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Brownian search for targets hidden in cusp-like pockets: Progress and Applications

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Abstract

We report here recent progress in computing the search time for a stochastic particle to find a small target hidden in cusp-like pockets. The target is a small segment in dimension two, a small hole or a narrow ribbon in dimension three, placed at the end of a cusp. The asymptotic analysis of the diffusion equation reveals the role of the local geometry, and a mathematical difficulty comes from the boundary layer near the target. The methods are conformal mapping and matching asymptotic. We present applications in cell biology where cellular activation occurs when a diffusing particle finds a hidden site. This is the case during vesicular fusion initiated after a protein located between the vesicular and cell membranes binds to several diffusing calcium ions. Another example is a drug activation site located inside a deep molecular pocket. The analytical formulas clarify the role of small parameters.

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  1. Applied Mathematics and Computational Biology, Ecole Normale Supérieure, 46 rue d’Ulm, 75005, Paris, France

    C. Guerrier & D. Holcman

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  1. C. Guerrier
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  2. D. Holcman
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Guerrier, C., Holcman, D. Brownian search for targets hidden in cusp-like pockets: Progress and Applications. Eur. Phys. J. Spec. Top. 223, 3273–3285 (2014). https://doi.org/10.1140/epjst/e2014-02332-6

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  • DOI: https://doi.org/10.1140/epjst/e2014-02332-6

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