Non-markovian transport of DNA in microfluidic post arrays.
We present an analytically solvable model for the transport of long DNA through microfluidic arrays of posts. The motion is a repetitive three-part cycle: (i) collision with the post and extension of the arms; (ii) rope-over-pulley post disengagement; and (iii) a random period of uniform translation before the next collision. This cycle, inspired by geometration, is a nonseparable (Scher-Lax) continuous-time random walk on a lattice defined by the posts. Upon adopting a simple model for the transition probability density on the lattice, we analytically compute the mean DNA velocity and dispersivity in the long-time limit without any adjustable parameters. The results compare favorably with the limited amount of experimental data on separations in self-assembled arrays of magnetic beads. The Scher-Lax formalism provides a template for incorporating more sophisticated microscale models.
Minc
Nicolas
N
Laboratoire Physicochimie-Curie, CNRS/UMR 168, Institut Curie, Paris, France.
Viovy
Jean-Louis
JL
Dorfman
Kevin D
KD
D017122:Bacteriophage T4 / Q000737:chemistry / Q000235:genetics; D004279:DNA, Viral / Q000737:chemistry* / Q000302:isolation & purification; D008390:Markov Chains; D044085:Microfluidics / Q000379:methods; D008956:Models, Chemical; D013816:Thermodynamics
D004279:DNA, Viral