Compact Modeling of Allosteric Multisite Proteins: Application to a Cell Size Checkpoint

We explore a framework to model the dose response of allosteric multisite phosphorylation proteins using a single auxiliary variable. This reduction can closely replicate the steady state behavior of detailed multisite systems such as the Monod-Wyman-Changeux allosteric model or rule-based models. Optimal ultrasensitivity is obtained when the activation of an allosteric protein by its individual sites is concerted and redundant. The reduction makes this framework useful for modeling and analyzing biochemical systems in practical applications, where several multisite proteins may interact simultaneously. As an application we analyze a newly discovered checkpoint signaling pathway in budding yeast, which has been proposed to measure cell growth by monitoring signals generated at sites of plasma membrane growth. We show that the known components of this pathway can form a robust hysteretic switch. In particular, this system incorporates a signal proportional to bud growth or size, a mechanism to read the signal, and an all-or-none response triggered only when the signal reaches a threshold indicating that sufficient growth has occurred.Author Summary: A large number of proteins in the cell are modified post-translationally by phosphorylation at multiple specific locations. This can help bring about interesting dynamical behaviors such as bistability or all-or-none responses to stimuli. Such behaviors are in turn important for cellular decision-making, differentiation, or the regulation of cellular processes. In this paper we propose the use of a specific technique for modeling allosteric multisite proteins, which can be thought of as the reduced version of a more detailed set of reactions. After validating this technique computationally by comparison to more detailed systems, we apply it to a new model of a signal transduction pathway with several multisite proteins. The model is concerned with a mechanism in budding yeast that is thought to measure the extent of daughter bud growth and send a signal to initiate mitosis when sufficient growth has occurred. Using the given framework we derive an analytically tractable model that creates the desired all-or-none signal. Overall, we give quantitative support to a newly discovered biochemical pathway, and we show the utility of the new modeling framework in the context of a realistic biological problem.