BackgroundFluorescence loss in photobleaching (FLIP) is a widely used imaging technique, which provides information about protein dynamics in various cellular regions. In FLIP, a small cellular region is repeatedly illuminated by an intense laser pulse, while images are taken with reduced laser power with a time lag between the bleaches. Despite its popularity, tools are lacking for quantitative analysis of FLIP experiments. Typically, the user defines regions of interest (ROIs) for further analysis which is subjective and does not allow for comparing different cells and experimental settings.ResultsWe present two complementary methods to detect and quantify protein transport and aggregation in living cells from FLIP image series. In the first approach, a stretched exponential (StrExp) function is fitted to fluorescence loss (FL) inside and outside the bleached region. We show by reaction–diffusion simulations, that the StrExp function can describe both, binding/barrier–limited and diffusion-limited FL kinetics. By pixel-wise regression of that function to FL kinetics of enhanced green fluorescent protein (eGFP), we determined in a user-unbiased manner from which cellular regions eGFP can be replenished in the bleached area. Spatial variation in the parameters calculated from the StrExp function allow for detecting diffusion barriers for eGFP in the nucleus and cytoplasm of living cells. Polyglutamine (polyQ) disease proteins like mutant huntingtin (mtHtt) can form large aggregates called inclusion bodies (IB’s). The second method combines single particle tracking with multi-compartment modelling of FL kinetics in moving IB’s to determine exchange rates of eGFP-tagged mtHtt protein (eGFP-mtHtt) between aggregates and the cytoplasm. This method is self-calibrating since it relates the FL inside and outside the bleached regions. It makes it therefore possible to compare release kinetics of eGFP-mtHtt between different cells and experiments.ConclusionsWe present two complementary methods for quantitative analysis of FLIP experiments in living cells. They provide spatial maps of exchange dynamics and absolute binding parameters of fluorescent molecules to moving intracellular entities, respectively. Our methods should be of great value for quantitative studies of intracellular transport.

A third order conservative reconstruction, in the context of finite volume schemes for hyperbolic conservation laws, is constructed based on logarithmic functions. This logarithmic method reconstructs without the use of a limiter, any preprocessing of input data, special treatments for local extrema, or shock solutions. Also the method is local in the sense that data from only the nearest neighbors are required.We test the new reconstruction method in several numerical experiments, including nonlinear systems in one and two space dimensions.

A straightforward semi-implicit finite-difference method approximating a system of conservation laws including a stiff relaxation term is analyzed. We show that the error, measured in L 1 , is bounded by O( √ ∆t) independent of the stiffness, where the time step ∆t represents the mesh size. As a simple corollary we obtain that solutions of the stiff system converge toward the solution of an equilibrium model at a rate of O(δ 1/3 ) in L 1 as the relaxation time δ tends to zero.

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A class of high-order reconstruction methods based on logarithmic functions is presented. Inspired by Marquina's hyperbolic method, we introduce a double logarithmic ansatz of fifth order of accuracy. Low variation is guaranteed by the ansatz and (slope-) limiting is avoided. The method can reconstruct smooth extrema without order reduction. Fifth order of convergence is verified in a numerical experiment governed by the nonlinear Euler system. Numerical experiments, including the Osher-Shu shock/acoustic interaction, are presented.