title: Equilibrium state of molecular breeding.
abstract: We investigate the equilibrium state of the model of Peng, et al. for molecular breeding. In the model, a population of DNA sequences is successively culled by removing the sequences with the lowest binding affinity to a particular target sequence. The remaining sequences are then amplified to restore the original population size, undergoing some degree of point-substitution of nucleotides in the process. Working in the infinite population size limit, we derive an equation for the equilibrium distribution of binding affinity, here modeled by the number of matches to the target sequence. The equation is then solved approximately in the limit of large sequence length, in the three regimes of strong, intermediate and weak selection. The approximate solutions are verified via comparison to exact numerical results.
authors.affiliation: Dept. of Physics, Bar-Ilan University, Ramat-Gan, IL, 52900, Israel.
authors.forename: Elisheva
authors.initials: E
authors.lastname: Cohen
authors.forename: David A
authors.initials: DA
authors.lastname: Kessler
mesh_terms: D020137:Base Pair Mismatch; D001665:Binding Sites; D004247:DNA / Q000235:genetics* / Q000378:metabolism; D019143:Evolution, Molecular; D008957:Models, Genetic; D009154:Mutation
chemical_list: D004247:DNA