Continuous fluorescence microphotolysis of anthracene-labeled phospholipids in membranes. Theoretical approach of the simultaneous determination of their photodimerization and lateral diffusion rates.

Anthracene is a fluorescent and photoactivatable (dimerization) group which can be used for investigating the lateral distribution and dynamics of lipids in membranes. In fluorescence recovery after photobleaching or in microphotolysis experiments, and when using this fluorophore, the bleaching (or microphotolysis) step in the illuminated part of the membrane is in fact the sum of two antagonistic processes: fluorescence decay, which is due to dimerization of anthracene residues, and fluorescence recovery, which is due to a diffusion mediated exchange of bleached and unbleached particles between the illuminated and diffusion area in the membrane. Here, we propose a new mathematical algorithm that enables such a second-order reaction-diffusion process to be analyzed. After coupling a fluorescence recovery step to a microphotolysis step, this algorithm allows us to calculate the lateral diffusion coefficient D and the photodimerization constant K of anthracene-labeled lipids in membranes, two parameters which contribute to the understanding of the fluidity of the lipid phase in membranes. This algorithm also provides us with a complete description of the anthracene-labeled molecules distribution in the illuminated and diffusion area, at any time of the experiment. The fluorescence recovery after microphotolysis procedure we propose was tested with an anthracene-labeled phosphatidylcholine inserted in egg-phosphatidylcholine multilayers, in monolayers adsorbed onto alkylated glass surfaces and in the plasma membrane of Chinese hamster ovary cells. It is shown that this procedure can also be used to evaluate the important parameters of probe mobile fraction and to determine the relative size of the illuminated and diffusion areas. This will enable membranes to be explored in terms of microdomains and/or macrodomains

lsmear : a variable selection strategy for interval branch and bound solvers

International audienceSmear-based variable selection strategies are well-known and commonly used bybranch-and-prune interval-based solvers. They estimate the impact of the variables on eachconstraint of the system by using the partial derivatives and the sizes of the variable domains.Then they aggregate these values, in some way, to estimate the impact of each variable onthe whole system. The variable with the greatest impact is then selected. A problem of thesestrategies is that they, generally, consider all constraints equally important. In this work, wepropose a new variable selection strategy which first weights the constraints by using theoptimal Lagrangian multipliers of a linearization of the original problem. Then, the impactof the variables is computed with a typical smear-based function but taking into accountthe weights of the constraints. The strategy isg tested on a set of well-known benchmarkinstances outperforming significantly the classical variable selection strategie