DNA electrophoresis model. Alexander van Heukelum, Utrect Univ, The Netherlands.
Date: Wed, 5 Jun 2002 14:12:02 +0200 (MET DST)
From: Alexander van Heukelum
To: davis :at the domain: cise.ufl.edu
Subject: Sparse matrix library
-- Alexander van Heukelum -- Institute for Theoretical Physics
Room: Minnaert Building 307 Utrecht University
Phone: (+31) (30) 253 4622 Leuvenlaan 4
Fax: (+31) (30) 253 5937 3584 CE Utrecht
Email: heukelum :at the domain: phys.uu.nl The Netherlands
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The cage model of DNA electrophoresis
The cage model of DNA electrophoresis describes the drift, induced by a
constant electric field, of homogeneously charged polymers through a
gel. The gel forms an effective "tube", from which the polymers can only
escape by reptation, i.e., motion of stored length along the chain. The
polymer chain is modeled as a random walk on a cubic lattice, and stored
length is represented by two adjacent segments with opposite directions
(a kink). The dynamics consists of single-monomer moves: only
configurations which differ by the direction of a kink or the direction
of an end segment have a finite transition probability.
The direction of the field is chosen in the direction of the main body
diagonal of the lattice, such that many polymer configurations become
equivalent. The matrices presented here describe the transition
probabilities between such equivalence-classes of the configurations,
for an applied field of E = (0.1, 0.1, 0.1) for polymers of L = 3 to 15
monomers.
name length rows columns nonzeros
-------- -------- -------- -------- --------
cage3 3 5 5 19
cage4 4 9 9 49
cage5 5 37 37 233
cage6 6 93 93 785
cage7 7 340 340 3084
cage8 8 1015 1015 11003
cage9 9 3534 3534 41594
cage10 10 11397 11397 150645
cage11 11 39082 39082 559722
cage12 12 130228 130228 2032536
cage13 13 445315 445315 7479343
cage14 14 1505785 1505785 27130349
cage15 15 5154859 5154859 99199551
For more information on the matrices, see A. van Heukelum, G. T.
Barkema, and R. H. Bisseling, "DNA electrophoresis studied with
the cage model", J. Comp. Phys. 180, 313-326 (2002), or
http://arxiv.org/format/cond-mat/0101467.