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DYNAMICS OF REACTION- DIFFUSION SYSTEMS mathematical description, numerical methods, FRAP data and parameter estimation Alejandro Lara, Jaroslav Kysela 28. 7. 2011

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Aims of the Project Consideration of inward flux boundary conditions Use COMSOL optimization module for solving the inverse problem Getting to know COMSOL Multiphysics and its features

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Fluorescence Recovery After Photobleaching FRAP

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Comsol- Optimization Module Powerful tool that can solve elaborate problems in many fields of physics Provides strong tools to optimize parameters It is able to compute “parameter determination” (inverse problems) Last year this project did not have access to the Optimization Module Research in forums states that optimization is not possible in time-dependent problems

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Experimental Data Red algae porphyridium cruentum He-Ne laser (633 nm) Observed for 480 seconds, each 8 seconds

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Fluorescence

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Boundary Conditions No flux Flux as a gradient of concentration on the boundaries Approximately constant concentration on the boundaries of an observed area Flux as a time derivative of experimentally obtained concentration curve

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Total Intensity Immobile fraction Mobile fraction

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Diffusion Dynamics

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Alternative Optimization Linear interpolation can be assumed at the beginning D test can be found This routine is very to write and implement However, it is not very robust and might have some problems with the experimental data.

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Future Approach Finite Difference Method

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Future Approach Computational routine can be arranged A variable D can be included

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Conclusions, Future Goals Implementation of nonzero inward flux in the model of diffusion of phycobilisomes in a thylakoid membrane Alternative procedures were used to solve the inverse problem, but they proved to be insufficient Develop more expertise in the use of COMSOL optimization module Use other numerical methods that include the flux and variable diffusion coefficient

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References http://www.iiserpune.ac.in/~cathale/lects/201101_bio435/bio435 -expt/bio435-FRAP-protocol.html http://iws.collin.edu/biopage/faculty/mcculloch/1406/outlines/cha pter%2010/chap10.htm http://www.comsol.eu/papers/459/chemical-engineering/ http://www.me.ucsb.edu/~moehlis/APC591/tutorials/tutorial5/nod e5.html

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Acknowledgement Ing. Štěpán Papáček, PhD. Thank you for your attention

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