TY - JOUR

T1 - Solution of the quasispecies model for an arbitrary gene network

AU - Tannenbaum, Emmanuel

AU - Shakhnovich, Eugene I.

N1 - Funding Information:
This research was supported by the National Institutes of Health. The authors would also like to thank Eric J. Deeds for helpful discussions.

PY - 2004/1/1

Y1 - 2004/1/1

N2 - In this paper, we study the equilibrium behavior of Eigen’s quasispecies equations for an arbitrary gene network. We consider a genome consisting of [Formula presented] genes, so that the full genome sequence [Formula presented] may be written as [Formula presented], where [Formula presented] are sequences of individual genes. We assume a single fitness peak model for each gene, so that gene [Formula presented] has some “master” sequence [Formula presented] for which it is functioning. The fitness landscape is then determined by which genes in the genome are functioning and which are not. The equilibrium behavior of this model may be solved in the limit of infinite sequence length. The central result is that, instead of a single error catastrophe, the model exhibits a series of localization to delocalization transitions, which we term an “error cascade.” As the mutation rate is increased, the selective advantage for maintaining functional copies of certain genes in the network disappears, and the population distribution delocalizes over the corresponding sequence spaces. The network goes through a series of such transitions, as more and more genes become inactivated, until eventually delocalization occurs over the entire genome space, resulting in a final error catastrophe. This model provides a criterion for determining the conditions under which certain genes in a genome will lose functionality due to genetic drift. It also provides insight into the response of gene networks to mutagens. In particular, it suggests an approach for determining the relative importance of various genes to the fitness of an organism, in a more accurate manner than the standard “deletion set” method. The results in this paper also have implications for mutational robustness and what C.O. Wilke termed “survival of the flattest.”.

AB - In this paper, we study the equilibrium behavior of Eigen’s quasispecies equations for an arbitrary gene network. We consider a genome consisting of [Formula presented] genes, so that the full genome sequence [Formula presented] may be written as [Formula presented], where [Formula presented] are sequences of individual genes. We assume a single fitness peak model for each gene, so that gene [Formula presented] has some “master” sequence [Formula presented] for which it is functioning. The fitness landscape is then determined by which genes in the genome are functioning and which are not. The equilibrium behavior of this model may be solved in the limit of infinite sequence length. The central result is that, instead of a single error catastrophe, the model exhibits a series of localization to delocalization transitions, which we term an “error cascade.” As the mutation rate is increased, the selective advantage for maintaining functional copies of certain genes in the network disappears, and the population distribution delocalizes over the corresponding sequence spaces. The network goes through a series of such transitions, as more and more genes become inactivated, until eventually delocalization occurs over the entire genome space, resulting in a final error catastrophe. This model provides a criterion for determining the conditions under which certain genes in a genome will lose functionality due to genetic drift. It also provides insight into the response of gene networks to mutagens. In particular, it suggests an approach for determining the relative importance of various genes to the fitness of an organism, in a more accurate manner than the standard “deletion set” method. The results in this paper also have implications for mutational robustness and what C.O. Wilke termed “survival of the flattest.”.

UR - http://www.scopus.com/inward/record.url?scp=45849154871&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.70.021903

DO - 10.1103/PhysRevE.70.021903

M3 - Article

C2 - 15447511

AN - SCOPUS:45849154871

SN - 1063-651X

VL - 70

SP - 15

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

IS - 2

ER -