MATHEMATICAL MODEL OF UV-INDUCED RESPONSE OF EPIDERMIS Mikhail M. Stolnitz Saratov State University,...
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Transcript of MATHEMATICAL MODEL OF UV-INDUCED RESPONSE OF EPIDERMIS Mikhail M. Stolnitz Saratov State University,...
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MATHEMATICAL MODELMATHEMATICAL MODELOF UV-OF UV-INDUCED RESPONSE INDUCED RESPONSE
OF OF EPIDERMIS EPIDERMIS
Mikhail M. Stolnitz
Saratov State University, Saratov, Russia
SaratovState
University
International Institute of
Optics & Biophotonics
Optics & Biomedical
Physics Departmen
t
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AbstractAbstract UV-induced response of epidermis is considered as result of reaction of nonlinear dynamic system with negative feedback on external action. Des-cribed mathematical model has a block structure with modules for calculation of
1)UV-radiation propagation through epidermis;
2)changes in the number of keratinocytes and melanocytes and number of melanosomes in different types of cells;
3)variation of melanin content in lower and upper layers of epidermis.
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INTRODUCTION
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UV-radiation
(From SpringerImages and [1].)
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UV-photons Keratinocytes Melanocytes Langergans cells Lymfocytes Cell membrane DNA, DNA-fragments UV-chromophores Activators of cell signa-
ling pathways
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“DRAMATIS PERSONAE” Melanin granules Melanosomes Tyrosinase Motor proteins ROS, NO Cytokines Caspases, p53 Kinases, phosphatases Vitamin D Others…
INTRODUCTION
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I. UVR penetration through upper epidermal layers
II. UVR interaction with cell membranes and DNA
III.Immediate response. Molecular levelIV.Cell signaling pathways activation. DNA
repairV. Response on cell level. ApoptosisVI.Delayed response. Intracellular level.
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VII. Tissue level response. Hyperplasia of upper layers of epidermis. Melanin screen formation
Melanogenesis, inflammation
Attenuation of UVR actionPhotoaging, carcinogenesis
SHORT LIST OF PROCESSES
INTRODUCTION
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Nonlinear Hierarchical «Mechanistic»
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Now there are many partial models and only two attempts to develop “general” models [2, 3].
MODEL REQUIREMENTS
INTRODUCTION
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INTRODUCTION
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“STAIR OF MODELS”
UV0
UV1
M K
dXX
dt
“Physical”Structural
Mathematical
Decompositionand synthesis
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Epidermis
Dermis
UVR
E
D
UVR
TISSUE LEVELSTRUCTURE OF MODEL
Eupp
Eliv
Eupp – upper epidermal layersEliv – “living” epidermis
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D
UVR
CELLULAR LEVELSTRUCTURE OF MODEL
Eliv
M K Lf
K – keratinocytes; M – melanocytes; Lf – lymphocytes
Eupp
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UVR
INTRA CELLULAR LEVEL
STRUCTURE OF MODEL
K M
Mb Nc
dendrite length
Ms
Mb – membrane; Nc – nuclei; Ms – melanosome
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MOLECULAR LEVEL
STRUCTURE OF MODEL
K M
TsPK DNA Mel
PK – protein kinases; Ts – tyrosinase; Mel – melanines
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METHODS OF SOLUTION
I. Volterra Series (See [4]).II.Analytical solutions for
simplified models (See [2]).III.Numerical solutions.IV.Monte-Carlo methods.
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ACKNOWLEDGMENTS:
The research has been made possible by
grant #224014 Network of Excellence for Biophotonics (PHOTONICS4LIFE) of the Seventh Framework Programme of Commission of the European Communities
grant 06-02-16740 of Russian Foundation of Basis Research
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REFERENCES
1. Farage M. A., Miller K. W., Maibach H. I. Determinants in the Rate of Skin Aging: Ethnicity, Gender, and Lifestyle Influences. // Textbook of Aging Skin, Chapter 92, Springer, 2010, pp. 983–997.
2. Thingnes J., Øyehaug L., Hovig E., Omholt S. W. The mathematics of tanning // BMC Systems Biology, 2009, Vol. 3, Article No. 60.
3. Stolnitz M. M., Peshkova A. Yu. Mathematical model of UV-induced melanin screen // Izvestiya VUZ. Applied Nonlinear Dynamics, 2001, Vol. 9, No. 3, pp. 73–84 (In Russian).
4. Giri F., Bai Er-Wei. Block-oriented Nonlinear System Identification (Lecture Notes in Control and Information Sciences, Volume 404). – Springer, 2010.
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