Analysis of Actin FLAP Dynamics in the Leading Lamella

BACKGROUND. The transport of labeled G-actin from the mid-lamella region to the leading edge in a highly motile malignant rat fibroblast line has been studied using fluorescence localization after photobleaching or FLAP, and the transit times recorded in these experiments were so fast that simple diffusion was deemed an insufficient explanation (see Zicha et al., Science, v. 300, pp. 142-145 [1]). METHODOLOGY/PRINCIPAL FINDINGS. We re-examine the Zicha FLAP experiments using a two-phase reactive interpenetrating flow formalism to model the cytoplasm and the transport dynamics of bleached and unbleached actin. By allowing an improved treatment of effects related to the retrograde flow of the cytoskeleton and of the geometry and finite thickness of the lamella, this new analysis reveals a mechanism that can realistically explain the timing and the amplitude of all the FLAP signals observed in [1] without invoking special transport modalities. CONCLUSIONS/SIGNIFICANCE. We conclude that simple diffusion is sufficent to explain the observed transport rates, and that variations in the transport of labeled actin through the lamella are minor and not likely to be the cause of the observed physiological variations among different segments of the leading edge. We find that such variations in labeling can easily arise from differences and changes in the microscopic actin dynamics inside the edge compartment, and that the key dynamical parameter in this regard is the so-called "dilatation rate" (the velocity of cytoskeletal retrograde flow divided by a characteristic dimension of the edge compartment where rapid polymerization occurs). If our dilatation hypothesis is correct, the transient kinetics of bleached actin relocalization constitute a novel and very sensitive method for probing the cytoskeletal dynamics in leading edge micro-environments which are otherwise very difficult to directly interrogate.Whitaker biomedical engineering research grant (RG-02-0714); National Institutes of Health (RO1 GM7200

A mathematical model of the vertical dual-mass hydroimpulsive mechanism

In this paper, the model of a hydroimpulsive mechanism for boring machines was presented. Differential equations describing the processes occurring in the mechanism were derived

A "saddle-node" bifurcation scenario for birth or destruction of a Smale-Williams solenoid

Formation or destruction of hyperbolic chaotic attractor under parameter variation is considered with an example represented by Smale--Williams solenoid in stroboscopic Poincar\'{e} map of two alternately excited non-autonomous van der Pol oscillators. The transition occupies a narrow but finite parameter interval and progresses in such way that periodic orbits constituting a "skeleton" of the attractor undergo saddle-node bifurcation events involving partner orbits from the attractor and from a non-attracting invariant set, which forms together with its stable manifold a basin boundary of the attractor.Comment: 7 pages, 7 figures, 1 tabl