Abstracts of selected references

AU - Tietz D
TI - Analysis of one-dimensional gels and two-dimensional Serwer-type gels on the basis of the
extended Ogston model using personal computers.
AB - This report presents the stand-alone computer application ElphoFit, a software package for the analysis of gel electrophoretic data based on Ferguson plots. Either conventional one-dimensional gels or two-dimensional agarose gels (Serwer-type) can be evaluated. Special emphasis is on the latter gel type, which has been applied previously for the separation of DNA, intact viruses and polydisperse meningitis vaccines. ElphoFit is designed for Macintosh PCs and for the IBM XT, AT, PS/2 and compatibles. The program operates interactively with the user, who determines the course of evaluation. Data input is in the format of files providing values of gel electrophoretic migration distances or particle mobility (absolute or relative). Data processing involves a simultaneous least-square curve fitting algorithm (Newton-Gauss, Marquardt-Levenberg) which uses equations derived from the extended Ogston model. Functions are fit to the database by adjusting their variables, representing physical parameters of the gel and the electrophoresed particle. The program output consists of tables and graphics accompanied by an explanatory text providing the following information: (i) radius and free mobility of the electrophoresed particle, (ii) fiber radius, length and volume, mean or median pore radius of the gel, (iii) linear Ferguson plots, (iv) iso-free-mobility/iso-size nomogram for two-dimensional gels, (v) confidence ellipses, (vi) required parameters for image processing program GELFIT and (vii) goodness-of-fit and other statistical parameters, such as standard errors, dependency values, root-mean-square (RMS) error and determination coefficient. Other features of the program are (i) simulation of Serwer-type two-dimensional electrophoresis, (ii) standardization according to size, or size and free mobility, (iii) the conversion of particle radii to molecular (or particle) weight and vice versa, (iv) interconversion of DNA size specifications, i.e. the number of base pairs and the geometric mean radii, (v) computation of gel concentration for optimal resolution of two components, (vi) option to obtain a session record, (viii) option to establish a data output file containing the information of generated graphics (IBM only) and (ix) a text editing facility, e.g., for creating data files. Graphics (Macintosh version, PICT format) and text output files (both IBM and Macintosh versions, standard ASCII format) generated by ElphoFit are compatible with commercially available software.
SO - Electrophoresis 1991 Jan;12(1):28-39

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AU - Tietz D
AU - Aldroubi A
AU - Schneerson R
AU - Unser M
AU - Chrambach A
TI - The distribution of particles characterized by size and free mobility within polydisperse populations of protein-polysaccharide conjugates, determined from two-dimensional agarose electro- pherograms.

AB - New approaches for the characterization of polydisperse particle populations are presented*. The investigated samples contain virus-sized protein-polysaccharide conjugates which had previously been prepared as immunogens against bacterial meningitis (Hib). The analysis is based on two-dimensional agarose
electrophoresis (Serwer-type). This method, like the one of O'Farrell, achieves a separation according to size and charge. It relies on a different principle, however, and is applicable to nondenatured particles which are 100 to more than 1000 times larger in mass than regular uncrosslinked proteins. Data from stained gel patterns are evaluated by the computer program ElphoFit, which makes it possible to standardize the gel and to construct a nomogram which defines every position on the gel in terms of particle size and free mobility (related to surface net charge density). The output of ElphoFit, consisting of nomogram parameters, is transferred to the image processing program GELFIT. This software is used to evaluate the computer images obtained by digitizing the stained gel patterns: (i) The nomogram is electronically superimposed on the computer image. (ii) The gel pattern is transformed from a curvilinear to a rectangular coordinate system of particle size and free mobility. The center of gravity as well as density maxima are given in coordinates of particle size and free mobility. Ranges of gray levels can be accentuated by adding 16 pseudocolors. (iii) Using surface-stripping techniques, GELFIT provides an estimate for the number of major subpopulations within each preparation. (iv) Numerical values for the distribution of particle size and free mobility are determined. Using program IMAGE, the quantitative physical assessment of a given conjugate preparation is presented in the form of a computer-generated three-dimensional plot, the shape of which serves to identify and characterize the preparation visually. The data analysis based on digitized two-dimensional gel patterns is automated to an extent that a technician can perform routine evaluations. It uses the Macintosh II personal computer.
SO - Electrophoresis 1991 Jan;12(1):46-54

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AU - Aldroubi A
AU - Unser M
AU - Tietz D
AU - Trus B
TI - Computerized methods for analyzing two-dimensional agarose gel electropherograms.

AB - Previous methods interpret zonal or polydisperse gel patterns of two-dimensional Serwer-type gels in terms of size and free mobility (surface net charge density). These two parameters have been determined for each component without quantitatively measuring the abundance of the components. The present study advances these previous methods by determining the relative concentration of each component by computer evaluation of densitometrically analyzed gel patterns. Suitable procedures and their underlying algorithms are presented. The mathematical routines are implemented in a user-friendly software package, called
GelFit and designed for a Macintosh personal computer. The program input consists of digitized images of gel staining patterns exemplified by those obtained from electrophoresis of native subcellular-sized particles. The data are processed through the following steps: (i) Noise reduction and calibration. (ii) Geometrical transformation of the pattern onto a rectangular size/free mobility coordinate system using rationales of the extended Ogston model. (iii) Analysis of the transformed image to determine density maxima, density profiles along iso-free-mobility or iso-size lines, curve fitting of one-dimensional profiles or two-dimensional surfaces using Gaussian functions and curve stripping of surfaces to determine the possible number of particle populations.
SO - Electrophoresis 1991 Jan;12(1):39-46

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AU - Tietz D
AU - Chrambach A
TI - Concave
Ferguson plots of DNA fragments and convex Ferguson plots of bacteriophages: evaluation of molecular and fiber properties, using desktop computers.
AB - A desktop computer program evaluating physical properties of DNA and bacteriophages is presented. The analysis is based on data obtained from capillary and submarine-type agarose electrophoresis. Native molecular/particle properties and properties of the gel (or polymer) medium can be derived from electrophoresis at several gel concentrations. This is done conveniently by a computerized evaluation of the semi-logarithmic plot of mobility vs. gel concentration, designated the Ferguson plot. In application to most proteins, this plot is linear and computer programs exist to evaluate it. However, nonlinear Ferguson plots have assumed great importance in view of the fact that the plots are concave for DNA. Similarly, convex plots are important since they prevail in the electrophoresis of large particles in agarose. The computer program reported here is the first to (i) address concave Ferguson plots and (ii) allow for the evaluation of both cases using a desktop computer. Program ElphoFit version 2.0, a Macintosh application, is available upon request.
SO - Electrophoresis 1992 May;13(5):286-94

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AU - Orban L
AU - Garner MM
AU - Wheeler D
AU - Tietz D
AU - Chrambach A
TI - Characterization of the electrophoretic properties of nucleosome core particles by transverse polyacrylamide pore gradient gel
electrophoresis.
AB - Transverse pore gradient gel electrophoresis, previously applied to bent DNA, has extended the usefulness of the gel retardation assay in two ways: (i) by differentiating between different DNA conformations; (ii) by providing information regarding the physical properties of DNA. In the present study, similarly extended information is obtained with regard to a well-characterized DNA-protein complex, the chicken erythrocyte nucleosome core particle. (i) The winding of DNA around the protein core constrains the DNA which renders its Ferguson curve (migration distance vs. gel concentration) similar to that of kinetoplast DNA, i.e. it intersects sharply with the Ferguson curves of linear DNA standards. By contrast, the deproteinized nucleosome DNA exhibits a Ferguson curve similar to linear standards of the same length. (ii) Interpretation of the Ferguson curve based on a mathematical model shows that the nucleosome exhibits a linear Ferguson plot [log(mobility) vs. gel concentration]. This is similar to and characteristic of spherical proteins, contrasting with the concave plot typical for linear and bent DNA. (iii) The effective size of the nucleosome, evaluated in terms of an equivalent sphere (i.e. a hypothetical spherical particle with a radius, Res, having the same electrophoretic mobility as DNA for a particular set of experimental conditions), remains invariant across the gel concentration range of 3-9%T. This is similar to proteins and bacteriophages and contrasts with the progressive decline of Res with increasing gel concentration observed for linear DNA and the deproteinized nucleosomal DNA.
SO - Electrophoresis 1993 Aug;14(8):720-4

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AU - Tietz D
AU - Chrambach A
TI - DNA shape and separation efficiency in polymer media: a computerized method based on electrophoretic mobility data.

AB - The computer program
ElphoFit for evaluation of the nonlinear plots of log-(mobility) vs. polymer concentration (Ferguson plots) in terms of molecular and polymer properties has been extended to yield a measure of the molecular sieving capacity of he polymer medium. The usefulness of the extended program, version 2.2, was exemplified by the evaluation of DNA shape and separation efficiency in solutions and gels of agarose and polyacrylamide, using previous reports in the literature as a data base. That application of the extended program yields the following results:(i) The size of migrating DNA can be compared with an equivalent sphere having the same free mobility for a particular set of experimental conditions. The decrease in size of the equivalent sphere with polymer concentration previously demonstrated for agarose solutions applies to all of these polymer media; it reveals a steep, hyperbolic decline of that radius in uncrosslinked polyacrylamide solutions in contrast to he shallow decline in the other three media. (ii) The separation efficiency of polyacrylamide gels exceeds that of uncrosslinked polyacrylamide solutions; the separation efficiency of agarose solutions for DNA smaller than 1 kb in length is higher than that of polyacrylamide solutions. Program ElphoFit 2.2 is available on request from the first author.
SO - Electrophoresis 1993 Mar;14(3):185-90

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AU - Tietz D
AU - Chrambach A
TI - Computer simulation of the variable agarose fiber dimensions on the basis of mobility data derived from
gel electrophoresis and using the Ogston theory.
AB - Agarose gel electrophoresis of viruses and proteins was evaluated for estimating fiber dynamics of agarose by computer simulation based on the extended Ogston theory. By introducing functions, in place of previously used constant parameters, into the equations derived from the Ogston theory it was demonstrated that the effective fiber properties are variable as a function of both gel concentration and the size of the particle passing through the gel. This variability accounts for the curvature of plots of log(mobility) vs gel concentration in agarose gel electrophoresis as well as for the apparent dichotomy between fiber properties obtained from the electrophoresis of either viruses or proteins. Specifically, computer simulation based on the electrophoretic mobility values of five viruses and seven proteins by use of an eight (gel-specific) parameter model yielded functions relating gel concentration and/or particle size with electrophoretic mobility of particles, the retardation coefficient, K'R, and effective fiber radius, length, and volume. The simulations give further insights into, as well as mathematical basis for, a number of previously made assumptions (such as variation of agarose fiber structure with gel concentration, variation of fiber volume with particle size, continuity of the K'R vs radius plot from 0 to 45 nm), thus demonstrating the continued usefulness of the Ogston model. The mathematical model provides the elements for an improved method for the determination of particle size, charge, and potentially shape by agarose gel electrophoresis, and can be regarded as the basis for future elaboration of a computer program for the routine determination of these parameters.
SO - Anal Biochem 1987 Mar;161(2):395-411

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AU - Tietz D
TI -
Gel electrophoresis of intact subcellular particles. (Review)
AB - The review describes the application of gel electrophoresis to the characterization and separation of viruses, ribosomes, vesicles and other subcellular particles. The preparation of the sample, the choice of the buffer, the gel medium, the apparatus and the detection of the particle (staining and scanning) as well as the necessary theory are discussed. This includes the mathematical evaluation of experimental data on the basis of Ferguson plots using the extended Ogston theory. Simple methods and sophisticated computer simulation techniques are described and exemplified in application to the determination of particle size and charge, the pore size of the gel (unpublished data) and the two-dimensional agarose electrophoresis (unpublished). It is shown that the nature of the particle (e.g. spherical or rod-shaped, pliable or rigid texture) determines the shape of the non-linear Ferguson plot. In addition, the review gives a number of practical applications of gel electrophoresis, isoelectric focusing, titration curves and immuno-electrophoresis to subcellular particles. Pros and cons are evaluated. A comparison with other analytical procedures is made. The review is concluded by a futuristic outlook.
SO - J Chromatogr 1987 Jul 17;418:305-44

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AU - Tietz D
TI - Evaluation of mobility data obtained from
gel electrophoresis: Strategies in the computation of particle and gel properties on the basis of the extended Ogston model (Review)
AB - Structural analysis is usually performed by analyzing electromagnetic wave intensities (light, electron beams, X-rays) after passage through or reflection from the object of investigation. This review discusses structural characterization by electrophoretic sieving of macromolecules or subcellular particles in gel matrices, a method which does not require denaturing conditions. It is a two step procedure and can be performed consecutively  or simultaneously.   i) Migrating objects of known size acting as a kind of measuring probe are used to calculate the effective radius and total length of the gel fiber (standardization). The size of the probe determines the degree of resolution.  ii) The size, charge and shape of unknown samples is estimated on the basis of their retardation pattern.
This approach involves gel electrophoresis at well defined experimental conditions ("Quantitative Gel Electrophoresis")? and the determination of mobility values at different gel concentrations (gels at single concentrations) or different duration of electrophoresis (pore gradient gels). The obtained mobility data are evaluated on basis of the Ogston theory which describes the distribution of spacings in a random network of fibers. Its applicability to gel electrophoresis is discussed and the underlying mathematics is explained in the Appendix which also contains original information with regard to i) evaluation of gradient gels, ii) interpretation of electron microscopic pictures of polyacrylamide gel and iii) computer programs in BASIC for curve fitting and numerical solutions.
SO - Advances in Electrophoresis, Vol. 2, 109-169 (1988).

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AU - Tietz D
TI - Evidence against recent challenges of the
extended Ogston model
AB - The extended Ogston model has frequently been applied to characterize particles in biological samples according to size and free mobility (surface net charge density). The analysis rests on the computer-assisted evaluation of the semi-logarithmic plot of mobility, m, vs. gel concentration, T [g/100 mL] (Ferguson plot). The model originates from the work of Chrambach and Rodbard [Proc. Natl. Acad. Sci. USA 1970, 65, 970-977; The Practice of Quantitative Gel Electrophoresis, VCH Verlagsgesellschaft, Weinheim FRG, 1985, pp. 1-265] and is based on experimental observations of Morris [Protides of the Biological fluids, Vol. 14, Elsevier, New York 1966, pp. 543-551] and mathematical rationales of Ogston [Trans. Faraday Soc. 1958, 54, 1754-1757]. Recently, this model has been challenged in a short communication by Slater and Guo [Electrophoresis 1995, 16, 11-15]. This letter is a preliminary response to that article stating that Slater and Guo's objections appear not sufficiently substantiated.
SO - Electrophoresis 1995 Mar;16(3):460-1

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Further information is provided in the Readme files of the ElphoFit sofware package. Please address requests to:

Dietmar Tietz
E-M-A-I-L

Transfer to Computer Program ElphoFit