Exploring cyclic networks of multisite modification reveals origins of information processing characteristics

In distributive phosphorylation catalytic constants enable non-trivial dynamics

Ordered distributive double phosphorylation is a recurrent motif in intracellular signaling and control. It is either sequential (where the site phosphorylated last is dephosphorylated first) or cyclic (where the site phosphorylated first is dephosphorylated first). Sequential distributive double phosphorylation has been extensively studied and an inequality involving only the catalytic constants of kinase and phosphatase is known to be sufficient for multistationarity. As multistationarity is necessary for bistability it has been argued that these constants enable bistability. Here we show for cyclic distributive double phosphorylation that if its catalytic constants satisfy an analogous inequality, then Hopf bifurcations and hence sustained oscillations can occur. Hence we argue that in distributive double phosphorylation (sequential or distributive) the catalytic constants enable non-trivial dynamics. In fact, if the rate constant values in a network of cyclic distributive double phosphorylation satisfy this inequality, then a network of sequential distributive double phosphorylation with the same rate constant values will show multistationarity-albeit for different values of the total concentrations. For cyclic distributive double phosphorylation we further describe a procedure to generate rate constant values where Hopf bifurcations and hence sustained oscillations can occur. This may, for example, allow for an efficient sampling of oscillatory regions in parameter space. Our analysis is greatly simplified by the fact that it is possible to reduce the network of cyclic distributive double phosphorylation to what we call a network with a single extreme ray. We summarize key properties of these networks.

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.