Diffusive filament motion

In both cases the experiments are very rough and a proper accounting of errors would probably show that these two outcomes are not really distinguishable in any case the reactant s diffusion coefficients are not equal and theory makes no distinct prediction for that case, so it may be that there remains little to improve here. The conclusion seems to be that chemical experiments have not yet detected important deviations of circular filament motion in chemical media from Equation (15). 

Accumulating evidence clearly points at involvement of the cell cytoskeleton in the compartmentalization of the membrane, in particular, the fine cytoskeleton filaments formed by actin in most eukaryotic cells or spectrin in mammalian red blood cells. However, single-particle tracking experiments show the same patterns of hop-diffusion for lipid molecules located in the extracellular leaflet of the plasma membrane. How can the membrane skeleton, which is located only on the cytoplasmic surface of the membrane, suppress the motion of lipids on the extracellular side ... 

Peskin et al [1993] have proposed the Brownian ratchet theory to describe the active force production. The main component of that theory was the interaction between a rigid protein and a diffusing object in front of it. If the object undergoes a Brownian motion, and the fiber undergoes polymerization, there are rates at which the polymer can push the object and overcome the external resistance. The problem was formulated in terms of a system of reaction-diffusion equations for the probabilities of the polymer to have certain number of monomers. Two limiting cases, fast diffusion and fast polymerization, were treated analytically that resulted in explicit force/velocity relationships. This theory was subsequently extended to elastic objects and to the transient attachment of the filament to the object. The correspondence of these models to recent experimental data is discussed in the article by Mogilner and Oster [2003]. 

Amblard, et al., used videomicroscopy and magnetic tweezers to study probe motion in viscoelastic F-actin systems(95). Videomicroscopy determines particle positions the tweezers apply known forces to a particle. The F-actin filaments had an estimated length of 20 p.m, persistence length c. 14 p.m, and at 0.1 g/1 a mesh size 1 p.m. With small beads (diameter d < ), diffusion followed x t)) t. ... 

It was appreciated two decades ago when scroll rings were first measured and timed in Belousov-Zhabotinsky media [24] that they contract and vanish, possibly faster the greater the curvature it was supposed that they would collapse in time 0(diameter / >) [43, p. 255]. But it was not until one decade ago that Yakushevitch [68] and Panfilov and Pertsov [69] noticed and confirmed numerically (in the case of equal diffusion of all reactants, and radius of curvature/wavelength large and slowly varying or constant along the filament) that the reaction-diffusion equation prescribes such motion strictly in proportion to curvature, with coefficient equal to the diffusion coefficient ... 

As discussed above, in agar gel the ratio of ferroin/bromous acid diffusion coefficients is thought to be about 0.6, so formula = D/r is not strictly applicable the appropriate D might be smaller than the bromous acid diffusion coefficient. Taking D (for bromous acid) as 1.1 x 10 cm /sec at 5°C, then with 20 = 0.08 cm we expect unilateral contraction at speed 1.1 X 10 cm /sec x 7t/(2 x 0.08 cm) = 0.000216 cm/sec (or less). The experimental result [72] was 0.0005 cm/sec 2.3 times faster than anticipated. If we do not use 1.1 x 10 cm /sec but 30% less as inferred from our measurements of rings shrinking in the identical medium (Section 6.A.1 just above), then the observed retraction is still 1.7 times faster than expected on this basis - at the level of precision of observations, twice as fast . Proportionality of the filament s motion (in the plane of curvature) to local curvature thus substantially exceeds the expectation of Equation (15) we find an enhancement of motion during this perpetually-sustained near-terminal collapse at the extremely small radii here stably maintained (0.05 cm = Aq/5). 

We are interested in the diffusive motion of relatively stiff chains made of magnetic particles either when the filaments are under the presence of a constant field or when the magnetic field is turned off. In the presence of an external magnetic field, the linear aggregates are forced to align along the field direction, so rotational chain diffusion is forbidden. Conseqnently, only the translational diffusion coefficients D and have to be considered for the theoretical analysis. 

In our experimental setup, an external magnetic field is applied perpendicularly to the scattering plane, forcing the filaments to align in the same direction. Due to this geometry, the measurements are only sensitive to the transversal motion of the linear aggregates, and the parallel diffusion coefficient D may also be neglected." ... 

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