Pathway switching explains the sharp response characteristic of hypoxia response network

Hypoxia induces the expression of genes that alter metabolism through the hypoxia-inducible factor (HIF). A theoretical model based on differential equations of the hypoxia response network has been previously proposed in which a sharp response to changes in oxygen concentration was observed but not quantitatively explained. That model consisted of reactions involving 23 molecular species among which the concentrations of HIF and oxygen were linked through a complex set of reactions. In this paper, we analyze this previous model using a combination of mathematical tools to draw out the key components of the network and explain quantitatively how they contribute to the sharp oxygen response. We find that the switch-like behavior is due to pathway-switching wherein HIF degrades rapidly under normoxia in one pathway, while the other pathway accumulates HIF to trigger downstream genes under hypoxia. The analytic technique is potentially useful in studying larger biomedical networks.     

Predicted Functions of MdmX in Fine-Tuning the Response of p53 to DNA Damage

Tumor suppressor protein p53 is regulated by two structurally homologous proteins, Mdm2 and MdmX. In contrast to Mdm2, MdmX lacks ubiquitin ligase activity. Although the essential interactions of MdmX are known, it is not clear how they function to regulate p53. The regulation of tumor suppressor p53 by Mdm2 and MdmX in response to DNA damage was investigated by mathematical modeling of a simplified network. The simplified network model was derived from a detailed molecular interaction map (MIM) that exhibited four coherent DNA damage response pathways. The results suggest that MdmX may amplify or stabilize DNA damage-induced p53 responses via non-enzymatic interactions. Transient effects of MdmX are mediated by reservoirs of p53∶MdmX and Mdm2∶MdmX heterodimers, with MdmX buffering the concentrations of p53 and/or Mdm2. A survey of kinetic parameter space disclosed regions of switch-like behavior stemming from such reservoir-based transients. During an early response to DNA damage, MdmX positively or negatively regulated p53 activity, depending on the level of Mdm2; this led to amplification of p53 activity and switch-like response. During a late response to DNA damage, MdmX could dampen oscillations of p53 activity. A possible role of MdmX may be to dampen such oscillations that otherwise could produce erratic cell behavior. Our study suggests how MdmX may participate in the response of p53 to DNA damage either by increasing dependency of p53 on Mdm2 or by dampening oscillations of p53 activity and presents a model for experimental investigation.     

Membrane localization of scaffold proteins promotes graded signaling in the yeast MAP kinase cascade

BACKGROUND: Signaling through mitogen-activated protein kinase (MAPK) cascade pathways can show various input-output behaviors, including either switch-like or graded responses to increasing levels of stimulus. Prior studies suggest that switch-like behavior is promoted by positive feedback loops and nonprocessive phosphorylation reactions, but it is unclear whether graded signaling is a default behavior or whether it must be enforced by separate mechanisms. It has been hypothesized that scaffold proteins promote graded behavior. RESULTS: Here, we experimentally probe the determinants of graded signaling in the yeast mating MAPK pathway. We find that graded behavior is robust in that it resists perturbation by loss of several negative-feedback regulators. However, the pathway becomes switch-like when activated by a crosstalk stimulus that bypasses multiple upstream components. To dissect the contributing factors, we developed a method for gradually varying the signal input at different pathway steps in vivo. Input at the beginning of the kinase cascade produced a sharp, threshold-like response. Surprisingly, the scaffold protein Ste5 increased this threshold behavior when limited to the cytosol. However, signaling remained graded whenever Ste5 was allowed to function at the plasma membrane. CONCLUSIONS: The results suggest that the MAPK cascade module is inherently ultrasensitive but is converted to a graded system by the pathway-specific activation mechanism. Scaffold-mediated assembly of signaling complexes at the plasma membrane allows faithful propagation of weak signals, which consequently reduces pathway ultrasensitivity. These properties help shape the input-output properties of the system to fit the physiological context.     

Multitasking by pVHL in tumour suppression

Functional inactivation of the von Hippel-Lindau (VHL) tumour suppressor gene product, pVHL, leads to cancer in humans. It is widely accepted that pVHL functions to destabilise hypoxia inducible factor alpha (HIFalpha) subunits, key effectors of the hypoxia signalling pathway. However, growing evidence indicates that tumour suppression by pVHL also involves the control of a wide variety of HIFalpha-independent processes including microtubule dynamics, primary cilium maintenance, cell proliferation, neuronal apoptosis, extracellular matrix deposition and responses to DNA damage. Moreover, it is becoming apparent that tumour initiation requires not only VHL mutation but also the alteration of additional cooperating cancer pathways. These studies are beginning to provide insights into the signalling networks involving pVHL that normally control diverse cellular processes and how disruption of these networks leads to tumour formation.     

Structural Analysis to Determine the Core of Hypoxia Response Network

The advent of sophisticated molecular biology techniques allows to deduce the structure of complex biological networks. However, networks tend to be huge and impose computational challenges on traditional mathematical analysis due to their high dimension and lack of reliable kinetic data. To overcome this problem, complex biological networks are decomposed into modules that are assumed to capture essential aspects of the full network''s dynamics. The question that begs for an answer is how to identify the core that is representative of a network''s dynamics, its function and robustness. One of the powerful methods to probe into the structure of a network is Petri net analysis. Petri nets support network visualization and execution. They are also equipped with sound mathematical and formal reasoning based on which a network can be decomposed into modules. The structural analysis provides insight into the robustness and facilitates the identification of fragile nodes. The application of these techniques to a previously proposed hypoxia control network reveals three functional modules responsible for degrading the hypoxia-inducible factor (HIF). Interestingly, the structural analysis identifies superfluous network parts and suggests that the reversibility of the reactions are not important for the essential functionality. The core network is determined to be the union of the three reduced individual modules. The structural analysis results are confirmed by numerical integration of the differential equations induced by the individual modules as well as their composition. The structural analysis leads also to a coarse network structure highlighting the structural principles inherent in the three functional modules. Importantly, our analysis identifies the fragile node in this robust network without which the switch-like behavior is shown to be completely absent.     

Phosphatase Specificity and Pathway Insulation in Signaling Networks

Phosphatases play an important role in cellular signaling networks by regulating the phosphorylation state of proteins. Phosphatases are classically considered to be promiscuous, acting on tens to hundreds of different substrates. We recently demonstrated that a shared phosphatase can couple the responses of two proteins to incoming signals, even if those two substrates are from otherwise isolated areas of the network. This finding raises a potential paradox: if phosphatases are indeed highly promiscuous, how do cells insulate themselves against unwanted crosstalk? Here, we use mathematical models to explore three possible insulation mechanisms. One approach involves evolving phosphatase K_M values that are large enough to prevent saturation by the phosphatase’s substrates. Although this is an effective method for generating isolation, the phosphatase becomes a highly inefficient enzyme, which prevents the system from achieving switch-like responses and can result in slow response kinetics. We also explore the idea that substrate degradation can serve as an effective phosphatase. Assuming that degradation is unsaturatable, this mechanism could insulate substrates from crosstalk, but it would also preclude ultrasensitive responses and would require very high substrate turnover to achieve rapid dephosphorylation kinetics. Finally, we show that adaptor subunits, such as those found on phosphatases like PP2A, can provide effective insulation against phosphatase crosstalk, but only if their binding to substrates is uncoupled from their binding to the catalytic core. Analysis of the interaction network of PP2A’s adaptor domains reveals that although its adaptors may isolate subsets of targets from one another, there is still a strong potential for phosphatase crosstalk within those subsets. Understanding how phosphatase crosstalk and the insulation mechanisms described here impact the function and evolution of signaling networks represents a major challenge for experimental and computational systems biology.     

Multiscale modelling of vascular tumour growth in 3D: the roles of domain size and boundary conditions

We investigate a three-dimensional multiscale model of vascular tumour growth, which couples blood flow, angiogenesis, vascular remodelling, nutrient/growth factor transport, movement of, and interactions between, normal and tumour cells, and nutrient-dependent cell cycle dynamics within each cell. In particular, we determine how the domain size, aspect ratio and initial vascular network influence the tumour's growth dynamics and its long-time composition. We establish whether it is possible to extrapolate simulation results obtained for small domains to larger ones, by constructing a large simulation domain from a number of identical subdomains, each subsystem initially comprising two parallel parent vessels, with associated cells and diffusible substances. We find that the subsystem is not representative of the full domain and conclude that, for this initial vessel geometry, interactions between adjacent subsystems contribute to the overall growth dynamics. We then show that extrapolation of results from a small subdomain to a larger domain can only be made if the subdomain is sufficiently large and is initialised with a sufficiently complex vascular network. Motivated by these results, we perform simulations to investigate the tumour's response to therapy and show that the probability of tumour elimination in a larger domain can be extrapolated from simulation results on a smaller domain. Finally, we demonstrate how our model may be combined with experimental data, to predict the spatio-temporal evolution of a vascular tumour.     

Hill coefficient-based stochastic switch-like signal directly governs damage-recovery dynamics in freshwater fish in response to pulse copper

Growing evidence demonstrates that fluctuating metal stressors can have profound impact on the ecophysiological responses in aquatic species. However, how environmental stochasticity affects the complex damage-recovery dynamics in organisms remains difficult to predict. The objective of this paper was to investigate the stochastic behavior in the damage-recovery dynamics in tilapia in response to pulse waterborne copper (Cu). We developed a mathematical framework that allows discrimination between damage and recovery processes in tilapia exposed to designed pulse Cu scenarios. We built deterministic nonlinear models for the damage-recovery dynamics that produce response surfaces describing killing/recovery rate–Cu-pulse interval interactions. Here we showed that the stochastic switching behavior arose from competition among killing, recovery rates, and Cu pulse frequency. This competition resulted in an ultrasensitivity appeared in whole body, gills, muscle, liver, and kidney with Hill coefficients of ≥7, 4, 7, 5, and 5, respectively, at Cu 3 mg L⁻¹, dilution rate 0.05 h⁻¹, and pulse interval 72 h, indicating that a stochastic switch-like response was generated. We argue that the role of gill-associated Hill coefficient as a direct signal of the stochastic switch-like response in the damage-recovery dynamics in response to pulse metal stressor can serve as a sensitive indicator for risk detection in fluctuating environments. Our approach constitutes a general method to identify the stochastic switch-like response for aquatic species exposed to fluctuating metal stressors, which may help to predict and, eventually, expand our understanding of the damage-recovery dynamics. Finally, we implicate that Hill coefficient-based switch-like signal and its damage with hazard response can be linked in an information theoretic framework to handle environmental stochasticity.     

Crosstalk and Competition in Signaling Networks

Signaling networks have evolved to transduce external and internal information into critical cellular decisions such as growth, differentiation, and apoptosis. These networks form highly interconnected systems within cells due to network crosstalk, where an enzyme from one canonical pathway acts on targets from other pathways. It is currently unclear what types of effects these interconnections can have on the response of networks to incoming signals. In this work, we employ mathematical models to characterize the influence that multiple substrates have on one another. These models build off of the atomistic motif of a kinase/phosphatase pair acting on a single substrate. We find that the ultrasensitive, switch-like response these motifs can exhibit becomes transitive: if one substrate saturates the enzymes and responds ultrasensitively, then all substrates will do so regardless of their degree of saturation. We also demonstrate that the phosphatases themselves can induce crosstalk even when the kinases are independent. These findings have strong implications for how we understand and classify crosstalk, as well as for the rational development of kinase inhibitors aimed at pharmaceutically modulating network behavior.     

Functional neuroimaging of genetic variation in serotonergic neurotransmission

Serotonin (5-hydroxytryptamine; 5-HT) is a potent modulator of the physiology and behavior involved in generating appropriate responses to environmental cues such as danger or threat. Furthermore, genetic variation in 5-HT subsystem genes can impact upon several dimensions of emotional behavior including neuroticism and psychopathology, but especially anxiety traits. Recently, functional neuroimaging has provided a dramatic illustration of how a promoter polymorphism in the human 5-HT transporter (5-HTT) gene, which has been weakly related to these behaviors, is strongly related to the engagement of neural systems, namely the amygdala, subserving emotional processes. In this commentary, we discuss how functional neuroimaging can be used to characterize the effects of polymorphisms in 5-HT subsystem genes on the response of neural circuits underlying the generation and regulation of mood and temperament as well as susceptibility to affective illness. We argue that in time, such knowledge will allow us to not only transcend phenomenological diagnosis and represent mechanisms of disease, but also identify at-risk individuals and biological pathways for the development of new treatments.