Gradual Crossover from Subdiffusion to Normal Diffusion: A Many-Body Effect in Protein Surface Water

Abstract

Dynamics of hydration water is essential for the function of biomacromolecules. Previous studies have demonstrated that water molecules exhibit subdiffusion on the surface of biomacromolecules; yet the microscopic mechanism remains vague. Here, by performing neutron scattering, molecular dynamics simulations, and analytic modeling on hydrated perdeuterated protein powders, we found water molecules jump randomly between trapping sites on protein surfaces, whose waiting times obey a broad distribution, resulting in subdiffusion. Moreover, the subdiffusive exponent gradually increases with observation time towards normal diffusion due to a many-body volume-exclusion effect.

Geometric universality and anomalous diffusion in frictional fingers

“…The fourth column shows the value of various exponents based on direct measurements in the frictional finger trees. The last two columns shows the values for frictional finger trees and for MST based on expected scaling relations from equations (16)- (18). The values for MST are based on the value for d m given in [4], and the values for the frictional finger trees are based on the direct measurement of the Hack exponent.…”

“…By contrast, in complex geometries or under flow, the diffusion exponent α may depart from unity, being subdiffusive 0<α<1 or superdiffusive 1<α<2. This type of anomalous transport is typical in complex systems [11][12][13][14][15][16][17][18]. The most famous example of subdiffusion is perhaps de Gennes 'la fourmi dans le labyrinthe' (the ant in the labyrinth), referring to a random walker on a 2D critical percolation cluster [9].…”

Quenched and annealed disorder mechanisms in comb models with fractional operators

“…In particular, they obtained an empirical MSD ∼ t 0.2 for the transversal direction and a MSD ∼ t 0.9 for the parallel direction of such macromolecules. Liang Hong and co-workers also reported a gradual crossover from subdiffusion to Brownian diffusion on the mobility of water molecules on protein surfaces [85]. They further argued that a broad distribution of trapping times causes the subdiffusion; however, water molecules start jumping to the empty sites as the trappings become occupied, resulting in the Brownian diffusion.…”

Analytic approaches of the anomalous diffusion: A review

“…Analysing the trajectory of one stochastic system we can describe if the movement is classified as anomalous or not. Recently Pan Tan et al made a combination of techniques, including the analytic, experimental and simulation, to describe the anomalous diffusion of water molecules around two biomolecules [185]. The techniques converge to a unique result, showing to the reader that the greater the number of techniques the greater the chances of unravelling some complex behaviour of nature.…”