Dynamics of post-translational modification systems: recent progress and future directions

Abstract

Post-translational modification (PTM) of proteins plays a key role in signal transduction, and hence significant effort has gone toward understanding how PTM networks process information. This involves, on the theory side, analyzing the dynamical systems arising from such networks. Which networks are, for instance, bistable? Which networks admit sustained oscillations? Which parameter values enable such behaviors? In this Perspective, we highlight recent progress in this area and point out some important future directions. Along the way, we summarize several techniques for analyzing general networks, such as eliminating variables to obtain steady-state parametrizations, and harnessing results on how incorporating intermediates affects dynamics.

13 pages, 3 figures

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• Multistationarity in the space of total concentrations for systems that admit a monomial parametrization
• Absolute concentration robustness: Algebra and geometry
• The kinetic space of multistationarity in dual phosphorylation
• On the reaction rate constants that enable multistationarity in the two-site phosphorylation cycle
• The inheritance of local bifurcations in mass action networks