/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Tight control of cell-cell communication is essential for the generation of a normally patterned embryo. A critical mediator of key cell-cell signaling events during embryogenesis is the highly conserved Wnt family of secreted proteins. Recent biochemical and genetic analyses have greatly enriched our understanding of how Wnts signal, and the list of canonical Wnt signaling components has exploded. The data reveal that multiple extracellular, cytoplasmic, and nuclear regulators intricately modulate Wnt signaling levels. In addition, receptor-ligand specificity and feedback loops help to determine Wnt signaling outputs. Wnts are required for adult tissue maintenance, and perturbations in Wnt signaling promote both human degenerative diseases and cancer. The next few years are likely to see novel therapeutic reagents aimed at controlling Wnt signaling in order to alleviate these conditions.

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The Wnt signaling pathway in development and disease.

https://www.cell.com/cell/pdf/S0092-8674(06)01344-4.pdf

Wnt/beta-catenin signaling in development and disease.

Wnt/β-catenin signaling: components, mechanisms, and diseases

If carcinogenesis occurs by somatic evolution, then common components of the cancer phenotype result from active selection and must, therefore, confer a significant growth advantage. A near-universal property of primary and metastatic cancers is upregulation of glycolysis, resulting in increased glucose consumption, which can be observed with clinical tumour imaging. We propose that persistent metabolism of glucose to lactate even in aerobic conditions is an adaptation to intermittent hypoxia in pre-malignant lesions. However, upregulation of glycolysis leads to microenvironmental acidosis requiring evolution to phenotypes resistant to acid-induced cell toxicity. Subsequent cell populations with upregulated glycolysis and acid resistance have a powerful growth advantage, which promotes unconstrained proliferation and invasion.

Why do cancers have high aerobic glycolysis

A theoretical analysis of linear enzymatic chains is presented By linear approximation simple analytical solutions can be obtained for the metabolite concentrations and the flux through the chain for steady-state conditions The equations are greatly simplified if the common kinetic constants are expressed as functions of two parameters, ie the thermodynamic equilibrium constant and the “characteristic time” Three cardinal terms are proposed for the quantitative description of enzyme systems The first two are the control strength and the control matrix; these indicate the dependence of the flux and the metabolite concentrations, respectively, on the kinetic properties of a given enzyme The third is the effector strength, which defines the dependence of the velocity of an enzyme on the concentration of an effector; it expresses the importance of an effector By linear approximation simple analytical expressions were derived for the control strength, the control matrix and the mass-action ratios The effector strength was calculated for two cases: for a competitive inhibitor and for allosteric effectors according to the Monod (1965) model The influence of an effector on the concentrations of the metabolites was considered

/pdf/a-linear-steady-state-treatment-of-enzymatic-chains-fsstil97lz.pdf

A Linear Steady‐State Treatment of Enzymatic Chains

Introduction Fundamentals of biochemical modeling Balance equations Rate laws Generalized mass-action kinetics Various enzyme kinetic rate laws Thermodynamic flow-force relationships Power-law approximation Steady states of biochemical networks General considerations Stable and unstable steady states Multiple steady states Metabolic oscillations Background Mathematical conditions for oscillations Glycolytic oscillations Models of intracellular calcium oscillations A simple three-variable model with only monomolecular and bimolecular reactions Possible physiological significance of oscillations Stoichiometric analysis Conservation relations Linear dependencies between the rows of the stoichiometry matrix Non-negative flux vectors Elementary flux modes Thermodynamic aspects A generalized Wegscheider condition Strictly detailed balanced subnetworks Onsager's reciprocity reactions for coupled enyme reactions Time hierarchy in metabolism Time constants The quasi-steady-state approximation The Rapid equilibrium approximation Modal analysis Metabolic control analysis Basic definitions A systematic approach Theorems of metabolic control analysis Summation theorems Connectivity theorems Calculation of control coefficients using the theorems Geometrical interpretation Control analysis of various systems General remarks Elasticity coefficients for specific rate laws Control coefficients for simple hypothetical pathways Unbranched chains A branched system Control of erythrocyte energy metabolism The reaction system Basic model Interplay of ATP production and ATP consumption Glycolytic energy metabolism and osmotic states A simple model of oxidative phosphorylation A three-step model of serine biosynthesis Time-dependent control coefficients Are control coefficients always parameter independent? Posing the problem A system without conserved moieties A system with a conserved moiety A system including dynamic channeling Normalized versus non-normalized coefficients Analysis in terms of variables other than steady-state concentrations and fluxes General analysis Concentration ratios and free-energy-differences as state variables Entropy production as response variable Control of transient times Control of oscillations A second-order approach A quantitative approach to metabolic regulations Co-response coefficients Fluctuations of internal variables versus parameter perturbations Internal response coefficients Rephrasing the basic equations of metabolic control analysis in terms of co-response coefficients and internal response coefficients Control within and between subsystems Modular approach Overall elasticities Overall control coefficients Flux control insusceptibility Control exerted by elementary steps in enzyme catalysis Control analysis of metabolic channeling Comparison of metabolic control analysis and power-law formalism Computational aspects Application of optimization methods and the interrelation with evolution Optimization of the catalytic properties of single enzymes Basic assumptions Optimal values of elementary rate constants Optimal Michaelis constants Optimization of multienzyme systems Maximization of steady-state flux Influence of osmotic constraints and minimization of intermediate concentrations Minimization of transient times Optimal stoichiometries.

The Regulation of Cellular Systems

Wnt signaling plays an important role in both oncogenesis and development. Activation of the Wnt pathway results in stabilization of the transcriptional coactivator β-catenin. Recent studies have demonstrated that axin, which coordinates β-catenin degradation, is itself degraded. Although the key molecules required for transducing a Wnt signal have been identified, a quantitative understanding of this pathway has been lacking. We have developed a mathematical model for the canonical Wnt pathway that describes the interactions among the core components: Wnt, Frizzled, Dishevelled, GSK3β, APC, axin, β-catenin, and TCF. Using a system of differential equations, the model incorporates the kinetics of protein–protein interactions, protein synthesis/degradation, and phosphorylation/dephosphorylation. We initially defined a reference state of kinetic, thermodynamic, and flux data from experiments using Xenopus extracts. Predictions based on the analysis of the reference state were used iteratively to develop a more refined model from which we analyzed the effects of prolonged and transient Wnt stimulation on β-catenin and axin turnover. We predict several unusual features of the Wnt pathway, some of which we tested experimentally. An insight from our model, which we confirmed experimentally, is that the two scaffold proteins axin and APC promote the formation of degradation complexes in very different ways. We can also explain the importance of axin degradation in amplifying and sharpening the Wnt signal, and we show that the dependence of axin degradation on APC is an essential part of an unappreciated regulatory loop that prevents the accumulation of β-catenin at decreased APC concentrations. By applying control analysis to our mathematical model, we demonstrate the modular design, sensitivity, and robustness of the Wnt pathway and derive an explicit expression for tumor suppression and oncogenicity.

/pdf/the-roles-of-apc-and-axin-derived-from-experimental-and-58iybttpvv.pdf

The roles of APC and Axin derived from experimental and theoretical analysis of the Wnt pathway.

Mathematical models of protein kinase signal transduction.

Publisher Summary
This chapter discusses the study of the regulation of metabolism by mathematical models. There has grown a sizable literature on the theoretical analysis of biological regulation, mostly by means of mathematical models. Modeling is an advanced technique for the study of the regulation. It involves the quantitative consideration of the multitude of data and interactions characteristic for biological systems. Modeling is useful for the deduction of the essential relations in metabolism that constitute a characteristic dynamic structure. The most important precondition for modeling is the knowledge of the main metabolic routes. It requires the identification of the stoichiometric relations in the various enzymatic reactions, branching and merging points, bypasses, and most of the intermediates. The chapter discusses different types of models and the methods of modeling.

Reinhart Heinrich

Papers

A Linear Steady‐State Treatment of Enzymatic Chains

The Regulation of Cellular Systems

The roles of APC and Axin derived from experimental and theoretical analysis of the Wnt pathway.

Mathematical models of protein kinase signal transduction.

Metabolic regulation and mathematical models