Open Access
Translator Disclaimer
February 2007 Waiting for regulatory sequences to appear
Richard Durrett, Deena Schmidt
Ann. Appl. Probab. 17(1): 1-32 (February 2007). DOI: 10.1214/105051606000000619


One possible explanation for the substantial organismal differences between humans and chimpanzees is that there have been changes in gene regulation. Given what is known about transcription factor binding sites, this 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 [Mol. Biol. Evol. 18 (2001) 1764–1770] computed 5,950 years as the answer for six letter words. Here, 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 has mean 375,000 years when there is a 7 out of 8 letter match in the population consensus sequence (an event of probability roughly 5/16) and has mean 650 million years when there is not. Fortunately, 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 a 7 out of 8 letter match is good enough, the mean reduces to about 60,000 years.


Download Citation

Richard Durrett. Deena Schmidt. "Waiting for regulatory sequences to appear." Ann. Appl. Probab. 17 (1) 1 - 32, February 2007.


Published: February 2007
First available in Project Euclid: 13 February 2007

zbMATH: 1128.92024
MathSciNet: MR2292578
Digital Object Identifier: 10.1214/105051606000000619

Primary: 92D10
Secondary: 60F05

Keywords: clumping heuristic , Moran model , Poisson approximation , Population genetics , Regulatory sequence

Rights: Copyright © 2007 Institute of Mathematical Statistics


Vol.17 • No. 1 • February 2007
Back to Top