INTERDISCIPLINARY STOCHASTIC PROCESSES COLLOQUIUM

Tuesday January 17, room 60 Evans, 4.10 - 5.00pm

Speaker: Rick Durrett (Cornell)

Title: Waiting for ATCAAAG

Abstract: 
One possible explanation for the substantial organismal differences that
have developed in the 6 million years since the divergence of humans and
chimpanzees is that there have been changes in gene regulation. The word
in the title is a sample transcription factor binding sites and motivates
the following probability question: given a 1000 nucleotide region in our
genome, how long does it take for a specified six to nine letter word to
appear in that region in some individual? Stone and Wray (2001) computed
5949 years as the answer for six letter words in the human population. We
will show that for words of length 6, the average waiting time is 100,000
years while for words of length 8, the waiting time is roughly a 1/3 -
2/3 mixture of exponentials with means 375,000 years and 625 million
years. In biological reality, the match to the target word does not have
to be perfect for binding to occur. If we model this by saying that we
allow mismatch, then almost all of the mass in the probability
distribution shifts to the smaller mean.