Deterministic and stochastic models of NFkappaB pathway.

In the article, we discuss the state of art and perspectives in deterministic and stochastic models of NFkappaB regulatory module. The NFkappaB is a transcription factor controlling various immune responses including inflammation and apoptosis. It is tightly regulated by at least two negative feedback loops involving IkappaBalpha and A20. This mode of regulation results in nucleus-to-cytoplasm oscillations in NFkappaB localization, which induce subsequent waves of NFkappaB responsive genes. Single cell experiments carried by several groups provided comprehensive evidence that stochastic effects play an important role in NFkappaB regulation. From modeling point of view, living cells might be considered noisy or stochastic biochemical reactors. In eukaryotic cells, in which the number of protein or mRNA molecules is relatively large, stochastic effects primarily originate in regulation of gene activity. Transcriptional activity of a gene can be initiated by trans-activator molecules binding to the specific regulatory site(s) in the target gene. The stochastic event of gene activation is amplified by transcription and translation, since it results in a burst of mRNA molecules, and each copy of mRNA then serves as a template for numerous protein molecules. Another potential source of variability can be receptors activation. At low-dose stimulation, important in cell-to-cell signaling, the number of active receptors can be low enough to introduce substantial noise to downstream signaling. Stochastic modeling confirms the large variability in cell responses and shows that no cell behaves like an "average" cell. This high cell-to-cell variability can be one of the weapons of the immune defense. Such non-deterministic defense may be harder to overcome by relatively simple programs coded in viruses and other pathogens.