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Thresholds to RNA virus stability
RNA viruses are known to replicate at very high mutation
rates. These rates are actually known to be close to their so-called
error threshold. This threshold is in fact a critical point beyond
which genetic information is lost through a so called
error catastrophe .
However, the transition from a stable quasispecies to genetic drift
and loss of information can also occur by crossing replication thresholds:
below some replication rates, the viral population gets suddenly unable
to survive. Available data from
hepatitis C virus population analysis
(see A. Mas et al., J. Gen. Virol. vol 85 (2004) pp. 3619-3626)
can be interpreted through this theoretical view, providing evidence for
such a replication threshold.

Left: hepatitis C virus. Right: the two phases of a simple quasispecies model
In its simplest form, we can consider a reduced system of equations
defining a population as formed by two basic groups: the master
sequence x1 and the other sequences, which we assume to be grouped into
an "average" sequence with population x2 (Swetina and Schuster, 1982).
Let us also assume (as a first approximation) that mutations occur from
the master to the second compartment but not in the
reverse sense. The enormous size of the sequence space makes this assumption
a good first approximation. The model is given by the next two
ordinary differential equations set:

It can be shown that the stability condition for the master sequence to persist
is given by the inequality:

In the previous figure (right) we show the two possible phases, separated by the critical line,
using a fixed f2 value (here f_2=0.25). Once such boundary is crossed,
we shift from one type of qualitative dynamics to the other. The standard error
threshold condition is associated to an increase in mutation rate.
Increased mutation rates crossing the critical line drive the master sequence into extinction.
But another possibility becomes obvious by considering the second parameter: as the
master sequence replication rate decreases, we can also perform the same type
of phase transition. Such scenario is consistent with a successful immune response
against the dominant sequence, which leads to a decreased viability of the master
sequence. This actually explains several
key features of the observed quasispecies complexity observed in the HCV infected
patients.
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FITNESS LANDSCAPES AND VIRAL EVOLUTION
Viral evolution takes place on fitness landscapes. The structure of such
landscapes is one of the key topics to be explored by our Lab and
collaborating teams. How the neutrality and rugeddness of landscapes
affects and is affected by viral dynamics will be explored using
different theoretical approaches.

See our related papers:
Climb every mountain?
Elena, S.F. and Sanjuán, R. (2003). Science 302: 2074-2075.
Evolution experiments with microorganisms: the dynamics and genetic bases of adaptation.
Elena, S.F. and Lenski, R.E. (2003). Nature Rev. Genetics 4: 457-469.
VIRUS AND DIGITAL EVOLUTION RELATED WEBSITES
Big Picture Book of Viruses
The Big Picture Book of Viruses is intended to serve as both a catalog of
virus pictures on the Internet and as an educational resource to those
seeking more information about viruses. To this end, it is intimately
linked to All the Virology on the WWW, and our collection of Virology Courses and Tutorials.
There are several ways to access the information in the Big Picture Book
of Viruses. All viruses are listed according to the family to which they
have been assigned by the International Committee on Taxonomy of Viruses
(ICTV). The images and other data can be obtained by the routes listed.
All the Virology in the WWW
All the Virology on the WWW seeks to be the best single site for Virology
information on the Internet. We have collected all the virology related Web
sites that might be of interest to our fellow virologists, and others
interested in learning more about viruses. Additionally, we have created
an index to virus pictures on the web, The Big Picture Book of Viruses,
which also functions as a resource for viral taxonomy. A collection of some
of the best Online Virology and Microbiology Course Notes available can also
be found here. If you're interested in even more information, we have The
Virology Bookshop, an on-line microbiology and virology bookstore
with a significant discount for our users.
Evolutionary Biology and Biocomplexity: Chris Adami's Lab
We study fundamental properties of the evolutionary process, using
theoretical and computational methods. Evolutionary theory has a claim
of universality, in the sense that the theory does not make any reference
to its instantiation, that is, how information is encoded. We therefore
often use populations of self-replicating computer programs (also known
as digital life) to perform simple evolutionary experiments. We believe
that evolutionary theory can be treated just like any theory in physics,
where theories inspire experiments, who in turn can be designed to validate of falsify theories.
Digital virus evolution: Claus Wilke
RNA viruses (such as influenza virus, human immunodeficiency virus,
or hepatitis A, B, C virus) tend to have very high mutation rates. As a
consequence, they can evolve rapidly in reaction to immune response or
treatment. Frequently, they adapt to new hosts, and the majority of newly
emerging infectious diseases are RNA viruses that cross the species barrier
from animal host to human (examples are SARS or the avian influenza).
However, a high mutation rate also implies frequent deleterious mutations.
I am studying questions such as how RNA viruses can thrive under high
rates of deleterious mutations, how they can mask the effect of deleterious
mutations under coinfection, and how they adapt to changing hosts.
In silico and in vitro microbial evolution: Lenski's Lab
The main focus of my lab is on experimental evolution. Evolution is usually
investigated using the comparative method or by studying fossils.
Our approach is to watch evolution as it happens, in the context of
experiments that are replicated and performed under controlled conditions.
The idea of watching evolution in action is not new. In fact, Charles Darwin,
in the first edition of On the Origin of Species (1859, p. 187), said
In looking for the gradations by which an organ in any species has been
perfected, we ought to look exclusively to its lineal ancestors ; but this
is scarcely ever possible, and we are forced in each case to look to species
of the same group, that is to the collateral descendants from the same
original parent-form.
In order to study evolution as it happens we are now performing experiments with two different fast-evolving systems: (a) Bacteria, primarily Escherichia coli; and (b) Digital organisms in the Avida system.
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