Biphasic responses in multi-site phosphorylation systems

Ligand bias underlies differential signaling of multiple FGFs via FGFR1

The differential signaling of multiple FGF ligands through a single fibroblast growth factor (FGF) receptor (FGFR) plays an important role in embryonic development. Here, we use quantitative biophysical tools to uncover the mechanism behind differences in FGFR1c signaling in response to FGF4, FGF8, and FGF9, a process which is relevant for limb bud outgrowth. We find that FGF8 preferentially induces FRS2 phosphorylation and extracellular matrix loss, while FGF4 and FGF9 preferentially induce FGFR1c phosphorylation and cell growth arrest. Thus, we demonstrate that FGF8 is a biased FGFR1c ligand, as compared to FGF4 and FGF9. Förster resonance energy transfer experiments reveal a correlation between biased signaling and the conformation of the FGFR1c transmembrane domain dimer. Our findings expand the mechanistic understanding of FGF signaling during development and bring the poorly understood concept of receptor tyrosine kinase ligand bias into the spotlight.

A unified approach to dissecting biphasic responses in cell signaling

Biphasic responses are encountered at all levels in biological systems. At the cellular level, biphasic dose-responses are widely encountered in cell signaling and post-translational modification systems and represent safeguards against overactivation or overexpression of species. In this paper, we provide a unified theoretical synthesis of biphasic responses in cell signaling systems, by assessing signaling systems ranging from basic biochemical building blocks to canonical network structures to well-characterized exemplars on one hand, and examining different types of doses on the other. By using analytical and computational approaches applied to a range of systems across levels (described by broadly employed models), we reveal (i) design principles enabling the presence of biphasic responses, including in almost all instances, an explicit characterization of the parameter space (ii) structural factors which preclude the possibility of biphasic responses (iii) different combinations of the presence or absence of enzyme-biphasic and substrate-biphasic responses, representing safeguards against overactivation and overexpression, respectively (iv) the possibility of broadly robust biphasic responses (v) the complete alteration of signaling behavior in a network due to biphasic interactions between species (biphasic regulation) (vi) the propensity of different co-existing biphasic responses in the Erk signaling network. These results both individually and in totality have a number of important consequences for systems and synthetic biology.

Network regulation meets substrate modification chemistry

Biochemical networks are at the heart of cellular information processing. These networks contain distinct facets: (i) processing of information from the environment via cascades/pathways along with network regulation and (ii) modification of substrates in different ways, to confer protein functionality, stability and processing. While many studies focus on these factors individually, how they interact and the consequences for cellular systems behaviour are poorly understood. We develop a systems framework for this purpose by examining the interplay of network regulation (canonical feedback and feed-forward circuits) and multisite modification, as an exemplar of substrate modification. Using computational, analytical and semi-analytical approaches, we reveal distinct and unexpected ways in which the substrate modification and network levels combine and the emergent behaviour arising therefrom. This has important consequences for dissecting the behaviour of specific signalling networks, tracing the origins of systems behaviour, inference of networks from data, robustness/evolvability and multi-level engineering of biomolecular networks. Overall, we repeatedly demonstrate how focusing on only one level (say network regulation) can lead to profoundly misleading conclusions about all these aspects, and reveal a number of important consequences for experimental/theoretical/data-driven interrogations of cellular signalling systems.

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.

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

Multisite phosphorylation (and generally multisite modification) is a basic way of encoding substrate function and circuits/networks of post-translational modifications (PTM) are ubiquitous in cell signalling. The information processing characteristics of PTM systems are a focal point of broad interest. The ordering of modifications is a key aspect of multisite modification, and a broad synthesis of the impact of ordering of modifications is still missing. We focus on a basic class of multisite modification circuits: the cyclic mechanism, which corresponds to the same ordering of phosphorylation and dephosphorylation, and examine multiple variants involving common/separate kinases and common/separate phosphatases. This is of interest both because it is encountered in concrete cellular contexts, and because it serves as a bridge between ordered (sequential) mechanisms (representing one type of ordering) and random mechanisms (which have no ordering). We show that bistability and biphasic dose response curves of the maximally modified phosphoform are ruled out for basic structural reasons independent of parameters, while oscillations can result with even just one shared enzyme. We then examine the effect of relaxing some basic assumptions about the ordering of modification. We show computationally and analytically how bistability, biphasic responses and oscillations can be generated by minimal augmentations to the cyclic mechanism even when these augmentations involved reactions operating in the unsaturated limit. All in all, using this approach we demonstrate (1) how the cyclic mechanism (with single augmentations) represents a modification circuit using minimal ingredients (in terms of shared enzymes and sequestration of enzymes) to generate bistability and oscillations, when compared to other mechanisms, (2) new design principles for rationally designing PTM systems for a variety of behaviour, (3) a basis and a necessary step for understanding the origins and robustness of behaviour observed in basic multisite modification systems.

Exploring the intrinsic behaviour of multisite phosphorylation systems as part of signalling pathways

Multisite phosphorylation is a basic way of chemically encoding substrate function and a recurring feature of cell signalling pathways. A number of studies have explored information processing characteristics of multisite phosphorylation, through studies of the intrinsic kinetics. Many of these studies focus on the module in isolation. In this paper, we build a bridge to connect the behaviour of multisite modification in isolation to that as part of pathways. We study the effect of activation of the enzymes (which are basic ways in which the module may be regulated), as well the effects of the modified substrates being involved in further modifications or exiting reaction compartments. We find that these effects can induce multiple kinds of transitions, including to behaviour not seen intrinsically in the multisite modification module. We then build on these insights to investigate how these multisite modification systems can be tuned by enzyme activation to realize a range of information processing outcomes for the design of synthetic phosphorylation circuits. Connecting the complexity of multisite modification kinetics, with the pathways in which they are embedded, serves as a basis for teasing out many aspects of their interaction, providing insights of relevance in systems biology, synthetic biology/chemistry and chemical information processing.

Substrate complex competition is a regulatory motif that allows NFκB RelA to license but not amplify NFκB RelB

Signaling pathways often share molecular components, tying the activity of one pathway to the functioning of another. In the NFκB signaling system, distinct kinases mediate inflammatory and developmental signaling via RelA and RelB, respectively. Although the substrates of the developmental, so-called noncanonical, pathway are induced by inflammatory/canonical signaling, crosstalk is limited. Through dynamical systems modeling, we identified the underlying regulatory mechanism. We found that as the substrate of the noncanonical kinase NIK, the nfkb2 gene product p100, transitions from a monomer to a multimeric complex, it may compete with and inhibit p100 processing to the active p52. Although multimeric complexes of p100 (IκBδ) are known to inhibit preexisting RelA:p50 through sequestration, here we report that p100 complexes can inhibit the enzymatic formation of RelB:p52. We show that the dose-response systems properties of this complex substrate competition motif are poorly accounted for by standard Michaelis-Menten kinetics, but require more detailed mass action formulations. In sum, although tonic inflammatory signaling is required for adequate expression of the noncanonical pathway precursors, the substrate complex competition motif identified here can prevent amplification of the active RelB:p52 dimer in elevated inflammatory conditions to ensure reliable RelB-dependent developmental signaling independent of inflammatory context.

When More Is Less: Dual Phosphorylation Protects Signaling Off State against Overexpression

Kinases in signaling pathways are commonly activated by multisite phosphorylation. For example, the mitogen-activated protein kinase Erk is activated by its kinase Mek by two consecutive phosphorylations within its activation loop. In this article, we use kinetic models to study how the activation of Erk is coupled to its abundance. Intuitively, Erk activity should rise with increasing amounts of Erk protein. However, a mathematical model shows that the signaling off state is robust to increasing amounts of Erk, and Erk activity may even decline with increasing amounts of Erk. This counterintuitive, bell-shaped response of Erk activity to increasing amounts of Erk arises from the competition of the unmodified and single phosphorylated form of Erk for access to its kinase Mek. This shows that phosphorylation cycles can contain an intrinsic robustness mechanism that protects signaling from aberrant activation e.g., by gene expression noise or kinase overexpression after gene duplication events in diseases like cancer.

A mathematical model of multisite phosphorylation of tau protein

Abnormal tau metabolism followed by formation of tau deposits causes a number of neurodegenerative diseases called tauopathies including Alzheimer's disease. Hyperphosphorylation of tau protein precedes tau aggregation and is a topic of interest for the development of pharmacological interventions to prevent pathology progression at early stages. The development of a mathematical model of multisite phosphorylation of tau would be helpful for searching for the targets of pharmacological interventions and candidates for biomarkers of pathology progression. In the present study, we for the first time developed a model of multisite phosphorylation of tau protein and elucidated the relative contribution of kinases to phosphorylation of distinct sites. The model describes phosphorylation of tau or PKA-prephosphorylated tau by GSK3β and CDK5 and dephosphorylation by PP2A, accurately reproducing the data for short-term kinetics of tau (de)phosphorylation. Our results suggest that kinase inhibition may more specifically prevent tau hyperphosphorylation, e.g., on PHF sites, which are key biomarkers of pathological changes in Alzheimer's disease. The main features of our model are partial phosphorylation of tau residues and merging of random and sequential mechanisms of multisite phosphorylation within the framework of the probability-based approach assuming independent phosphorylation events.

Sequence Determinants of the Conformational Properties of an Intrinsically Disordered Protein Prior to and upon Multisite Phosphorylation

Many cell signaling events are coordinated by intrinsically disordered protein regions (IDRs) that undergo multisite Serine/Threonine phosphorylation. The conformational properties of these IDRs prior to and following multisite phosphorylation are directly relevant to understanding their functions. Here, we present results from biophysical studies and molecular simulations that quantify the conformational properties of an 81-residue IDR from the S. cerevisiae transcription factor Ash1. We show that the unphosphorylated Ash1 IDR adopts coil-like conformations that are expanded and well-solvated. This result contradicts inferences regarding global compaction that are derived from heuristics based on amino acid compositions for IDRs with low proline contents. Upon phosphorylation at ten distinct sites, the global conformational properties of pAsh1 are indistinguishable from those of unphosphorylated Ash1. This insensitivity derives from compensatory changes to the pattern of local and long-range intrachain contacts. We show that the conformational properties of Ash1 and pAsh1 can be explained in terms of the linear sequence patterning of proline and charged residues vis-à-vis all other residues. The sequence features of the Ash1 IDR are shared by many other IDRs that undergo multisite phosphorylation. Accordingly, we propose that our findings might be generalizable to other IDRs involved in cell signaling.

Mixed mechanisms of multi-site phosphorylation

Multi-site phosphorylation is ubiquitous in cell biology and has been widely studied experimentally and theoretically. The underlying chemical modification mechanisms are typically assumed to be distributive or processive. In this paper, we study the behaviour of mixed mechanisms that can arise either because phosphorylation and dephosphorylation involve different mechanisms or because phosphorylation and/or dephosphorylation can occur through a combination of mechanisms. We examine a hierarchy of models to assess chemical information processing through different mixed mechanisms, using simulations, bifurcation analysis and analytical work. We demonstrate how mixed mechanisms can show important and unintuitive differences from pure distributive and processive mechanisms, in some cases resulting in monostable behaviour with simple dose-response behaviour, while in other cases generating new behaviour-like oscillations. Our results also suggest patterns of information processing that are relevant as the number of modification sites increases. Overall, our work creates a framework to examine information processing arising from complexities of multi-site modification mechanisms and their impact on signal transduction.

Context-specific flow through the MEK/ERK module produces cell- and ligand-specific patterns of ERK single and double phosphorylation

The same pathway, such as the mitogen-activated protein kinase (MAPK) pathway, can produce different cellular responses, depending on stimulus or cell type. We examined the phosphorylation dynamics of the MAPK kinase MEK and its targets extracellular signal-regulated kinase 1 and 2 (ERK1/2) in primary hepatocytes and the transformed keratinocyte cell line HaCaT A5 exposed to either hepatocyte growth factor or interleukin-6. By combining quantitative mass spectrometry with dynamic modeling, we elucidated network structures for the reversible threonine and tyrosine phosphorylation of ERK in both cell types. In addition to differences in the phosphorylation and dephosphorylation reactions, the HaCaT network model required two feedback mechanisms, which, as the experimental data suggested, involved the induction of the dual-specificity phosphatase DUSP6 and the scaffold paxillin. We assayed and modeled the accumulation of the double-phosphorylated and active form of ERK1/2, as well as the dynamics of the changes in the monophosphorylated forms of ERK1/2. Modeling the differences in the dynamics of the changes in the distributions of the phosphorylated forms of ERK1/2 suggested that different amounts of MEK activity triggered context-specific responses, with primary hepatocytes favoring the formation of double-phosphorylated ERK1/2 and HaCaT A5 cells that produce both the threonine-phosphorylated and the double-phosphorylated form. These differences in phosphorylation distributions explained the threshold, sensitivity, and saturation of the ERK response. We extended the findings of differential ERK phosphorylation profiles to five additional cultured cell systems and matched liver tumor and normal tissue, which revealed context-specific patterns of the various forms of phosphorylated ERK.

Biosensor architectures for high-fidelity reporting of cellular signaling

Understanding mechanisms of information processing in cellular signaling networks requires quantitative measurements of protein activities in living cells. Biosensors are molecular probes that have been developed to directly track the activity of specific signaling proteins and their use is revolutionizing our understanding of signal transduction. The use of biosensors relies on the assumption that their activity is linearly proportional to the activity of the signaling protein they have been engineered to track. We use mechanistic mathematical models of common biosensor architectures (single-chain FRET-based biosensors), which include both intramolecular and intermolecular reactions, to study the validity of the linearity assumption. As a result of the classic mechanism of zero-order ultrasensitivity, we find that biosensor activity can be highly nonlinear so that small changes in signaling protein activity can give rise to large changes in biosensor activity and vice versa. This nonlinearity is abolished in architectures that favor the formation of biosensor oligomers, but oligomeric biosensors produce complicated FRET states. Based on this finding, we show that high-fidelity reporting is possible when a single-chain intermolecular biosensor is used that cannot undergo intramolecular reactions and is restricted to forming dimers. We provide phase diagrams that compare various trade-offs, including observer effects, which further highlight the utility of biosensor architectures that favor intermolecular over intramolecular binding. We discuss challenges in calibrating and constructing biosensors and highlight the utility of mathematical models in designing novel probes for cellular signaling.

Dominant negative inhibition data should be analyzed using mathematical modeling--re-interpreting data from insulin signaling

As our ability to measure the complexity of intracellular networks has evolved, it has become increasingly clear that we need new methods for data analysis: methods involving mathematical modeling. Nevertheless, it is still uncontroversial to publish and interpret experimental results without a model-based proof that the reasoning is correct. In the present study, we argue that this attitude probably needs to change in the future. We illustrate this need for modeling by considering the common experimental technique of using dominant-negative constructs. More specifically, we consider published time-series and dose-response data which previously have been used to argue that the protein S6 kinase does not phosphorylate insulin receptor substrate-1 at a specific serine residue. Using a presented general approach to interpret such data, we now demonstrate that the given dominant-negative data are not conclusive (i.e. that in the absence of other proofs, S6 kinase still may be the kinase). Using simulations with uncertainty analysis and analytical solutions, we show that an alternative explanation is centered around depletion of substrate, which can be tested experimentally. This analysis thus illustrates both the necessity and the benefits of using mathematical modeling to fully understand the implications of biological data, even for a small system and relatively simple data.