Ultrasensitivity and bistability in covalent-modification cycles with positive autoregulation.

Cailan Jeynes-Smith,Robyn P Araujo

doi:10.1098/rspa.2021.0069

Abstract

Switch-like behaviours in biochemical networks are of fundamental significance in biological signal processing, and exist as two distinct types: ultra-sensitivity and bistability. Here we propose two new models of a reversible covalent-modification cycle with positive autoregulation (PAR), a motif structure that is thought to be capable of both ultrasensitivity and bistability in different parameter regimes. These new models appeal to a modelling framework that we call complex-complete, which accounts fully for the molecular complexities of the underlying signalling mechanisms. Each of the two new models encodes a specific molecular mechanism for PAR. We demonstrate that the modelling simplifications for PAR models that have been used in previous work, which rely on Michaelian approximations, are unable to accurately recapitulate the qualitative signalling responses supported by our detailed models. Strikingly, we show that complex-complete PAR models are capable of new qualitative responses such as one-way switches and a ‘prozone’ effect, depending on the specific PAR-encoding mechanism, which are not supported by Michaelian simplifications. Our results highlight the critical importance of accurately representing the molecular details of biochemical signalling mechanisms, and strongly suggest that the Michaelian approximation is inadequate for predictive models of enzyme-mediated chemical reactions with added regulations such as PAR.

Highlights

The capacity for collections of biochemical reactions to respond in a switch-like, or all-or-none, manner is of fundamental significance in biological signal processing, and has been widely observed in many different signalling contexts [1,2,3]
Bistability is thought to arise from a variety of underlying mechanisms, including: positive autoregulation (PAR) and positive feedback, where a molecule either directly or indirectly promotes its own creation [54,59,60,62,68,69,74,75]; cooperative binding, where the binding of one molecule enhances the binding of subsequent molecules [66,76]; antagonism, where one molecule benefits at the loss of another [65,77]; and double negative feedback, a cycle in which two interacting molecules mutually inhibit each other [54]
With this goal in mind, we commenced our study with a preliminary exploratory parameter search in which we classified the qualitative nature of the dose–response profiles for both the PAR-d and PAR-i motifs for approximately 1000 random parameter sets, each parameter taking values in the range (10−6, 106)

Summary

Introduction

The capacity for collections of biochemical reactions to respond in a switch-like, or all-or-none, manner is of fundamental significance in biological signal processing, and has been widely observed in many different signalling contexts [1,2,3]. The more complicated enzyme–substrate interactions that readily arise in biological networks, involving multisite chemical modifications, positive or negative autoregulation of substrate molecules, and other molecular intricacies, are currently beyond the reach of most modelling simplifications involving alternative QSSAs [14,15] Even small such collections of relatively simple enzyme-mediated reactions can involve the formation of a number of transient, intermediate molecular states and protein–protein (a). Goldbeter & Koshland’s seminal work on zero-order ultrasensitivity [46] has suggested that the Michaelian model of a covalent-modification cycle, equation (1.3), provides a good approximation to the ultrasensitive behaviour of the complex-complete mass-action model provided that E1tot, E2tot Wtot, a parametric condition unlikely to obtain in many signal transduction networks, or other highly complex bionetworks in nature [14].

Results

Discussion and concluding remarks

Methods