A mathematical analysis of nuclear intensity dynamics for Mig1-GFP under consideration of bleaching effects and background noise in Saccharomyces cerevisiae

Fluorescence microscopy is an imaging technique that provides insights into signal transduction pathways through the generation of quantitative data, such as the spatiotemporal distribution of GFP-tagged proteins in signaling pathways. The data acquired are, however, usually a composition of both the GFP-tagged proteins of interest and of an autofluorescent background, which both undergo photobleaching during imaging. We here present a mathematical model based on ordinary differential equations that successfully describes the shuttling of intracellular Mig1-GFP under changing environmental conditions regarding glucose concentration. Our analysis separates the different bleaching rates of Mig1-GFP and background, and the background-to-Mig1-GFP ratio. By applying our model to experimental data, we can thus extract the Mig1-GFP signal from the overall acquired signal and investigate the influence of kinase and phosphatase on Mig1. We found a stronger regulation of Mig1 through its kinase than through its phosphatase when controlled by the glucose concentration, with a constant (de)phosphorylation rate independent of the glucose concentration. By replacing the term for decreasing excited Mig1-GFP concentration with a constant, we were able to reconstruct the dynamics of Mig1-GFP, as it would occur without bleaching and background noise. Our model effectively demonstrates how data, acquired with an optical microscope, can be processed and used for a systems biology analysis of signal transduction pathways.