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