Decoding the quantitative nature of TGF-beta/Smad signaling.

How transforming growth factor-beta (TGF-beta) signaling elicits diverse cell responses remains elusive, despite the major molecular components of the pathway being known. We contend that understanding TGF-beta biology requires mathematical models to decipher the quantitative nature of TGF-beta/Smad signaling and to account for its complexity. Here, we review mathematical models of TGF-beta superfamily signaling that predict how robustness is achieved in bone-morphogenetic-protein signaling in the Drosophila embryo, how changes in receptor-trafficking dynamics can be exploited by cancer cells and how the basic mechanisms of TGF-beta/Smad signaling conspire to promote Smad accumulation in the nucleus. These studies demonstrate the power of mathematical modeling for understanding TGF-beta biology.

[1]  Jeffrey L. Wrana,et al.  Mechanism of activation of the TGF-β receptor , 1994, Nature.

[2]  Jeffrey L. Wrana,et al.  TGFβ signals through a heteromeric protein kinase receptor complex , 1992, Cell.

[3]  C. Hill.  TGF-β signalling pathways in early Xenopus development , 2001 .

[4]  E. Klipp,et al.  Mathematical modeling of intracellular signaling pathways , 2006, BMC Neuroscience.

[5]  N. Barkai,et al.  Variability and robustness in biomolecular systems. , 2007, Molecular cell.

[6]  J. Massagué,et al.  Type I receptors specify growth-inhibitory and transcriptional responses to transforming growth factor beta and activin , 1994, Molecular and cellular biology.

[7]  Steven Dyson,et al.  The Interpretation of Position in a Morphogen Gradient as Revealed by Occupancy of Activin Receptors , 1998, Cell.

[8]  Wei He,et al.  Hematopoiesis Controlled by Distinct TIF1γ and Smad4 Branches of the TGFβ Pathway , 2006, Cell.

[9]  Jan Ellenberg,et al.  Dissecting the contribution of diffusion and interactions to the mobility of nuclear proteins. , 2006, Biophysical journal.

[10]  Sang Gyun Kim,et al.  The endogenous ratio of Smad2 and Smad3 influences the cytostatic function of Smad3. , 2005, Molecular biology of the cell.

[11]  Xueyan Duan,et al.  PPM1A Functions as a Smad Phosphatase to Terminate TGFβ Signaling , 2006, Cell.

[12]  O. Piepenburg,et al.  Nuclear accumulation of Smad complexes occurs only after the midblastula transition in Xenopus , 2007, Development.

[13]  M. Ringnér,et al.  Gene expression profiling demonstrates that TGF-β1 signals exclusively through receptor complexes involving Alk5 and identifies targets of TGF-β signaling , 2005 .

[14]  Carsten Peterson,et al.  A rate equation approach to elucidate the kinetics and robustness of the TGF-beta pathway. , 2006, Biophysical journal.

[15]  J. Wrana,et al.  Smad7 binds to Smurf2 to form an E3 ubiquitin ligase that targets the TGF beta receptor for degradation. , 2000, Molecular cell.

[16]  A. Kicheva,et al.  Postsynaptic Mad Signaling at the Drosophila Neuromuscular Junction , 2006, Current Biology.

[17]  I. Taylor,et al.  SnapShot: The TGFβ Pathway Interactome , 2008, Cell.

[18]  Yu-Chiun Wang,et al.  Spatial bistability of Dpp–receptor interactions during Drosophila dorsal–ventral patterning , 2005, Nature.

[19]  Paul A. Bates,et al.  Mathematical modeling identifies Smad nucleocytoplasmic shuttling as a dynamic signal-interpreting system , 2008, Proceedings of the National Academy of Sciences.

[20]  A. Mogilner,et al.  Quantitative modeling in cell biology: what is it good for? , 2006, Developmental cell.

[21]  M. Sporn,et al.  Type beta transforming growth factor: a bifunctional regulator of cellular growth. , 1985, Proceedings of the National Academy of Sciences of the United States of America.

[22]  C. Heldin,et al.  Non-Smad TGF-β signals , 2005, Journal of Cell Science.

[23]  L M Wakefield,et al.  Transforming growth factor type beta induces monocyte chemotaxis and growth factor production. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[24]  A. Arkin,et al.  Simulating cell biology , 2006, Current Biology.

[25]  A. Hinck,et al.  Cooperative assembly of TGF-beta superfamily signaling complexes is mediated by two disparate mechanisms and distinct modes of receptor binding. , 2008, Molecular cell.

[26]  张强,et al.  TGFβ , 2000 .

[27]  C. Wernstedt,et al.  Phosphorylation of Ser465 and Ser467 in the C Terminus of Smad2 Mediates Interaction with Smad4 and Is Required for Transforming Growth Factor-β Signaling* , 1997, The Journal of Biological Chemistry.

[28]  N. Rosenblum,et al.  BMP7 controls collecting tubule cell proliferation and apoptosis via Smad1-dependent and -independent pathways. , 2001, American journal of physiology. Renal physiology.

[29]  S. Schnell,et al.  A multiscale mathematical model of cancer, and its use in analyzing irradiation therapies , 2006, Theoretical Biology and Medical Modelling.

[30]  D. C. Clarke,et al.  Systems theory of Smad signalling. , 2006, Systems biology.

[31]  J. Smith,et al.  Responses of embryonic xenopus cells to activin and FGF are separated by multiple dose thresholds and correspond to distinct axes of the mesoderm , 1992, Cell.

[32]  C. Heldin,et al.  Smad signal transduction : Smads in proliferation, differentiation and disease , 2006 .

[33]  H. Moses,et al.  Stimulation of the chemotactic migration of human fibroblasts by transforming growth factor beta , 1987, Journal of Experimental Medicine.

[34]  Osamu Shimmi,et al.  Facilitated Transport of a Dpp/Scw Heterodimer by Sog/Tsg Leads to Robust Patterning of the Drosophila Blastoderm Embryo , 2005, Cell.

[35]  Y. Ip,et al.  Msk is required for nuclear import of TGF-β/BMP-activated Smads , 2007, The Journal of cell biology.

[36]  Edda Klipp,et al.  Constraint-Based Modeling and Kinetic Analysis of the Smad Dependent TGF-β Signaling Pathway , 2007, PloS one.

[37]  L. Mathews,et al.  Identification and characterization of constitutively active Smad2 mutants: evaluation of formation of Smad complex and subcellular distribution. , 2000, Molecular endocrinology.

[38]  Nicos Nicola,et al.  Cytokine reference : a compendium of cytokines and other mediators of host defence , 2001 .

[39]  M. Sporn,et al.  Transforming growth factor type beta: rapid induction of fibrosis and angiogenesis in vivo and stimulation of collagen formation in vitro. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[40]  James Briscoe,et al.  The interpretation of morphogen gradients , 2006, Development.

[41]  R. Weinberg,et al.  Transforming growth factor beta-induced phosphorylation of Smad3 is required for growth inhibition and transcriptional induction in epithelial cells. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[42]  C. Hill,et al.  Nucleocytoplasmic shuttling of Smads 2, 3, and 4 permits sensing of TGF-beta receptor activity. , 2002, Molecular cell.

[43]  Gregory T. Reeves,et al.  Quantitative models of developmental pattern formation. , 2006, Developmental cell.

[44]  C. Hill,et al.  Attenuation of the TGF-beta-Smad signaling pathway in pancreatic tumor cells confers resistance to TGF-beta-induced growth arrest. , 2003, Oncogene.

[45]  John J Tyson,et al.  Mathematical modeling as a tool for investigating cell cycle control networks. , 2007, Methods.

[46]  M. Goumans,et al.  Functional analysis of the TGFbeta receptor/Smad pathway through gene ablation in mice. , 2000, The International journal of developmental biology.

[47]  Jeffrey L. Wrana,et al.  Distinct endocytic pathways regulate TGF-β receptor signalling and turnover , 2003, Nature Cell Biology.

[48]  Mark P. de Caestecker,et al.  Structural Basis of Heteromeric Smad Protein Assembly in TGF-β Signaling , 2004 .

[49]  David M. Umulis,et al.  Shaping BMP morphogen gradients in the Drosophila embryo and pupal wing , 2005, Development.

[50]  C. Cunningham,et al.  Cross‐talk between the bone morphogenetic protein pathway and other major signaling pathways results in tightly regulated cell‐specific outcomes , 2007, The FEBS journal.

[51]  Bernhard Schmierer,et al.  Kinetic Analysis of Smad Nucleocytoplasmic Shuttling Reveals a Mechanism for Transforming Growth Factor β-Dependent Nuclear Accumulation of Smads , 2005, Molecular and Cellular Biology.

[52]  Markus Affolter,et al.  The Decapentaplegic morphogen gradient: from pattern formation to growth regulation , 2007, Nature Reviews Genetics.

[53]  Qing Nie,et al.  Formation of the BMP activity gradient in the Drosophila embryo. , 2005, Developmental cell.

[54]  M. Sporn,et al.  Peptide growth factors are multifunctional , 1988, Nature.

[55]  J. Massagué,et al.  The transforming growth factor-beta family. , 1990, Annual review of cell biology.

[56]  Bernhard Schmierer,et al.  Analysis of Smad nucleocytoplasmic shuttling in living cells , 2004, Journal of Cell Science.

[57]  J. Massagué,et al.  Partnership between DPC4 and SMAD proteins in TGF-β signalling pathways , 1996, Nature.

[58]  L. Baudhuin,et al.  Sphingosylphosphorylcholine is a ligand for ovarian cancer G-protein-coupled receptor 1 , 2000, Nature Cell Biology.

[59]  R. Pagano,et al.  Ligand-dependent and -independent transforming growth factor-beta receptor recycling regulated by clathrin-mediated endocytosis and Rab11. , 2004, Molecular biology of the cell.

[60]  R. Kucherlapati,et al.  Hierarchical model of gene regulation by transforming growth factor β , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[61]  Chris Sander,et al.  Signal Processing in the TGF-β Superfamily Ligand-Receptor Network , 2005, PLoS Comput. Biol..

[62]  J A Sherratt,et al.  Modeling the effects of transforming growth factor‐β on extracellular matrix alignment in dermal wound repair , 2001, Wound repair and regeneration : official publication of the Wound Healing Society [and] the European Tissue Repair Society.

[63]  R. Derynck,et al.  Specificity and versatility in tgf-beta signaling through Smads. , 2005, Annual review of cell and developmental biology.

[64]  Marta Ibañes,et al.  Theoretical and experimental approaches to understand morphogen gradients , 2008, Molecular systems biology.

[65]  L. Orci,et al.  Biphasic Effect of Transforming Growth Factor-β1 on in Vitro Angiogenesis , 1993 .

[66]  J. Gurdon,et al.  A changing morphogen gradient is interpreted by continuous transduction flow. , 2002, Development.

[67]  Fumiko Itoh,et al.  Smad7 and protein phosphatase 1α are critical determinants in the duration of TGF-β/ALK1 signaling in endothelial cells , 2006, BMC Cell Biology.

[68]  J. Massagué,et al.  Transforming growth factor-beta stimulates the expression of fibronectin and collagen and their incorporation into the extracellular matrix. , 1986, The Journal of biological chemistry.

[69]  M. O’Connor-McCourt,et al.  Transforming growth factor-beta (TGF-beta) binding to the extracellular domain of the type II TGF-beta receptor: receptor capture on a biosensor surface using a new coiled-coil capture system demonstrates that avidity contributes significantly to high affinity binding. , 2003, Journal of molecular biology.

[70]  C. Deng,et al.  Genetic Disruptions within the Murine Genome Reveal Numerous Roles of the Smad Gene Family in Development, Disease, and Cancer , 2006 .

[71]  C. Hill,et al.  Smad4 Dependency Defines Two Classes of Transforming Growth Factor β (TGF-β) Target Genes and Distinguishes TGF-β-Induced Epithelial-Mesenchymal Transition from Its Antiproliferative and Migratory Responses , 2005, Molecular and Cellular Biology.

[72]  M. Laiho,et al.  Enhanced production and extracellular deposition of the endothelial- type plasminogen activator inhibitor in cultured human lung fibroblasts by transforming growth factor-beta , 1986, The Journal of cell biology.

[73]  N. Barkai,et al.  Robustness of the BMP morphogen gradient in Drosophila embryonic patterning , 2022 .

[74]  David M. Umulis,et al.  Robust, bistable patterning of the dorsal surface of the Drosophila embryo. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[75]  Jonathan G. Rud,et al.  Nuclear Targeting of Transforming Growth Factor-β-activated Smad Complexes* , 2005, Journal of Biological Chemistry.

[76]  C. Hill,et al.  Transforming Growth Factor β-Independent Shuttling of Smad4 between the Cytoplasm and Nucleus , 2000, Molecular and Cellular Biology.

[77]  P. Dijke,et al.  Negative regulation of TGF-β receptor/Smad signal transduction , 2007 .

[78]  J. Gurdon,et al.  Morphogen gradient interpretation , 2001, Nature.

[79]  C. Heldin,et al.  The Mechanism of Nuclear Export of Smad3 Involves Exportin 4 and Ran , 2006, Molecular and Cellular Biology.

[80]  M. Mehler,et al.  Multiple Roles of Bone Morphogenetic Protein Signaling in the Regulation of Cortical Cell Number and Phenotype , 1999, The Journal of Neuroscience.

[81]  R. A. Rahimi,et al.  TGF-beta signaling: a tale of two responses. , 2007, Journal of cellular biochemistry.

[82]  J. Massagué,et al.  The nuclear import function of Smad2 is masked by SARA and unmasked by TGFb-dependent phosphorylation , 2000, Nature Cell Biology.

[83]  Jeremy B. A. Green,et al.  Morphogen gradients, positional information, and Xenopus: Interplay of theory and experiment , 2002, Developmental dynamics : an official publication of the American Association of Anatomists.