Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation, and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.Comment: Submitted to 'Systems Medicine' as a book chapte

Synthetic Activation of Endogenous PI3K and Rac Identifies an AND-Gate Switch for Cell Polarization and Migration

Phosphatidylinositol 3-OH kinase (PI3K) has been widely studied as a principal regulator of cell polarization, migration, and chemotaxis [1], [2], [3], [4]. Surprisingly, recent studies showed that mammalian neutrophils and Dictyostelium discoideum cells can polarize and migrate in the absence of PI3K activity [5], [6], [7]. Here we directly probe the roles of PI3K and its downstream effector, Rac, in HL-60 neutrophils by using a chemical biology approach whereby the endogenously present enzymes are synthetically activated in less than one minute [8], [9], [10]. We show that uniform activation of endogenous PI3K is sufficient to polarize previously unpolarized neutrophils and trigger effective cell migration. After a delay following symmetrical phosphatidylinositol (3,4,5)-triphosphate (PIP3) production, a polarized distribution of PIP3 was induced by positive feedback requiring actin polymerization. Pharmacological studies argue that this process does not require receptor-coupled trimeric G proteins. Contrary to the current working model, rapid activation of endogenous Rac proteins triggered effective actin polymerization but failed to feed back to PI3K to generate PIP3 or induce cell polarization. Thus, the increase in PIP3 concentration at the leading edge is generated by positive feedback with an AND gate logic with a PI3K-Rac-actin polymerization pathway as a first input and a PI3K initiated non-Rac pathway as a second input. This AND-gate control for cell polarization can explain how Rac can be employed for both PI3K-dependent and -independent signaling pathways coexisting in the same cell

A Mechanism for the Polarity Formation of Chemoreceptors at the Growth Cone Membrane for Gradient Amplification during Directional Sensing

Accurate response to external directional signals is essential for many physiological functions such as chemotaxis or axonal guidance. It relies on the detection and amplification of gradients of chemical cues, which, in eukaryotic cells, involves the asymmetric relocalization of signaling molecules. How molecular events coordinate to induce a polarity at the cell level remains however poorly understood, particularly for nerve chemotaxis. Here, we propose a model, inspired by single-molecule experiments, for the membrane dynamics of GABA chemoreceptors in nerve growth cones (GCs) during directional sensing. In our model, transient interactions between the receptors and the microtubules, coupled to GABA-induced signaling, provide a positive-feedback loop that leads to redistribution of the receptors towards the gradient source. Using numerical simulations with parameters derived from experiments, we find that the kinetics of polarization and the steady-state polarized distribution of GABA receptors are in remarkable agreement with experimental observations. Furthermore, we make predictions on the properties of the GC seen as a sensing, amplification and filtering module. In particular, the growth cone acts as a low-pass filter with a time constant ∼10 minutes determined by the Brownian diffusion of chemoreceptors in the membrane. This filtering makes the gradient amplification resistent to rapid fluctuations of the external signals, a beneficial feature to enhance the accuracy of neuronal wiring. Since the model is based on minimal assumptions on the receptor/cytoskeleton interactions, its validity extends to polarity formation beyond the case of GABA gradient sensing. Altogether, it constitutes an original positive-feedback mechanism by which cells can dynamically adapt their internal organization to external signals

Multifaceted roles of GSK-3 and Wnt/β-catenin in hematopoiesis and leukemogenesis: opportunities for therapeutic intervention

Glycogen synthase kinase-3 (GSK-3) is well documented to participate in a complex array of critical cellular processes. It was initially identified in rat skeletal muscle as a serine/threonine kinase that phosphorylated and inactivated glycogen synthase. This versatile protein is involved in numerous signaling pathways that influence metabolism, embryogenesis, differentiation, migration, cell cycle progression and survival. Recently, GSK-3 has been implicated in leukemia stem cell pathophysiology and may be an appropriate target for its eradication. In this review, we will discuss the roles that GSK-3 plays in hematopoiesis and leukemogenesis as how this pivotal kinase can interact with multiple signaling pathways such as: Wnt/β-catenin, phosphoinositide 3-kinase (PI3K)/phosphatase and tensin homolog (PTEN)/Akt/mammalian target of rapamycin (mTOR), Ras/Raf/MEK/extracellular signal-regulated kinase (ERK), Notch and others. Moreover, we will discuss how targeting GSK-3 and these other pathways can improve leukemia therapy and may overcome therapeutic resistance. In summary, GSK-3 is a crucial regulatory kinase interacting with multiple pathways to control various physiological processes, as well as leukemia stem cells, leukemia progression and therapeutic resistance. GSK-3 and Wnt are clearly intriguing therapeutic targets

The Indian cobra reference genome and transcriptome enables comprehensive identification of venom toxins

Snakebite envenoming is a serious and neglected tropical disease that kills ~100,000 people annually. High-quality, genome-enabled comprehensive characterization of toxin genes will facilitate development of effective humanized recombinant antivenom. We report a de novo near-chromosomal genome assembly of Naja naja, the Indian cobra, a highly venomous, medically important snake. Our assembly has a scaffold N50 of 223.35 Mb, with 19 scaffolds containing 95% of the genome. Of the 23,248 predicted protein-coding genes, 12,346 venom-gland-expressed genes constitute the \u27venom-ome\u27 and this included 139 genes from 33 toxin families. Among the 139 toxin genes were 19 \u27venom-ome-specific toxins\u27 (VSTs) that showed venom-gland-specific expression, and these probably encode the minimal core venom effector proteins. Synthetic venom reconstituted through recombinant VST expression will aid in the rapid development of safe and effective synthetic antivenom. Additionally, our genome could serve as a reference for snake genomes, support evolutionary studies and enable venom-driven drug discovery

The regulation of glycogen synthase kinase-3 nuclear export by Frat/GBP

Previous studies have shown that nuclear levels of glycogen synthase kinase-3 (GSK-3) are dynamically regulated and may affect access of GSK-3 to its substrates. In this study we show that the GSK-3-binding protein Frat/GBP regulates the nuclear export of GSK-3. We show that Frat/GBP contains a nuclear export sequence that promotes its own nuclear export and that of associated GSK-3. Treating cells with leptomycin B increased nuclear levels of endogenous GSK-3 suggesting that an endogenous process targets GSK-3 for nuclear export. To investigate this further, we used two approaches to disrupt the interaction between GSK-3 and endogenous Frat. First we isolated mutants of GSK-3 that selectively interfered with Frat binding and found that these mutants were poorly exported. Second we expressed a peptide that competes with Frat for GSK-3 binding and found that it caused endogenous GSK-3 to accumulate in the nucleus. Together these data suggest that Frat may be the endogenous factor that targets GSK-3 for nuclear export. The dynamic expression patterns of Frat mRNAs together with the role of Frat in mediating GSK-3 nuclear export have important implications for the control of the substrate access of GSK-3 in several signaling pathways

Seduced by the dark side: integrating molecular and ecological perspectives on the influence of light on plant defence against pests and pathogens.

Plants frequently suffer attack from herbivores and microbial pathogens, and have evolved a complex array of defence mechanisms to resist defoliation and disease. These include both preformed defences, ranging from structural features to stores of toxic secondary metabolites, and inducible defences, which are activated only after an attack is detected. It is well known that plant defences against pests and pathogens are commonly affected by environmental conditions, but the mechanisms by which responses to the biotic and abiotic environments interact are only poorly understood. In this review, we consider the impact of light on plant defence, in terms of both plant life histories and rapid scale molecular responses to biotic attack. We bring together evidence that illustrates that light not only modulates defence responses via its influence on biochemistry and plant development but, in some cases, is essential for the development of resistance. We suggest that the interaction between the light environment and plant defence is multifaceted, and extends across different temporal and biological scales

Identification of the Axin and Frat binding region of glycogen synthase kinase-3

Glycogen synthase kinase-3 (GSK-3) is a key component of several signaling pathways including those regulated by Wnt and insulin ligands. Specificity in GSK-3 signaling is thought to involve interactions with scaffold proteins that localize GSK-3 regulators and substrates. This report shows that GSK-3 forms a low affinity homodimer that is disrupted by binding to Axin and Frat. Based on the crystal structure of GSK-3, we have used surface-scanning mutagenesis to identify residues that differentially affect GSK-3 interactions. Mutations that disrupt Frat and Axin cluster at the dimer interface explaining their effect on homodimer formation. Loss of the Axin binding site blocks the ability of dominant negative GSK-3 to cause axis duplication in Xenopus embryos. The Axin binding site is conserved within all GSK-3 proteins, and its loss affects both cell motility and gene expression in the nonmetazoan,Dictyostelium. Surprisingly, we find no genetic interaction between a non-Axin-binding GSK-3 mutant and T-cell factor activity, arguing that Axin interactions alone cannot explain the regulation of T-cell factor-mediated gene expression

A secreted protein is an endogenous chemorepellant in Dictyostelium discoideum

Chemorepellants may play multiple roles in physiological and pathological processes.However, few endogenous chemorepellants have been identified, and how they function is unclear. We found that the autocrine signal AprA, which is produced by growing Dictyostelium discoideum cells and inhibits their proliferation, also functions as a chemorepellant.Wild-type cells at the edge of a colony show directed movement outward from the colony, whereas cells lacking AprA do not. Cells show directed movement away from a source of recombinant AprA and dialyzed conditioned media from wild-type cells, but not dialyzed conditionedmedia fromaprA− cells. The secreted protein CfaD, the G protein Gα8, and the kinase QkgA are necessary for the chemorepellant activity of AprA as well as its proliferation-inhibiting activity, whereas the putative transcription factor BzpN is dispensable for the chemorepellant activity of AprA but necessary for inhibition of proliferation. Phospholipase C and PI3 kinases 1 and 2, which are necessary for the activity of at least one other chemorepellant in Dictyostelium, are not necessary for recombinant AprA chemorepellant activity. Starved cells are not repelled by recombinant AprA, suggesting that aggregation-phase cells are not sensitive to the chemorepellant effect. Cell tracking indicates that AprA affects the directional bias of cell movement, but not cell velocity or the persistence of cell movement. Together, our data indicate that the endogenous signal AprA acts as an autocrine chemorepellant for Dictyostelium cells