Micellization of casein-graft-dextran copolymer prepared through Maillard reaction

Casein is almost insoluble at around pH 4.6, which is its isoelectric point (pI). Grafting copolymer, casein-g-dextran, was prepared through the Amadori rearrangement of the Maillard reaction. The copolymer has a reversible pH sensitive property: micellization at the pI of casein forming a casein core and dextran shell structure and dissociation when pH differs from the pI. The micelles produced at pH 4.6 have a spherical shape and their size is dependent on the Maillard reaction: reaction time, molar ratio of casein to dextran, and molecular weight of dextran used. Typically, the hydrodynamic diameter of the micelles is about 100 nm and the critical micelle concentration is about 10 mg/L. The micelles are very stable in aqueous solution and can be stored as lyophiled powder. The micelles are able to encapsulate hydrophobic compounds such as pyrene.     

The biological functions of low-frequency vibrations (phonons). VI. A possible dynamic mechanism of allosteric transition in antibody molecules

By means of the quasi-continuity theory developed recently [Chou, K.-C. (1983) Biochem. J. 209 , 573–580; Chou, K.-C. (1984) Biochem. J. 221 , 27–31; Chou, K.-C. (1985) Biophys. J. 48 , 289–297], the low-frequency breathing motions of the β-barrels in the 12 domains of an IgG antibody molecule have been calculated. The results are in very good agreement with the observed low-frequency peaks in the Raman spectra. Based on this, the resonant couplings among the domains located at its different regions are discussed. It turns out that some very interesting functions of antibody molecules, such as the “chelate effect” and “trigger effect” whose dynamic principle has been so far unknown, can be clearly elucidated in terms of a fundamental natural law; i.e., it is through the channel of low-frequency resonance that the “signal” (or energy) in an antibody is transmitted from one location to the other, so as to be able to induce the relevant conformational change required for operating those important biological functions. The physical picture illustrated here once again provides us with a classic example that structure and function in nature are highly harmonized.     

Design of a nonuniformly distributed biocatalyst

The properties of a nonuniformly distributed biocatalyst, where the active enzymes are immobilized on the exterior or the interior portions o a solid support, are compared with those of a conventional biocatalyst which is uniformly distributed in a spherical geometry. To investigate the performance of nonuniformly distributed biocatalysts their effectiveness factors are computed and compared for six different enzyme distribution configurations: one-half core, one-half shell, one-third center space, one-third middle annulus, one-third outer shell, and the uniformly distributed. According to the results of numerical analysis, the biocatalyst performance of the exterior "shell" configuration is always far more effective for the immobilized enzymes with positive order reaction kinetics such as Michaelis-Menten and competitive product inhibition. However, in the case of negative order enzymatic reaction kinetics such as substrate inhibition, the interior "core" configuration of the biocatalyst can render far greater enzyme utilization efficiency.     

Prediction of femoral head collapse in osteonecrosis

The femoral head deteriorates in osteonecrosis. As a consequence of that, the cortical shell of the femoral head can buckle into the cancellous bone supporting it. In order to examine the buckling scenario we performed numerical analysis of a realistic femoral head model. The analysis included a solution of the hip contact problem, which provided the contact pressure distribution, and subsequent buckling simulation based on the given contact pressure. The contact problem was solved iteratively by approximating the cartilage by a discrete set of unilateral linear springs. The buckling calculations were based on a finite element mesh with brick elements for the cancellous bone and shell elements for the cortical shell. Results of 144 simulations for a variety of geometrical, material, and loading parameters strengthen the buckling scenario. They, particularly, show that the normal cancellous bone serves as a strong supporting foundation for the cortical shell and prevents it from buckling. However, under the development of osteonecrosis the deteriorating cancellous bone is unable to prevent the cortical shell from buckling and the critical pressure decreases with the decreasing Young modulus of the cancellous bone. The local buckling of the cortical shell seems to be the driving force of the progressive fracturing of the femoral head leading to its entire collapse. The buckling analysis provides an additional criterion of the femoral head collapse, the critical contact pressure. The buckling scenario also suggests a new argument in speculating on the femoral head reinforcement. If the entire collapse of the femoral head starts with the buckling of the cortical shell then it is reasonable to place the reinforcement as close to the cortical shell as possible.     

Size regulation of ss-RNA viruses

While a monodisperse size distribution is common within one kind of spherical virus, the size of viral shells varies from one type of virus to another. In this article, we investigate the physical mechanisms underlying the size selection among spherical viruses. In particular, we study the effect of genome length and genome and protein concentrations on the size of spherical viral capsids in the absence of spontaneous curvature and bending energy. We find that the coat proteins could well adjust the size of the shell to the size of their genome, which in turn depends on the number of charges on it. Furthermore, we find that different stoichiometric mixtures of proteins and genome can produce virus particles of various sizes, consistent with in vitro experiments.     

An optimization approach to predicting protein structural class from amino acid composition.

Proteins are generally classified into four structural classes: all-alpha proteins, all-beta proteins, alpha + beta proteins, and alpha/beta proteins. In this article, a protein is expressed as a vector of 20-dimensional space, in which its 20 components are defined by the composition of its 20 amino acids. Based on this, a new method, the so-called maximum component coefficient method, is proposed for predicting the structural class of a protein according to its amino acid composition. In comparison with the existing methods, the new method yields a higher general accuracy of prediction. Especially for the all-alpha proteins, the rate of correct prediction obtained by the new method is much higher than that by any of the existing methods. For instance, for the 19 all-alpha proteins investigated previously by P.Y. Chou, the rate of correct prediction by means of his method was 84.2%, but the correct rate when predicted with the new method would be 100%! Furthermore, the new method is characterized by an explicable physical picture. This is reflected by the process in which the vector representing a protein to be predicted is decomposed into four component vectors, each of which corresponds to one of the norms of the four protein structural classes.     

Fast ignition upon the implosion of a thin shell onto a precompressed deuterium-tritium ball

Fast ignition of a precompressed inertial confinement fusion (ICF) target by a hydrodynamic material flux is investigated. A model system of hydrodynamic objects consisting of a central deuterium-tritium (DT) ball and a concentric two-layer shell separated by a vacuum gap is analyzed. The outer layer of the shell is an ablator, while the inner layer consists of DT ice. The igniting hydrodynamic flux forms as a result of laser-driven acceleration and compression of the shell toward the system center. A series of one-dimensional numerical simulations of the shell implosion, the collision of the shell with the DT ball, and the generation and propagation of thermonuclear burn waves in both parts of the system are performed. Analytic models are developed that describe the implosion of a thin shell onto a central homogeneous ball of arbitrary radius and density and the initiation and propagation of a thermonuclear burn wave induced by such an implosion. Application of the solution of a model problem to analyzing the implosion of a segment of a spherical shell in a conical channel indicates the possibility of fast ignition of a spherical ICF target from a conical target driven by a laser pulse with an energy of 500?C700 kJ.     

A micelle model for the sedimentation behavior of bovine beta-casein

The monomer-single polymer model of G.A. Gilbert (Disc. Faraday Soc. 20 (1955) 68) for moving boundary sedimentation has been used by Payens and colleagues to explain the observed results for bovine caseins, and by Harrington and colleagues to explain the observed results for myosin fibrils. Electron microscope pictures of Buchheim and Schmidt have subsequently revealed micellar beta-casein in the form of slightly elongated or spherical particles having a bimodal size distribution, but with a broad range of particle sizes, at concentrations not too far above the critical micelle concentration. The equilibrium properties of a broadly distributed micellar system can be fitted by the shell model developed by one of us, and in the present article, the shell model is extended to predict the moving boundary sedimentation behavior of such a system. The observed sedimentation patterns, as well as the critical concentration predictions of the monomer-single polymer Gilbert sedimentation model, are satisfactorily described with the present model, based on a continuous distribution of intermediates between monomers and the largest possible spherical micelles. For one example considered, the predicted frequency distribution of molecular weight is in qualitative agreement with the frequency distribution of particle volume found by Buchheim and Schmidt.     

Modeling and analysis of diffusion and reaction in legume nodules

Diffusion of gases through legume nodules is important for nitrogen fixation. A mathematical model is presented for diffusion and enzymatic reaction for legume nodules with a reactive core and an inert shell. The transient model is solved numerically for spherical geometry for acetylene reduction by nitrogenase enzyme. The results are used to estimate the diffusivities of acetylene and ethylene in the nodules by comparing predicted and experimental lag times. The experimental results are also analyzed using an effectiveness factor plot for spherical nodules with inert shells and reactive cores. The results show that the diffusivities are slightly higher than those for acetylene and ethylene in water because of some contribution of gas phase diffusion. Applications to oxygen diffusion through nodule tissue are suggested.     

Contributions to the mathematical theory of organic form. II Asymmetric metabolism of cellular aggregates

The case is studied of a cellular aggregate forming a hollow spherical shell, the physical constants and the metabolic rate being non-uniform throughout the shell. This leads to asymmetries of concentration distributions, which are calculated here for some simple cases.     

Optimization of Nanoparticle Size for Plasmonic Enhancement of Fluorescence

This paper reports on the enhancement of fluorescence that can result from the proximity of fluorophores to metallic nanoparticles (NPs). This plasmonic enhancement, which is a result of the localized surface plasmon resonance at the metal surface, can be exploited to improve the signal obtained from optical biochips and thereby lower the limits of detection. There are two distinct enhancement effects: an increase in the excitation of the fluorophore and an increase in its quantum efficiency. This study focuses on the first of these effects where the maximum enhancement occurs when the NP plasmon resonance wavelength coincides with the fluorophore absorption band. In this case, the excitation enhancement is proportional to the square of the amplitude of the electric field. The scale of the enhancement depends on many parameters, such as NP size and shape, metal type, and NP–fluorophore separation. A model system consisting of spherical gold/silver alloy NPs, surrounded by a silica spacer shell, to which is attached a fluorescent ruthenium dye, was chosen and the dependence of the fluorescence enhancement on NP diameter was investigated. Theoretical calculations, based on Mie theory, were carried out to predict the maximum possible enhancement factor for spherical NPs with a fixed composition and a range of diameters. Spherical NPs of the same composition were fabricated by chemical preparation techniques. The NPs were coated with a thin silica shell to overcome quenching effects and the dye was attached to the shell.     

ADAPTATION FROM RESTRICTED GEOMETRIES: THE SHELL INCLINATION OF TERRESTRIAL GASTROPODS

The adaptations that occur for support and protection can be studied with regard to the optimal structure that balances these objectives with any imposed constraints. The shell inclination of terrestrial gastropods is an appropriate model to address this problem. In this study, we examined how gastropods improve shell angles to well‐balanced ones from geometrically constrained shapes. Our geometric analysis and physical analysis showed that constantly coiled shells are constrained from adopting a well‐balanced angle; the shell angle of such basic shells tends to increase as the spire index (shell height/width) increases, although the optimum angle for stability is 90° for flat shells and 0° for tall shells. Furthermore, we estimated the influences of the geometric rule and the functional demands on actual shells by measuring the shell angles of both resting and active snails. We found that terrestrial gastropods have shell angles that are suited for balance. The growth lines of the shells indicated that this adaptation depends on the deflection of the last whorl: the apertures of flat shells are deflected downward, whereas those of tall shells are deflected upward. Our observations of active snails demonstrated that the animals hold their shells at better balanced angles than inactive snails.     

Immobilization of lipase using egg shell and alginate as carriers: optimization of reaction conditions

The use of egg shell and alginate as carriers for lipase were studied and the kinetic parameters K _m and V _max were found out. These values were compared with those obtained for free lipase. The reaction conditions were optimized at a pH of 6.0–6.5, temperature at 40?°C and the time of reaction for 40 minutes. 600?μl of free enzyme, 30 numbers of alginate beads with lipase and 2.5?mg of egg shell loaded with lipase. The critical reaction velocity in case of free lipase, lipase adsorbed on egg shell and entrapped in alginate was found to be 53.779 I.U., 37.450 I.U., 31.543 I.U. respectively. It was found that the egg shell loaded with lipase could be reused for 8 times while the alginate beads only for 4 times. It was finally concluded that egg shell was an efficient carrier as far as lipase was concerned, especially in presence of an insoluble substrate.     

Self-organizing mechanism for development of space-filling neuronal dendrites

Neurons develop distinctive dendritic morphologies to receive and process information. Previous experiments showed that competitive dendro-dendritic interactions play critical roles in shaping dendrites of the space-filling type, which uniformly cover their receptive field. We incorporated this finding in constructing a new mathematical model, in which reaction dynamics of two chemicals (activator and suppressor) are coupled to neuronal dendrite growth. Our numerical analysis determined the conditions for dendritic branching and suggested that the self-organizing property of the proposed system can underlie dendritogenesis. Furthermore, we found a clear correlation between dendrite shape and the distribution of the activator, thus providing a morphological criterion to predict the in vivo distribution of the hypothetical molecular complexes responsible for dendrite elongation and branching.     

Electromechanical stresses produced in the plasma membranes of suspended cells by applied electric fields

Summary We analyze the electrical and mechanical stress in the bounding membrane of a cell (or vesicle) in suspension which is deformed by an external applied field. The membrane is treated as a thin, elastic, initially spherical, dielectric shell and the analysis is valid for frequencies less than the reciprocal of the charging time (i.e. less than MHz), or for constant fields. A complete analytic solution is obtained, and expressions are given which relate the deformation, the surface tension and the transmembrane potential difference to the applied field. We show that mechanical tensions in the range which lyse membranes are induced at values of the external field which are of the same order as those which are reported to lyse the plasma membranes of cells in suspension.     

Critical amino acids responsible for conferring calcium channel characteristics are located on the surface and aroundβ-turn potentials of channel proteins

Calcium ion is thought to be one of the initial signals in the process of synaptic modification. Various reports have described that the critical amino acids responsible for determining calcium permeability of ion channels are glutamic acid, glutamine, arginine, and asparagine. By using a computational method (MacPROT) distinguishing transmembrane, globular, and surface sequences of proteins, the present work predicts that the critical amino acids exist within surface regions of the proteins. Furthermore, occurrence ofβ-turn probabilities can be predicted around these critical residues by the protein conformational prediction method of Chou and Fasman. The results suggest that the critical amino acids exist at hydrophilic spaces or canals of membranous channel proteins and that the redirection potential of the protein chain induced by the turn structures provides the conformational change requisite for the ion selectivity and gating (opening/closing) of the channels.     

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.     

Stress field in actin gel growing on spherical substrate

Polymerization of actin to form an elastic gel is one of the main mechanisms responsible for cellular motility. The particular problem addressed here stems from the need to model theoretically the growth of actin gel under controlled conditions, as observed in experiments. A biomimetic in vitro system which consists of a spherical latex bead, coated by the enzymatic protein ActA, and a reconstituted cytoplasm within which such beads are placed, induces polymerization of actin on the surface of the bead in the form of successive elastic thin spherical layers. Each newly formed layer pushes outward, and is pushed inward by, the already formed spherical layers which altogether constitute an elastic spherical shell of thickness h varying with time. Thus, a stress field is created in the shell which in turn affects the rate of polymerization as well as that of dissociation of actin gel. Given this bio-chemo-mechanical coupling, the accurate determination of the stress field becomes a subject of great importance for the understanding of the process, and it is the main objective of this work. The problem is addressed by first assuming appropriate constitutive laws for the actin gel elastic material, and then solving the only non-trivial stress equilibrium differential equation along the radial direction assuming spherical symmetry. A linear and a non-linear constitutive model for isotropic elasticity is used, appropriate for small and finite strains, respectively, and the solution is found in closed analytical forms in both cases. Two important conclusions are reached. First, the stress field depends strongly on the compressibility of the actin gel medium via the value of the Poisson ratio, for both linear and non-linear analysis. Second, the linear and non-linear solutions are very close for small strains, but they diverge progressively as the strains increase from small to large. Guided by available experimental data on the observed strain levels, the analytical results are illustrated by selected graphs of stress variation along the radial direction. At the end some comments and suggestions on the bio-chemo-mechanical coupling of actin gel growth and resorption are presented, where the role of properly defined joint isotropic invariants of stress and a unit vector along the predominant direction of free ends of actin filaments at the polymerization site is introduced.     

The influence of macromolecular crowding on thermodynamic activity: solubility and dimerization constants for spherical and dumbbell-shaped molecules in a hard-sphere mixture

Macromolecules in solution can have large effects on the properties of other solutes through nonideal excluded-volume (crowding) interactions. Minton has calculated such effects by treating the macromolecules as a hard-sphere fluid in a background of an inert structureless solvent. In the present paper these calculations are extended by including the primary solvent as a separate component in a hard-sphere mixture. The results are in good agreement with experimental data. However, some predictions of this model differ drastically from those based on Minton's approach. Thus, much smaller effects from macromolecular crowding, particularly by smaller molecules, are expected. The present results also predict a much larger dependence on the shape of the molecules under study; notably for a dimerization reaction, it is found that the excluded-volume effects actually can destabilize side-by-side binding of two spherical molecules, while a dimerization to a spherical complex is stabilized. Therefore there will exist intermediate shapes of complexes whose stability is insensitive to crowded-volume effects. The consequences for crowding effects inside the living cell are also discussed.     

Neutron spin echo studies on ferritin: free-particle diffusion and interacting solutions

The dynamics of proteins are often studied by means of quasielastic neutron scattering (QENS), for example by time-of-flight methods. The spatial dimensions (10-20 nm) present in protein solutions are accessible by neutron scattering. In this article, a systematic study of diffusive dynamics of ferritin and apoferritin (=ferritin without iron core) is presented. Apoferritin consists of a spherical shell built of 24 protein units and carries net negative charge at pH 5. We have studied diffusive dynamics of ferritin solutions by neutron spin echo (NSE). We pay attention to an important feature of this technique compared to other QENS methods, which being the usage of a broad wavelength band. Using a more sophisticated fit function than usually used in NSE, we find as expected in low concentrated systems that the diffusion coefficient approaches the free-particle value of apoferritin and coincides with the diameter of the apoferritin shell (12.2 nm). In interacting solutions, the NSE results reveal that the dynamic picture of this complex liquid is dominated by slowing down of the dynamics. In low-salt solutions, a structure factor peak appears due to ordering of the ferritin molecules on the length scale of several intermolecular distances. We discuss the usage of different NSE fit functions for interacting solutions near the structure factor peak. Comparison of the dependence of elastic and dynamic data on the scattering vector value shows the influence of indirect interactions on the dynamic picture, irrespective of the way of data analysis, which being necessary due to the broad wavelength spectrum.