Bell-shaped and ultrasensitive dose-response in phosphorylation-dephosphorylation cycles: the role of kinase-phosphatase complex formation

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.

Ultrasensitive dose-response for asbestos cancer risk implied by new inflammation-mutation model

Alterations in complex cellular phenotype each typically involve multistep activation of an ultrasensitive molecular switch (e.g., to adaptively initiate an apoptosis, inflammasome, Nrf2-ARE anti-oxidant, or heat-shock activation pathway) that triggers expression of a suite of target genes while efficiently limiting false-positive switching from a baseline state. Such switches exhibit nonlinear signal-activation relationships. In contrast, a linear no-threshold (LNT) dose-response relationship is expected for damage that accumulates in proportion to dose, as hypothesized for increased risk of cancer in relation to genotoxic dose according to the multistage somatic mutation/clonal-expansion theory of cancer, e.g., as represented in the Moolgavkar-Venzon-Knudsen (MVK) cancer model by a doubly stochastic nonhomogeneous Poisson process. Mesothelioma and lung cancer induced by exposure to carcinogenic (e.g., certain asbestos) fibers in humans and experimental animals are thought to involve modes of action driven by mutations, cytotoxicity-associated inflammation, or both, rendering ambiguous expectations concerning the nature of model-implied shape of the low-dose response for above-background increase in risk of incurring these endpoints. A recent Inflammation Somatic Mutation (ISM) theory of cancer posits instead that tissue-damage-associated inflammation that epigenetically recruits, activates and orchestrates stem cells to engage in tissue repair does not merely promote cancer, but rather is a requisite co-initiator (acting together with as few as two somatic mutations) of the most efficient pathway to any type of cancer in any reparable tissue (Dose-Response 2019; 17(2):1-12). This theory is reviewed, implications of this theory are discussed in relation to mesothelioma and lung cancer associated with chronic asbestos inhalation, one of the two types of ISM-required mutations is here hypothesized to block or impede inflammation resolution (e.g., by doing so for GPCR-mediated signal transduction by one or more endogenous autacoid specialized pro-resolving mediators or SPMs), and supporting evidence for this hypothesis is discussed.

ATP-powered molecular recognition to engineer transient multivalency and self-sorting 4D hierarchical systems

Biological systems organize multiple hierarchical structures in parallel, and create dynamic assemblies and functions by energy dissipation. In contrast, emerging artificial non-equilibrium self-assembling systems have remained relatively simplistic concerning hierarchical design, and non-equilibrium multi-component systems are uncharted territory. Here we report a modular DNA toolbox allowing to program transient non-equilibrium multicomponent systems across hierarchical length scales by introducing chemically fueled molecular recognition orchestrated by reaction networks of concurrent ATP-powered ligation and cleavage of freely programmable DNA building blocks. Going across hierarchical levels, we demonstrate transient side-chain functionalized nucleic acid polymers, and further introduce the concept of transient cooperative multivalency as a key to bridge length scales to pioneer fuel-driven encapsulation, self-assembly of colloids, and non-equilibrium transient narcissistic colloidal self-sorting on a systems level. The fully programmable and functionalizable DNA components pave the way to design chemically fueled 4D (3 space, 1 time) molecular multicomponent systems and autonomous materials.

Linear-No-Threshold Default Assumptions are Unwarranted for Cytotoxic Endpoints Independently Triggered by Ultrasensitive Molecular Switches

Crump's response in this issue to my critique of linear-no-threshold (LNT) default assumptions for noncancer and nongenotoxic cancer risks (Risk Analysis 2016; 36(3):589-604) is rebutted herein. Crump maintains that distinguishing between a low-dose linear dose response and a threshold dose response on the basis of dose-response data is impossible even for endpoints involving increased cytotoxicity. My rebuttal relies on descriptions and specific illustrations of two well-characterized ultrasensitive molecular switches that govern two key cytoprotective responses to cellular stress-heat shock response and antioxidant response element activation, respectively-each of which serve to suppress stress-induced apoptotic cell death unless overwhelmed. Because detailed dose-response data for each endpoint is shown to be J- or inverted-J-shaped with high confidence, and because independent pathways can explain background rates of apoptosis, LNT assumptions for this cytotoxic endpoint are unwarranted, at least in some cases and perhaps generally.

Quinoline based mono- and bis-(thio)carbohydrazones: synthesis, anticancer activity in 2D and 3D cancer and cancer stem cell models

Study of antitumor activity of mono- and bis-quinoline based (thio)carbohydrazones on THP-1 and AsPC-1 cancer stem cells, revealed that thiocarbohydrazones had superior pro-apoptotic activity than carbohydrazones with multi-target profile activities.

A systems model of phosphorylation for inflammatory signaling events

Phosphorylation is a fundamental biochemical reaction that modulates protein activity in cells. While a single phosphorylation event is relatively easy to understand, multisite phosphorylation requires systems approaches for deeper elucidation of the underlying molecular mechanisms. In this paper we develop a mechanistic model for single- and multi-site phosphorylation. The proposed model is compared with previously reported studies. We compare the predictions of our model with experiments published in the literature in the context of inflammatory signaling events in order to provide a mechanistic description of the multisite phosphorylation-mediated regulation of Signal Transducer and Activator of Transcription 3 (STAT3) and Interferon Regulatory Factor 5 (IRF-5) proteins. The presented model makes crucial predictions for transcription factor phosphorylation events in the immune system. The model proposes potential mechanisms for T cell phenotype switching and production of cytokines. This study also provides a generic framework for the better understanding of a large number of multisite phosphorylation-regulated biochemical circuits.

Small G proteins Rac1 and Ras regulate serine/threonine protein phosphatase 5 (PP5)·extracellular signal-regulated kinase (ERK) complexes involved in the feedback regulation of Raf1

Serine/threonine protein phosphatase 5 (PP5, PPP5C) is known to interact with the chaperonin heat shock protein 90 (HSP90) and is involved in the regulation of multiple cellular signaling cascades that control diverse cellular processes, such as cell growth, differentiation, proliferation, motility, and apoptosis. Here, we identify PP5 in stable complexes with extracellular signal-regulated kinases (ERKs). Studies using mutant proteins reveal that the formation of PP5·ERK1 and PP5·ERK2 complexes partially depends on HSP90 binding to PP5 but does not require PP5 or ERK1/2 activity. However, PP5 and ERK activity regulates the phosphorylation state of Raf1 kinase, an upstream activator of ERK signaling. Whereas expression of constitutively active Rac1 promotes the assembly of PP5·ERK1/2 complexes, acute activation of ERK1/2 fails to influence the phosphatase-kinase interaction. Introduction of oncogenic HRas (HRas(V12)) has no effect on PP5-ERK1 binding but selectively decreases the interaction of PP5 with ERK2, in a manner that is independent of PP5 and MAPK/ERK kinase (MEK) activity, yet paradoxically requires ERK2 activity. Additional studies conducted with oncogenic variants of KRas4B reveal that KRas(L61), but not KRas(V12), also decreases the PP5-ERK2 interaction. The expression of wild type HRas or KRas proteins fails to reduce PP5-ERK2 binding, indicating that the effect is specific to HRas(V12) and KRas(L61) gain-of-function mutations. These findings reveal a novel, differential responsiveness of PP5-ERK1 and PP5-ERK2 interactions to select oncogenic Ras variants and also support a role for PP5·ERK complexes in regulating the feedback phosphorylation of PP5-associated Raf1.

Zero-order ultrasensitivity: a study of criticality and fluctuations under the total quasi-steady state approximation in the linear noise regime

Zero-order ultrasensitivity (ZOU) is a long known and interesting phenomenon in enzyme networks. Here, a substrate is reversibly modified by two antagonistic enzymes (a 'push-pull' system) and the fraction in modified state undergoes a sharp switching from near-zero to near-unity at a critical value of the ratio of the enzyme concentrations, under saturation conditions. ZOU and its extensions have been studied for several decades now, ever since the seminal paper of Goldbeter and Koshland (1981); however, a complete probabilistic treatment, important for the study of fluctuations in finite populations, is still lacking. In this paper, we study ZOU using a modular approach, akin to the total quasi-steady state approximation (tQSSA). This approach leads to a set of Fokker-Planck (drift-diffusion) equations for the probability distributions of the intermediate enzyme-bound complexes, as well as the modified/unmodified fractions of substrate molecules. We obtain explicit expressions for various average fractions and their fluctuations in the linear noise approximation (LNA). The emergence of a 'critical point' for the switching transition is rigorously established. New analytical results are derived for the average and variance of the fractional substrate concentration in various chemical states in the near-critical regime. For the total fraction in the modified state, the variance is shown to be a maximum near the critical point and decays algebraically away from it, similar to a second-order phase transition. The new analytical results are compared with existing ones as well as detailed numerical simulations using a Gillespie algorithm.

Ultrasensitivity in phosphorylation-dephosphorylation cycles with little substrate

Cellular decision-making is driven by dynamic behaviours, such as the preparations for sunrise enabled by circadian rhythms and the choice of cell fates enabled by positive feedback. Such behaviours are often built upon ultrasensitive responses where a linear change in input generates a sigmoidal change in output. Phosphorylation-dephosphorylation cycles are one means to generate ultrasensitivity. Using bioinformatics, we show that in vivo levels of kinases and phosphatases frequently exceed the levels of their corresponding substrates in budding yeast. This result is in contrast to the conditions often required by zero-order ultrasensitivity, perhaps the most well known means for how such cycles become ultrasensitive. We therefore introduce a mechanism to generate ultrasensitivity when numbers of enzymes are higher than numbers of substrates. Our model combines distributive and non-distributive actions of the enzymes with two-stage binding and concerted allosteric transitions of the substrate. We use analytical and numerical methods to calculate the Hill number of the response. For a substrate with phosphosites, we find an upper bound of the Hill number of , and so even systems with a single phosphosite can be ultrasensitive. Two-stage binding, where an enzyme must first bind to a binding site on the substrate before it can access the substrate's phosphosites, allows the enzymes to sequester the substrate. Such sequestration combined with competition for each phosphosite provides an intuitive explanation for the sigmoidal shifts in levels of phosphorylated substrate. Additionally, we find cases for which the response is not monotonic, but shows instead a peak at intermediate levels of input. Given its generality, we expect the mechanism described by our model to often underlay decision-making circuits in eukaryotic cells.

Effects of multiple enzyme-substrate interactions in basic units of cellular signal processing

Covalent modification cycles are a ubiquitous feature of cellular signalling networks. In these systems, the interaction of an active enzyme with the unmodified form of its substrate is essential for signalling to occur. However, this interaction is not necessarily the only enzyme-substrate interaction possible. In this paper, we analyse the behaviour of a basic model of signalling in which additional, non-essential enzyme-substrate interactions are possible. These interactions include those between the inactive form of an enzyme and its substrate, and between the active form of an enzyme and its product. We find that these additional interactions can result in increased sensitivity and biphasic responses, respectively. The dynamics of the responses are also significantly altered by the presence of additional interactions. Finally, we evaluate the consequences of these interactions in two variations of our basic model, involving double modification of substrate and scaffold-mediated signalling, respectively. We conclude that the molecular details of protein-protein interactions are important in determining the signalling properties of enzymatic signalling pathways.