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This article is part of the supplement: Proceedings of the Eighth Annual MCBIOS Conference. Computational Biology and Bioinformatics for a New Decade

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First-passage time analysis of a one-dimensional diffusion-reaction model: application to protein transport along DNA

Michael L Mayo1*, Edward J Perkins1 and Preetam Ghosh2

Author Affiliations

1 Environmental Laboratory, US Army Engineer Research and Development Center, Vicksburg, MS 39180, USA

2 Department of Computer Science, Virginia Commonwealth University, Richmond, VA 23284, USA

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BMC Bioinformatics 2011, 12(Suppl 10):S18  doi:10.1186/1471-2105-12-S10-S18

Published: 18 October 2011



Proteins search along the DNA for targets, such as transcription initiation sequences, according to one-dimensional diffusion, which is interrupted by micro- and macro-hopping events and intersegmental transfers that occur under close packing conditions.


A one-dimensional diffusion-reaction model in the form of difference-differential equations is proposed to analyze the nonequilibrium protein sliding kinetics along a segment of bacterial DNA. A renormalization approach is used to derive an expression for the mean first-passage time to arrive at sites downstream of the origin from the occupation probabilities given by the individual transport equations. Monte Carlo simulations are employed to assess the validity of the proposed approach, and all results are interpreted within the context of bacterial transcription.


Mean first-passage times decrease with increasing reaction rates, indicating that, on average, surviving proteins more rapidly locate downstream targets than their reaction-free counterparts, but at the price of increasing rarity. Two qualitatively different screening regimes are identified according to whether the search process operates under “small” or “large” values for the dissociation rate of the protein-DNA complex. Lower bounds are placed on the overall search time for varying reactive conditions. Good agreement with experimental estimates requires the reaction rate reside near the transition between both screening regimes, suggesting that biology balances a need for rapid searches against maximum exploration during each round of the sliding phase.