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New cellular automaton designed to simulate geometration in gel electrophoresis. (English) Zbl 0995.92021

Summary: We propose a new kind of cellular automaton to simulate transportation of molecules of DNA through agarose gel. Two processes are taken into account: reputation at strong electric field \(E\), described in the particle model, and geometration, i.e., subsequent hookings and releases of long molecules at and from gel fibres. The automaton rules are deterministic and they are designed to describe both processes within one unified approach. Thermal fluctuations are not taken into account. The number of simultaneous hookings is limited by the molecule length.
The features of the automaton are: (i) the size of the cell neighbourhoods for the automaton rule varies dynamically, from nearest neighbors to the entire molecule; (ii) the length of the time step is determined at each step according to dynamic rules. Calculations are made up to \(N=244\) reptons in a molecule.
Two subsequent stages of the motion are found. Firstly, an initial set of random configurations of molecules is transformed into a more ordered phase, where most molecules are elongated along the applied field direction. After some transient time, the mobility \(\mu\) reaches a constant value. Then, it varies with \(N\) as \(1/N\) for long molecules. The band dispersion varies with time \(t\) approximately as \(Nt^{1/2}\). Our results indicate that the well-known plateau of the mobility \(\mu\) vs. \(N\) does not hold at large electric fields.

MSC:

92C40 Biochemistry, molecular biology
68U20 Simulation (MSC2010)
92C05 Biophysics
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