In search for theoretical physiology - A mathematical theory of living systems. Comment on "Toward a mathematical theory of living systems focusing on developmental biology and evolution: A review and perspectives" by N. Bellomo and B. Carbonaro

Physics of Life Reviews

Volumn 8, Issue 1, 2011, Pages 24-27

  Mamontov, Eugen ^a  

^a Insightasy AB   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMAL; BIOLOGICAL MODEL; DEVELOPMENTAL BIOLOGY; EVOLUTION; GENOME; HOMEOSTASIS; HUMAN; KINETICS; MATHEMATICS; METHODOLOGY; MOLECULAR EVOLUTION; NEOPLASM; NOTE; PATHOLOGY; STATISTICS; SYSTEMS BIOLOGY; THEORETICAL MODEL; THERMODYNAMICS;

ANIMALS; BIOLOGICAL EVOLUTION; DEVELOPMENTAL BIOLOGY; EVOLUTION, MOLECULAR; GENOME; HOMEOSTASIS; HUMANS; KINETICS; MATHEMATICS; MODELS, BIOLOGICAL; MODELS, THEORETICAL; NEOPLASMS; STOCHASTIC PROCESSES; SYSTEMS BIOLOGY; THERMODYNAMICS;

EID: 79952191740     PISSN: 15710645     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.plrev.2011.01.007     Document Type: Note

References (21)

1. Bassingthwaighte J.B. Strides in the technology of systems physiology and the art of testing complex hypotheses. Federation Proceedings 1987, 46(8):2473-2476.
2. Bellomo N., Carbonaro B. Toward a mathematical theory of living systems focusing on developmental biology and evolution: a review and perspectives. Physics of Life Reviews 2011, 8(1):1-18. [in this issue].
3. Mamontov E. Homeorhesis and evolutionary properties of living systems: From ordinary differential equations to the active-particle generalized kinetics theory. 10th evolutionary biology meeting at Marseilles 2006, 28-29. Association pour l'Etude de l'Evolution Biologique, Centre Régional de Documentation Pédagogique, Marseille, France, [abstract].
4. Mamontov E. Modelling homeorhesis by ordinary differential equations. Mathematical and Computer Modelling 2007, 45(5-6):694-707.
5. Trosko J.E., Chang C.C., Madhukar B.V. Modulation of intercellular communication during radiation and chemical carcinogenesis. Radiation Research 1990, 123:241-251.
6. Mamontov E., Koptioug A., Psiuk-Maksymowicz K. The minimal phase-transition model for the cell-number maintenance by the hyperplasia-extended homeorhesis. Acta Biotheoretica 2006, 54(2):61-101.
7. O'Neill R.V., DeAngelis D.L., Waide J.B., Allen T.F.H. A hierarchical concept of ecosystems 1986, Princeton University Press, Princeton, NJ, USA.
8. Hanahan D., Weinberg R.A. The hallmarks of cancer. Cell 2000, 100(1):57-70.
9. Trosko J.E., Chang C.C., Upham B.L., Tai M.H. Ignored hallmarks of carcinogenesis: stem cells and cell-cell communication. Annals of the New York Academy of Sciences 2004, 1028(Dec):192-201.
10. Iversen O.H. Cybernetic aspects of the cancer problem. Progress in biocybernetics 1965, vol. 2:76-110. Elsevier, Amsterdam.
11. Nowak M.A, Sigmund K. Evolutionary dynamics of biological games. Science 2004, 303(5659):793-799.
12. Kolomiets V.G., Mel'nikov A.I. Integral manifolds of systems of differential equations with a random right-hand side in a Banach space. Ukrainian Mathematical Journal 1992, 44(1):12-16.
13. Baris J.S., Fodčuk V.I. The integral manifold for an irregularly perturbed differential system in a Banach space. Mathematical Physics 1970, (8):23-30. [in Russian (Mathematical Reviews 45 #3901)].
14. Mamontov Y.V., Willander M. Asymptotic method of finite equation for bounded solutions of nonlinear smooth ODEs. Mathematica Japonica 1997, 46(3):451-461.
15. Frank S.A. Dynamics of cancer: incidence, inheritance, and evolution 2007, Princeton University Press, Princeton, NJ, USA.
16. Komarova N.L. Stochastic modeling of loss- and gain-of-function mutations in cancer. Mathematical Models and Methods in Applied Sciences 2007, 17(suppl):1647-1674.
17. Komarova N.L. Spatial stochastic models for cancer initiation and progression. Bulletin of Mathematical Biology 2006, 68(7):1573-1599.
18. Quintana E., Shackleton M., Sabel M.S., Fullen D.R., Johnson T.M., Morrison S.J. Efficient tumour formation by single human melanoma cells. Nature 2008, 456(7222):593-598.
19. Rashevsky N. An approach to the mathematical biophysics of biological self-regulation and of cell polarity. Acta Biotheoretica 1938, 4:133-153.
20. Balescu R. Statistical dynamics: matter out of equilibrium 1997, Imperial College Press, London.
21. Mamontov E. The "mean-field" ordinary differential equation for a population of individuals and the resulting kinetic-equation-type dynamical model for living systems. In: Ordinary differential equations: theory, analysis and applications, Hauppauge, NY, USA: Nova Science Publishers; 2011 [in press].