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

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].)

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

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

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

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.

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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