PHYSICAL MATHEMATICS SEMINAR

TOPIC:			STOCHASTIC EVOLUTION OF HAPLOID POPULATIONS: 
			REVIEW AND APPLICATIONS TO VIROLOGY

SPEAKERS:		I.M. ROUZINE* and J.M. COFFIN
			Department of Molecular Biology and Microbiology
			Tufts University

ABSTRACT:

Due to easily controlled conditions of growth, enormous population sizes,
and extremely high mutation rates, RNA viruses represent an ideal
experimental system to test methods and models of population biology.
There exists a considerable amount of data on genetic diversity of HIV and
less notorious viruses, impressive research facilities to obtain such
data, and a pressing need to predict effects of genetic evolution of HIV
on the prospects of drug and vaccine development. We analyze a broad range
of problems of population genetics with a view to virological
applications, such as accumulation of deleterious mutants and fixation of
advantageous genetic virus variants in vitro, and evolution of HIV within
and between infected patients.

In the first part of the project, we focus on one- and two-locus models
including random genetic drift, mutation, and selection. Evolutionary
behavior of the frequency of deleterious mutants is analyzed using a
stochastic equation of diffusion (Wright-Fisher) type predicting the
time-dependent probability density of the mutant frequency, as well as
direct Monte-Carlo simulation. We show that evolution becomes almost
deterministic is controlled by selection at very large population sizes,
$N >> 1/ \mu$, while smallest populations, $N << 1/s$, exhibit "neutral"
behavior, in the sense that selection does not matter much, and random
drift dominates. In the intermediate, broad interval, $1/ \mu << N <<
1/s$, termed the selection-drift regime, populations almost uniform
genetically behave essentially randomly, while highly polymorphic
populations exhibit almost deterministic behavior.

Based on these findings, we apply a specially designed linkage
disequilibrium test to several two-locus population models to show that an
effective HIV population, in a typical untreated patient, is larger than
$1/ \mu ~ 10^{5}$ infected cells, i.e., either at the border or within the
deterministic regime. We also studied a cluster of models describing
random sampling during transmission between patients to show, by excluding
alternative models, that the observed high level of genetic diversity in
the pro gene of HIV is, most likely, due to strong differences in the
best-fit sequence between individuals, 16%. We also discuss our ongoing
effort to account for linkage and biological interaction (epistasis)
between multiple loci. We propose a novel method to trace evolution of
individual sequences as a percolation in multi-dimensional space of
genetic variants.

DATE:			TUESDAY, NOVEMBER 7, 2000

TIME:			2:30 PM

LOCATION:		Building 2, Room 338


Refreshments will be served at 3:30 PM in Room 2-349



						Massachusetts Institute of Technology
						Department of Mathematics
						Cambridge, MA  02139