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

Symmetry breaking meets multisite modification

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; and (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.

Proteins help our cells perform the chemical reactions necessary for life. Once proteins are made, they can also be modified in different ways. This can simply change their activity, or otherwise make them better suited for their specific jobs within the cell. Biological ‘catalysts’ called enzymes carry out protein modifications by reversibly adding (or removing) chemical groups, such as phosphate groups.

‘Multisite modifications’ occur when a protein has two or more modifications in different areas, which can be added randomly or in a specific sequence. The combination of all the modifications attached to a protein acts like a chemical barcode and confers a specific function to the protein.

Modification networks add levels of complexity above individual proteins. These encompass not only the proteins in a cell or tissue, but also the different enzymes that can modify them, and how they all interact with each other. Although our knowledge of these networks is substantial, basic aspects, such as how the ordering of multisite modification systems emerges, is still not well understood.

Using a simple set of multisite modifications, Ramesh and Krishnan set out to study the potential mechanisms allowing the creation of order in this context. Symmetry is a pervasive theme across the sciences. In biology, symmetry and how it may be broken, is important to understand, for example, how organism develop. Ramesh and Krishnan used the perspective of symmetry in protein networks to uncover the origins of ordering.

First, mathematical models of simple modification networks were created based on their basic descriptions. This system centred on proteins that could have phosphate modifications at two possible sites. The network was ‘symmetric’, meaning that the rate of different sets of chemical reactions was identical, as were the amounts of all the enzymes involved.

Dissecting the simulated network using a variety of mathematical approaches showed that its initial symmetry could break, giving rise to sets of ordered multisite modifications. Breaking symmetry did not require any additional features or factors; the basic chemical ‘ingredients’ of protein modification were all that was needed. The prism of symmetry also revealed other aspects of these multisite modification networks, such as robustness and oscillations.

This study sheds new light on the mechanism behind ordering of protein modifications. In the future, Ramesh and Krishnan hope that this approach can be applied to the study of not just proteins but also a wider range of biochemical networks.

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

Protein activity is often regulated by ligand binding or by post-translational modifications such as phosphorylation. Moreover, proteins that are regulated in this way often contain multiple ligand binding sites or modification sites, which can operate to create an ultrasensitive dose response. Here, we consider the contribution of the individual modification/binding sites to the activation process, and how their individual values affect the ultrasensitive behavior of the overall system. We use a generalized Monod-Wyman-Changeux (MWC) model that allows for variable conformational free energy contributions from distinct sites, and associate a so-called activation parameter to each site. Our analysis shows that the ultrasensitivity generally increases as the conformational free energy contribution from one or more sites is strengthened. Furthermore, ultrasensitivity depends on the mean of the activation parameters and not on their variability. In some cases, we find that the best way to maximize ultrasensitivity is to make the contribution from all sites as strong as possible. These results provide insights into the performance objectives of multiple modification/binding sites and thus help gain a greater understanding of signaling and its role in diseases.

A measure to quantify the degree of cooperativity in overall titration curves

In the framework of the grand canonical ensemble, different definitions of cooperativity commonly used in the context of ligand binding are not equivalent. A unifying definition is the existence of non-real roots of the binding polynomial. Using this qualitative criterion, an open question is how to quantify the degree of cooperativity. In this work, we introduce a theoretical measure to quantify the degree of cooperativity of a titriation curve. Its definition is based on a minimal energy approach mapping a given binding polynomial to the minimal interaction energy which is required to generate it. We show that the degree of cooperativity can be calculated easily, if the molecule under consideration is assumed to consist of energetically identical binding sites. Moreover, the property of sub-multiplicativity allows us to determine upper bounds for the degree of cooperativity in asymmetric systems. The approach is consistent with the qualitative definition of cooperativity based on the existence of non-real roots of the binding polynomial, and thus helps to put the concept of cooperativity on a solid theoretical ground. It connects macro- and microstates, but takes here also into account that an infinite number of different molecules can cause the same macroscopic ligand binding behavior, which means that the underlying microsystem cannot be uniquely identified based on the titration curve only.

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

The activation of retinoic acid-inducible gene I (RIG-I), an indispensable viral RNA sensor in mammals, is subtly regulated by ubiquitination. Although multiple ubiquitination sites at the amino terminus of RIG-I have been identified, their functional allocations in RIG-I activation remain elusive. We identified a stratified model for RIG-I amino-terminal ubiquitination, in which initiation at either Lys164 or Lys172 allows subsequent ubiquitination at other lysines, to trigger and amplify RIG-I activation. Experimental and mathematical modeling showed that multisite ubiquitination provides robustness in RIG-I-mediated type I interferon (IFN) signaling. Furthermore, the flexibly controlled ultrasensitivity and IFN activation intensity determine the specificity of the IFN-stimulated gene transcription and manipulate cell fate in antiviral immune response. Our work demonstrates that tunable type I IFN signaling can be regulated through multisite RIG-I ubiquitination and elucidates a new paradigm for dynamic regulation in RIG-I-mediated antiviral signaling.