ARTICLE Survival and Apoptotic Pathways Initiated By TNF-a: Modeling and Predictions

ABSTRACT: We present a mathematical model which includes TNF-a initiated survival and apoptotic cascades, as well as nuclear transcription of IkB. These pathways play a crucial role in deciding cell fate in response to inflammation and infection. Our model incorporates known specific protein–protein interactions as identified by experiments. Using these biochemical interactions, we develop a mathematical model of the NF-kB-mediated survival and caspasemediated apoptosis pathways. Using mass action kinetics, we follow the formation of the survival and late complexes as well as the dynamics of DNA fragmentation. The effect of TNF-a concentration on DNA fragmentation is modeled and compares well with experiment. Nuclear transcription is also modeled phenomenologically by means of time lagged cytosolic concentrations. This results in transcription related concentrations undergoing under-damped oscillations, in qualitative and quantitative agreement with experiment. Using a tumor cell as a hypothetical model, we explore the interplay between the components of the survival and apoptotic pathways. Results are presented which make predictions on the limits of cellular oscillations in terms of time delay, initial concentration ratios and other features of the model. The model also makes clear predictions on cell viability in terms of DNA damage within the framework of TNF-a stimulus duration