## Role of substrate unbinding in Michaelis-Menten enzymatic reactions.

- Shlomi Reuveni, Michael Urbakh, Joseph Klafter
- Proceedings of the National Academy of Sciences…
- 2014

- Published 2012 in Physical review letters

Motivated by novel experimental work and the lack of an adequate theory, we study the dynamic structure factor S(k,t) of large vibrating fractal networks at large wave numbers k. We show that the decay of S(k,t) is dominated by the spatially averaged mean square displacement of a network node, which evolves subdiffusively in time, ((u[over →](i)(t)-u[over →](i)(0))(2))∼t(ν), where ν depends on the spectral dimension d(s) and fractal dimension d(f). As a result, S(k,t) decays as a stretched exponential S(k,t)≈S(k)e(-(Γ(k)t)(ν)) with Γ(k)∼k(2/ν). Applications to a variety of fractal-like systems are elucidated.

@article{Reuveni2012DynamicSF,
title={Dynamic structure factor of vibrating fractals.},
author={Shlomi Reuveni and Joseph Klafter and Rony Granek},
journal={Physical review letters},
year={2012},
volume={108 6},
pages={068101}
}