Single-file diffusion of uncharged particles

An equation for unidirectional fluxes of nonelectrolytes and for the total flux in the single-file transport through a narrow pore has been derived. The equation obtained accounts for the correlations of the population of the pore in the coordinate of transport. The problem has been solved using superposition approximation and unidirectional fluxes has been found. The population profile in the pore was shown to have nonlinear shape; this is principally different from the results of the classical diffusion approach.     

An equation to determine the practical tilt angle of a double-tilt specimen holder and its application to transmission electron microscopy

In this short communication an equation has been used to calculate the practical tilt angles of TEM specimens using a double-tilt holder. By using the equation, the determination of the normal direction of TEM thin foil specimens and the orientation difference between two phases or grains were found to be more convenient and less time consuming when compared to other methods.     

Physicochemical aspects of the antiseptic action of nanohydroxyapatite

The mechanism of interaction of nanocrystals of hydroxyapatite with Staphylococcus aureus bacteria has been investigated. It was shown that the growth of bacteria and their colonies both in the presence and absence of hydroxyapatite nanocrystals can be described using the Fokker-Planck equation. It was found that hydroxyapatite nanocrystals adhere in a particular orientation on the surface of bacteria, decreasing substantially their colony-forming ability.     

A compact model to predict quantized sub-band energy levels and inversion layer centroids of MOSFETs with a parabolic potential well approximation

A compact model to predict sub-band energy levels and inversion charge centroids in the MOSFET surface inversion layer has been presented in this paper for parabolic potential well approximation. Based on a coupled solution of the Schrödinger equation and the Poisson equation following the WKB method, one transcendental equation of the sub-band energy level has been rigorously derived and then the approximate analytical solutions for the sub-band energy levels and the inversion charge centroids have been obtained. The analytical results are compared with the numerical data and a good agreement between the analytical and numerical is found.     

Conversion of benzylpenicillin to 6-aminopenicillanic acid in a batch reactor and continuous feed stirred tank reactor using immobilized penicillin amidase

A rate equation has been derived to describe the hydrolysis of benzylpenicillin to 6-aminopenicillanic acid by penicillin amidase. The integrated from of the rate equation has been shown to predict satisfactorily the progress of the reaction in a batch reactor using either soluble or immobilized penicillin amidase. The rate equation was also used to predict the performance of a continuous feed stirred tank reactor containing immobilized enzyme. There was good agreement with experimental measurements.     

脱脂菌紫质与天然紫膜水合变化的比较

本实验通过不同水合度下天然紫膜、脱脂菌紫质吸附等温线分析、红外光谱对比,讨论了天然紫膜小磷脂、蛋白质、水三者作用关系,认为磷脂对天然紫膜中蛋白质表而一些极性基团的分布及水合有重要作用,这些位点的水合对蛋白质进一步水合变化起重要作用.     

Absolute reaction rate and kinetics of protein adsorption at solid-liquid interfaces.

Extents of adsorption of bovine serum albumin from aqueous solution to the surface of alumina, silica, carbon and chromium powder have been studied as function of time for various values of bulk protein concentration, pH, ionic strength and temperature. The rates of adsorption in all cases have been observed to fit in the first order rate equation with two different rate constants Ka1 and Ka2. Effects of addition of SDS, CTAB and neutral salts on values of Ka1 and Ka2 have also been studied. Using Arrhenius equation the activation energy values Ea1 and Ea2 have been evaluated from the values of Ka1 and Ka2 at three different temperatures, respectively. The corresponding values of enthalpy of activation (delta H*), entropy of activation (delta S*), and free energy of activation (delta G*) have been evaluated using Eyring's equation of absolute reaction rate. The mechanism of protein adsorption has been discussed in the light of basic principles of absolute reaction rate. It has been found that for Ka1 the delta H*1 greater than T delta S*1 and for Ka2 T delta S*2 greater than H*2, i.e. the anchorage and binding of protein to the surface are enthalpy controlled processes whereas the surface denaturation as well as rearrangement and folding is an entropy controlled process. The role of diffusion on rate of adsorption has also been discussed.     

19F nuclear magnetic resonance as a probe of the spatial relationship between the heme iron of cytochrome P-450 and its substrate

The distance between the heme iron of ferrous cytochrome P-450-CAM and a fluorine label attached to the 9-methyl carbon of its substrate, (1R)-(+)-camphor, has been determined using 19F NMR. This investigation uses the Solomon-Bloembergen equation to measure the distance from a paramagnetic heme iron to a fluorine probe incorporated into a substrate that is not in fast exchange. The structural identity of the substrate analogue, 9-fluorocamphor, has been established using one- and two-dimensional NMR methods and mass spectrometry. The relaxation rate of 9-fluorocamphor bound to high-spin paramagnetic ferrous P-450-CAM has been studied at 188, 282, and 376 MHz, and the correlation time has been directly determined from the frequency dependence of the relaxation rate. When the substrate analogue was bound to the low-spin diamagnetic ferrous-CO derivative of the enzyme, the relaxation rate was found to be 100 times slower and was therefore neglected in the distance calculation. The relaxation data for the paramagnetic system and the correlation time have been used to calculate a distance of 3.8 A between the heme iron and the C-9 fluoride. A fit of the distance and the chemical shift data to the pseudocontact shift equation predicts an angle of approximately 52 degrees between the heme normal and the Fe-F vector. The solution state Fe-F distance is somewhat shorter and the angle between the heme normal and the Fe-F vector slightly larger for the substrate-bound ferrous enzyme reported herein than the analogous values for the substrate-bound ferric enzyme determined in the solid state by x-ray crystallography. These differences may reflect a structural change at the substrate-binding site upon reduction of the iron.     

THE KINETICS OF OSMOSIS

It is shown that by combining the osmotic pressure and rate of diffusion laws an equation can be derived for the kinetics of osmosis. The equation has been found to agree with experiments on the rate of osmosis for egg albumin and gelatin solutions with collodion membranes.     

Oscillating growth patterns of multicellular tumour spheroids

The growth kinetics of 9L (rat glioblastoma cell line) and U118 (human glioblastoma cell line) multicellular tumour spheroids (MTS) have been investigated by non-linear least square fitting of individual growth curves with the Gompertz growth equation and power spectrum analysis of residuals. Residuals were not randomly distributed around calculated growth trajectories. At least one main frequency was found for all analysed MTS growth curves, demonstrating the existence of time-dependent periodic fluctuations of MTS volume dimensions. Similar periodic oscillations of MTS volume dimensions were also observed for MTS generated using cloned 9L cells. However, we found significant differences in the growth kinetics of MTS obtained with cloned cells if compared to the growth kinetics of MTS obtained with polyclonal cells. Our findings demonstrate that the growth patterns of three-dimensional tumour cell cultures are more complex than has been previously predicted using traditional continuous growth models.     

The determination of the kinetics of polysaccharide thermal degradation using high temperature viscosity measurements

Information about the thermal degradation of the polysaccharides sodium alginate, carrageenan and carboxymethyl cellulose has been obtained from the time dependence of the viscosity at high temperatures measured using a slit viscometer. The viscosity is related to the molecular weight using previously-published relations between the zero shear specific viscosity and the coil overlap parameter in conjunction with the appropriate Mark-Houwink equation. It is found that alginate is much less stable than carboxymethyl cellulose and carrageenan. Activation energies for depolymerisation obtained from Arrhenius plots in the presence of oxygen ranged from 50 kJ/mol for alginate to 105 kJ/mol for κ-carrageenan.     

Stochastic model of population growth and spread

A stochastic model for the population regulated by logistic growth and spreading in a given region of two-or three-dimensional space has been introduced. For many-species population the interactions among the species have also been icorporated in this model. From the random variables that describe stochastic processes of a Wiener type the space-dependent random population densities have been formed and shown to satisfy the Langevin equations. The Fokker-Planck equation corresponding to these Langevin equations has been approximately solved for the transition probability of the population spreading and it has been found that such approximate expressions of the transition probability depend on the solutions of the deterministic equations of the diffusion model with logistic growth and interactions. Also, the stationary or equilibrium solutions of the Fokker-Planck equation together with the special discussion on the pattern of single-species population spreading have been made.     

On the solution of the non-linear bio-heat equation

With reference to microwave localized hyperthermia, a non-linear model of the thermal behavior of living tissues, where local thermoregulating convective and conducting effects due to blood flow are taken into account, has been assumed. The non-linear operator equation for the space and time temperature distribution, which describes local energy balance (bio-heat equation), has been linearized and solved by using a variant of the Newton iterative method. Numerical calculations for plane stratified structures simulating living bodies, irradiated by plane electromagnetic waves, have been carried out.     

Slip boundaries in nanopores

The flow of liquid water confined within slit pores formed from amorphous surfaces of carbon and polydimethylsiloxane (PDMS) has been investigated using molecular dynamics techniques. For PDMS (including plasma treated forms) the slip length is found to be very small, and there are essentially stick boundary conditions. The slip lengths for amorphous carbon surfaces are significant; however, they are much smaller than those measured experimentally for nanopipes. We show, for the first time, that the slip length can be predicted using the Sokhan–Quirke equation for amorphous surfaces using only equilibrium properties.     

Degradation of Tectilon Yellow 2G by hybrid technique: combination of sonolysis and biodegradation using mutant Pseudomonas putida

Degradation of Tectilon Yellow 2G (TY2G), an azo dye has been studied by hybrid technique involving pretreatment by sonochemical method and further biological treatment by Pseudomonas putida mutant. Pretreatment experiments were carried out by sonolysis of the dye solution at different concentrations (100-1000 mg/L). Wild type Gram-negative P. putida species isolated from the textile effluent contaminated soil, which was found to be effective towards dye degradation, has been acclimatized so as to consume TY2G as the sole source of nutrition. Mutant strain was obtained from the acclimatized species by random mutagenesis using the chemical mutagen ethidium bromide for various time intervals (6-30 min). The optimum mutagenesis exposure time for obtaining the most efficient species for dye degradation was found to be 18 min. An efficient mutant strain P. putida ACT 1 has been isolated and was used for growth experiments. The mutant strain showed a better growth compared to the wild strain. The substrate utilization kinetics has been modeled using Monod and Haldane model equations of which the Haldane model provided a better fit. The enzyme kinetics of the mutant and wild species was obtained using Michaelis-Menten equation. The mutated species showed better enzyme kinetics towards the degradation of TY2G.     

Simplified calculation of cell water content during freezing and thawing in nonideal solutions of cryoprotective agents and its possible application to the study of “solution effects” injury

A simplified equation has been derived which reduces the time and complexity of calculating subzero cell water content during freezing and thawing as compared to calculation by means of the Mazur equation. The simplified equation also allows inclusion of the effects of nonideality of glycerol and dimethyl sulfoxide aqueous electrolyte solutions. Furthermore, a very simple, iterative method of solving the simplified equation has been shown to give results which are equivalent to those obtained using the far more difficult and involved Runge-Kutta technique. It is hoped that these simplifications will make calculation of cell water content accessible to more cryobiologists. In addition, possible applications of such calculations to mechanistic issues in the area of “solution effects” injury are discussed.     

The dynamics of continuous microbial culture described by cell age distribution and concentration of one substrate

A mathematical model has been considered in which the known equation of McKendrick and Von Foerster for cell age distribution is combined with that for substrate concentration. The dependence of cell division rate on cell age has been taken as a step function. The interrelation between culture parameters describing the substrate consumption and cell division has been found. The shape of cell age distribution as well as the values of substrate and cell concentrations in steady and transient states have been investigated. Stationary regimes at the initial culture state synchronized by ages have been found to be established as damped oscillations and age waves. Under definite conditions the transition from one steady growth regime to another includes sharp single-time age synchronization of the culture.     

Effect of counterion concentration on the dielectric behavior of a polypeptidic chain in the helix–coil transition

On the basis of the two-state model of a polyelectrolyte solution, the ion concentration in the polymer domain has been calculated by using the spherical Poisson–Boltzmann equation. The ion accumulation in the neighboring of the polyion influences, on different time scales, various electrical properties of the solution, in particular the low-frequency electrical conductivity and the high-frequency dielectric dispersion. These predictions have been compared with recent dielectric measurements on poly (L -glutamic acid) aqueous solutions during the conformational transition from the α-helix to random coil, and a satisfactory agreement has been found. This finding suggests that counterion distribution plays a different role in determining the electrical properties of charged polymer solutions, causing a electrophoretic contribution of the polymer domain to the electrical conductivity and influencing the high-frequency dielectric dispersion. © 1993 John Wiley & Sons, Inc.     

Volume of the conducting airways calculated from morphometric parameters

A method of calculating the volume of a tree distal to a cut at the origin of a branch, using branching, diameter and length ratios, has been developed. The method was applied to bronchial tree casts from human, dog, sheep, hamster, and rat lungs. It was found that the exponenta in the equation weight=k×diameter ^a is approximately equal to 3.0 in sheep lung casts, as found by Hooper (1977), but it is greater than 3.0 in casts from the other four species.     

Equations and calculations for fermentations of butyric acid bacteria

A stoichiometric equation has been derived which describes the interrelations among the various products and biomass in fermentations of butyric acid bacteria. The derivation of the equation is based on an assumed ATP yield, two biological regularities, and the biochemistry of product formation of the fermentations. The equation obeys the constraints imposed on growth and product formation by thermodynamics and the biochemical topology. The validity of the equation is tested using a variety of fermentation data from the literature. The uses, improvements, limitations, and extensions of the equation are also discussed in detail. For example, the fermentation equation is used to calculate the maximal possible yields of the main fermentation products.