Robust homeostasis of cellular cholesterol is a consequence of endogenous antithetic integral control

Although cholesterol is essential for cellular viability and proliferation, it is highly toxic in excess. The concentration of cellular cholesterol must therefore be maintained within tight tolerances, and is thought to be subject to a stringent form of homeostasis known as Robust Perfect Adaptation (RPA). While much is known about the cellular signalling interactions involved in cholesterol regulation, the specific chemical reaction network structures that might be responsible for the robust homeostatic regulation of cellular cholesterol have been entirely unclear until now. In particular, the molecular mechanisms responsible for sensing excess whole-cell cholesterol levels have not been identified previously, and no mathematical models to date have been able to capture an integral control implementation that could impose RPA on cellular cholesterol. Here we provide a detailed mathematical description of cholesterol regulation pathways in terms of biochemical reactions, based on an extensive review of experimental and clinical literature. We are able to decompose the associated chemical reaction network structures into several independent subnetworks, one of which is responsible for conferring RPA on several intracellular forms of cholesterol. Remarkably, our analysis reveals that RPA in the cholesterol concentration in the endoplasmic reticulum (ER) is almost certainly due to a well-characterised control strategy known as antithetic integral control which, in this case, involves the high-affinity binding of a multi-molecular transcription factor complex with cholesterol molecules that are excluded from the ER membrane. Our model provides a detailed framework for exploring the necessary biochemical conditions for robust homeostatic control of essential and tightly regulated cellular molecules such as cholesterol.