Parameter identification problem based on FRAP images: From data processing to optimal design of photobleaching experiments

Abstract

The aim of this study is to make a step towards optimal design of photobleaching experiments. The photobleaching techniques, mainly FRAP (Fluorescence Recovery After Photobleaching), are widely used since 1970’s to determine the mobility of fluorescent molecules within the living cells. While many rather empirical recommendations for the experimental setup have been made in past decades, no rigorous mathematical study concerning optimal design of FRAP experiments exists. In this paper, we formulate and solve the inverse problem of data processing of FRAP images leading to the underlaying model parameter identification. The key concept relies on the analysis of sensitivity of the measured outputs on the model parameters. It permits to represent the resulting parameter estimate as random variable, i.e., we can provide both the mean value and standard error or corresponding confidence interval. Based on the same sensitivity-based approach we further optimize experimental design factors, e.g., the radius of bleach spot. The reliability of our new approach is shown on a numerical example.