Molecular dynamics simulation study of the static and dynamic properties of a model colloidal suspension with explicit solvent

Molecular dynamics simulation was used to study a colloidal suspension with explicit solvent to determine how inclusion of the solvent affects the structure and dynamics of the system. The solute was modelled as a hard-core particle enclosed in a Weeks–Chandler–Andersen (WCA) potential shell, while the solvent was modelled as a simple WCA fluid. We found that when the solute–solvent interaction included a hard core equal to half of the solute hard-core diameter, large depletion effects arose, leading to an effective attraction and large deviations from hard-sphere structure for the colloidal component. It was found that these effects could be eliminated by reducing the hard-core distance parameter in the solute–solvent interaction, thus allowing the solvent to penetrate closer to the colloidal particles. Three different values for the solute–solvent hard-core parameter were systematically studied by comparing the static structure factor and radial distribution function to the predictions of the Percus–Yevick theory for hard spheres. When the optimal value of the solute–solvent hard-core interaction parameter was found, this model was then used to study the dynamical behaviour of the colloidal suspension. This was done by first measuring the velocity autocorrelation function (VACF) over a large range of packing fractions. We found that this model predicted the sign of the long-time tail in the VACF in agreement with experimental values, something that single component hard-sphere systems have failed to do. The intermediate scattering functions at low wavevector were briefly studied to determine their behaviour in a dilute system. It was found that they could be modelled using a simple diffusion equation with a wavevector independent diffusion coefficient, making this model an excellent analogue of experimentally studied hard-sphere colloids.     

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.     

Convective diffusion in parallel flow fields

Laminar motion of two viscous incompressible fluids through each other is treated for two cases: flow along the axis of a circular cylinder, and flow between parallel flat plates. Motion of either fluid entails that of the other. Regarding one fluid as a solvent, the other as a solute, and supposing the system to have ends impermeable to the former, it is found that the solvent streams with the solute down the center of the system, to return in the opposite direction out nearer the walls. Thus diffusion of a dissolved substance through a region in which the solvent is confined produces continual streaming in the latter.     

Convection and Diffusion in Charged Hydrated Soft Tissues: A Mixture Theory Approach

The extracellular matrix of cartilage is a charged porous fibrous material. Transport phenomena in such a medium are very complex. In this study, solute diffusive flux and convective flux in porous fibrous media were investigated using a continuum mixture theory approach. The intrinsic diffusion coefficient of solute in the mixture was defined and its relation to drag coefficients was presented. The effect of mechanical loading on solute diffusion in cartilage under unconfined compression with a frictionless boundary condition was analyzed numerically using the model developed. Both strain-dependent hydraulic permeability and diffusivity were considered. Analyses and results show that (1) In porous media, the convective velocity for each solute phase is different. (2) The solute convection in tissue is governed by the relative convective velocity (i.e., relative to solid velocity). (3) Under the assumption that all the frictional interactions among solutes are negligible, the relative convective velocity for α-solute phase is equal to the relative solvent velocity multiplied by its convective coefficient (H ^α) which is also known as the hindrance factor in the literature. The relationship between the convective coefficient and the relative diffusivity of solute is presented. (4) Solute concentration profile within the cartilage sample depends on the phase of dynamic compression.     

Coupling of Solute and Solvent Flows in Porous Lipid Bilayer Membranes

The present experiments were designed to evaluate coupling of water and nonelectrolyte flows in porous lipid bilayer membranes (i.e., in the presence of amphotericin B) in series with unstirred layers. Alterations in solute flux during osmosis, with respect to the flux in the absence of net water flow, could be related to two factors: first, changes in the diffusional component of solute flux referable to variations in solute concentrations at the membrane interfaces produced by osmotic flow through the unstirred layers; and second, coupling of solute and solvent flows within the membrane phase. Osmotic water flow in the same direction as solute flow increased substantially the net fluxes of glycerol and erythritol through the membranes, while osmotic flow in the opposite direction to glycerol flow reduced the net flux of that solute. The observed effects of osmotic water flow on the fluxes of these solutes were in reasonable agreement with predictions based on a model for coupling of solute and solvent flows within the membrane phase, and considerably in excess of the prediction for a diffusion process alone.     

A multiscale theoretical model for diffusive mass transfer in cellular biological media

An integrated methodology is developed for the theoretical analysis of solute transport and reaction in cellular biological media, such as tissues, microbial flocs, and biofilms. First, the method of local spatial averaging with a weight function is used to establish the equation which describes solute conservation at the cellular biological medium scale, starting with a continuum-based formulation of solute transport at finer spatial scales. Second, an effective-medium model is developed for the self-consistent calculation of the local diffusion coefficient in the cellular biological medium, including the effects of the structural heterogeneity of the extra-cellular space and the reversible adsorption to extra-cellular polymers. The final expression for the local effective diffusion coefficient is: D(Abeta)=lambda(beta)D(Aupsilon), where D(Aupsilon) is the diffusion coefficient in water, and lambda(beta) is a function of the composition and fundamental geometric and physicochemical system properties, including the size of solute molecules, the size of extra-cellular polymer fibers, and the mass permeability of the cell membrane. Furthermore, the analysis sheds some light on the function of the extra-cellular hydrogel as a diffusive barrier to solute molecules approaching the cell membrane, and its implications on the transport of chemotherapeutic agents within a cellular biological medium. Finally, the model predicts the qualitative trend as well as the quantitative variability of a large number of published experimental data on the diffusion coefficient of oxygen in cell-entrapping gels, microbial flocs, biofilms, and mammalian tissues.     

Transient solute diffusion in articular cartilage

The one-dimensional transient diffusion of glucose, inulin and dextran into adult bovine knee articular cartilage was determined for transport times of 1, 5, 15 and 60 min, and 4, 12, 24 and 48 h. The apparent diffusion coefficient and apparent interface partition coefficient were calculated from the concentration-depth profiles within the tissue using a theoretical model for non-steady state solute diffusion. The diffusion coefficient was found to decrease with both solute size and transport time. The partition coefficient also decreased with solute size but increased with transport time. Neither coefficient was dependent on normal tissue fluid or proteoglycan content variations.     

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

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

Picosecond-nanosecond laser photolysis studies of a photoacid generator in solutions: Transient absorption spectroscopy and transient grating measurements.

Photochemical reaction profiles of a photoacid generator, N-trifluoromethylsulfonyloxy-1,8-naphthalimide (NI-Sf), in solution phase were investigated by means of picosecond and nanosecond transient absorption spectroscopy as well as transient grating measurements. Picosecond transient absorption spectroscopy directly revealed that the lifetime of the S1 state and the intersystem-crossing yield decreased with increasing solvent polarity. On the other hand, photochemical reaction yield increased with an increase in the solvent polarity. These results indicated that the photochemical reaction started in the S1 state. Transient grating measurement directly detected the diffusion process of the proton and its diffusion coefficient was obtained to be 3.9 x 10(-9) m2 s(-1), which was several times larger than those of the usual solute molecules.     

Effects of solvent and solute drag on transmembrane diffusion

The present study compares and quantitates both solvent drag and solute drag forces in a system with both heteropore and homopore membranes. It is shown that tracer solute permeability can be increased if solution flow or driver solute flux is in the direction of tracer diffusion. Either force can decrease tracer permeability if the force can decrease tracer permeability if the force is opposite to the direction of tracer diffusion. The two forces can be additive or one force may reduce the effect of the other force. In the particular system quantitated, solute drag is shown to be some 300 times more effective than solvent drag on a mole-to-mole basis. The use of a number of solute pairs on other homopore and heteropore membranes confirms the finding that the two drag forces can be analyzed or manipulated in a variety of systems.     

The permeation of organic acids through lecithin bilayers. Resemblance to diffusion in polymers.

1. The fluxes of aliphatic acids and their derivatives through black lipid membranes made of egg lecithin in decane were measured by means of a proton titration method. 2. Permeability coefficients were calculated and these were divided by the partition coefficient of the diffusing solute in different solvent systems: n-decane, olive oil, ether and octanol. The logarithms of the diffusion coefficients thus obtained were plotted against the logarithm of the molecular weight. The data could not be fitted to a single regression line in any solvent system. 3. When the logarithm of the diffusion coefficients were correlated to the logarithm of the molecular volume (equals molecular weight/ specific gravity) all the diffusants could be fitted to the same regression line, indicating that the molecular volume is a better index of molecular size and shape than the molecular weight. 4. Analysis of the experimental results assuming a model of diffusion through soft polymers (Lieb, W.R. and Stein, W. D. (1971) Current Topics in Membranes and Transport, vol. 2, pp. 1-39, Academic Press, New York) showed that decane and olive oil are not adequate model solvents for planar lecithin membranes but ether and octanol are good models. 5. The differential mass selectivity coefficient was found to be similar to that for soft polymers and biological membranes, i.e. greater than 3.0. 6. Water could be fitted by the same regression line, thus emphasizing the generality of passive transfer and implying that water crosses lipid membranes as single molecules.     

Theory of Diffusion in Gels

It has been shown that when concentration of solute is expressed as amount per unit volume of gel—solvent—solute system, Fick's laws for diffusion in a gel take the same form as for diffusion in solvent alone, except that the usual coefficient must be replaced by a new coefficient, D′, equal to D(1 - α)/(1 - ), where is the effective volume fraction of the gel substance and α is a coefficient of obstruction equal to 5/3 if the gel substance can be considered to be made up of randomly oriented rods. An equation was derived for the total amount of solute entering the gel, which is analogous to but not identical with the equation for the total amount of solute crossing the initial boundary in free diffusion. The effect of slice thickness was investigated by a mathematical procedure involving the solutions of approximate differential equations. It was shown that even for slices so thick that 95 per cent of the solute in the gel is contained in the first two, a correction factor equal to the square of the slice thickness divided by 48D't permits one to obtain accurate measurement of D′ from the mean concentration and the position of the midplane of the slice.     

Transport of neutral solute in articular cartilage: effect of microstructure anisotropy

Due to the avascular nature of articular cartilage, solute transport through its extracellular matrix is critical for the maintenance and the functioning of the tissue. What is more, diffusion of macromolecules may be affected by the microstructure of the extracellular matrix in both undeformed and deformed cartilage and experiments demonstrate diffusion anisotropy in the case of large solute. However, these phenomena have not received sufficient theoretical attention to date. We hypothesize here that the diffusion anisotropy of macromolecules is brought about by the particular microstructure of the cartilage network. Based on this hypothesis, we then propose a mathematical model that correlates the diffusion coefficient tensor with the structural orientation tensor of the network. This model is shown to be successful in describing anisotropic diffusion of macromolecules in undeformed tissue and is capable of clarifying the effects of network reorientation as the tissue deforms under mechanical load. Additionally, our model explains the anomaly that at large strain, in a cylindrical plug under unconfined compression, solute diffusion in the radial direction increases with strain. Our results indicate that in cartilage the degree of diffusion anisotropy is site specific, but depends also on the size of the diffusing molecule. Mechanical loading initiates and/or further exacerbates this anisotropy. At small deformation, solute diffusion is near isotropic in a tissue that is isotropic in its unstressed state, becoming anisotropic as loading progresses. Mechanical loading leads to an attenuation of solute diffusion in all directions when deformation is small. However, loading, if it is high enough, enhances solute transport in the direction perpendicular to the load line, instead of inhibiting it.     

The nonelectrolyte permeability of planar lipid bilayer membranes

The permeability of lecithin bilayer membranes to nonelectrolytes is in reasonable agreement with Overton's rule. The is, Pd alpha DKhc, where/Pd is the permeability coefficient of a solute through the bilayer, Khc is its hydrocarbon:water partition coefficient, and D is its diffusion coefficient in bulk hydrocarbon. The partition coefficients are by far the major determinants of the relative magnitudes of the permeability coefficients; the diffusion coefficients make only a minor contribution. We note that the recent emphasis on theoretically calculated intramembranous diffusion coefficients (Dm'S) has diverted attention from the experimentally measurable and physiologically relevant permeability coefficients (Pd'S) and has obscured the simplicity and usefulness of Overton's rule.     

Diffusion in immobilized-cell gels

Summary The relationship between the diffusion coefficient, the effective diffusion coefficient and the partition coefficient for a solute in a cell-containing gel is discussed. The use of correlation equations that are based on some kind of physical model is recommended when the effect of cell concentration on diffusion is interpreted.     

Bipartite expressions for diffusional mass transport in biomembranes

Analytical expressions for solute diffusion through a membrane barrier for different initial and boundary conditions are available in the literature. The three commonest initial and boundary conditions are for a membrane without solute respectively immersed in a solution of constant concentration, immersed in such a solution for one side but with the other side isolated, and immersed in such a solution for one side and with the other side kept at zero concentration. The physical quantities for the first two initial and boundary conditions are concentration and average concentration (the total solute entering the membrane) with amperometric current (flux) and solute that permeates through the membrane (charge passed) for the third initial and boundary condition. Expressions for these methods in the literature are inconvenient for practical applications because of the infinite mathematical series required. An investigation of convergence of these expressions was therefore carried out. Simple but accurate bipartite expressions for these methods were constructed and provided theoretical support for studies on mass transport characterization of biomembranes. As a specific application, these expressions enabled a direct fit of the simulated observables to experimental values to obtain diffusion coefficients. For these initial and boundary conditions and corresponding physical quantities, simple one point methods for diffusion coefficient estimation are also suggested. These latter diffusion coefficients can be initial values for numerical fit methods.     

An automated method for rapid determination of diffusion coefficients via measurements of boundary spreading

The use of a simple device by which a layer of solvent may be deposited onto a solution of an optically absorbing solute in a cylindrical quartz tube, without substantial mixing of solution and solvent, is described. The spreading of the boundary thus formed may be monitored as a function of time using an automated absorbance scanning device previously described [A. K. Attri and A. P. Minton (1983) Anal. Biochem. 133, 142-152]. A semiautomatic procedure for determining the diffusion coefficient from the time dependence of the shape of the boundary is described and is particularly well-suited for real-time data analysis with a laboratory microcomputer. The diffusion coefficients of several proteins have been measured using the technique reported, and the results are generally in good agreement with values reported in the literature. The feasibility of using this technique in combination with a previously described method for measuring the sedimentation coefficient [A. K. Attri and A. P. Minton (1984) Anal. Biochem. 136, 407-415] to rapidly determine the molecular weight of a protein is established.     

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.     

Red Cell Membrane Permeability Deduced from Bulk Diffusion Coefficients

The permeability coefficients of dog red cell membrane to tritiated water and to a series of[¹⁴C]amides have been deduced from bulk diffusion measurements through a "tissue" composed of packed red cells. Red cells were packed by centrifugation inside polyethylene tubing. The red cell column was pulsed at one end with radiolabeled solute and diffusion was allowed to proceed for several hours. The distribution of radioactivity along the red cell column was measured by sequential slicing and counting, and the diffusion coefficient was determined by a simple plotting technique, assuming a one-dimensional diffusional model. In order to derive the red cell membrane permeability coefficient from the bulk diffusion coefficient, the red cells were assumed to be packed in a regular manner approximating closely spaced parallelopipeds. The local steady-state diffusional flux was idealized as a one-dimensional intracellular pathway in parallel with a one-dimensional extracellular pathway with solute exchange occurring within the series pathway and between the pathways. The diffusion coefficients in the intracellular and extracellular pathways were estimated from bulk diffusion measurements through concentrated hemoglobin solutions and plasma, respectively; while the volume of the extracellular pathway was determined using radiolabeled sucrose. The membrane permeability coefficients were in satisfactory agreement with the data of Sha'afi, R. I., C. M. Gary-Bobo, and A. K. Solomon (1971. J. Gen. Physiol. 58:238) obtained by a rapid-reaction technique. The method is simple and particularly well suited for rapidly permeating solutes.