The critical micelle condition revisited.

Several simple alternatives have been examined as a possible basis for micellar size distributions which are internally consistent with the experimentally required concept of a threshold concentration, the critical micelle condition. Among these are the two-state system, monomer in equilibrium with a single high polymer, indefinite self-association, and continuous self-association with an arbitrary upper limit beyond which all further association is absolutely prohibited. Of these, only the last is a possible choice, although lacking experimental support. This report considers in deeper detail a thermodynamic model for micelle distributions, the so-called shell model of the present author, which is in basic agreement with an earlier statistic-mechanical study [Hoeve CA & Benson GC (1957), Colloid Polym Sci, 252, 56] in predicting the possibility of broad distributions of micellar species. A self-consistent distribution model which predicts a critical micelle condition must also predict a location with respect to degree of polymerization having a minimum concentration. Thus, the molar distribution function for the shell model satisfies this requirement, whereas the equivalent concentration distribution function fails to do so, as would the statistical models for multiple ligand binding. Moreover, the position of this minimum is predicted to change with concentration.     

The effect of the propagation coefficient on size distribution in micellar systems

In this study the effect of the propagation coefficient on the molar distribution function in a modified shell model for micellar systems was examined. The sharpness of the micelle size distribution boundary was found to depend less on the degree of polymerization, n, than on the propagation coefficient, P. Although Kegeles (J. Phys. Chem. 83 (1979) 1728) has reported a marked sharpening of the distribution boundary when P = 2.0. we found the boundary to be fairly broad at this point. However, as values of the propagation coefficient were increased from 3 to 10, the micelle distribution boundary became increasingly sharp. The possibility of such a change in the reaction boundary arising from a structural transition, accompanied by a change in the rate of dissociation of monomer from the shell, is also discussed.     

Interparticle interactions and structural changes of nucleosome core particles in low-salt solution

The structural behavior of the nucleosome core particles in the range of solvent Na+ concentration from 10.45 to 0.45 mM has been studied by small-angle neutron and synchroton radiation X-ray scattering, sedimentation, atomic absorption spectroscopy, density measurements, and circular dichroism. With decreasing salt concentration, the appearance of a scattering peak that is assignable to interparticle interactions, an intraparticle structural transition, a decrease in the sedimentation velocity of the particle, and a release of bound Na+ ions from the particle are all observed concurrently when the ratio of solvent Na+ ions per particle is below approximately 1000. These observations are interpreted to indicate that a release of bound Na+ ions from the particle brings about structural rearrangements and weakens the electrostatic shielding of the particle, and this introduces long-range repulsive ordering of the particle in low-salt solution. Analyses of the scattering data indicate that the rearrangement within the core particle in low-salt solution is slight, changing the particle's shape slightly from cylindrical to a more spherical form by moving the center of the mass of the DNA somewhat inward with accompanying small decreases in the radii of gyration of both the DNA and the histones.     

A new approximate whole boundary solution of the Lamm differential equation for the analysis of sedimentation velocity experiments

Sedimentation velocity is one of the best-suited physical methods for determining the size and shape of macromolecular substances or their complexes in the range from 1 to several thousand kDa. The moving boundary in sedimentation velocity runs can be described by the Lamm differential equation. Fitting of suitable model functions or solutions of the Lamm equation to the moving boundary is used to obtain directly sedimentation and diffusion coefficients, thus allowing quick determination of size, shape and other parameters of macromolecules. Here we present a new approximate whole boundary solution of the Lamm equation that simultaneously allows the specification of sedimentation and diffusion coefficients with deviations smaller than 1% from the expected values.     

Nanoparticles containing ketoprofen and acrylic polymers prepared by an aerosol flow reactor method

The purpose of this study was to outline the effects of interactions between a model drug and various acrylic polymers on the physical properties of nanoparticles prepared by an aerosol flow reactor method. The amount of model drug, ketoprofen, in the nanoparticles was varied, and the nanoparticles were analyzed for particle size distribution, particle morphology, thermal properties, IR spectroscopy, and drug release. The nanoparticles produced were spherical, amorphous, and had a matrix-type structure. Ketoprofen crystallization was observed when the amount of drug in Eudragit L nanoparticles was more than 33% (wt/wt). For Eudragit E and Eudragit RS nanoparticles, the drug acted as an effective plasticizer resulting in lowering of the glass transition of the polymer. Two factors affected the preparation of nanoparticles by the aerosol flow reactor method, namely, the solubility of the drug in the polymer matrix and the thermal properties of the resulting drug-polymer matrix.     

Diffusion-controlled reactions of enzymes. An approximate analytic solution of Chou's model

Based on Chou's model, a criterion was derived, by which one can judge whether or not the physical picture of the critical spherical shell described by Chou for an enzyme-substrate fast reaction system can emerge. Furthermore, for those reaction systems with such a physical picture, an approximate analytical solution was presented, which can be easily handled to calculate the upper limit of the diffusion-controlled reaction and the corresponding concentration distribution of substrate molecules on the surface of the major protein outside the active site. The results thus obtained are in good agreement with those computed by Chou et al. through the approach of numerical solution. Furthermore, the physical significance of the criterion and its relation to the critical spherical shell are substantiated during the process of derivation, which is very helpful for gaining an insight into this kind of biomolecular system with surprisingly high reaction rates.     

Sedimentation velocity analysis of heterogeneous protein-protein interactions: sedimentation coefficient distributions c(s) and asymptotic boundary profiles from Gilbert-Jenkins theory

Interacting proteins in rapid association equilibrium exhibit coupled migration under the influence of an external force. In sedimentation, two-component systems can exhibit bimodal boundaries, consisting of the undisturbed sedimentation of a fraction of the population of one component, and the coupled sedimentation of a mixture of both free and complex species in the reaction boundary. For the theoretical limit of diffusion-free sedimentation after infinite time, the shapes of the reaction boundaries and the sedimentation velocity gradients have been predicted by Gilbert and Jenkins. We compare these asymptotic gradients with sedimentation coefficient distributions, c(s), extracted from experimental sedimentation profiles by direct modeling with superpositions of Lamm equation solutions. The overall shapes are qualitatively consistent and the amplitudes and weight-average s-values of the different boundary components are quantitatively in good agreement. We propose that the concentration dependence of the area and weight-average s-value of the c(s) peaks can be modeled by isotherms based on Gilbert-Jenkins theory, providing a robust approach to exploit the bimodal structure of the reaction boundary for the analysis of experimental data. This can significantly improve the estimates for the determination of binding constants and hydrodynamic parameters of the complexes.     

Determination of the asymptotic shapes of sedimentation velocity patterns for reversibly polymerizing solutes

A simple method is described for the determination of the asymptotic boundary shape from a series of schlieren patterns taken during a sedimentation velocity experiment on a rapidly and reversibly associating solute. The form of the boundary so obtained reflects effects of sedimentation and chemical reaction but is free from effects of diffusion. The procedure is illustrated with analyses of experiments on diisopropyl fluorophosphate-inhibited α-chymotrypsin in 0.29 I phosphate, pH 7.9 (a monomer-dimer system), and on β-lactoglobulin A in 0.1 I acetate, pH 4.65 (a monomer-dimer-trimer-tetramer system). Asymptotic patterns so determined exhibit close agreement with those predicted by Gilbert theory.     

Analysis of brush-particle interactions using self-consistent-field theory

Non-specific protein adsorption can be reduced by attaching polymer chains by one end to a sorbent surface. End-grafted polymer modified surfaces have also found application in size-based chromatographic bioseparations. To better understand how to tailor surfaces for these applications, a numerical SCF model has been used to calculate theoretical results for the polymer density distribution of interacting polymer chains around a solute particle positioned at a fixed distance from a surface. In addition, the excess energy required to move the particle into the polymer chains (interaction energy) is calculated using a statistical mechanical treatment of the lattice model. The effect of system variables such as particle size, chain length, surface density and Flory interaction parameters on density distributions and interaction energies is also studied. Calculations for the interaction of a solute particle with a surface covered by many polymer chains (a brush) show that the polymer segments will fill in behind the particle quite rapidly as it moves toward the surface. When there is no strong energetic attraction between the polymer and solute we predict that the interaction energy will be purely repulsive upon compression due to losses in conformational entropy of the polymer chains. Above a critical chain length, which depends upon particle size, a maximum in the force required to move the particle toward the surface is observed due to an engulfment of the particle as chains attempt to access the free volume behind the particle. If an attraction exists between the polymer and solute, such that a minimum in the interaction energy is seen, the optimum conditions for solute repulsion occur at the highest surface density attainable. Long chain length can lead to increased solute concentration within the polymer layer due to the fact that an increased number of favourable polymer–solute contacts are able to occur than with short chains at a similar entropic penalty.     

Ketal cross-linked poly(ethylene glycol)-poly(amino acid)s copolymer micelles for efficient intracellular delivery of doxorubicin

A biocompatible, robust polymer micelle bearing pH-hydrolyzable shell cross-links was developed for efficient intracellular delivery of doxorubicin (DOX). The rationally designed triblock copolymer of poly(ethylene glycol)-poly(L-aspartic acid)-poly(L-phenylalanine) (PEG-PAsp-PPhe) self-assembled to form polymer micelles with three distinct domains of the PEG outer corona, the PAsp middle shell, and the PPhe inner core. Shell cross-linking was performed by the reaction of ketal-containing cross-linkers with Asp moieties in the middle shells. The shell cross-linking did not change the micelle size and the spherical morphology. Fluorescence quenching experiments confirmed the formation of shell cross-linked diffusion barrier, as judged by the reduced Stern-Volmer quenching constant (K(SV)). Dynamic light scattering and fluorescence spectroscopy experiments showed that shell cross-linking improved the micellar physical stability even in the presence of micelle disrupting surfactants, sodium dodecyl sulfate (SDS). The hydrolysis kinetics study showed that the hydrolysis half-life (t(1/2)) of ketal cross-links was estimated to be 52 h at pH 7.4, whereas 0.7 h at pH 5.0, indicating the 74-fold faster hydrolysis at endosomal pH. Ketal cross-linked micelles showed the rapid DOX release at endosomal pH, compared to physiological pH. Confocal laser scanning microscopy (CLSM) showed that ketal cross-linked micelles were taken up by the MCF-7 breast cancer cells via endocytosis and transferred into endosomes to hydrolyze the cross-links by lowered pH and finally facilitate the DOX release to inhibit proliferation of cancer cells. This ketal cross-linked polymer micelle is promising for enhanced intracellular delivery efficiency of many hydrophobic anticancer drugs.     

Use of a membrane-bound fluorophore to characterize diffusion boundary layers around human erythrocytes.

A novel method is used to demonstrate the presence of diffusion boundary layers around erythrocytes following rapid mixing in a stopped-flow spectrophotometer and to estimate the apparent dimensions of the diffusion boundary layers. Pink erythrocyte ghosts labeled on their external surfaces with tetramethyl rhodamine isothiocyanate (TRITC) were mixed in a stopped-flow apparatus with 50 mM NaI in Ringer's solutions. I- is an effective collisional quencher of TRITC fluorescence. TRITC fluorescence after flow stopped decreased monoexponentially with time. The concentration of I- at the cell surface as a function of time was estimated from the dependence of TRITC fluorescence on I- concentration in steady-state experiments. The kinetics of the increase in I- concentration at the cell surface was fit to two diffusional models: a planar erythrocyte ghost bounded by planar diffusion boundary layer and a spherical erythrocyte surrounded by a spherical shell diffusion boundary layer. The planar model best fits the experimental data with a diffusion boundary layer 4.68 microns thick. Using the spherical model the experimental data is best fit by a 6.9 microns diffusion boundary layer.     

Drug-polymer microparticles produced by supercritical assisted atomization

The supercritical assisted atomization (SAA) was proposed as a new technique to produce composite microparticles for drug controlled release. Ampicillin trihydrate and chitosan were selected as model drug and carrier, respectively, and 1% v/v acetic acid aqueous solution was used as solvent. The effect of the polymer/drug ratio on particle morphology and drug release rate was evaluated. SEM analysis indicated that non-coalescing spherical microparticles formed by chitosan/ampicillin were produced by SAA. All coprecipitates produced have a sharp particle distribution, with diameters ranging between about 0.1 and 6 microm. SAA composite microparticles were characterized by X-ray, DSC, EDX and UV-vis analysis. A solid solution of the chitosan and ampicillin was produced and a stabilizing effect of the polymer on the drug has resulted that protects ampicillin from thermal degradation. A prolonged release from SAA coprecipitates with respect to raw drug and physical mixtures of chitosan and ampicillin was obtained; moreover, the polymer/drug ratio has revealed to be a controlling parameter for drug release. Drug release mechanisms characteristic of swelling-controlled systems were observed, with ampicillin release depending on both relaxation and diffusive mechanisms. An empirical binomial equation was used to describe experimental data, showing a fair good agreement with ampicillin release data if both the relaxational and the diffusional parameters are function of the polymer/drug ratio.     

An investigation of the structure of Alfalfa mosaic virus by small-angle neutron scattering

Small-angle neutron scattering experiments have been performed on the tubular bottom component of Alfalfa mosaic virus (AMV) and the “30 S” particle (a quasispherical reassembled AMV coat protein particle) with the aim of determining the internal structure of the virus. Scattering curves were obtained out to a resolution of $\text{1}\text{50}\text{A}\text{?}{}^{\mathrm{?1}}$ at a number of H₂O/²H₂O ratios and were analysed using a model fitting technique. This involves calculating the scattering intensity due to a parameterised distribution of scattering density representing the particle and comparing this to the experimental data after taking into account the effect of instrumental smearing. The use of the contrast variation method enables the internal consistency of the model to be well tested.Three models are used in an attempt to explain the scattering curve of the 30 S particle. A single homogeneous shell is shown to be inadequate and two other models introducing the presumed T = 1 icosahedral symmetry of the particle are presented and discussed. The most satisfactory of these consists of 60 spherical monomers of radius 19 Å symmetrically placed in pairs about the 2-fold icosahedral positions.The analysis of the bottom component data has yielded a low resolution model for the virus, which is shown to be consistent with its composition as given by earlier physico-chemical measurements. In the model the RNA is uniformly packed throughout the interior of the capsid (which is cylindrical with hemispherical ends) out to a radius of about 65 Å and with a packing fraction of 20%. Within the limitations of an homogeneous shell model, the protein capsid has an outer radius of 94 Å and thickness of 23 Å, but arguments are presented based on the marked lattice structure of the cylindrical capsid and the analysis of the scattering data of the 30 S particle, that this model underestimates the thickness of the protein shell and that it in fact makes contact with the RNA at about 65 Å.     

A comparison of weight average and direct boundary fitting of sedimentation velocity data for indefinite polymerizing systems

Analysis of sedimentation velocity data for indefinite self-associating systems is often achieved by fitting of weight average sedimentation coefficients (s(20,w)) However, this method discriminates poorly between alternative models of association and is biased by the presence of inactive monomers and irreversible aggregates. Therefore, a more robust method for extracting the binding constants for indefinite self-associating systems has been developed. This approach utilizes a set of fitting routines (SedAnal) that perform global non-linear least squares fits of up to 10 sedimentation velocity experiments, corresponding to different loading concentrations, by a combination of finite element simulations and a fitting algorithm that uses a simplex convergence routine to search parameter space. Indefinite self-association is analyzed with the software program isodesfitter, which incorporates user provided functions for sedimentation coefficients as a function of the degree of polymerization for spherical, linear and helical polymer models. The computer program hydro was used to generate the sedimentation coefficient values for the linear and helical polymer assembly mechanisms. Since this curve fitting method directly fits the shape of the sedimenting boundary, it is in principle very sensitive to alternative models and the presence of species not participating in the reaction. This approach is compared with traditional fitting of weight average data and applied to the initial stages of Mg(2+)-induced tubulin self-associating into small curved polymers, and vinblastine-induced tubulin spiral formation. The appropriate use and limitations of the methods are discussed.     

Synthesis and Characterization of PLGA Shell Microcapsules Containing Aqueous Cores Prepared by Internal Phase Separation

The preparation of microcapsules consisting of poly(d,l-lactide-co-glycolide) (PLGA) polymer shell and aqueous core is a clear challenge and hence has been rarely addressed in literature. Herein, aqueous core-PLGA shell microcapsules have been prepared by internal phase separation from acetone-water in oil emulsion. The resulting microcapsules exhibited mean particle size of 1.1?±?0.39 μm (PDI?=?0.35) with spherical surface morphology and internal poly-nuclear core morphology as indicated by scanning electron microscopy (SEM). The incorporation of water molecules into PLGA microcapsules was confirmed by differential scanning calorimetry (DSC). Aqueous core-PLGA shell microcapsules and the corresponding conventional PLGA microspheres were prepared and loaded with risedronate sodium as a model drug. Interestingly, aqueous core-PLGA shell microcapsules illustrated 2.5-fold increase in drug encapsulation in comparison to the classical PLGA microspheres (i.e., 31.6 vs. 12.7%), while exhibiting sustained release behavior following diffusion-controlled Higuchi model. The reported method could be extrapolated to encapsulate other water soluble drugs and hydrophilic macromolecules into PLGA microcapsules, which should overcome various drawbacks correlated with conventional PLGA microspheres in terms of drug loading and release.     

Structure of an insect virus at 3.0 A resolution

We report the first atomic resolution structure of an insect virus determined by single crystal X-ray diffraction. Black beetle virus has a bipartite RNA genome encapsulated in a single particle. The capsid contains 180 protomers arranged on a T = 3 surface lattice. The quaternary organization of the protomers is similar to that observed in the T = 3 plant virus structures. The protomers consist of a basic, crystallographically disordered amino terminus (64 residues), a beta-barrel as seen in other animal and plant virus subunits, an outer protrusion composed predominantly of beta-sheet and formed by three large insertions between strands of the barrel, and a carboxy terminal domain composed of two distorted helices lying inside the shell. The outer surfaces of quasi-threefold related protomers form trigonal pyramidyl protrusions. A cleavage site, located 44 residues from the carboxy terminus, lies within the central cavity of the protein shell. The structural motif observed in BBV (a shell composed of 180 eight-stranded antiparallel beta-barrels) is common to all nonsatellite spherical viruses whose structures have so far been solved. This highly conserved shell architecture suggests a common origin for the coat protein of spherical viruses, while the primitive genome structure of BBV suggests that this insect virus represents an early stage in the evolution of spherical viruses from cellular genes.     

黄土丘陵区林草景观界面雨后土壤水分空间变异规律

对黄土丘陵区刺槐林-草地景观界面上雨后土壤表层(0～10 cm)和亚表层(10～20 cm)水分的空间变异规律进行了研究.经典统计学分析表明,草地两层的土壤含水量分别高于林地;林草界面两层的土壤含水量均为弱变异程度,并具有明显的生态梯度.移动窗口法分析表明,林草界面对土壤表层和亚表层的水分影响范围为边界两侧4 m、3 m,影响域分别为8 m、6m.地统计学分析表明,草地两层土壤含水量空间分布均表现为纯块金效应,林地两层均可拟合成线性模型,而林草界面两层均可拟合成球状模型;林草界面土壤表层、亚表层水分空间依赖性和空间自相关较强,其空间结构异质性明显高于林地和草地.克立格制图描述的林草界面土壤水分的空间分布格局为从边界处向两侧的一定距离范围内,土壤含水量呈条带状分布,而在较远的距离,水分的空间分布呈现出几个明显的斑块状.     

Stability of molecular adhesion mediated by confined polymer repellers and ligand-receptor bonds

Experiments have shown that stable adhesion of a variety of animal cells on substrates prepared with precisely controlled ligand distribution can be formed only if the ligand spacing is below 58 nm. To explain this phenomenon, here we propose a confined polymer model to study the stability of molecular adhesion mediated by polymer repellers and ligand-receptor bonds. In this model, both repellers and binders are treated as wormlike chains confined in a nanoslit, and the stability of adhesion is considered as a competition between attractive interactions of ligand-receptor binding and repulsive forces due to the size mismatch between repellers and binders. The force on each ligand-receptor bond is calculated from the confined polymer model, and the classic model of Bell is used to describe the association/dissociation reactions of ligand-receptor bonds. The calculated equilibrium bond distribution shows that there exists a critical ligand density for stable adhesion, corresponding to a critical ligand spacing which agrees not only qualitatively but also quantitatively with the experimental observation. In the case of stable adhesion, the model predicts an equilibrium separation between adhesion surfaces below 60% of the contour length of the ligand-receptor bonds.     

Effect of bending on the axisymmetric vibrations of a spheroidal model of the head

The head is modelled as an elastic prolate spheroidal shell filled with an inviscid, compressible fluid. Bending effects are included, and the free vibration frequency spectrum obtained is compared with that of an earlier spheroidal model using extensional (membrane) shell theory and with a spherical model including bending. The differences between the present results and those reported previously are significant.