General analysis of mathematical models for bone remodeling

Bone

Volumn 48, Issue 4, 2011, Pages 910-917

  Zumsande, Martin ^a   Stiefs, Dirk ^a   Siegmund, Stefan ^b,c   Gross, Thilo ^a,c  

^a MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

^b DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

^c Center for Dynamics   (Germany)

Author keywords

Bone remodeling; Modelling; Osteoblast; Osteoclast

Indexed keywords

OSTEOCLAST DIFFERENTIATION FACTOR; OSTEOPROTEGERIN; TRANSFORMING GROWTH FACTOR BETA;

ARTICLE; BONE REMODELING; CELL SURVIVAL; MATHEMATICAL MODEL; OSTEOBLAST; OSTEOCLAST; PAGET BONE DISEASE; STEM CELL;

ANIMALS; BONE REMODELING; HUMANS; MODELS, THEORETICAL; OSTEOBLASTS; OSTEOCLASTS;

EID: 79952697360     PISSN: 87563282     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.bone.2010.12.010     Document Type: Article

References (32)

1. Manolagas S.C. Birth and death of bone cells: basic regulatory mechanisms and implications for the pathogenesis and treatment of osteoporosis. Endocr Rev 2000, 21(2):115.
2. Robling A.G., Castillo A.B., Turner C.H. Biomechanical and molecular regulation of bone remodeling. Annu Rev Biomed Eng 2006, 8:455-498.
3. Anandarajah A.P. Role of RANKL in bone diseases. Trends Endocrinol Metab 2009, 20(2):88-94.
4. Boyce B.F., Xing L. Functions of RANKL/RANK/OPG in bone modeling and remodeling. Arch Biochem Biophys 2008, 473:139-146.
5. Janssens K., ten Dijke P., Janssens S., Van Hul W. Transforming growth factor-β1 to the bone. Endocr Rev 2005, 26(6):743-774.
6. Reddy S.V., Kurihara N., Menaa C., Roodman G.D. Paget's disease of bone: a disease of the osteoclast. Rev Endocr Metab Disord 2001, 2:195-201.
7. Whyte M.P. Paget's disease of bone and genetic disorders of RANKL/OPG/RANK/NF-κB signaling. Ann N Y Acad Sci 2006, 1068:143-164.
8. Kearns A.E., Khosla S., Kostenuik P.J. Receptor activator of nuclear factor κB ligand and osteoprotegerin regulation of bone remodeling in health and disease. Endocr Rev 2008, 29(2):155-192.
9. McNamara L.M. Perspective on post-menopausal osteoporosis: establishing an interdisciplinary understanding of the sequence of events from the molecular level to whole bone fractures. J R Soc Interface 2010, 7(44):353-372.
10. Frost H.M. Tetracycline-based histological analysis of bone remodeling. Calcif Tissue Int 1969, 3(1):211-237.
11. Komarova S.V., Smith R.J., Dixon S.J., Sims S.M., Wahl L.M. Mathematical model predicts a critical role for osteoclast autocrine regulation in the control of bone remodeling. Bone 2003, 33(2):206-215.
12. Lemaire V., Tobin F.L., Greller L.D., Cho C.R., Suva L.J. Modeling the interactions between osteoblast and osteoclast activities in bone remodeling. J Theor Biol 2004, 229(3):293-309.
13. Pivonka P., Zimak J., Smith D.W., Gardiner B.S., Dunstan C.R., Sims N.A., Martin T.J., Mundy G.R. Model structure and control of bone remodeling: a theoretical study. Bone 2008, 43(2):249-263.
14. Pivonka P., Zimak J., Smith D.W., Gardiner B.S., Dunstan C.R., Sims N.A., Martin T.J., Mundy G.R. Theoretical investigation of the role of the RANK-RANKL-OPG system in bone remodeling. J Theor Biol 2010, 262(2):306-316.
15. Guckenheimer J., Holmes P. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields 1997, Springer, New York. 3rd Edition.
16. Kuznetsov Y.A. Elements of Applied Bifurcation Theory 1995, Springer Verlag, New York. 3rd Edition.
17. Gross T., Feudel U. Generalized models as an universal approach to the analysis of nonlinear dynamical systems. Phys Rev E 2006, 73:16205-16214.
18. Steuer R., Gross T., Selbig J., Blasius B. Structural kinetic modeling of metabolic networks. Proc Natl Acad Sci 2006, 103:11868-11874.
19. Gross T., Rudolf L., Levin S.A., Dieckmann U. Generalized models reveal stabilizing factors in food webs. Science 2009, 325:747-750.
20. Zumsande M., Gross T. Bifurcations and chaos in the MAPK signaling cascade. J Theor Biol 2010, 265:481-491.
21. Fell D.A. Metabolic control analysis: a survey of its theoretical and experimental development. Biochem J 1992, 286:313-330.
22. Gross T., Feudel U. Analytical search for bifurcation surfaces in parameter space. Phys D 2004, 195:292-302.
23. Hughes D.E., Dai A., Tiffee J.C., Li H.H., Mundy G.R., Boyce B.F. Estrogen promotes apoptosis of murine osteoclasts mediated by TGF-β. Nat Med 1996, 2(10):1132-1136.
24. Murakami T., Yamamoto M., Yamamoto M., Ono K., Nishikawa M., Nagata N., Motoyoshi K., Akatsu T. Transforming growth factor-β1 increases mRNA levels of osteoclastogenesis inhibitory factor in osteoblastic/stromal cells and inhibits the survival of murine osteoclast-like cells. Biochem Biophys Res Commun 1998, 252:747-752.
25. Houde N., Chamoux E., Bisson M., Roux S. Transforming growth factor-β1 (TGF-β1) induces human osteoclast apoptosis by up-regulating Bim. J Biol Chem 2009, 284(35):23397-23404.
26. Fuller K., Lean J.M., Bayley KE.., Wani M.R., Chambers T.J. A role for TGFβ1 in osteoclast differentiation and survival. J Cell Sci 2000, 113(13):2445.
27. Ruan M., Pederson L., Bradley E.W., Bamberger A.M., Oursler M.J. Transforming growth factor-β coordinately induces suppressor of cytokine signaling 3 and leukemia inhibitory factor to suppress osteoclast apoptosis. Endocrinology 2010, 151(4):1713-1722.
28. Gori F., Hofbauer L.C., Dunstan C.R., Spelsberg T.C., Khosla S., Riggs B.L. The expression of osteoprotegerin and RANK ligand and the support of osteoclast formation by stromal-osteoblast lineage cells is developmentally regulated. Endocrinology 2000, 141(12):4768-4776.
29. Thomas G.P., Baker S.U.K., Eisman J.A., Gardiner E.M. Changing RANKL/OPG mRNA expression in differentiating murine primary osteoblasts. J Endocrinol 2001, 170(2):451.
30. Gross T., Ebenhöh W., Feudel U. Long food chains are in general chaotic. Oikos 2005, 109(1):135-144.
31. Akchurin T., Aissiou T., Prosk E., Nigam N., Komarova S.V. Complex dynamics of osteoclast formation and death in long-term cultures. PLoS ONE 2008, 3:e2104.
32. Ralston S.H., Hoey S.A., Gallacher S.J., Adamson B.B., Boyle I.T. Cytokine and growth factor expression in Paget's disease: analysis by reverse-transcription/polymerase chain reaction. Br J Rheumatol 1994, 33(7):620.