The effect of site-to-site variability in ultrasensitive dose responses.

In this paper we study the ultrasensitive behavior of multisite phosphorylation or ligand binding systems, under site-to-site variations in the modification rates. Using computational methods and mathematical analysis, we prove that the Hill coefficient reaches its maximum value when all sites are identical to each other. This is shown for a non-cooperative multisite system with arbitrary activation function as well as for the well known MWC model. We also show that the Hill coefficient of the dose response is locally robust to variations in individual modification rates. The results suggest that maximal ultrasensitivity is reached when sites are similar to each other but not necessarily identical, a conformation found in unstructured modification domains present in many experimental systems.

Ultrasensitivity in independent multisite systems.

Multisite modifications are widely recognized as an essential feature of many switch-like responses in signal transduction. It is usually assumed that the modification of one site directly or indirectly increases the rate of modification of neighboring sites. In this paper we provide a new set of assumptions for a multisite system to become highly ultrasensitive even in the absence of cooperativity or allostery. We assume that the individual sites are modified independently of each other, and that protein activity is an ultrasensitive function of the fraction of modified sites. These assumptions are particularly useful in the context of multisite systems with a large (8+) number of sites. We estimate the apparent Hill coefficient of the dose responses in the sequential and nonsequential cases, highlight their different qualitative properties, and discuss a formula to approximate dose responses in the nonsequential case. As an example we describe a model of bacterial chemotaxis that features robust ultrasensitivity and perfect adaptation over a wide range of ligand concentrations, based on non-allosteric multisite behavior at the level of receptors and flagella. We also include a model of the inactivation of the yeast pheromone protein Ste5 by cell cycle proteins.