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

Global burden of 288 causes of death and life expectancy decomposition in 204 countries and territories and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

BACKGROUND Regular, detailed reporting on population health by underlying cause of death is fundamental for public health decision making. Cause-specific estimates of mortality and the subsequent effects on life expectancy worldwide are valuable metrics to gauge progress in reducing mortality rates. These estimates are particularly important following large-scale mortality spikes, such as the COVID-19 pandemic. When systematically analysed, mortality rates and life expectancy allow comparisons of the consequences of causes of death globally and over time, providing a nuanced understanding of the effect of these causes on global populations. METHODS The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 cause-of-death analysis estimated mortality and years of life lost (YLLs) from 288 causes of death by age-sex-location-year in 204 countries and territories and 811 subnational locations for each year from 1990 until 2021. The analysis used 56 604 data sources, including data from vital registration and verbal autopsy as well as surveys, censuses, surveillance systems, and cancer registries, among others. As with previous GBD rounds, cause-specific death rates for most causes were estimated using the Cause of Death Ensemble model-a modelling tool developed for GBD to assess the out-of-sample predictive validity of different statistical models and covariate permutations and combine those results to produce cause-specific mortality estimates-with alternative strategies adapted to model causes with insufficient data, substantial changes in reporting over the study period, or unusual epidemiology. YLLs were computed as the product of the number of deaths for each cause-age-sex-location-year and the standard life expectancy at each age. As part of the modelling process, uncertainty intervals (UIs) were generated using the 2·5th and 97·5th percentiles from a 1000-draw distribution for each metric. We decomposed life expectancy by cause of death, location, and year to show cause-specific effects on life expectancy from 1990 to 2021. We also used the coefficient of variation and the fraction of population affected by 90% of deaths to highlight concentrations of mortality. Findings are reported in counts and age-standardised rates. Methodological improvements for cause-of-death estimates in GBD 2021 include the expansion of under-5-years age group to include four new age groups, enhanced methods to account for stochastic variation of sparse data, and the inclusion of COVID-19 and other pandemic-related mortality-which includes excess mortality associated with the pandemic, excluding COVID-19, lower respiratory infections, measles, malaria, and pertussis. For this analysis, 199 new country-years of vital registration cause-of-death data, 5 country-years of surveillance data, 21 country-years of verbal autopsy data, and 94 country-years of other data types were added to those used in previous GBD rounds. FINDINGS The leading causes of age-standardised deaths globally were the same in 2019 as they were in 1990; in descending order, these were, ischaemic heart disease, stroke, chronic obstructive pulmonary disease, and lower respiratory infections. In 2021, however, COVID-19 replaced stroke as the second-leading age-standardised cause of death, with 94·0 deaths (95% UI 89·2-100·0) per 100 000 population. The COVID-19 pandemic shifted the rankings of the leading five causes, lowering stroke to the third-leading and chronic obstructive pulmonary disease to the fourth-leading position. In 2021, the highest age-standardised death rates from COVID-19 occurred in sub-Saharan Africa (271·0 deaths [250·1-290·7] per 100 000 population) and Latin America and the Caribbean (195·4 deaths [182·1-211·4] per 100 000 population). The lowest age-standardised death rates from COVID-19 were in the high-income super-region (48·1 deaths [47·4-48·8] per 100 000 population) and southeast Asia, east Asia, and Oceania (23·2 deaths [16·3-37·2] per 100 000 population). Globally, life expectancy steadily improved between 1990 and 2019 for 18 of the 22 investigated causes. Decomposition of global and regional life expectancy showed the positive effect that reductions in deaths from enteric infections, lower respiratory infections, stroke, and neonatal deaths, among others have contributed to improved survival over the study period. However, a net reduction of 1·6 years occurred in global life expectancy between 2019 and 2021, primarily due to increased death rates from COVID-19 and other pandemic-related mortality. Life expectancy was highly variable between super-regions over the study period, with southeast Asia, east Asia, and Oceania gaining 8·3 years (6·7-9·9) overall, while having the smallest reduction in life expectancy due to COVID-19 (0·4 years). The largest reduction in life expectancy due to COVID-19 occurred in Latin America and the Caribbean (3·6 years). Additionally, 53 of the 288 causes of death were highly concentrated in locations with less than 50% of the global population as of 2021, and these causes of death became progressively more concentrated since 1990, when only 44 causes showed this pattern. The concentration phenomenon is discussed heuristically with respect to enteric and lower respiratory infections, malaria, HIV/AIDS, neonatal disorders, tuberculosis, and measles. INTERPRETATION Long-standing gains in life expectancy and reductions in many of the leading causes of death have been disrupted by the COVID-19 pandemic, the adverse effects of which were spread unevenly among populations. Despite the pandemic, there has been continued progress in combatting several notable causes of death, leading to improved global life expectancy over the study period. Each of the seven GBD super-regions showed an overall improvement from 1990 and 2021, obscuring the negative effect in the years of the pandemic. Additionally, our findings regarding regional variation in causes of death driving increases in life expectancy hold clear policy utility. Analyses of shifting mortality trends reveal that several causes, once widespread globally, are now increasingly concentrated geographically. These changes in mortality concentration, alongside further investigation of changing risks, interventions, and relevant policy, present an important opportunity to deepen our understanding of mortality-reduction strategies. Examining patterns in mortality concentration might reveal areas where successful public health interventions have been implemented. Translating these successes to locations where certain causes of death remain entrenched can inform policies that work to improve life expectancy for people everywhere. FUNDING Bill & Melinda Gates Foundation

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