Biased reptation model

In the reptation region the electrophoretic mobility depends on the solute s molecular size NP and on the field strength E according to the biased reptation model [13] ... 

Slater, GW. and Noolandi, J., The biased reptation model of DNA gel electrophoresis mobility vs. molecular size and gel concentration, Biopolymers, 28, 1781, 1989. 

The mobility of flexible chains in gels is well described by the biased reptation model [1], which is indicated schematically in Fig. 4. In the model, the fibers of the gel are coarse grained into a reptation tube that confines the chain. The chain thus slithers along the tube contour (the reptation part) under the influence of the electric field, which provides a tendency for the slithering motion to be in the direction of the electric field (the biased part). 

DNA gel electrophoresis is one of the most widely used tools of molecular genetics research. The biased reptation model has proven to be useful to understand most continuous field and low-frequency pulsed field effects. In this paper, we review how we have generalized the reptation model to include the electric forces acting on the DNA polymer, and we give an analysis of the main results obtained from analytical and numerical calculations. 

Finally, the biased reptation model (BRM) predicts that under some conditions of field strengths and gel concentrations, the electrophoretic mobility becomes a non-monotonic function of the... 

Fig.4 In the biased reptation model, the biased walk of the chain in its tube, which creates new tube sections, is similar to the motion of a point-like particle between two absorbing walls. A biased Jump ends when the molecule has migrated over a distance a along the tube axis, i.e., when it has reached the next point defining the end of the next pore. This process is similar to the absorbtion of the particle by one of the walls, each at distance a from the starting position. The particle and the chain both have a one-dimensional velocity and diffusion constant D.

The biased reptation model provides a good framework to discuss the experimental results of the various gel electrophoresis techniques used to separate nucleic acids. Although more experiments are needed to fully characterize these techniques, available results indicate that the simplified version of the model discussed in this paper is satisfactory when low-frequency pulsed fields are used, or when transient intra-tube effects are not dominant. This is the case in continuous fields, for small molecules in intermittent fields, and possibly also for crossed fields. However, intra-tube effects are observed to play a role in field-inversion electrophoresis, for long molecules in intermittent fields, and during the first stages of an experiment (where an orientation overshoot is observed). 

The large number of cases where the biased reptation model is reliable indicates that the intra-tube effects do not rule out reptation as the basic migration mechanism. Further theoretical advances will include the effects of both intra-tube molecular orientation and tube orientation on the electrophoretic properties of large nucleic acids. 

Numerical simulations have been very helpful in the understanding of electrophoretic transport mechanisms in gels. As a first contribution, numerical simulations of the biased reptation model have permitted progress beyond the... 

III.3.2 Biasing the Reptation Model The reptation process is fully defined by the four elements present in the basic stochastic equations (8) and (9). These are the probabilities that the next Jump will be made towards the end of the tube, the time duration and the length 0 =0 of this Jump, and finally the vector c( ) giving the properties of the new tube section created by this Jump. The fact that p =i, x =XBrown (c(0>=0 in absence of a field reflects the fact that we then have Brownian motion. The tube concept and the assumption of a constant pore size a are implicit in Eq.(8). 

The BRM is a natural generalization of the original reptation model where the motion of the primitive chain in its "tube is considered to become biased when an electric field is applied. The electrophoretic properties of the DNA molecules are related in the BRM to the effect of the field on the conformation of the reptation tube since this conformation tends to orient in the field direction when the primitive chain creates new tube sections, the electrophoretic velocity becomes a nonlinear function of the electric field. This tube alignment also reduces the effectiveness of the entanglements in opposing the electrophoretic drift, with the consequence that, except for transient effects or very small molecules, the mobility becomes molecular-size independent in continuous fields. 

The models described above, biased reptation and lattice chains, assume a homogeneous geL An opposite approach, in which gel inhomogeneities play a dominant role, was recently proposed by Zimm [139]. In this model, the tube is represented by a series of lakes in which the chmn can expand, and straits in which it is strongly confined. Finally, simulations of dectophoretic drift in 3D random percolation clustem of obstacles, have started [173]. 

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