Anomalous versus slowed-down Brownian diffusion in the ligand-binding equilibrium

Hédi Soula 1, 2, * Bertrand Caré 1, 2, 3, * Guillaume Beslon 1, 3 Hugues Berry 4, 1, 3, *
* Auteur correspondant
1 BEAGLE - Artificial Evolution and Computational Biology
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information, Inria Grenoble - Rhône-Alpes, LBBE - Laboratoire de Biométrie et Biologie Evolutive, CarMeN - Laboratoire de recherche en cardiovasculaire, métabolisme, diabétologie et nutrition
Abstract : Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) which converges back to a Brownian motion with reduced diffusion coefficient at long times, after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed-down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in 2d. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte-Carlo simulations, we show that those three scenarios have distinctive effects on the apparent affinity of the reaction. While continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hinderance by obstacles both improve it. However, only in the case of slowed-down Brownian motion, the affinity is maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes.
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Hédi Soula, Bertrand Caré, Guillaume Beslon, Hugues Berry. Anomalous versus slowed-down Brownian diffusion in the ligand-binding equilibrium. Biophysical Journal, Biophysical Society, 2013, 105 (9), pp.2064-2073. 〈10.1016/j.bpj.2013.07.023〉. 〈hal-00720515v3〉

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