title: Shepherd model for knot-limited polymer ejection from a capsid.
abstract: We construct a tractable model to describe the rate at which a knotted polymer is ejected from a spherical capsid via a small pore. Knots are too large to fit through the pore and must reptate to the end of the polymer for ejection to occur. The reptation of knots is described by symmetric exclusion on the line, with the internal capsid pressure represented by an additional biased particle that drives knots to the end of the chain. We compute the exact ejection speed for a finite number of knots L and find that it scales as 1/L. We establish a mapping to the solvable zero-range process. We also construct a continuum theory for many knots that matches the exact discrete theory for large L.
authors.affiliation: Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA. tibor_antal@harvard.edu
authors.forename: Tibor
authors.initials: T
authors.lastname: Antal
authors.forename: P L
authors.initials: PL
authors.lastname: Krapivsky
authors.forename: S
authors.initials: S
authors.lastname: Redner
mesh_terms: D000818:Animals; D002213:Capsid / Q000378:metabolism*; D004279:DNA, Viral / Q000378:metabolism; D008954:Models, Biological; D011108:Polymers / Q000378:metabolism*; D013269:Stochastic Processes
chemical_list: D004279:DNA, Viral; D011108:Polymers