Limitations of methods of determining effective diffusion coefficients in cell immobilization matrices

Various techniques are available for determining the effective diffusivity D(e) of solutes such as glucose in cell immobilization matrices. Nearly all, if not all, are subject to errors and limitations as regards the ranges of temperature, pressure, and/or concentration over which they give reliable results. It is the purpose of this article to compare three of these methods, designated (a) thin disc, (b) cylinder, and (c) beads types, and to show by means of a sensitivity and error analysis of the equation used in each method that the thin-disc and cylindrical techniques give more accurate results of D(e) than does the bead method.     

Minimizing the errors associated with the determination of effective diffusion coefficients when using spherical cell immobilization matrices

Gel materials are often used to entrap biological catalysts. Several experimental methods have been proposed to estimate the diffusion coefficient of important chemical species within these materials. An error analysis for the bead method was performed and, contrary to previously reported results, when proper experimental conditions were employed, the error associated with the bead method was similar to that obtained using the other common methods.     

The determination of local cell membrane diffusion coefficients

Solutions applicable to the measurement of cell membrane diffusion coefficients are derived using an approximate integral method.     

Macroporous gel particles as robust macroporous matrices for cell immobilization

A new design of robust matrices for cell immobilization is described. Macroporous gels (MGs) with immobilized microbial cells were prepared at subzero temperatures and were formed inside a plastic core (so-called, protective housing). Due to the protective housing the macroporous gel particles with immobilized cells can be used in well-stirred bioreactors. High retained activity of yeast (77-92%) and Escherichia coli (50-91%) cells immobilized in MGs after drying and storage in the dried state was due to the high structural stability and heterogeneous porous structure of the MGs.     

Cell growth patterns in immobilization matrices

Within an immobilized cell matrix, mass transfer limitations on substrate delivery or product removal can often lead to a wide range of local chemical environments. As immobilized living cell populations actively grow and adapt to their surroundings, these mass transfer effects often lead to strong, time-dependent spatial variations in substrate concentration and biomass densities and growth rates. This review focuses on the methods that have been devised, both experimentally and theoretically, to study the non-uniform growth patterns that arise in the mass transfer limited environment of an immobilization matrix, with particular attention being paid to cell growth in polysaccharide gels.     

Electronic speckle pattern interferometry: a tool for determining diffusion and partition coefficients for proteins in gels

The aim of this study was to demonstrate electronic speckle pattern interferometry (ESPI) as a powerful tool in determining diffusion coefficients and partition coefficients for proteins in gels. ESPI employs a CCD camera instead of a holographic plate as in conventional holographic interferometry. This gives the advantage of being able to choose the reference state freely. If a hologram at the reference state is taken and compared to a hologram during the diffusion process, an interferometric picture can be generated that describes the refraction index gradients and thus the concentration gradients in the gel as well as in the liquid. MATLAB is then used to fit Fick's law to the experimental data to obtain the diffusion coefficients in gel and liquid. The partition coefficient is obtained from the same experiment from the flux condition at the interface between gel and liquid. This makes the comparison between the different diffusants more reliable than when the measurements are performed in separate experiments. The diffusion and partitioning coefficients of lysozyme, BSA, and IgG in 4% agarose gel at pH 5.6 and in 0.1 M NaCl have been determined. In the gel the diffusion coefficients were 11.2 +/- 1.6, 4.8 +/- 0.6, and 3.0 +/- 0.3 m(2)/s for lysozyme, BSA, and IgG, respectively. The partition coefficients were determined to be 0.65 +/- 0.04, 0.44 +/- 0.06, and 0.51 +/- 0.04 for lysozyme, BSA, and IgG, respectively. The current study shows that ESPI is easy to use and gives diffusion coefficients and partition coefficients for proteins with sufficient accuracy from the same experiment.     

Evaluation of Taylor dispersion injections: determining kinetic/affinity interaction constants and diffusion coefficients in label-free biosensing

In label-free biomolecular interaction analysis, a standard injection provides an injection of uniform analyte concentration. An alternative approach exploiting Taylor dispersion produces a continuous analyte titration allowing a full analyte dose response to be recorded in a single injection. The enhanced biophysical characterization that is possible with this new technique is demonstrated using a commercially available surface plasmon resonance-based biosensor. A kinetic interaction model was fitted locally to Taylor dispersion curves for estimation of the analyte diffusion coefficient in addition to affinity/kinetic constants. Statistical confidence in the measured parameters from a single Taylor dispersion injection was comparable to that obtained for global analysis of multiple standard injections. The affinity constants for multisite interactions were resolved with acceptable confidence limits. Importantly, a single analyte injection could be treated as a high-resolution real-time affinity isotherm and was demonstrated using the complex two-site interaction of warfarin with human serum albumin. In all three model interactions tested, the kinetic/affinity constants compared favorably with those obtained from standard kinetic analysis and the estimates of analyte diffusion coefficients were in good agreement with the expected values.     

Swelling behavior of poly(vinyl alcohol) cryogels employed as matrices for cell immobilization

Poly(vinyl alcohol) cryogels are prepared from aqueous solutions of the polymer by freezing and thawing and are employed as matrices for cell immobilization. The swelling behavior of these macroporous gel carriers in pure water and in solutions of certain compounds (salts, amino acids, and glucose) was studied to elucidate the osmotic properties of the cryogels during long-term exposure to aqueous media. It was shown that after the initial sol fraction was washed out, the residual gel matrix possessed high stability even at extreme pH conditions (acid or alkali concentration up to 1.0 mol l⁻¹) or in the presence of strong chaotropic salts such as sodium rhodanide. Although the macroporous supermolecular structure of the carriers under consideration underwent certain changes as a result of aging processes during prolonged washing of the gel, the high porous morphology of the material was retained.     

Comparison of two methods for determining human adipose cell size

The mean cell sizes of specimens of human adipose tissue were determined on sectioned slices according to the method described by Sj?str?m et al. (J. Lipid Res. 1971. 12: 521-530) and on adipocytes isolated after treatment of the tissue with collagenase. The average mean cell sizes from 11 biopsy specimens were 94.4 and 94.0 micro m, respectively (r = 0.964; P(t(b)) < 0.001; y = 0.90x + 9.74), for the two methods. There was no indication of an increased rupture of isolated large human adipose cells. Thus, with precautions (freshly siliconized glassware and omitting the centrifugation of the isolated cells), the collagenase method may be used for metabolic as well as morphologic studies of human adipose tissue.     

Estimation of diffusion coefficients of proteins

A correlation for estimating the diffusion coefficients of protein molecules is presented. The correlation is based upon literature values of the protein diffusion coefficients and molal volumes for 143 proteins. The correlation can be used for the estimation of diffusion coefficients using only molecular weight. Accuracy is such that a linear regression on 301 proteins showed 75% of the diffusion coefficients estimated fell within 20% of the experimental values. The relationship between this correlation, the Stokes–Einstein equation, and the Wilke–Chang correlation is discussed.     

Prediction of diffusion coefficients of plasmids

The ability to predict diffusion coefficients is important in the design, analysis, and operation of plasmid downstream processing operations such as membrane and fixed-bed chromatography. A correlation is proposed to predict the diffusion coefficient, D, of supercoiled plasmid DNA molecules in dilute solutions on the basis of the molecular weight, M, or size. Experimental data (18 points) collected from the literature confirmed the proposed variation of D with plasmid molecular weight as D proportional, variant M(-2/3), for molecules within the 1,800-287,100 base-pair range. The correlation was able to estimate the available experimental results with an average error of 6.3%.     

Prediction of diffusion coefficients of proteins

A correlation for predicting the diffusion coefficients of proteins at standard conditions is proposed by adapting the Stokes-Einstein equation to a model for the equivalent hydrodynamic sphere. The radius of gyration, which accounts for the size and shape of protein molecules in solution, was used in deriving the new correlation. The correlation successfully predicted the diffusion coefficients of proteins, for which experimental data were available, with a higher degree of accuracy than achieved by previous correlation methods.     

The use of flow cytofluorometry for determining antisperm antibodies by sperm immobilization and sperm toxicity methods]

During antisperm antibody detection by conventional methods of immobilization and cytotoxicity investigators used flow cytometry to detect dead and/or immovable sperm cells. It was shown that after incubation of sperm cells with low antiserum dilution immovable spermatozoa are still living. Evidently, cytotoxicity test in this case brings about false-negative results. Therefore, flow cytometry will be a success for ASAB detection through immobilization test.     

Determination of diffusion and permeability coefficients in muscle

A theory is presented for the study of diffusion in heterogeneous tissue-like structures. It is applicable to a common type of measurement in which the change of the amount of substance remaining in the tissue is determined as the substance diffuses from the tissue into an adjacent medium, for instance, Ringer's solution. The main objective of this paper is to obtain a method for the calculation of the diffusion coefficient in the intercellular space and of the permeability coefficients between this space and the cells, based on the type of measurement mentioned above. Although the fundamental ideas upon which the theory is based are applicable to any type of tissue, the formulae derived are limited to the case in which the cells form a flat bundle of parallel fibers. The theory is applied to the experimental results of E. J. Harris and G. P. Burn on diffusion of sodium in the sartorius muscle of the frog. We find that if we know the ratio of the cellular and intercellular volumes of the muscle the ratio of the equilibrium concentrations of sodium outside and inside the cells can be determined. A very simple mathematical analysis of the experimental relation between the amount of substance diffusing out of the muscle and the time of diffusion gives us this ratio. The ratio of the equilibrium sodium concentrations in the case of the sartorius frog muscle is between about 10 and 30, depending on the muscle used. The same mathematical analysis makes it possible to obtain the permeability coefficients of muscle fibers through simple calculations, if their sizes are known. The permeability coefficients for the experimental work mentioned above using sodium are 1.25 to 11.5×10⁻⁸ cm/sec for the flow into the fibers and 3.2 to 16×10⁻⁷ cm/sec for the flow in the opposite direction. The determination of the diffusion coefficient in the intercellular space is more laborious and yields only an order of magnitude: 10⁻⁶ cm²/sec.     

Characterization of sugar diffusion coefficients in alginate membranes

The diffusivity of several monosaccharides and disaccharides in calcium alginate gels was determined using a specially designed diaphragm cell. The diffusion coefficients of the tested sugars are 4 to 18% smaller in alginate gel than in water and, with the exception of fructose, this difference increases with increasing sugar molecular weight. Also the position of the carbonyl group seems to be determined in the value of the diffusion coefficient - ketoses have lower diffusion coefficients than aldoses.