A simple mathematical model to aid quantification of electrophoresis gels by image analysis

In many scientific disciplines, measurements are taken from films that have been exposed to energetic sources. Examples include radiographs where the source is an X-ray tube, autoradiography where the source is a radioactive isotope and electrophoresis gels where the source is an enhanced chemiluminescence reaction. In these situations it is of interest to quantify the darkening of the film and compute the strength of the source which in the cases of autoradiography and electrophoresis can be used to compute unknown concentrations of biochemicals. We developed a simple mathematical model of the darkening of films in radiography, autoradiography and electrophoresis bands disclosed by enhanced chemiluminescence, and present formulae to calculate the strength of the source from measurement of film blackening by image analysis. A simple model is used in two examples to predict blackening of film exposed to electromagnetic radiation. This blackening is measured by image analysis. Results show reasonable agreement between predictions of the model and blackening of film for the examples chosen. This model is proposed as an aid to quantification of electrophoresis gels.