Diffusion of Particles in the Extracellular Matrix: The Effect of Repulsive Electrostatic Interactions

Diffusive transport of macromolecules and nanoparticles in charged fibrous media is of interest in many biological applications, including drug delivery and separation processes. Experimental findings have shown that diffusion can be significantly hindered by electrostatic interactions between the diffusing particle and charged components of the extracellular matrix. The implications, however, have not been analyzed rigorously. Here, we present a mathematical framework to study the effect of charge on the diffusive transport of macromolecules and nanoparticles in the extracellular matrix of biological tissues. The model takes into account steric, hydrodynamic, and electrostatic interactions. We show that when the fiber size is comparable to the Debye length, electrostatic forces between the fibers and the particles result in slowed diffusion. However, as the fiber diameter increases the repulsive forces become less important. Our results explain the experimental observations that neutral particles diffuse faster than charged particles. Taken together, we conclude that optimal particles for delivery to tumors should be initially cationic to target the tumor vessels and then change to neutral charge after exiting the blood vessels.     

The Electrodynamics of Current-Current Interaction in a Double Helix

General expressions for the tangential and radial forces for two current elements moving contra-wise to each other in a helical manner are derived. The two repulsive forces are calculated as a function of velocity, with explicit values given for parameters, appropriate to DNA. The calculated electrodynamic respulsive forces oppose the stabilizing standard radial and tangential forces in the helix and, if large enough, can result in strand separation. The currents required are of the same order of magnitude as observed intra-cellular currents and as passed recently through short segments of duplex DNA. A speculative mechanism involving a resistance-capacitance membrane network in series with a resistance DNA network is formulated. Strand separation in DNA may well originate in such an electrodynamic system.     

Using the ratio of means as the effect size measure in combining results of microarray experiments

Background  

Development of efficient analytic methodologies for combining microarray results is a major challenge in gene expression analysis. The widely used effect size models are thought to provide an efficient modeling framework for this purpose, where the measures of association for each study and each gene are combined, weighted by the standard errors. A significant disadvantage of this strategy is that the quality of different data sets may be highly variable, but this information is usually neglected during the integration. Moreover, it is widely known that the estimated standard deviations are probably unstable in the commonly used effect size measures (such as standardized mean difference) when sample sizes in each group are small.     

Evidences of Changes in Surface Electrostatic Charge Distribution during Stabilization of HPV16 Virus-Like Particles

The stabilization of human papillomavirus type 16 virus-like particles has been examined by means of different techniques including dynamic and static light scattering, transmission electron microscopy and electrophoretic mobility. All these techniques provide different and often complementary perspectives about the aggregation process and generation of stabilized virus-like particles after a period of time of 48 hours at a temperature of 298 K. Interestingly, static light scattering results point towards a clear colloidal instability in the initial systems, as suggested by a negative value of the second virial coefficient. This is likely related to small repulsive electrostatic interactions among the particles, and in agreement with relatively small absolute values of the electrophoretic mobility and, hence, of the net surface charges. At this initial stage the small repulsive interactions are not able to compensate binding interactions, which tend to aggregate the particles. As time proceeds, an increase of the size of the particles is accompanied by strong increases, in absolute values, of the electrophoretic mobility and net surface charge, suggesting enhanced repulsive electrostatic interactions and, consequently, a stabilized colloidal system. These results show that electrophoretic mobility is a useful methodology that can be applied to screen the stabilization factors for virus-like particles during vaccine development.     

Spectrum of Physical Properties Among the Virions of a Whole Population of Vaccinia Virus Particles

Populations of virions released from cultures of L cells infected with vaccinia virus are composed of particles which differ substantially from each other in sedimentation rate and buoyant density. Clumps of two and three virions sediment enough faster than single particles so that fractions containing only singles and others with predominantly pairs can be isolated. The observed velocity range for single particles is much greater than that attributable to diffusion and convection in the centrifuge. Plaquing efficiency is three times higher in a small fraction of the slowest-moving virions than in the major part of the population, even though no size difference can be seen in the electron microscope. Isopycnic densities in potassium tartrate range from 1.15 to 1.23, enough to account for the observed range in velocities. Centrifugation was done in the BXIV zonal rotor at very low virion concentration (less than 10⁸ per ml at any point in the spectrum). Virus count and state of aggregation were determined by electron microscopy.     

The role of convection in the standard fluid-mechanical model for morphogenesis

The effect of convection on reaction-diffusion instabilities in a visco-elastic medium is studied by using the standard continuum theory of a fluid mixture. The medium is assumed to be in local mechanical equilibrium, and convection is generated by pressure forces which arise if the equilibrium density of the medium changes with its composition. A linear stability analysis shows that reaction-diffusion instabilities proceeding from homogeneous steady states at rest are unmodified by induced convection to first order in concentration changes. We suggest that a non-linear analysis would show convection produces no new instabilities, as a linear analysis of inhomogeneous non-convecting stationary states shows that reaction-diffusion growth rates are reduced by convection at long wavelengths and are otherwise unchanged. For applications in embryology, numerical estimates suggest that convection can be ignored in reaction-diffusion mechanisms for pattern formation, and this conclusion is supported by a dimensional analysis.On leave from Department of Physics, Monash University, Clayton, Victoria 3168, Australia     

Cell transport in model extracellular matrices

The rapid transport of cells has been shown to occur by ordered countercurrent convection. This convection can be created by mixtures of macromolecules which make up the extracellular matrix and by the degradation and aggregation products of these macromolecules. The ordered countercurrent convection is manifested in the form of structured flows and arises in isothermal systems with small concentration gradients of solutes. The flows are gravity driven but may rapidly move at angles close to the horizontal axis if they are mechanically constrained to do so. These flows have been shown to rapidly transport cells at rates ranging from 1 to 100 mm h-1, depending on the conditions of the experiment. The transport of cells is nonspecific in that various cell types (chondrocytes, fibroblasts, endothelial cells, and red blood cells) as well as inert particles of similar size (latex beads 6-microns diam) are transported at similar rates. Latex bead transport by structured flow has also been demonstrated to occur in confined spaces in the form of Teflon tubing down to 200 microns in diameter and at angles in the range of 45-90 degrees to the horizontal axis. The flows may also occur over relatively long distances for a prolonged period of time. The conditions for flow formation are simple and widespread. It is suggested that it may contribute to the forces involved in the movement of cells in the extracellular matrix in vivo especially during remodeling and embryogenesis.     

Dung feeding in adult scarabaeines (tunnellers and endocoprids): even large dung beetles eat small particles

Abstract 1. The maximum size of ingested particles was determined in 15 species of adult dung beetle (Scarabaeidae: Scarabaeinae) by mixing small latex or glass balls of known diameter into the dung used as food. Twelve species (tribes Coprini, Onitini, Oniticellini, and Onthophagini) were tunnellers (making dung stores for feeding and breeding in the soil below the pat) and three species (tribe Oniticellini) were endocoprids (feeding and breeding in the dung pat itself).
2. The test species, covering a wide range of body size (fresh weights 0.05–7.4 g), ingested minute particles only (maximum diameter 8–50 µm), and there was a statistically significant but numerically small increase in particle size with body weight.
3. When the effect of body size was taken into account, taxon (tribe), ecological group (tunneller/endocoprid), and dung preference (coarse/fine) had no significant effect on the size of ingested particles.
4. Tests using two tunnelling species did not indicate that beetles use their mandibles to grind dung particles prior to ingestion.
5. The results suggest essentially the same feeding mechanism in all adult tunnelling or endocoprid scarabaeines that eat fresh dung. Larger, indigestible plant fragments are avoided by filtration, and ingestion is confined to very small particles of higher nutritional value.     

A theoretical model to study the effect of convection and leaky junctions on macromolecule transport in artery walls

A mathematical model is presented herein to determine the effect of convection on macromolecular transport across an artery wall due to transmural or osmotic pressure differences. The model is based on an extension of the leaky junction-cell turnover model of Weinbaum et al. (1985) to take into account a combined transport mechanism of convection and diffusion and also to provide the leaky junctions in the model with a finite resistance, thus allowing the results to be extended to intercellular clefts with a retarding extracellular matrix or to macromolecules whose dimensions are nearly the same as the junctional width. The results from this improved model show that the effect of pressure on transarterial macromolecular transport is important especially for cell turnover rates greater than 1% and that significant changes in the equilibrium balance of the cholesterol carrying LDL molecules in the arterial wall can occur due to a very small fraction of leaky junctions. At very high turnover rates (large fraction of leaky junctions) the effect of convection on macromolecular transport becomes dramatic and explains the very large increases in uptake observed experimentally after artificially inducing extensive endothelial damage.     

Using quantitative trait loci results to discriminate among crosses on the basis of their progeny mean and variance

To develop inbred lines, parents are crossed to generate segregating populations from which superior inbred progeny are selected. The value of a particular cross thus depends on the expected performance of its best progeny, which we call the superior progeny value. Superior progeny value is a linear combination of the mean of the cross's progeny and their standard deviation. In this study we specify theory to predict a cross's progeny standard deviation from QTL results and explore analytically and by simulation the variance of that standard deviation under different genetic models. We then study the impact of different QTL analysis methods on the prediction accuracy of a cross's superior progeny value. We show that including all markers, rather than only markers with significant effects, improves the prediction. Methods that account for the uncertainty of the QTL analysis by integrating over the posterior distributions of effect estimates also produce better predictions than methods that retain only point estimates from the QTL analysis. The utility of including estimates of a cross's among-progeny standard deviation in the prediction increases with increasing heritability and marker density but decreasing genome size and QTL number. This utility is also higher if crosses are envisioned only among the best parents rather than among all parents. Nevertheless, we show that among crosses the variance of progeny means is generally much greater than the variance of progeny standard deviations, restricting the utility of estimates of progeny standard deviations to a relatively small parameter space.     

Direct force measurements between cellulose surfaces and colloidal silica particles

The interaction of cellulose layers with colloidal silica particles was investigated by direct force measurements with the atomic force microscope (AFM). Upon approach, repulsive forces were found between the negatively charged silica particles and the cellulose surface. The forces were interpreted quantitatively in terms of electrostatic interactions due to overlap of diffuse layers originating from negatively charged carboxylic groups on the cellulose surface. The diffuse layer charge density of cellulose was estimated to be 0.80 mC/m2 at pH 9.5 and 0.21 mC/m2 at pH 4. The forces upon retraction are characterized by molecular adhesion events, whereby individual cellulose chains desorb from the probe surface. The retraction profiles are dominated by well-defined force plateaus, which correspond to single-chain desorption forces of 35-42 pN. We surmise that adsorption of cellulose to probe surfaces is dominated by nonelectrostatic forces, probably originating from hydrogen bonding. Electrostatic contributions to desorption force could be detected only at high pH, where the silica surface is highly charged.     

First-Leaflet Phase Effect on Properties of Phospholipid Bilayer Formed Through Vesicle Adsorption on LB Monolayer

Phospholipid bilayers were formed on mica using the Langmuir–Blodgett technique and liposome fusion, as a model system for biomembranes. Nanometer-scale surface physical properties of the bilayers were quantitatively characterized upon the different phases of the first leaflets. Lower hydration/steric forces on the bilayers were observed at the liquid phase of the first leaflet than at the solid phase. The forces appear to be related to the low mechanical stability of the lipid bilayer, which was affected by the first leaflet phase. The first leaflet phase also influenced the long-range repulsive forces over the second leaflet. Surface forces, measured using a modified probe with an atomic force microscope, showed that lower long-range repulsive forces were also found at the liquid phase of the first leaflet. Force measurements were performed at 300 mM sodium chloride solution so that the effect of the phase on the long-range repulsive forces could be investigated by reducing the effect of the repulsion between the second-leaflet lipid headgroups on the long-range repulsive forces. Forces were analyzed using the Derjaguin–Landau–Verwey–Overbeek theory so that the surface potential and surface charge density of the lipid bilayers were quantitatively acquired for each phase of the first leaflet.     

Exclusion of alcohols from spermidine-DNA assemblies: probing the physical basis of preferential hydration

The interaction of the alcohols 2-methyl-2,4-pentanediol (MPD) and 2-propanol and of glycerol with condensed spermidine(3+)-DNA arrays are investigated with direct force measurements using osmotic stress coupled with X-ray scattering. Thermodynamic forces between DNA helices are measured from the dependence of helical interaxial spacings on the osmotic pressure applied by poly(ethylene glycol) solutions in equilibrium with the DNA phase. The sensitivity of these forces to solute concentration can be transformed into a change in the number of excess or deficit solutes or waters in the DNA phase by applying the Gibbs-Duhem equation. The alcohols examined are excluded from the condensed DNA array and strongly affect the osmotic stress force curves. DNA is preferentially hydrated. MPD is significantly more excluded than 2-propanol. The exclusion of these alcohols, however, is not due to a steric repulsion since glycerol that is intermediate in size between MPD and 2-propanol does not observably affect DNA force curves. As the distance between DNA helices varies, the change in the number of excess waters is independent of alcohol concentration for each alcohol. These solutes are acting osmotically on the condensed array. The distance dependence of exclusion indicates that repulsive water structuring forces dominate the interaction of alcohols with the DNA surface. The exclusion measured for these condensed arrays can quantitatively account for the effect of these alcohols on the precipitation of DNA from dilute solution by spermidine(3+).     

Functional aspects of shell geometry in some British land snails

Allometric relationships between the area of the shell mouth and live body weight are examined in 19 species of British land snails. Within species, the rate of increase of mouth area on weight is usually less than the isometric expectation, in spite of the logarithmic spiral pattern of growth in most species. It is suggested that this deviation is due mainly to changes in density with size. Two species which conform to isometric expectation alter the geometry of the shell as they pow.
Between species, the rate of increase in mouth area on weight in adults is much greater than isometric expectation, and the range of mouth areas at standard weight is considerable. These deviations are almost entirely accounted for by differences in shell geometry between large and small species, the former having higher rates of whorl expansion and smaller or non–existent umbilicuses.
The range of loading (weight per unit mouth area) on resting adult snails is thus much less than would be expected. It is suggested that large species are limited in the range of possible shell geometries by the need to minimize loading, while in small species other forces such as desiccation and predation may also be important: the range of geometries is generally larger. Observations on ecology and behaviour tend to support these conclusions.     

A precise analytical method for calculating the electrostatic energy of macromolecules in aqueous solution

A new method for calculating the total electrostatic free energy of a macromolecule in solution is presented. It is applicable to molecules of arbitrary shape and size, including membranes or macromolecular assemblies with substrate molecules and ions. The method is derived from integrating the energy density of the electrostatic field and is termed the field energy method. It is based on the dielectric model, in which the solute and the surrounding water are regarded as different continuous dielectrics. The field energy method yields both the interaction energy between all charge pairs and the self energy of single charges, effectively accounting for the interaction with water. First, the dielectric boundary and mirror charges are determined for all charges of the solute. The energy is then given as a simple function of the interatomic distances, and the standard atomic partial charges and volumes. The interaction and self energy are shown to result from three-body and pairwise interactions. Both energy terms explicitly involve apolar atoms, revealing that apolar groups are also subject to electrostatic forces. We applied the field energy method to a spherical model protein. Comparison with the Kirkwood solution shows that errors are within a small percentage. As a further test, the field energy method was used to calculate the electrostatic potential of the protein superoxide dismutase. We obtained good agreement with the result from a program that implements the numerical finite difference algorithm. The field energy method provides a basis for energy minimization and dynamics programs that account for the solvent and screening effect of water at little computational expense.     

Model of cochlear microphonic explores the tuning and magnitude of hair cell transduction current

The mammalian cochlea relies on the active forcing of sensory outer hair cells (OHCs) to amplify traveling wave responses along the basilar membrane. These forces are the result of electromotility, wherein current through the OHCs leads to conformational changes in the cells that provide stresses on surrounding structures. OHC transducer current can be detected via the voltage in the scala tympani (the cochlear microphonic, CM), and the CM can be used as an indicator of healthy cochlear operation. The CM represents a summation of OHC currents (the inner hair cell contribution is known to be small) and to use CM to probe the properties of OHC transduction requires a model that simulates that summation. We developed a finite element model for that purpose. The pattern of current generators (the model input) was initially based on basilar membrane displacement, with the current size based on in vitro data. The model was able to reproduce the amplitude of experimental CM results reasonably well when the input tuning was enhanced slightly (peak increased by ∼6 dB), which can be regarded as additional hair bundle tuning, and with a current/input value of 200–260 pA/nm, which is ∼4 times greater than the largest in vitro measures.     

Strategy for selection of methods for separation of bioparticles from particle mixtures

The desired product of bioprocesses is often produced in particulate form, either as an inclusion body (IB) or as a crystal. Particle harvesting is then a crucial and attractive form of product recovery. Because the liquid phase often contains other bioparticles, such as cell debris, whole cells, particulate biocatalysts or particulate by-products, the recovery of product particles is a complex process. In most cases, the particulate product is purified using selective solubilization or extraction. However, if selective particle recovery is possible, the already high purity of the particles makes this downstream process more favorable. This work gives an overview of typical bioparticle mixtures that are encountered in industrial biotechnology and the various driving forces that may be used for particle-particle separation, such as the centrifugal force, the magnetic force, the electric force, and forces related to interfaces. By coupling these driving forces to the resisting forces, the limitations of using these driving forces with respect to particle size are calculated. It shows that centrifugation is not a general solution for particle-particle separation in biotechnology because the particle sizes of product and contaminating particles are often very small, thus, causing their settling velocities to be too low for efficient separation by centrifugation. Examples of such separation problems are the recovery of IBs or virus-like particles (VLPs) from (microbial) cell debris. In these cases, separation processes that use electrical forces or fluid-fluid interfaces show to have a large potential for particle-particle separation. These methods are not yet commonly applied for large-scale particle-particle separation in biotechnology and more research is required on the separation techniques and on particle characterization to facilitate successful application of these methods in industry.     

Two-phase formation in solutions of tobacco mosaic virus and the problem of long-range forces

In a nearly salt-free medium, a dilute tobacco mosaic virus solution of rod-shaped virus particles of uniform length forms two phases; the bottom optically anisotropic phase has a greater virus concentration than has the top optically isotropic phase. For a sample containing particles of various lengths, the bottom phase contains longer particles than does the top and the concentrations top and bottom are nearly equal. The longer the particles the less the minimum concentration necessary for two-phase formation. Increasing the salt concentration increases the minimum concentration. The formation of two phases is explained in terms of geometrical considerations without recourse to the concept of long-range attractive forces. The minimum concentration for two-phase formation is that concentration at which correlation in orientation between the rod-shaped particles begins to take place. This concentration is determined by the thermodynamically effective size and shape of the particles as obtained from the concentration dependence of the osmotic pressure of the solutions measured by light scattering. The effective volume of the particles is introduced into the theory of Onsager for correlation of orientation of uniform size rods and good agreement with experiment is obtained. The theory is extended to a mixture of non-uniform size rods and to the case in which the salt concentration is varied, and agreement with experiment is obtained. The thermodynamically effective volume of the particles and its dependence on salt concentration are explained in terms of the shape of the particles and the electrostatic repulsion between them. Current theories of the hydration of proteins and of long-range forces are critically discussed. The bottom layer of freshly purified tobacco mosaic virus samples shows Bragg diffraction of visible light. The diffraction data indicate that the virus particles in solution form three-dimensional crystals approximately the size of crystalline inclusion bodies found in the cells of plants suffering from the disease.     

Global structure analysis of acid-unfolded myoglobin with consideration to effects of intermolecular coulomb repulsion on solution X-ray scattering

To obtain information on the global structure of protein in the acid-unfolded (AU) state, the structure of apomyoglobin (apoMb) was analyzed by using the solution X-ray scattering (SXS) method. SXS profiles were obtained over a wide range of protein concentrations, 1-18 mg mL-1, under strongly acidic conditions. From analysis of the SXS profile extrapolated to a zero protein concentration, the mean square radius, Rsq, of AU-apoMb at 20 mM HCl was estimated to be 4.81 +/- 0.31 nm. This estimate is more than 1.3 nm larger than those of 3.0-3.5 nm reported thus far. The difference originates from the fact that effects of Coulomb repulsive forces acting between AU-apoMb molecules have not been correctly taken into account in the conventional analysis. In fact, even at a low protein concentration of 1 mg mL-1 close to the limit of measurement in the present SXS method, the solution condition applicable to estimating accurately structural parameters of AU-apoMb is very limited. At HCl concentrations lower than 10 mM, the scattering intensity at a small scattering vector decreases remarkably through the effect of intermolecular repulsive forces and the forward scattering intensity is significantly lower than the estimate from the partial specific volume of protein. On the other hand, at HCl concentrations higher than 50 mM, some compact molten-globule-like structures emerge. As a result, the intermediate concentration of 20 mM HCl is the best choice of the solution condition for determining Rsq of AU-apoMb. The effect of intermolecular Coulomb repulsion on the SXS profile of AU-apoMb is at its maximum for forward scattering and decreases monotonously with an increase in the scattering angle to be virtually negligible at K approximately 0.63 nm(-1). Whereas urea-denatured apoMb shows a SXS profile typical of Gaussian chains, the intrinsic SXS profile of AU-apoMb differs significantly from those of Gaussian chains.