Bioinformatics Preprint 07-006
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Titel:
The transient probability distribution of M/M/&infty;:
a stochastic model for transcription factor binding
site evolution
Author(s):
Günter P. Wagner,
Wolfgang Otto,
Vincent Lynch,
Peter F. Stadler
Submitted
Abstract:
Both experimental as well as sequence evolution evidence suggests that
transcription factor binding sites can undergo divergence and turnover even
when the transcriptional output remains conserved. Furthermore it is likely
that there exist lineage specific differences in the retention rate of
binding sites that make it desirable to estimate the rate of acquisition
and decay of transcription factor binding sites from comparative sequence
data. In this paper we propose a stochastic, phenomenological model for
binding site turnover. For a given genomic region we assume a constant rate
of binding site origination /lambda/ and a constant per site decay rate of
/mu/. We derived an explicit expression for the conditional probability
distribution of the number of binding sites n at time t given
n0 binding sites at t=0. The analytical result was
compared to a simulation model and we found that it closely predicts the
simulated sequence evolution. We then analyzed a small data set of the
number of estrogen response elements (ERE) in mammalian HoxA sequences and
showed that the data is broadly consistent with the assumption of a
stationary turnover process. A regression of shared EREÇs over the time
since divergence led to an estimate of the half life time for an ERE in the
primate HoxA clusters of about 27 myr, which corresponds to a per site
decay rate of 1.3*10-9/year and a rate of origination of
1.6*-7/year. We conclude that the model can be used to
estimate the rate of binding site turnover from comparative genomic data.
Keywords:
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