ABSTRACT

Alliances between experimental and computational disciplines are increasingly important to meet the challenges of modern live sciences. In laboratories all over the world, the precise quantification of ´colocalization` with microscopic imaging techniques has become a frequent task. Colocalization verifies the presence of biological molecules, structures, or organelles at the same physical location. So far, colocalization has not been resolved satisfactorily on a mathematic-statistical level. We therefore focus this project on the development of a coherent and robust approach to quantify the colocalization of fluorescently labeled biological structures with confocal laser scanning microscopy. In contrast to all preceding methods which calculate colocalization coefficients for an image set with rather simple, global mathematical coefficients (based on the theories of Manders or Pearson), our approach develops a consequent bottom-up algorithm based on the calculation of local scaling functions which we term Colocalization Scaling Index Methods (C-SIM). These local C-SIM are defined within a given radius r for every position xi in the image matrices. Our approach will account for the strong interdependence in adjacent pixel regions which are induced by the physical properties of the experiment-specific point spread functions (PSF) in the diffraction limited detection volume of contemporary light microscopes. The properties of the following mathematical approaches for the local estimation of colocalization will be investigated: the Scaling Index Method SIM(xi|r), the Correlation Coefficient of Raw Images CCRI(xi|r), the Joint Moment of Standardized Images JMSI(xi|r), the auto- and cross-correlation functions G(X)(xi|r), and coefficients based on the theories of Pearson and Manders. Based in our experience with SIM-related techniques we have strong evidences to believe that the success of all C-SIM will critically depend on the optimal selection of the sensitive C-SIM radii. Preliminary results indicate that global and local auto- and cross-correlation functions G(X)(xi|r) possess promising properties to determine the size of interdependent pixel regions. These properties will be investigated in a detailed manner in order to guarantee an operator independent approach for the optimal selection of C-SIM radii.
An important question concerns the probabilistic evaluation of the calculated C-SIM maps. A final decision has to be made if a local colocalization is coincidental or not. In this context we will implement a novel approach based on a defined displacement algorithm (DDA) for the entire set of the C-SIM(xi|r) descriptors. Local DDAs provide the possibility to generate local probability density functions (PDF), facilitating the definition of a precise statistical probability (p-values) which separates true versus coincidental colocalization. Local DDAs will lead to a robust probabilistic model where the initial regional interdependency between the subjacent biological structures is preserved and every pixel is evaluated in respect to its vicinity.
Our probabilistic approach will be validated from a theoretical level (simulation) up to an experimental level which will lead us to the best possible description of colocalization with C-SIM(xi|r). Last but not least, C-SIM will be applied to current issues in cell biology, ranging from experiments with different cell cultures to experiments which include transgenic animals. The experimental applications will culminate to resolve colocalization in vivo on a three dimensional level in cells within developing organisms such as the translucent embryo of zebrafish (Danio rerio). Our approach has a strong transdisciplinary focus. It combines facets from physical, mathematical, computational, and biological sciences. It finally aims to a successive implementation of the developed routines in form of a free cross-platform runtime utility based on IDL Virtual Machine and to the implementation as an interactive internet-based tool on our web-page for interactive Scientific Image Analysis (SCIAN, www.scian.cl). With this approach, we are defending the spirit of public domain software and the benefits of the development will be accessible to the entire scientific community. It should be empathized that our web-page is developed and maintained in collaboration with a local software company, Xperts Ltda. (Ingenieria en Informática y Comunicaciones, Valdivia, www.xperts.cl), which has originated important mutual benefits and strengthens the transfer of scientific image processing technologies into different areas.