摘要:

1IntroductionThe dynamics of the water molecules in the vicinity of a biological surface are found to be different from those in the bulk.1–10The dynamical properties of water around a protein surface are found to depend on the distance from the biomolecular surface.1–3,9Similar observations have been obtained from the computer simulations of water near micellar surface.10In particular, the mean square displacement (MSD) of water molecules close to biological surfaces is found to be sublinear with time.2,3,11These results have been confirmed by neutron scattering experiments also.12MSD can in general be written as below,1MSD = ⟨|Δr(t)|2⟩ =c+a×tαwhere |Δr(t)| is the displacement of a molecule at timet. For diffusive dynamics,α= 1. For sub-diffusive dynamicsα< 1, whereas the dynamics is called super-diffusive ifα> 1. Recent computer simulation studies by Cannistraroet al.showed that the dynamics of water near a constrained biological surface is sub-diffusive for short time (below 10 ps) with the exponentαvarying from 0.75 to 0.96 depending on the region of water molecules chosen at different distances from the protein surface.13,2Sub-diffusivity has been observed in many other types of systems also, such as membrane bound protein,14polymer melts,12,15–17and the transverse motion of membrane point due to the bending modes18etc.On the other hand, enhanced or super-diffusion with an exponent 1.5 has been observed in the mean square displacement of engulfed microsphere in a living eukaryotic cell,19,20with a sub-diffusive behavior at short times.21The occurrence of super-diffusion has been interpreted as the evidence for a generalized Einstein relation, whereby the motion of the particles along microtubules in a dense network require displacement of the surrounding filaments. The time dependent diffusion coefficient is related by time dependent viscosity of the medium.21Recently, Garcia and Hummer reported a study on the dynamics of cytochrome c which exhibits a crossover from sub-diffusive over a short period (below 100 ps) to super-diffusive dynamics in the longer time with exponents 0.5 and 1.75, respectively.22Origin of the crossover from sub-diffusive dynamics at short time (t≤ 10 ps) to super-diffusive dynamics at intermediate time (10 ps ≤t≤ 200 ps) for different systems is not yet fully understood.Observations for the sub-diffusive dynamics of water near the biological surface have often been attributed to enhanced stability of the water molecules at the surface due to hydrogen bonding to the biological surface.23–26Theoretical models have been developed in terms of bound ⇌ free equilibration.27The evidence of such exchange was obtained by a nuclear Overhauser effect experiment.28On the other hand, molecular dynamics simulations of water molecules at protein and micellar surfaces show the existence of sizable fraction of water molecules in the layer with residence time larger than the rest.29The binding energy distribution varies from 0.5 to 9 kcal mol−1. The trajectory of individual water molecules clearly shows a dynamic equilibrium, between a bound state and a free state.30,31To the best of of our knowledge, no simple explanation has been offered for the observed super-diffusive behavior.Note that no detailed numerical solutions of time dependent diffusion or time dependent mean square displacement (MSD) in the model bistable potential have been carried out, even though such a study can throw light on the origin of the observed behavior. However, purely analytical studies in these type of systems have been limited by the fact that the heterogeneous surface faced by the water molecules makes a general analytical solution virtually impossible.It is shown in recent simulations of a micelle that the bound water molecules are energetically stable with a potential energy contribution of 9–12 kcal mol−1while the quasi-free water molecules which surround the bound water are only stable by 5–6 kcal mol−1.32Radial distribution function (g(r)) shows that the first shell of water molecules shows a peak around 3.5 Å while the second shell shows a peak around 6–7 Å.32The structure ofg(r) suggests the existence of an effective binding potential which could be double well in nature because the effective potential is related to radial distribution function by the following well-known relation2βVeff(r) = −lng(r)In this work, we explain the origin ofboththe sub- and the super-diffusive behavior of the biological water by studying the diffusion over simple double well and Morse type of potentials. The double well potential represents the potential environment of the water close to a biomolecule. The first potential energy well corresponds to the bound water molecule and the second well corresponds to the quasi-free water molecule. The effective potential energy of interaction between the surface and the water molecules of course becomes negligible at a few layers from the surface and here the water is free and behaves as in bulk water. A model of free diffusion (without any potential) is studied to compare the dynamics of the biological water relative to the bulk water. We demonstrate by numerical computation of the probability densityP(r,t) on the potential energy landscape that this model is able to catch the dynamical anomalies present in the biological water. The sub-diffusive behavior is shown to originate not only because of the binding to the surface but also due to the bound ⇌ free dynamic equilibration present among the water molecules at the surface. The MSD calculated from the distributionP(r,t) shows a cross-over from sub-diffusive behavior over a short time to a super-diffusive nature over a long time, precisely of the type observed in computer simulations.22However, we find that a pronounced sub-diffusivity is present only when the exchange between the two wells is facile. Self intermediate scattering functionFs(k,t) calculated fromP(r,t) also shows a marked non-exponential relaxation.

ISSN:1460-2733    

DOI:10.1039/b212786e

出版商:RSC    

年代:2003

数据来源: RSC