DEPARTMENT OF MATHEMATICAL SCIENCES

APPLIED AND COMPUTATIONAL MATHEMATICS SEMINAR

**Speaker:** Tanya Kostova, NSF

**Title: ***
Genotype Dominance in the Molecular Quasispecies Model
*

**Abstract:**
A quasispecies is defined as "a dynamic distribution of nonidentical but closely related mutant and
recombinant viral genomes subjected to genetic variation, competition and selection and which acts as a
unit of selection". The concept is currently relatively widely adopted within the virology community
to qualify the variability of genetic sequences corresponding to the same virus species. The term "quasispecies"
originates from a mathematical model proposed in the 1970s by Eigen. The model is a system of ODEs for the
frequencies of the distinct genotypes, which obeys a mass conservation law and has a unique positive globally
stable equilibrium. Each genotype self-replicates but replication is error prone: thus there is a non-negative
probability that any genotype would mutate into any other genotype. In the absence of mutation the dynamic
equilibrium of the system is represented by the genotype with the highest "fitness" (i.e. productivity), while all
other types are extinct; in such a case the fittest genotype is dominant. Increase in the mutation rate leads to a
change in the position of the equilibrium in quasispecies space and may lead to the emergence of a new
dominant genotype.
We ask the question whether we can determine the dominant genotype when the mutation rate varies from 0 to
1 and whether the fittest genotype can remain dominant no matter what the mutation rate is. To answer this
question we analyze the dynamics of the system for value of the mutation rate equal to 1 and derive the
conditions under which a given genotype would be dominant for high mutation values.
Although the quasispecies model has been used to interpret and drive experimental work in virology, it does not
account for the complexity of real viral quasispecies. If time permits, I will shortly describe the replication cycle of
an RNA virus and will outline the requirements for a more realistic viral quasispecies model.

**Time:** Friday, Apr. 16, 2010, 1:30-2:30 p.m.

**Place:** Science and Tech I, Room 242

Department of Mathematical Sciences

George Mason University

4400 University Drive, MS 3F2

Fairfax, VA 22030-4444

http://math.gmu.edu/

Tel. 703-993-1460, Fax. 703-993-1491