–water potential caused slower hydrogen bonds dynamics and restricted the diffusion coefficient of water. Consequently, it was found that hydrogen bond breakage and formation rate with the repulsive r^?12 potential model, will increase compared to the corresponding water confined with the LJ(12-6) potential.     

Solute concentration effect on osmotic reflection coefficient

A theory for the effect of concentration on osmotic reflection coefficient, correct to first order, was developed at the molecular level by considering the effect of solute-solute interactions on solute concentration and the fluid stress tensor within a solvent-filled pore. The solvent was modeled as a continuous fluid and potential energies between solute molecules and the pore wall were assumed to be pairwise additive. Although the theory is more general, calculations are presented only for excluded volume effects (hard-sphere for solute, hard-wall for pore). The relationship between the first-order concentration effect and the infinite dilution value of reflection coefficient appears to be geometry independent. The theory is discussed in light of experimental studies of osmotic flow that have recently appeared in the literature.     

Diffusion constant of K+ inside Gramicidin A: a comparative study of four computational methods

The local diffusion constant of K(+) inside the Gramicidin A (GA) channel has been calculated using four computational methods based on molecular dynamics (MD) simulations, specifically: Mean Square Displacement (MSD), Velocity Autocorrelation Function (VACF), Second Fluctuation Dissipation Theorem (SFDT) and analysis of the Generalized Langevin Equation for a Harmonic Oscillator (GLE-HO). All methods were first tested and compared for K(+) in bulk water--all predicted the correct diffusion constant. Inside GA, MSD and VACF methods were found to be unreliable because they are biased by the systematic force exerted by the membrane-channel system on the ion. SFDT and GLE-HO techniques properly unbias the influence of the systematic force on the diffusion properties and predicted a similar diffusion constant of K(+) inside GA, namely, ca. 10 times smaller than in the bulk. It was found that both SFDT and GLE-HO methods require extensive MD sampling on the order of tens of nanoseconds to predict a reliable diffusion constant of K(+) inside GA.     

Further Observations on Asymmetrical Solute Movement across Membranes

The permeability of frog skin under the influence of urea hyperosmolarity has been studied. Flux ratio asymmetry has been demonstrated again for tracer mannitol. The inhibitors DNP, CN^-, and ouabain have been used to eliminate active sodium transport and it was found that urea hyperosmolarity produces asymmetrical mannitol fluxes on frog skins having no short-circuit current. These findings suggest that flux ratio asymmetry is due to solute interaction and is unrelated to sodium transport. Studies with a synthetic membrane show clearly that bulk flow of fluid can produce a "solvent drag" effect and change flux ratios. When bulk flow is blocked and solute gradients allowed their full expression, then solute interaction "solute drag" is easily demonstrable in a synthetic system.     

An effective solvent theory connecting the underlying mechanisms of osmolytes and denaturants for protein stability

An all-atom Gō model of Trp-cage protein is simulated using discontinuous molecular dynamics in an explicit minimal solvent, using a single, contact-based interaction energy between protein and solvent particles. An effective denaturant or osmolyte solution can be constructed by making the interaction energy attractive or repulsive. A statistical mechanical equivalence is demonstrated between this effective solvent model and models in which proteins are immersed in solutions consisting of water and osmolytes or denaturants. Analysis of these studies yields the following conclusions: 1), Osmolytes impart extra stability to the protein by reducing the entropy of the unfolded state. 2), Unfolded states in the presence of osmolyte are more collapsed than in water. 3), The folding transition in osmolyte solutions tends to be less cooperative than in water, as determined by the ratio of van 't Hoff to calorimetric enthalpy changes. The decrease in cooperativity arises from an increase in native structure in the unfolded state, and thus a lower thermodynamic barrier at the transition midpoint. 4), Weak denaturants were observed to destabilize small proteins not by lowering the unfolded enthalpy, but primarily by swelling the unfolded state and raising its entropy. However, adding a strong denaturant destabilizes proteins enthalpically. 5), The folding transition in denaturant-containing solutions is more cooperative than in water. 6), Transfer to a concentrated osmolyte solution with purely hard-sphere steric repulsion significantly stabilizes the protein, due to excluded volume interactions not present in the canonical Tanford transfer model. 7), Although a solution with hard-sphere interactions adds a solvation barrier to native contacts, the folding is nevertheless less cooperative for reasons 1–3 above, because a hard-sphere solvent acts as a protecting osmolyte.     

A note on the diffusion drag forces

A formal derivation of the expression for the diffusion drag force is given. The expression involves the coefficient of diffusion of the solute through the solvent and the coefficient of diffusion which the solute would posses if it diffused through itself in the form of a gas, in the absence of the solvent.     

Optimisation of solute transport in dialysers using a three-dimensional finite volume model

Dialyser manufacturers only provide limited information about mass removal under well-defined flow and solute conditions in commercially available dialysers for hemodialysis. This computational study aimed at assessing the solute transport efficiency in a dialyser for different geometries (fiber lengths and diameters).

A three-dimensional finite volume model of a single fiber in a high flux polysulphone dialyser (Fresenius F60) was developed. Different equations describe blood and dialysate flow (Navier–Stokes), radial filtration flow (Darcy) and solute transport (convection–diffusion). Fluid and membrane properties were derived from in vitro and in vivo tests as well as from literature data. Urea (MW60) was used as marker to simulate small molecule removal, while middle molecule transport was modelled using vitamin B12 (MW1355) and inulin (MW5200). Keeping the fluid velocity in a single fiber constant, fiber diameter and length were changed in a wide range for evaluation of solute removal efficiency. Clearances were found enhanced by 13% (urea), 50% (vitamin B12) and 89% (inulin) for a fiber twice as long as a standard one and by 5.5% (vitamin B12) and 21% (inulin) for a fiber diameter of 150 μm instead of 200 μm. The impact of fiber dimensions was more pronounced for the middle molecules compared to urea.     

Percolation Transition in the Parallel Hard-cube Model Fluid

Abstract

Pressure and self-diffusion calculations for a model fluid system of parallel hard cubes are reported. When viewed alongside equations of state incorporating the known coefficients in the virial expansion (b ₂ to b ₇), a weak phase change is postulated around 1/4 close-packing. Changes in behaviour are also seen at the same density for the self-diffusion coefficient and an associated single-particle free volume. It is conjectured that a transition may be identifiable with the low-density percolation transition that occurs in all hard-core fluids when the single particle configurational volume becomes extensive. If the hard-sphere model were to behave similarly, the observations may have implications for the general development of liquid-state theory.     

The temperature-dependent swelling of elastin

It is suggested that the temperature-dependent swelling behavior of water-swollen elastin is due entirely to the interaction of the numerous nonpolar groups in the elastin protein wiht the aqueous swelling solvent (i.e., ahydrophobic interaction). Flory-Rehner theory for network swelling was used to test this hypothesis. Calculated values for the solvent–polymer interaction parameter, χ1, derived from swelling data indicate that water is a very poor solvent for elastin at all temperatures over the range 0–70° C. Comparison of the calculated _χ1 values with theoretical values for the free energy of interaction of nonpolar solutes and water strongly suggests that the swelling behavior of elastin can be attributed quantitatively to hydrophobic interactions. The implications of these results for the structure and elastic mechanism of elastin are discussed.     

Secondary structure and dynamics of an intrinsically unstructured linker domain

The transient secondary structure and dynamics of an intrinsically unstructured linker domain from the 70 kDa subunit of human replication protein A was investigated using solution state NMR. Stable secondary structure, inferred from large secondary chemical shifts, was observed for a segment of the intrinsically unstructured linker domain when it is attached to an N-terminal protein interaction domain. Results from NMR relaxation experiments showed the rotational diffusion for this segment of the intrinsically unstructured linker domain to be correlated with the N-terminal protein interaction domain. When the N-terminal domain is removed, the stable secondary structure is lost and faster rotational diffusion is observed. The large secondary chemical shifts were used to calculate phi and psi dihedral angles and these dihedral angles were used to build a backbone structural model. Restrained molecular dynamics were performed on this new structure using the chemical shift based dihedral angles and a single NOE distance as restraints. In the resulting family of structures a large, solvent exposed loop was observed for the segment of the intrinsically unstructured linker domain that had large secondary chemical shifts.     

Fractionation of macromolecules in an alternating transverse electric field: simulation of the method

An electric field of alternating polarity applied in a direction transverse to the direction of solute transport is used as the basis of a method for the separation of biological macromolecules. The method derives directly from the ability of an electric field to induce movement of a charged macromolecule and from the physics of laminar fluid flow; no adsorptive immobile phase component is involved.

The method is simulated by computer for the case of solute molecules in a solvent flowing through a narrow chamber of recta generates an electric field orthogonal to the direction of solvent flow. Solute molecules repetitively traverse the solvent channel at rates determined by their electrophoretic mobility. During the transit across the channel, solute molecules are transported in the direction of solvent flow; at the channel wall, solvent velocity is negligible and solute transport is limited to that provided by transient diffusion into a mobile solvent zone. Molecules of different intrinsic electrophoretic mobility are separated.

The computer model was used to illustrate the process and to demonstrate the ‘tunability’ of the method as a function of the oscillation frequency and voltage wave form. Because of this tunability, a single instrument can function as the equivalent of several different chromatographic systems. Because fractionation is effected by direct physicochemical phenomena rather than via interaction with chromatographic sites, variations in fractionation results arising from formation of polymers for gel electrophoresis, packing of chromatography columns, or deterioration of columns with use are avoided. This method may be of particular use for the purification of nucleic acid fragments and for the analysis of protei: nucleic acid interactions.     

The Limitations of an Exclusively Colloidal View of Protein Solution Hydrodynamics and Rheology

Proteins are complex macromolecules with dynamic conformations. They are charged like colloids, but unlike colloids, charge is heterogeneously distributed on their surfaces. Here we overturn entrenched doctrine that uncritically treats bovine serum albumin (BSA) as a colloidal hard sphere by elucidating the complex pH and surface hydration-dependence of solution viscosity. We measure the infinite shear viscosity of buffered BSA solutions in a parameter space chosen to tune competing long-range repulsions and short-range attractions (2 mg/mL ≤ [BSA] ≤ 500 mg/mL and 3.0 ≤ pH ≤ 7.4). We account for surface hydration through partial specific volume to define volume fraction and determine that the pH-dependent BSA intrinsic viscosity never equals the classical hard sphere result (2.5). We attempt to fit our data to the colloidal rheology models of Russel, Saville, and Schowalter (RSS) and Krieger-Dougherty (KD), which are each routinely and successfully applied to uniformly charged suspensions and to hard-sphere suspensions, respectively. We discover that the RSS model accurately describes our data at pH 3.0, 4.0, and 5.0, but fails at pH 6.0 and 7.4, due to steeply rising solution viscosity at high concentration. When we implement the KD model with the maximum packing volume fraction as the sole floating parameter while holding the intrinsic viscosity constant, we conclude that the model only succeeds at pH 6.0 and 7.4. These findings lead us to define a minimal framework for models of crowded protein solution viscosity wherein critical protein-specific attributes (namely, conformation, surface hydration, and surface charge distribution) are addressed.     

Effect of cut-off distance used in molecular dynamics simulations on fluid properties

The effect of cut-off distance used in molecular dynamics (MD) simulations on fluid properties was studied systematically in both canonical (NVT) and isothermal–isobaric (NPT) ensembles. Results show that the cut-off distance in the NVT ensemble plays little role in determining the equilibrium structure of fluid if the ensemble has a high density. However, pressures calculated in the same NVT ensembles strongly depend on the cut-off distance used. In the NPT ensemble, cut-off distance plays a key role in determining fluid equilibrium structure, density and self-diffusion coefficient. The characteristic of the radial distribution function of fluid in NPT ensembles depending on the cut-off distance used in MD simulations means that the WCA theory (a perturbation theory developed by Weeks, Chandler and Andersen) is not suitable for NPT ensembles because the assumption (the effect of the attractive force in determining the liquid structure is negligible) used in the WCA theory is not valid. The dependence of fluid properties on the cut-off distance also indicates that using the WCA potential (the repulsive part of the intermolecular potential proposed in the WCA theory) to calculate fluid transport in heterogeneous systems could lead to significant errors or incorrect results.     

Excluded volume in solvation: sensitivity of scaled-particle theory to solvent size and density

Changes in solvent environment greatly affect macromolecular structure and stability. To investigate the role of excluded volume in solvation, scaled-particle theory is often used to calculate delta G(tr)(ev), the excluded-volume portion of the solute transfer free energy, delta G(tr). The inputs to SPT are the solvent radii and molarities. Real molecules are not spheres. Hence, molecular radii are not uniquely defined and vary for any given species. Since delta G(tr)(ev) is extremely sensitive to solvent radii, uncertainty in these radii causes a large uncertainty in delta G(tr)(ev)-several kcal/mol for amino acid solutes transferring from water to aqueous mixtures. This uncertainty is larger than the experimental delta G(tr) values. Also, delta G(tr)(ev) can be either positive or negative. Adding neutral crowding molecules may not necessarily reduce solubility. Lastly, delta G(tr)(ev) is very sensitive to solvent density, rho. A few percent error in rho may even cause qualitative deviations in delta G(tr)(ev). For example, if rho is calculated by assuming the hard-sphere pressure to be constant, then delta G(tr)(ev) values and uncertainties are now only tenths of a kcal/mol and are positive. Because delta G(tr)(ev) values calculated by scaled-particle theory are strongly sensitive to solvent radii and densities, determining the excluded-volume contribution to transfer free energies using SPT may be problematic.     

The Limitations of an Exclusively Colloidal View of Protein Solution Hydrodynamics and Rheology

Proteins are complex macromolecules with dynamic conformations. They are charged like colloids, but unlike colloids, charge is heterogeneously distributed on their surfaces. Here we overturn entrenched doctrine that uncritically treats bovine serum albumin (BSA) as a colloidal hard sphere by elucidating the complex pH and surface hydration-dependence of solution viscosity. We measure the infinite shear viscosity of buffered BSA solutions in a parameter space chosen to tune competing long-range repulsions and short-range attractions (2 mg/mL ≤ [BSA] ≤ 500 mg/mL and 3.0 ≤ pH ≤ 7.4). We account for surface hydration through partial specific volume to define volume fraction and determine that the pH-dependent BSA intrinsic viscosity never equals the classical hard sphere result (2.5). We attempt to fit our data to the colloidal rheology models of Russel, Saville, and Schowalter (RSS) and Krieger-Dougherty (KD), which are each routinely and successfully applied to uniformly charged suspensions and to hard-sphere suspensions, respectively. We discover that the RSS model accurately describes our data at pH 3.0, 4.0, and 5.0, but fails at pH 6.0 and 7.4, due to steeply rising solution viscosity at high concentration. When we implement the KD model with the maximum packing volume fraction as the sole floating parameter while holding the intrinsic viscosity constant, we conclude that the model only succeeds at pH 6.0 and 7.4. These findings lead us to define a minimal framework for models of crowded protein solution viscosity wherein critical protein-specific attributes (namely, conformation, surface hydration, and surface charge distribution) are addressed.     

Static compression is associated with decreased diffusivity of dextrans in cartilage explants

The chondrocytes of adult articular cartilage rely upon transport phenomena within their avascular extracellular matrix for many biological activities. Therefore, changes in matrix structure which influence cytokine transport parameters may be an important mechanism involved in the chondrocyte response to tissue compression. With this hypothesis in mind, partitioning and diffusion of 3-, 10-, and 40-kDa dextrans conjugated to tetramethylrhodamine, and 430-Da tetramethylrhodamine itself, were measured within statically compressed bovine articular cartilage explants using a novel experimental apparatus and desorption fluorescence method. Partitioning and diffusion were examined as functions of solute molecular weight and matrix proteoglycan density, and diffusion was measured versus static compression up to 35% volumetric strain. In general, partition coefficients and diffusivities were found to decrease with increasing solute molecular weight. In addition, for a given solute, diffusivities decreased significantly with increasing static compression. Results therefore suggest a possible role for transport limitations of relatively large molecular weight solutes within the extracellular matrix in mediating the biological response of chondrocytes to cartilage compression.     

Hydration effects on the electrostatic potential around tuftsin

The electrostatic potential and component dielectric constants from molecular dynamics (MD) trajectories of tuftsin, a tetrapeptide with the amino acid sequence Thr–Lys–Pro–Arg in water and in saline solution are presented. The results obtained from the analysis of the MD trajectories for the total electrostatic potential at points on a grid using the Ewald technique are compared with the solution to the Poisson–Boltzmann (PB) equation. The latter was solved using several sets of dielectric constant parameters. The effects of structural averaging on the PB results were also considered. Solute conformational mobility in simulations gives rise to an electrostatic potential map around the solute dominated by the solute monopole (or lowest order multipole). The detailed spatial variation of the electrostatic potential on the molecular surface brought about by the compounded effects of the distribution of water and ions close to the peptide, solvent mobility, and solute conformational mobility are not qualitatively reproducible from a reparametrization of the input solute and solvent dielectric constants to the PB equation for a single structure or for structurally averaged PB calculations. Nevertheless, by fitting the PB to the MD electrostatic potential surfaces with the dielectric constants as fitting parameters, we found that the values that give the best fit are the values calculated from the MD trajectories. Implications of using such field calculations on the design of tuftsin peptide analogues are discussed. © 1999 John Wiley & Sons, Inc. Biopoly 50: 133–143, 1999