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Non-Markovian polymer reaction kinetics

Nature Chemistry volume 4, pages 568–573 (2012)Cite this article

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Abstract

Describing the kinetics of polymer reactions, such as the formation of loops and hairpins in nucleic acids or polypeptides, is complicated by the structural dynamics of their chains. Although both intramolecular reactions, such as cyclization, and intermolecular reactions have been studied extensively, both experimentally and theoretically, there is to date no exact explicit analytical treatment of transport-limited polymer reaction kinetics, even in the case of the simplest (Rouse) model of monomers connected by linear springs. We introduce a new analytical approach to calculate the mean reaction time of polymer reactions that encompasses the non-Markovian dynamics of monomer motion. This requires that the conformational statistics of the polymer at the very instant of reaction be determined, which provides, as a by-product, new information on the reaction path. We show that the typical reactive conformation of the polymer is more extended than the equilibrium conformation, which leads to reaction times significantly shorter than predicted by the existing classical Markovian theory.

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Figure 1: Sketch of the examples of intramolecular and intermolecular reactions studied.
Figure 2: Theory and simulations of the cyclization reaction in three dimensions.
Figure 3: Theory and simulations of a diffusive variable in one dimension.
Figure 4: Theory and simulations of a diffusive variable in three dimensions.
Figure 5: Predicted polymer conformations at reaction.

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Acknowledgements

Support from European Research Council starting Grant FPTOpt-277998 and the French National Research Agency (ANR) Grants Micemico and DynRec are acknowledged.

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  1. Laboratoire de Physique Théorique de la Matière Condensée, CNRS/UPMC, 4 Place Jussieu, Paris, 75005, France

    T. Guérin, O. Bénichou & R. Voituriez

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  1. T. Guérin
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  2. O. Bénichou
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  3. R. Voituriez
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All authors contributed equally to this work.

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Correspondence to O. Bénichou.

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Guérin, T., Bénichou, O. & Voituriez, R. Non-Markovian polymer reaction kinetics. Nature Chem 4, 568–573 (2012). https://doi.org/10.1038/nchem.1378

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