Research Article On Data Space Selection and Data Processing for Parameter Identification in a Reaction-Diffusion Model Based on FRAP Experiments Stefan Kindermann 1 and Štjpán PapáIek 2 1 Industrial Mathematics Institute, Johannes Kepler University of Linz, Altenbergerstr 69, 4040 Linz, Austria 2 Institute of Complex Systems, South Bohemian Research Center of Aquaculture and Biodiversity of Hydrocenoses, Faculty of Fisheries and Protection of Waters, University of South Bohemia- ˇ Cesk´ e Budˇ ejovice, Z´ amek 136, 373 33 Nov´ e Hrady, Czech Republic Correspondence should be addressed to ˇ Stˇ ep´ an Pap´ aˇ cek; spapacek@frov.jcu.cz Received 2 January 2015; Revised 15 May 2015; Accepted 18 May 2015 Academic Editor: Benito M. Chen-Charpentier Copyright © 2015 S. Kindermann and ˇ S. Pap´ aˇ cek. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Fluorescence recovery afer photobleaching (FRAP) is a widely used measurement technique to determine the mobility of fuorescent molecules within living cells. While the experimental setup and protocol for FRAP experiments are usually fxed, data (pre)processing represents an important issue. Te aim of this paper is twofold. First, we formulate and solve the problem of relevant FRAP data selection. Te theoretical fndings are illustrated by the comparison of the results of parameter identifcation when the full data set was used and the case when the irrelevant data set (data with negligible impact on the confdence interval of the estimated parameters) was removed from the data space. Second, we analyze and compare two approaches of FRAP data processing. Our proposition, surprisingly for the FRAP community, claims that the data set represented by the FRAP recovery curves in form of a time series (integrated data approach commonly used by the FRAP community) leads to a larger confdence interval compared to the full (spatiotemporal) data approach. 1. Introduction Te method of fuorescence recovery afer photobleaching (FRAP) is based on the measurement of the change of fuores- cence emitted by autofuorescent molecules or fuorescently tagged compounds (e.g., green fuorescence proteins (GFP) in a region of interest (ROI), usually a 2D Euclidean bounded domain, in response to a high-intensity laser pulse provided by confocal laser scanning microscopy (CLSM). Te initial steady state is thus perturbed by an external stimulus, the so- called bleach. Te bleach (or bleaching) causes an irreversible loss of fuorescence in the bleached area, apparently with- out any signifcant damage to intracellular structures. Afer bleaching, the observed recovery in fuorescence refects the mobility of fuorescence compounds from the area outside the bleach [1]. To quantify the mobility of photosynthetic proteins of diferent microbial species is the main research interest of biologists. In Figure 1, we observe an example of FRAP data in form of a time series of both 2D and 1D fuorescence profles refecting the photosynthetic proteins mobility on a mem- brane [2, 3]. In the observed specimen (thylakoid membrane of the red algae Porphyridium cruentum, cf. Figure 1(a)), the experimentalists usually select a 2D rectangular ROI with the larger side perpendicular to the bleach strip in order to perform the averaging along the shorter axis. Te resulting 1D fuorescence profles (Gaussian-shaped signals in the central bleached region) are plotted on Figure 1(b). Based on spatiotemporal FRAP data, the difusion constant is usually estimated by ftting a closed form model to the preprocessed FRAP data; see, for example, [4–9]. Since all Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2015, Article ID 859849, 17 pages http://dx.doi.org/10.1155/2015/859849