Fredholm Integral Equations in Biophysical Data Analysis

Abstract

In the last decade, the abundant availability of computational resources has allowed for significant improvements in the interpretation of data in traditional disciplines of physical biochemistry. In particular, there are many examples where the data are fitted with a model describing a distribution of parameters, taking the form of a Fredholm integral equation. Algorithms traditionally applied in image analysis have proven highly useful to solve the corresponding ill-posed inverse problem. Two examples are presented from optical biosensing and sedimentation velocity analytical ultracentrifugation. In both examples, standard regularization techniques such as Tikhonov and maximum entropy regularization are applied, in conjunction with non-negativity constraints. Further, Bayesian adaptations of the regularization functional are possible that incorporate available prior knowledge on the system under study. Practical limitations and problems will be discussed.