Feedback Loops in Ultrasensitive Cascades

Understanding the flow of signals through stochastic bio-circuits of molecular interactions is important for both systems and synthetic biology. Here we analyze the stochastic signals produced by a bio-circuit that contains a feedback loop. The bio-circuit we study is a modification of the ultrasensitive mitogen-activated protein kinase (MAPK) cascade. The analysis is based on moment closure technique based on a novel procedure of splitting nonlinear nodes that represent product interactions in the bio-circuit's molecular diagram.