Many cancer-related pathways involve molecules that promote their own production, leading to nonlinear dynamics with positive feedback loops. This mechanism underlies bistability in signaling networks where stable states can drive tumor proliferation or suppression. Stochastic fluctuations can push a system to switch between such states, so that random noise can trigger transitions from a healthy to a malignant state, or vice versa. Such systems can be modeled using stochastic autocatalytic reaction networks. Understanding the sensitivity of such stochastic systems to small parameter changes is important for the formulation of models from data, for simulation of models and for drawing conclusions for real life systems. In this talk, we explore the sensitivity of a prototypical stochastic autocatalytic reaction network model that is known to exhibit dramatic switching behavior. The original model is called the Togashi–Kaneko model, and we consider a variant of it that allows for additional mutations. We establish a rigorous stochastic averaging principle that describes slow dynamics in terms of certain ergodic means of fast variables. For the two species model, we demonstrate a sensitivity of the model to even slight departures from symmetry in the autocatalytic reactions. We call this high sensitivity property “fragility”. Our preliminary explorations for models with more than two species point to a wealth of open questions for future research. Fragility appears to be an understudied phenomenon, which is likely to affect the formulation and interpretation of autocatalytic models across a spectrum of applications in the life sciences. Based on joint work with Y. Fu, H-W. Kang, W. Khudabukhsh, L. Popovic, G. Rempala.
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