Letter to the Editor
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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 [1,2] and is based on experimental observations of Morris [3] and mathematical rationales of Ogston [4]. Recently, this model has been challenged in a short communication by Slater and Guo [5]. This letter is a preliminary response to that article stating that Slater and Guo's objections appear not sufficiently substantiated as explained in the following.
(i) The system of [5] is a two-dimensional periodic grid of squared obstacles and a 'squared' migrating particle, the simplest possible system. This is not a principal objection against simplification. The question is: Is this simple approach adequate? Most likely not, since it is generally problematic to analyze 3-D motion (like gel electrophoretic migration) in a 2-D plane and to treat random structures of gels in terms of a periodic architecture (gels are not crystals).
(ii) The parameter f in Eqs.3 and 4 of [5] does not represent the fractional volume available for a squared 'particle' (as stated in [5]), but the fractional area which is called fa in this letter.
(iii) It is mentioned in [5] that the extended Ogston model would "predict a linear relationship (Eqs.3 and 4 of [5]) between the mobility and the concentration of a periodic gel" (actually not a gel, but a grid in [5]). However, the extended Ogston model is designed for a 3-D random pattern of obstacles and cannot make predictions for 2-D periodic grids.
(iv) For their system (Fig.1 of [5]), they find fa = 1 - c =1 - 1/p^2 (Eq.3 of [5]), where p is the periodicity of obstacles. Since fa is the fractional area and a dimensionless number, c must be dimensionless too. In fact, c is the fractional area of the grid occupied by the squared obstacles. It cannot be the gel concentration, as stated in [5], since this parameter would have the dimension g/100 mL. Therefore: c <> T, where T is the gel concentration used for Ferguson plots. Since the obstacles in [5] have an area, but 0 volume, their concentration cannot be expressed in terms of weight/volume and Ferguson plots cannot be constructed at all.
(v) Since a periodic grid is used, the 'squared' particle in Fig.1 of [5] can access 100% of fa as far as geometry is concerned. At a periodicity p=2 (every other square occupied by an obstacle), the 'concentration' (see item iv) c=1/p^2=0.25 and the available fractional area fa = 1 - c = 0.75. However a 'squared' particle having exactly the size of the squared spaces would be grid-locked and cannot access any volume. It is puzzling to see in Figs.3 and 6 of [5] that such a particle has a considerable mobility, for example, a relative mobility of 0.67 at c = 0.25 in Fig.3! If a more realistic cubic periodic grid with p=2 had been considered, grid-lock would have occurred at an available fractional volume f=1-1/2^3=0.875. According to the extended Ogston model, particles could still migrate at f=0.1. All these observations strongly indicate that the approach of [5] necessarily has to be in contrast to the extended Ogston model, where sieving elements are randomly distributed (3-D) and pore sizes follow a Poisson distribution (Fig.17 of [6]) with the consequence that migrating particles are sterically hindered to access all of the pores with radii smaller or equal to the radius of the migrating particle (probability of no contact). The larger the particles, the fewer pores can be accessed and the particle migration is increasingly retarded. This approximates the sieving effect of gels.
(vi) Slater and Guo's usage of the term retardation coefficient is completely different from the extended Ogston model.
The items in (i) to (vi) show that the approach in [5] cannot be compared with the extended Ogston model and, therefore, cannot be used to prove or disprove basic assumptions of that model and equations derived from it. Other statements in [5] are based purely on simulations without the support of experiments. Experimental observations in favor of the extended Ogston model are:
(vii) The equation m = mo xf, one of the basic assumption of the extended Ogston model, rests on work of Morris [3] (mo , particle free mobility).
(viii) The statement in [5] that Ferguson plots are intrinsically non-linear is in opposition to experimental findings. Ferguson plots giving the appearance of being linear have been published for more than two decades (in a concentration range wide enough to produce up to 50% and more retardation). Morris [3] tested the linearity and found no deviation larger than 2 to 5% at the most. It was only about ten years ago that significantly nonlinear plots were mentioned and were mathematically analyzed thereafter in terms of the extended Ogston model [7,6,8].
(ix) Predictions of the extended Ogston model are quite accurate regarding the fiber dimensions ([9], Section 7.1 of [6]) and pore sizes (Table 3 of [10]) for agarose gels, the supercoiled fibers of which appear to approximate Ogston's random fiber network. This agreement particularly holds in view of the fact that results from independent methods vary substantially.
Other support for the extended Ogston model comes from both mathematical and computer-assisted approaches:
(x) Arvanitidou et al. [11] state in their detailed study that the extended Ogston model appears well founded for rigid spherical particles such as globular proteins.
(xi) A simulation study confirms the extended Ogston model [12].
The arguments in (i) to (xi) present evidence for the validity of the extended Ogston model [1,2] and evidence against challenges of that model by a recent communication of Slater and Guo [5]. The discussion presented in this letter is by far not exhaustive and will be continued in a more detailed report on Ogston model-related issues and the adaptation of this model to nonlinear Ferguson plots including plots derived from DNA electrophoresis.
[1] Rodbard, D. and Chrambach, A., Proc. Natl. Acad. Sci. USA 1970, 65, 970-977.
[2] Chrambach, A., The Practice of Quantitative Gel Electrophoresis, VCH Verlagsgesellschaft, Weinheim FRG, 1985, pp. 1-265. ISBN 3-527-26039-0.
[3] Morris, C.J.O.R., in: Peeters, H. (Ed.), Protides of the Biological fluids, Vol. 14, Elsevier, New York 1966, pp. 543-551.
[4] Ogston, A.G., Trans. Faraday Soc. 1958, 54, 1754-1757.
[5] Slater, G.W. and Guo, H.L., Electrophoresis 1995, 16, 11-15. [6] Tietz, D., Adv. Electrophoresis 1988, 2, 109-169.
[7] Tietz, D. and Chrambach, A., Anal. Biochem. 1987, 161, 395-411.
[8] Tietz, D. and Chrambach, A., Electrophoresis 1992, 13, 286-294.
[9] Serwer, P., Electrophoresis, 4, 375-382, 1983
[10] Tietz, D., J. Chromatogr. 1987, 418, 305-344.
[11] Arvanitidou, E., Hoagland, D. and Smisek, D., Biopolymers 1991, 31, 435-447.
[12] Wheeler, D. and Chrambach, A., Electrophoresis 1993, 14, 993-996.