Symmetry breaking meets multisite modification

Abstract

Multisite modification is a basic way of conferring functionality to proteins, and a key component of post-translational modification networks. Additional interest in multisite modification stems from its capability of acting as complex information processors. In this paper we connect two seemingly disparate themes: symmetry and multisite modification. We examine different classes of random modification networks of substrates involving separate or common enzymes. We demonstrate that under different instances of symmetry of the modification network (invoked explicitly or implicitly and discussed in the literature), the biochemistry of multisite modification can lead to the symmetry being broken. This is shown computationally and consolidated analytically, revealing parameter regions where this can (and in fact does) happen, and characteristics of the symmetry broken state. We discuss the relevance of these results in situations where exact symmetry is not present. Overall, through our study we show how symmetry breaking (i) can confer new capabilities to protein networks, including concentration robustness of different combinations of species (in conjunction with multiple steady states) (ii) could have been the basis for ordering of multisite modification, which is widely observed in cells (iii) can significantly impact information processing in multisite modification and in cell signalling networks/pathways where multisite modification is present (iv) can be a fruitful new angle for engineering in synthetic biology and chemistry. All in all, the emerging conceptual synthesis provides a new vantage point for the elucidation and the engineering of molecular systems at the junction of chemical and biological systems.

Network regulation meets substrate modification chemistry

“…In addition, there are also other regulatory factors at the level of substrate modification, including scaffolding and enzymesubstrate feedback [9][10][11][12]. Interestingly, it has been found that post-translational modification of substrates themselves may be capable of generating non-trivial qualitative information processing [13][14][15][16][17][18][19][20][21].…”

The Double Phospho/Dephosphorylation Cycle as a Benchmark to Validate an Effective Taylor Series Method to Integrate Ordinary Differential Equations

“…Ordinary Differential Equation (ODE) models of DPDC use to combine in a symmetric fashion the four enzymatic reactions [8], providing a bistability regime where the non-phosphorylated or the doublephosphorylated versions of the substrate is predominant [9]. A primary motivation in investigating the computation of the system solutions is that, in a recent paper [10], it has been proven that symmetry breaking in the dynamical solutions of such a network may lead to modify its emergent properties, including concentration robustness of different stationary solutions. In this context, numerical integration of enzymatic reactions in ODE form has been a matter of investigation for more than a century [11,12], since the seminal works of Michaelis and Menten [13] providing an approximation (the celebrated Quasi Steady-State Approximation (QSSA) [14]) to cope with the double time scale arising whenever biologically meaningful parameters are assigned.…”