Motion of megabase deoxyribonucleic acid during field-inversion gel electrophoresis: Investigation by nonlocal Monte Carlo

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Abstract
We give a detailed description of a new Monte Carlo method for the simulation of the forced dynamics of long chain polymers in a constrictive environment. The model is based on the reptation theory but admits, in addition, the possibility that loops of the chain (‘‘hernias’’) may escape laterally out of the tube. A discrete representation of the molecule, in which individual chain segments are either taut or slack, permits the extensional mode of the molecule within the tube to be taken into consideration. The dynamics is modeled by the nonlocal hopping of ‘‘defects’’ (regions of slack) along the chain, with Monte Carlo rules based on the stochastic equations of motion of the taut portions of the molecule. We use the technique to investigate the motion of long deoxyribonucleic acid(DNA) molecules, containing millions of base pairs, during field‐inversion gelelectrophoresis. For the pulse ratios most commonly used in practice, we find that the separation patterns display two regions of band‐inversion. This anomalous behavior is linked to the strong transient response of the molecules when the field is reversed; sudden field inversion induces the formation of a chain configuration shaped like an extended V after an interval of time that increases linearly with the chain length. The DNA molecules that have the minimum and the maximum migration speeds are those whose transient response times are approximately equal to the forward and the reverse pulse time, respectively.