Anomalous Diffusion in Membranes
- PDF / 633,009 Bytes
- 12 Pages / 420.48 x 639 pts Page_size
- 51 Downloads / 223 Views
Abstract We study the undulations and the transverse diffusion of a tagged membrane point in both physical (passive) membranes and active biomembranes. In physical membranes thermal undulations generate a transverse subdiffusive motion, (r 2 ) t 2/3 . Active biomembranes include active sites that use chemical energy to pump ions or molecules from one side to the other. In this case we find a few regimes which show a strongly enhanced diffusion, (r 2 ) _ ta with 1 < a < 2.
1
Introduction
Lipid and surfactant membrane bilayers deserved much attention in the past two decades [1, 2]. While the interest in these membranes has been very wide, ranging from determining fundamental concepts of fluctuating surfaces to very practical applications, one key motivation has been their possible role as simple models for biomembranes. Most of
the studies focused on the stiffness of a membrane bilayer to bending and stretching, the statistics of its thermal undulations, and the different phases in which it appears in, and out of, equilibrium. Biomembranes include, however, among other additional constituents, carrier proteins that act as active transport sites [3], for example, the ATPase controlling the Na+-K+ pump. These sites use chemical energy (ATP), or sometimes the free-energy stored in a chemical potential gradient of another type of ions, in order to "pump" a solute ion or molecule against its chemical potential gradient. When an ion is transferred from one side of the membrane to the other through an active channel, the membrane is using force to do work on the ion. By "Newton's third law", the ion exerts the same force on the membrane in the opposite direction. Since ion transfer is a stochastic process, these ion transfers induce a force noise, in addition to the thermal noise which results from collisions of the solvent molecules with the membrane. In addition to their stochastic function, ion channels are also able to diffuse around within the 2 dimensional membrane surface, which leads to another source of force fluctuations. The effect of this active noise on the mean square amplitude of membrane undulations has been recently studied by Prost and Bruinsma [4, 5], who have put forward a
basic model and determined from it the mean square amplitude. They found that the 103 Mat. Res. Soc. Symp. Proc. Vol. 543 01999 Materials Research Society
active noise strongly enhances undulation fluctuations at long distances. Specifically, for small enough wavenumbers q it was found that (hqhq) q- q- 5 instead of (hqh q) - q-4 of the bending thermal undulations. Thi. is an important result which suggests that active membranes behave quite differently from passive membranes even in terms physical quantities which are not directly related to their activity. Even though this is certainly not the main reason for the presence of active centers in plasma membrane, nature may have been able to take advantage of this "side effect" behavior. The equal time correlation function (hqh-q) presents only part of the characteristics of the a
Data Loading...
