MATHEMATICAL MODEL OF UV- INDUCED RESPONSE OF EPIDERMIS

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

2. 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 UV-radiation propagation through epidermis; changes in the number of keratinocytes and melanocytes and number of melanosomes in different types of cells; variation of melanin content in lower and upper layers of epidermis. Saratov Fall Meeting 2011 2

3. INTRODUCTION UV-radiation (From SpringerImages and [1].) Saratov Fall Meeting 2011 3

4. INTRODUCTION “DRAMATIS PERSONAE” • UV-photons • Keratinocytes • Melanocytes • Langergans cells • Lymfocytes • Cell membrane • DNA, DNA-fragments • UV-chromophores • Activators of cell signa-ling pathways • Melanin granules • Melanosomes • Tyrosinase • Motor proteins • ROS, NO • Cytokines • Caspases, p53 • Kinases, phosphatases • Vitamin D • Others… Saratov Fall Meeting 2011 4

5. INTRODUCTION SHORT LIST OF PROCESSES UVR penetration through upper epidermal layers UVR interaction with cell membranes and DNA Immediate response. Molecular level Cell signaling pathways activation. DNA repair Response on cell level. Apoptosis 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 5 Saratov Fall Meeting 2011

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

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

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

9. STRUCTURE OF MODEL CELLULAR LEVEL Eupp UVR Eliv M K Lf D K – keratinocytes; M – melanocytes; Lf – lymphocytes Saratov Fall Meeting 2011 9

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

11. STRUCTURE OF MODEL MOLECULAR LEVEL K M PK DNA Ts Mel PK – protein kinases; Ts – tyrosinase; Mel – melanines Saratov Fall Meeting 2011 11

12. METHODS OF SOLUTION Volterra Series (See [4]). Analytical solutions for simplified models (See [2]). Numerical solutions. Monte-Carlo methods. Saratov Fall Meeting 2011 12

13. 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 Saratov Fall Meeting 2011 13

14. REFERENCES • 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 UV-induced 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. Saratov Fall Meeting 2011 14