MATHEMATICAL MODEL OF UV-INDUCED RESPONSE OF EPIDERMIS Mikhail M. Stolnitz Saratov State University, Saratov, Russia Saratov State University International Institute of Optics & Biophotonics Optics & Biomedical Physics Department

Abstract 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. Saratov Fall Meeting

INTRODUCTION 3 Saratov Fall Meeting 2011 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 4 Saratov Fall Meeting 2011 “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 level IV.Cell signaling pathways activation. DNA repair V.Response on cell level. Apoptosis VI.Delayed response. Intracellular level. 5 Saratov Fall Meeting 2011 VII. Tissue level response. Hyperplasia of upper layers of epidermis. Melanin screen formation Melanogenesis, inflammation Attenuation of UVR action Photoaging, carcinogenesis SHORT LIST OF PROCESSES INTRODUCTION

 Nonlinear  Hierarchical  «Mechanistic» 6 Saratov Fall Meeting 2011 Now there are many partial models and only two attempts to develop “general” models [2, 3]. MODEL REQUIREMENTS INTRODUCTION

7 Saratov Fall Meeting 2011 “STAIR OF MODELS” “Physical” Structural Mathematical Decomposition and synthesis

8 Saratov Fall Meeting 2011 Epidermis Dermis UVR E D TISSUE LEVEL STRUCTURE OF MODEL E upp E liv E upp – upper epidermal layers E liv – “living” epidermis

9 Saratov Fall Meeting 2011 D UVR CELLULAR LEVEL STRUCTURE OF MODEL E liv MKLf K – keratinocytes; M – melanocytes; Lf – lymphocytes E upp

10 Saratov Fall Meeting 2011 UVR INTRA CELLULAR LEVEL STRUCTURE OF MODEL KM Mb Nc dendrite length Ms Mb – membrane; Nc – nuclei; Ms – melanosome

11 Saratov Fall Meeting 2011 MOLECULAR LEVEL STRUCTURE OF MODEL KM TsPKDNAMel PK – protein kinases; Ts – tyrosinase; Mel – melanines

12 Saratov Fall Meeting 2011 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 # Network of Excellence for Biophotonics (PHOTONICS4LIFE) of the Seventh Framework Programme of Commission of the European Communities grant of Russian Foundation of Basis Research Saratov Fall Meeting

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– Thingnes J., Øyehaug L., Hovig E., Omholt S. W. The mathematics of tanning // BMC Systems Biology, 2009, Vol. 3, Article No 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, Saratov Fall Meeting 2011