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

Abstract

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.

Effect of magnitude and variability of energy of activation in multisite ultrasensitive biochemical processes

“…Previously, Enciso and Ryerson [8] asked the question "how can the microscopic ligand binding affinities (a.k.a. modification efficiencies) be tuned if the goal is to maximize ultrasensitivity?"…”

“…In this sense the current study is most relevant when the target structure is more heterogeneous, such as in the case of phosphorylation. Although phosphorylation consumes energy and is not thermodynamically closed, the MWC model is still a popular model to describe it [8,45,46]. It is also mathematically more amenable than the non-allosteric, independent model that we also included for completeness.…”

“…In this section, we use a non-allosteric model and carry out a similar study as for the generalized MWC model. The proposed model has been used elsewhere [8,33] but here it is generalized for the first time to have different activation parameters at different sites.…”

“…A common role for multisite modifications lies in the creation of switch-like, or ultrasensitive, dose response curves [7][8][9]. These are positive, monotonically increasing, sigmoidal functions that have two important properties: first, they respond minimally to low levels of input; second, once the input is sufficiently large, they switch from a low output to a near maximal output in response to a relatively small increase in the input.…”

Stratified ubiquitination of RIG-I creates robust immune response and induces selective gene expression

“…2 ). The ultrasensitivity behavior is relatively robust to site-to-site variations ( 30 ) or the sampling time ( 31 ), excluding the possibility of a specific parametric effect. Why does innate immune signaling mediated by RIG-I activation with multisite ubiquitination favor an analog but not a highly switch-like response?…”