Transcript Mathematical modelof UV-induced response of epidermis

Saratov
State
University
Optics &
Biomedical
Physics
Department
MATHEMATICAL MODEL
OF UV-INDUCED RESPONSE
OF EPIDERMIS
International
Institute of
Optics &
Biophotonics
Mikhail M. Stolnitz
Saratov State University, Saratov, Russia
Abstract
UV-induced response of epidermis is considered
as result of reaction of nonlinear dynamic system
with negative feedback on external action. Described 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
UV-radiation
(From SpringerImages and [1].)
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INTRODUCTION
“DRAMATIS PERSONAE”
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UV-photons
Keratinocytes
Melanocytes
Langergans cells
Lymfocytes
Cell membrane
DNA, DNA-fragments
UV-chromophores
Activators of cell signaling pathways
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Melanin granules
Melanosomes
Tyrosinase
Motor proteins
ROS, NO
Cytokines
Caspases, p53
Kinases, phosphatases
Vitamin D
Others…
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INTRODUCTION
SHORT LIST OF PROCESSES
I. UVR penetration through upper epidermal layers
II. UVR interaction with cell membranes and DNA
III.Immediate response. Molecular level
IV. Cell signaling pathways activation. DNA repair
V. Response on cell level. Apoptosis
VI. Delayed response. Intracellular level.
Melanogenesis, inflammation
VII. Tissue level response. Hyperplasia of upper layers of
epidermis. Melanin screen formation
Attenuation of UVR action
Photoaging, carcinogenesis
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INTRODUCTION
MODEL REQUIREMENTS
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Nonlinear
Hierarchical
«Mechanistic»
Now there are many partial models and only two
attempts to develop “general” models [2, 3].
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INTRODUCTION
“STAIR OF MODELS”
Mathematical
Structural
“Physical”
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dX 
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dt 
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X
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UV 0
Decomposition
and synthesis
UV 1
M
K
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STRUCTURE OF MODEL
TISSUE LEVEL
UVR
Epidermis
Dermis
UVR
E
Eupp
Eliv
D
Eupp – upper epidermal layers
Eliv – “living” epidermis
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STRUCTURE OF MODEL
CELLULAR LEVEL
Eupp
UVR
Eliv
M
K
Lf
D
K – keratinocytes; M – melanocytes; Lf – lymphocytes
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STRUCTURE OF MODEL
INTRA CELLULAR LEVEL
UVR
K
Mb
dendrite length
M
Nc
Ms
Mb – membrane; Nc – nuclei; Ms – melanosome
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STRUCTURE OF MODEL
MOLECULAR LEVEL
K
PK
M
DNA
Ts
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
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grant #224014 Network of Excellence for
Biophotonics (PHOTONICS4LIFE) of the
Seventh Framework Programme of Commission
of the European Communities
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grant 06-02-16740 of Russian Foundation of
Basis Research
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REFERENCES
1.
2.
3.
4.
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.
Thingnes J., Øyehaug L., Hovig E., Omholt S. W. The
mathematics of tanning // BMC Systems Biology, 2009, Vol.
3, Article No. 60.
Stolnitz M. M., Peshkova A. Yu. Mathematical model of UVinduced melanin screen // Izvestiya VUZ. Applied Nonlinear
Dynamics, 2001, Vol. 9, No. 3, pp. 73–84 (In Russian).
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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