Proteins molecules, Brownian motion

Globular proteins are found to rotate in solution at frequencies close to those calculated for rigid spheres. The frequencies are usually expressed in terms of a rotational correlation time, , which is the reciprocal of the rate constant for the randomization of the orientation of the molecule by Brownian motion. For a rigid sphere, 4> is given by... 

Membranes are two-dimensional flnids whose protein and lipid components continnonsly exchange positions because of Brownian motion, a process commoifly referred to as lateral diffusion. Lateral diffnsion enables proteins and lipids to explore their environment, which enconrages interactions between molecules. Thus, the speed of lateral diffusion is one of the limiting factors... 

How rapidly diffusion occurs is characterized by the diffusion coefficient D, a parameter that provides a measure of the mean of the squared displacement x of a molecule per unit time f. For diffusion in two dimensions such as a membrane, this is given by = 4Ht. The Saffman-Delbrtlck model of Brownian motion in biologic membranes describes the relationship between membrane viscosity, solvent viscosity, the radius R and height of the diffusing species, and D for both lateral and rotational diffusion of proteins in membranes (3, 4). This model predicts for example that for lateral diffusion, D should be relatively insensitive to the radius of the diffusing species, scaling with log (1/R). 

The general principle of BD is based on Brownian motion, which is the random movement of solute molecules in dilute solution that result from repeated collisions of the solute with solvent molecules. In BD, solute molecules diffuse under the influence of systematic intermolecular and intramolecular forces, which are subject to frictional damping by the solvent, and the stochastic effects of the solvent, which is modeled as a continuum. The BD technique allows the generation of trajectories on much longer temporal and spatial scales than is feasible with molecular dynamics simulations, which are currently limited to a time of about 10 ns for medium-sized proteins. 

In gel filtration, a protein mixture (the mobile phase) is applied to a column of small beads with pores of carefully controlled size (the stationary phase). The movement of the solute is dependent on the flow of the mobile phase and the Brownian motion of the solute molecules, causing their diffusion into and out of the chromatographic bed. Large proteins, above the exclusion limit of the gel, cannot enter the pores and are hence eluted in the void volume of the column. Small proteins enter the pores and are therefore eluted in the total volume" of the column and intermediate size proteins are eluted between the void and total volumes. Proteins are therefore eluted in order of decreasing molecular size. 

A. E. Cohen and W. E. Moemer, Controlling Brownian motion of single protein molecules and single fluorophores in aqueous buffer. Optics Express 16 p. 6941-6956 (2008). 

A common property of all cells Is motility, the ability to move in a specified direction. Many cell processes exhibit some type of movement at either the molecular or the cellular level all movements result from the application of a force. In Brownian motion, for Instance, thermal energy constantly buffets molecules and organelles in random directions and for very short distances. On the other hand, materials within a cell are transported in specific directions and for longer distances. This type of movement results from the mechanical work carried out by proteins that function as motors. We first briefly describe the types and general properties of molecular motors and then look at how one type of motor protein generates force for movement. 

Assuming a spherical shape for the fluorescent molecule, the degree of change in the rotational Brownian motion is given by Eq. (3.25), where v is the volume of the spherical molecule, r)0 is the solvent viscosity, r is the fluorescence lifetime of the chromophore, and T is the temperature. The values of r0 and r/v can be obtained from a plot of Mr versus T/rj0. Thus, if the fluorescence lifetime of the chromophore is known, it is possible to determine the hydrodynamic volume of the rotating molecule and its rotational diffusion constant D,. This data treatment is known as the Perrin-Weber approximation,25 after the two scientists who first derived the equations in the case of protein chromophores. 

If particles are known to be spherical in shape and nondeformable in the relatively weak flow fields associated with Brownian motion (this may be expected in the case of synthetic latex particles, many proteins, and viruses and probably also holds for certain emulsion particles with rigid ordered interfaces, the Stokes radius will closely correspond to the hard sphere radius R, related to Rg through Rg = 3/5 R and may also be similar to that observed in the electron microscope Rem. The value of Rg should, however, on detailed inspection be greater than the radii measured by the latter methods because it includes bound solvent molecules. The discrepancy can be used to estimate the degree of solvation 81 grams solvent/gram of the particle through the relation ... 

Dielectrophoresis has also been used to manipulate macromolecules such as DNA, viruses, proteins, and carbon nanotubes. The term colloids will be used here to generally describe a particle between 1 and 1,000 nm. At this scale we need to take into consideration additional parameters that will affect the efficiency and application of dielectrophoresis. The first is Brownian motion, or the random chaotic movement of molecules, which will introduce another destabilizing variable if we were to trap colloids. Second, electrostatic effects at the surface of colloids, created by the electrical double layer, will influence particle-particle interactions. Factors such as hydrodynamic drag, buoyancy, electrothermal effects, and a particle s double layer interactions need to be considered when applying dielectrophoresis to colloids. 

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