TY - JOUR

T1 - Equilibrium state of molecular breeding

AU - Cohen, Elisheva

AU - Kessler, David A.

PY - 2005/9

Y1 - 2005/9

N2 - 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.

AB - 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.

KW - Evolution

KW - Molecular Breeding

KW - Population dynamics

UR - http://www.scopus.com/inward/record.url?scp=24344502753&partnerID=8YFLogxK

U2 - 10.1007/s00285-005-0324-8

DO - 10.1007/s00285-005-0324-8

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C2 - 15868193

AN - SCOPUS:24344502753

SN - 0303-6812

VL - 51

SP - 281

EP - 301

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

IS - 3

ER -