Asymptotics of a Brownian ratchet for protein translocation |
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Authors: | Andrej Depperschmidt Peter Pfaffelhuber |
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Institution: | Albert-Ludwigs University Freiburg, Germany |
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Abstract: | Protein translocation in cells has been modelled by Brownian ratchets . In such models, the protein diffuses through a nanopore. On one side of the pore, ratcheting molecules bind to the protein and hinder it to diffuse out of the pore. We study a Brownian ratchet by means of a reflected Brownian motion (Xt)t≥0 with a changing reflection point (Rt)t≥0. The rate of change of Rt is γ(Xt−Rt) and the new reflection boundary is distributed uniformly between Rt− and Xt. The asymptotic speed of the ratchet scales with γ1/3 and the asymptotic variance is independent of γ. |
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Keywords: | primary 92C37 secondary 60J65 60G55 60K05 |
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