A theoretical analysis of the reptational motion of DNA in a gel that includes the effects of molecular fluctuations has been used to explain the main features found in experiments involving periodic inversion of the electric field. The resonance-like decrease of the electrophoretic mobility as a function of pulse duration is related to transient "undershoots" in the orientation of the molecule, in agreement with recent experimental data. These features arise from a delicate interplay of internal and center of mass motion of the molecules under pulsed field conditions, and are important for the separation of DNA molecules in the size range 0.2 to 10 million base pairs.

The collapse transition of selfavoiding walks on a square lattice: A computer simulation studyUsing the scanning simulation method we study the tricritical behavior at the Flory O-point of self-avoiding walks (SAWs) of N<250 steps with nearest neighbors attractions € (E < 0) on a simple cubic lattice (in the following paper we investigate tricritical trails on the same lattice). The tricritical temperature T t is -ElkBT t = 0.274±0.OO6 (one &tandard deviation). The results for the radius of gyration G and the end-to-end distance Rare consistent with the theo;etical prediction V t = 0.5 and with a logarithmic correction to scaling; the ratio (G 2 ) / (R2) = 0.1659 ± 0.000 1 (calculated without taking into account correction to scaling) is only slightly smaller than the theoretical asymptotic value 1/6 = 0.1666 .... The results for the partition function Z at T t lead to Yt = 1.005±0.017 in accord with theory and to I-'t = 5.058 ±0.014, where I-'t is the growth parameter; the correc,tion to scaling in Z is found to be relatively small. For the chain length studied the divergence of the specific heat at T t (a t "",0.3) is significantly larger than that predicted by theory, (In N)3/ll (i.e. at = 0). Also, at T t our data are affected by strong correction to scaling and are thus not consistent with the theoretical value of the crossover exponent tPt=0.5.

Employing the scanning simulation method, we study the tricritical behavior (at the Flory θ point) of self-avoiding walks with nearest-neighbors attraction energy ε(−‖ε‖) on a square lattice. We obtain −ε/kBTt=0.658±0.004, where Tt is the tricritical temperature and kB is the Boltzmann constant. The radius of gyration G and the end-to-end distance R lead to νt(G)=0.5795±0.0030 and νt(R) =0.574±0.006, respectively. We also obtain γt=1.11±0.022 and μt =3.213±0.013, where γt is the free energy exponent and μt is the growth parameter. Three estimates are calculated for the crossover exponent φt , based, respectively, on G, R and the specific heat C: φt (G)=0.597±0.008, φt(R)=0.564±0.009, and φt(C)=0.66±0.02. Our values for νt and γt are close to the Duplantier and Saleur exact values for the θ′ point, νt =4/7=0.571... and γt=8/7=1.142 ... . However, our values of φt are significantly larger than the exact value φt=3/7=0.42... . This suggests that the θ and θ′ points belong to different universality classes.

Linear dichroism and electric birefringence measurements show that when an electric field is applied to a DNA molecule at equilibrium in an agarose gel, the isotropic molecular conformation quickly orients in the field direction, reaching first a maximum ‘‘overshoot’’ orientation before it relaxes towards a somewhat less oriented but still anisotropic steady-state conformation. We present here a simple analytical model of this overshoot effect together with numerical results from a computer simulation of gel electrophoresis. The predicted dependence of the overshoot time and orientation upon field intensity and molecular size are in good agreement with experimental results. The dynamics of the overshoot involves U-shape conformations that disappear only after the internal elastic forces completely dominate the electric forces. It is also predicted that a different overshoot regime takes place for low electric fields and small molecular sizes, and that a primary and a secondary overshoot may appear for very large molecules.

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