Sedimentation equilibrium in macromolecular solutions of arbitrary concentration. I. Self-associating proteins

Relations describing sedimentation equilibrium in solutions of self-associating macromolecules at arbitrary concentration are presented. These relations are obtained by using scaled-particle theory to calculate the thermodynamic activity of each species present at a given radial distance. The results are expected to be valid for solutions of globular proteins under conditions such that interactions between individual solute molecules may be approximated by a hard-particle potential. Sedimentation equilibria in solutions containing either a nonassociating solute or a solute that self-associates according to several different schemes are simulated using the derived relations. The results of these simulations are presented in terms of the dependence of apparent weight-average molecular weight upon solute concentration. Simple empirical relations are presented for estimating the true weight-average molecular weight from the apparent weight-average molecular weight, without reference to any particular self-association scheme. The weight-average molecular weight estimated in this fashion is within a few percent of the true weight-average molecular weight at all experimentally realizable solute concentrations ( < 400 g/L).     

Numerical and series solutions of the peristaltic motion of an Oldroyd 8-constant fluid in an endoscope

In the present article, we have presented the peristaltic flow of an Oldroyd 8-constant fluid in an endoscope. The governing equations for the flow problem are simplified using long wavelength and low Reynold's number approximations. The solutions of the simplified problem are calculated using (i) Homotopy analysis method and (ii) Shooting method. The comparison of both the solutions shows a very good agreement between the results. The graphical results for the velocity field and stresses are presented to show the physical behaviour of all the parameters appearing in the problem.     

Numerical and series solutions of the peristaltic motion of an Oldroyd 8-constant fluid in an endoscope

In the present article, we have presented the peristaltic flow of an Oldroyd 8-constant fluid in an endoscope. The governing equations for the flow problem are simplified using long wavelength and low Reynold's number approximations. The solutions of the simplified problem are calculated using (i) Homotopy analysis method and (ii) Shooting method. The comparison of both the solutions shows a very good agreement between the results. The graphical results for the velocity field and stresses are presented to show the physical behaviour of all the parameters appearing in the problem.     

Periodic solutions of population models in a periodically fluctuating environment.

A periodically fluctuating environment is assumed in a population-modeling process that generates nonautonomous difference equations. The existence and uniqueness of periodic solutions are studied. A sufficient condition for existence and a necessary condition for uniqueness are obtained. Stability of the periodic solutions is investigated. Several numerical examples are given to illustrate the basic results, and a brief discussion is presented.     

On the analysis of oxygen diffusion and reaction in biological systems

An analysis of oxygen diffusion and reaction in multiregion biological systems is presented. This analysis considers a time-dependent flux boundary condition and oxygen consumption governed by Michaelis-Menten kinetics. The mathematical problem is developed in a uniform fashion, so as to include both the single cell and anisotropic systems with distinct regions which are characteristic of either a multicell spheroid or a tumor mass. Both transient and steady-state solutions are obtained, based on orthogonal collocation. Literature results on single-cell analysis are corroborated, and detailed transient solutions are presented for the oxygenation of a multicell spheroid, and for systemic oxygenation of both small and large tumors.     

Enzyme immobilization in porous solid supports-penetration of immobilized enzyme

The process of enzyme immobilization under the diffusion-controlled regime (i.e., fast attachment of enzyme compared to its diffusion) is modeled and theoretically solved in this article. Simple and compact solutions for the penetration depth of immobilized enzyme and the bulk enzyme concentration versus time are presented. Furthermore, the conditions for the validity of our solutions are also given in this article so that researchers can discover when the theoretical solutions can be applied to their systems.     

Facile Method for Monitoring Inhibition of Anaerobic Spore Outgrowth

A device is presented for the laboratory monitoring of spore outgrowth under controlled temperature and anaerobic conditions. Alterations in pH, redox potential, headspace composition, and optical density are followed as the activated spores grow out into vegetative cells. An interlock system allows the addition of test solutions or the removal of medium under anaerobic conditions. The device may also be used for rapid (<4 h) chemical inhibition studies or adapted for temperature injury studies of aerobic or anaerobic cells. Data on outgrowth of Clostridium sporogenes and inhibition by nitrite solutions are presented.     

Direct and inverse relationships between Riccati systems coupled with multiplicative terms

An analytical and computational framework for the derivation of solitary solutions to biological systems describing the cooperation and competition of species and expressed by the system of Riccati equations coupled with multiplicative terms is presented in this paper. It is demonstrated that relationships between these solitary solutions can be either direct or inverse. Thus, an infinitesimal perturbation of one population would lead to an infinitesimal change in the other population – if only both solitary solutions are coupled with the direct relationship. But, in general, that is not true if solitary solutions are coupled with the inverse relationship – an infinitesimal perturbation of one population may result into a non-infinitesimal change in the other population. Necessary and sufficient conditions for the existence of solitary solutions are derived in the space of the system's parameters and initial conditions.     

Dual Solutions for Nonlinear Flow Using Lie Group Analysis

`The aim of this analysis is to investigate the existence of the dual solutions for magnetohydrodynamic (MHD) flow of an upper-convected Maxwell (UCM) fluid over a porous shrinking wall. We have employed the Lie group analysis for the simplification of the nonlinear differential system and computed the absolute invariants explicitly. An efficient numerical technique namely the shooting method has been employed for the constructions of solutions. Dual solutions are computed for velocity profile of an upper-convected Maxwell (UCM) fluid flow. Plots reflecting the impact of dual solutions for the variations of Deborah number, Hartman number, wall mass transfer are presented and analyzed. Streamlines are also plotted for the wall mass transfer effects when suction and blowing situations are considered.     

Transport of ions of one kind through thin membranes

Summary The general equation for movement of ions of one kind through planar membranes and its equilibrium solutions are reviewed. A simple procedure to obtain exact numerical solutions is presented, and results are displayed as profiles of potential, field and concentration across the membrane. Finally, useful approximations for very low and very high ionic concentrations are given, and the limits of applicability of the constant-field approximation are indicated.     

The interaction of salts, amides, and water.

Infrared and Raman spectra are presented for salt solutions in N-methyl formamide and N,N'-dimethylformamide. Viscosities are reported for many of these solutions. Spectroscopic and viscosity data are also given for amide-salt solutions containing water. The three-component systems exhibit a hydrogen-bonding strength of water proton greater than amide proton, and an acceptor strength of Cl- greater than amide carbonyl oxygen greater than water oxygen. The salt cation is deduced by means of viscosity measurements to interact strongly with the amide carbonyl oxygen, even in the presence of appreciable quantities of water. Association of amides by hydrogen bonding through halide ions is also indicated.     

Extended Parker–Sochacki method for Michaelis–Menten enzymatic reaction model

In this article, a new approach—namely, the extended Parker–Sochacki method (EPSM)—is presented for solving the Michaelis–Menten nonlinear enzymatic reaction model. The Parker–Sochacki method (PSM) is combined with a new resummation method called the Sumudu–Padé resummation method to obtain approximate analytical solutions for the model. The obtained solutions by the proposed approach are compared with the solutions of PSM and the Runge–Kutta numerical method (RKM). The comparison proves the practicality, efficiency, and correctness of the presented approach. It serves as a basis for solving other nonlinear biochemical reaction models in the future.     

Acetylcholinesterase activity as an indicator of the content of stroma in infusable hemoglobin solutions in relation to the manner of their preparation

Acetylcholinesterase as an integral membrane part is a suitable indicator for characterizing the stroma in solutions of haemoglobin. The erythrocyte stroma cannot be fully eliminated because of the procedures of preparations for infundable haemoglobin solutions. The most favourable conditions with a stroma rest content of approximately 1% are presented by hypotonic haemolysis.     

Flow of a newtonian fluid through a permeable tube: The application to the proximal renal tubule

Creeping flow of a Newtonian fluid through a rigid permeable tube is considered and the transmural seepage is assumed to obey Darcy's law. Closed-form solutions for the pressure and velocity fields are presented and equations describing the axial variation of the mean cross-sectional pressure, the axial volumetric flow and the transmural fluid flux are derived. Approximate solutions for small seepage rates are given and are applied to the flow in the proximal renal tubule. Probable values for the epithelium permeability and the intraluminal hydrostatic pressure drop are obtained.     

The Application of Electromagnetic Theory to Electrocardiology: II. Numerical Solution of the Integral Equations

In an earlier paper exact integral equations were derived for the surface potentials resulting from sources within an irregularly shaped inhomogeneous body. These exact equations cannot usually be solved. In this paper a discrete analogue is constructed which is not straightforward to solve, but which can be treated by careful mathematical methods. In particular a deflation procedure greatly facilitates the iterative solution of the problem and overcomes the divergence encountered by other authors. Numerical solutions obtained for simple geometries are compared to the exact analytic solutions available in such cases. The necessary convergence of the solutions of the discrete analog towards the solution of the continuous problem is shown to occur only if the coefficients of the discrete analogue are carefully evaluated. Calculations are then presented for realistic thoracic geometries, typical results being presented as surface potential maps. Finally the important effect of the internal regional inhomogeneities, particularly a realistic cardiac blood mass, is demonstrated by obtaining vector loops with and without these effects.     

An analytic solution to the Förster energy transfer problem in two dimensions.

An analytic solution of the F?rster energy transfer problem in two dimensions is presented for the case in which the orientation factor is independent of the donor-acceptor distance, and both the donors and acceptors are randomly distributed in a plane. A general solution based on the method of F?rster is possible since all distances are measured in units of R0. The analytic solution is extended to the cases of donors embedded in structures that exclude acceptors, and donors that bind acceptors. The validity of the analytic solutions is demonstrated by comparison with numerical simulation calculations. Numerical approximations to the exact solutions are given for ease of computation. Specific applications to the case of fluorescence quenching of a membrane-bound donor by membrane-bound acceptors are presented.     

Aqueous solutions of some basic dyes--their use in the cytochemical detection of DNA

The paper contains results of staining DNA-aldehyde molecules with aqueous solutions of brilliant cresyl blue, thionin or neutral red, following Feulgen procedure and also reports on the use of aqueous solutions of these dyes, with primary amino group(s) in their molecules, for staining animal tissue nuclei after extraction of RNA with cold phosphoric acid. The pH of the dye solutions most suitable for optimum staining is 6.0. The time necessary for optimum staining of DNA-aldehydes and DNA-phosphate groups are 10 and 2 min respectively for tissues fixed in formalin, paraformaldehyde or Craf. Tissue fixed in Buin-fluid stain slower. The absorption curves of nuclei stained for DNA-aldehyde molecules and DNA-phosphate groups, stained with each of the three dyes are different from each other. The in vitro absorption curves of aqueous solutions of the three dyes have also been presented. Some implications of the results obtained are discussed.     

Derivation of general equations describing tracer diffusion in any two-compartment tissue with application to ionic diffusion in cylindrical muscle bundles

A set of generalized diffusion equations have been derived which describe radioactive tracer movement in any tissue that can be modeled as a distributed two-compartment system. These equations have been applied to ionic tracer movement in cylindrical muscle bundles, and the boundary conditions used correspond to experimental conditions during various ionic tracer diffusion experiments on cardiac papillary muscles. Specifically, solutions were obtained for extra- and intracellular tracer washout as well as for the extra- and intracellular steady-state tracer diffusion experiments of Weidmann (1966). These solutions are presented in series form as well as in graphical form and are compared with the corresponding experimental data. A comparison of these solutions with those obtained using simple exponential kinetics is presented, and it is shown that there is a marked discrepancy between these two methods of analysis for bundles of any appreciable diameter.     

Effectiveness factor calculations for immobilized enzyme catalysts

The steady state, nonlinear diffusion equations which describe reactions in constrained enzyme solutions are of great interest in many biological and engineering applications. As in other types of nonlinear differential equations, exact analytical solutions do not exist except in some simplified cases. In this paper, a general procedure is presented for solving numerically for the substrate concentration profile and effectiveness factor utilizing the transformation method suggested by Na and Na. Design correlations for enzyme solutions constrained within spherical membranes are included. The use of a unique definition of the Thiele Modulus in these charts permits the clear illustration of the effects of substrate concentration and external mass transfer resistances on the overall effectiveness factor for the catalyst particle.     

Linear Contrasts in Experimental Design with Non‐Identical Error Distributions

Estimation of linear contrasts in experimental design, and testing their assumed values, is considered when the error distributions from block to block are not necessarily identical. The normal‐theory solutions are shown to have low efficiencies as compared to the solutions presented here.