A mass action model of a fibroblast growth factor signaling pathway and its simplification

We consider a kinetic law of mass action model for Fibroblast Growth Factor (FGF) signaling, focusing on the induction of the RAS-MAP kinase pathway via GRB2 binding. Our biologically simple model suffers a combinatorial explosion in the number of differential equations required to simulate the system. In addition to numerically solving the full model, we show that it can be accurately simplified. This requires combining matched asymptotics, the quasi-steady state hypothesis, and the fact subsets of the equations decouple asymptotically. Both the full and simplified models reproduce the qualitative dynamics observed experimentally and in previous stochastic models. The simplified model also elucidates both the qualitative features of GRB2 binding and the complex relationship between SHP2 levels, the rate SHP2 induces dephosphorylation and levels of bound GRB2. In addition to providing insight into the important and redundant features of FGF signaling, such work further highlights the usefulness of numerous simplification techniques in the study of mass action models of signal transduction, as also illustrated recently by Borisov and co-workers (Borisov et al. in Biophys. J. 89, 951–66, 2005, Biosystems 83, 152–66, 2006; Kiyatkin et al. in J. Biol. Chem. 281, 19925–9938, 2006). These developments will facilitate the construction of tractable models of FGF signaling, incorporating further biological realism, such as spatial effects or realistic binding stoichiometries, despite a more severe combinatorial explosion associated with the latter

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

High-resolution temporal profiling of transcripts during Arabidopsis leaf senescence reveals a distinct chronology of processes and regulation

Leaf senescence is an essential developmental process that impacts dramatically on crop yields and involves altered regulation of thousands of genes and many metabolic and signaling pathways, resulting in major changes in the leaf. The regulation of senescence is complex, and although senescence regulatory genes have been characterized, there is little information on how these function in the global control of the process. We used microarray analysis to obtain a highresolution time-course profile of gene expression during development of a single leaf over a 3-week period to senescence. A complex experimental design approach and a combination of methods were used to extract high-quality replicated data and to identify differentially expressed genes. The multiple time points enable the use of highly informative clustering to reveal distinct time points at which signaling and metabolic pathways change. Analysis of motif enrichment, as well as comparison of transcription factor (TF) families showing altered expression over the time course, identify clear groups of TFs active at different stages of leaf development and senescence. These data enable connection of metabolic processes, signaling pathways, and specific TF activity, which will underpin the development of network models to elucidate the process of senescence

Dickkopf-3 is upregulated in osteoarthritis and has a chondroprotective role

Objective Dickkopf-3 (Dkk3) is a non-canonical member of the Dkk family of Wnt antagonists and its upregulation has been reported in microarray analysis of cartilage from mouse models of osteoarthritis (OA). In this study we assessed Dkk3 expression in human OA cartilage to ascertain its potential role in chondrocyte signaling and cartilage maintenance. Methods Dkk3 expression was analysed in human adult OA cartilage and synovial tissues and during chondrogenesis of ATDC5 and human mesenchymal stem cells. The role of Dkk3 in cartilage maintenance was analysed by incubation of bovine and human cartilage explants with interleukin-1 (IL1) and oncostatin-M (OSM). Dkk3 expression was measured in cartilage following murine hip avulsion. Whether Dkk3 influenced Wnt, TGF and activin cell signaling was assessed in primary human chondrocytes and SW1353 chondrosarcoma cells using RT-qPCR and luminescence assays. Results Increased gene and protein levels of Dkk3 were detected in human OA cartilage, synovial tissue and synovial fluid. DKK3 expression was decreased during chondrogenesis of both ATDC5 cells and humans MSCs. Dkk3 inhibited IL1 and OSM-mediated proteoglycan loss from human and bovine cartilage explants and collagen loss from bovine cartilage explans. Cartilage DKK3 expression was decreased following hip avulsion injury. TGF signaling was enhanced by Dkk3 and Wnt3a and activin signaling were inhibited. Conclusions We provide evidence that Dkk3 is upregulated in OA and may have a protective effect on cartilage integrity by preventing proteoglycan loss and helping to restore OA-relevant signaling pathway activity. Targeting Dkk3 may be a novel approach in the treatment of OA

Pharmacologic inhibition of RGD-binding integrins ameliorates fibrosis and improves function following kidney injury

Fibrosis is a final common pathway for many causes of progressive chronic kidney disease (CKD). Arginine-glycine-aspartic acid (RGD)-binding integrins are important mediators of the pro-fibrotic response by activating latent TGF-β at sites of injury and by providing myofibroblasts information about the composition and stiffness of the extracellular matrix. Therefore, blockade of RGD-binding integrins may have therapeutic potential for CKD. To test this idea, we used small-molecule peptidomimetics that potently inhibit a subset of RGD-binding integrins in a murine model of kidney fibrosis. Acute kidney injury leading to fibrosis was induced by administration of aristolochic acid. Continuous subcutaneous administration of CWHM-12, an RGD integrin antagonist, for 28 days improved kidney function as measured by serum creatinine. CWHM-12 significantly reduced Collagen 1 (Col1a1) mRNA expression and scar collagen deposition in the kidney. Protein and gene expression markers of activated myofibroblasts, a major source of extracellular matrix deposition in kidney fibrosis, were diminished by treatment. RNA sequencing revealed that inhibition of RGD integrins influenced multiple pathways that determine the outcome of the response to injury and of repair processes. A second RGD integrin antagonist, CWHM-680, administered once daily by oral gavage was also effective in ameliorating fibrosis. We conclude that targeting RGD integrins with such small-molecule antagonists is a promising therapeutic approach in fibrotic kidney disease

Dual positive and negative regulation of GPCR signaling by GTP hydrolysis

G protein-coupled receptors (GPCRs) regulate a variety of intracellular pathways through their ability to promote the binding of GTP to heterotrimeric G proteins. Regulator of G protein signaling (RGS) proteins increase the intrinsic GTPase activity of G-subunits and are widely regarded as negative regulators of G protein signaling. Using yeast we demonstrate that GTP hydrolysis is not only required for desensitization, but is essential for achieving a high maximal (saturated level) response. Thus RGS-mediated GTP hydrolysis acts as both a negative (low stimulation) and positive (high stimulation) regulator of signaling. To account for this we generated a new kinetic model of the G protein cycle where GGTP enters an inactive GTP-bound state following effector activation. Furthermore, in vivo and in silico experimentation demonstrates that maximum signaling output first increases and then decreases with RGS concentration. This unimodal, non-monotone dependence on RGS concentration is novel. Analysis of the kinetic model has revealed a dynamic network motif that shows precisely how inclusion of the inactive GTP-bound state for the G produces this unimodal relationship