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Egyptian Candidates

Egyptian Candidates. Ahmed Faramawy T.A in ASU, Cairo, Egypt. Hadeer ELHabashy TA in AUC, Cairo, Egypt. Mostafa Abo Elsoud National Research Center. Supervised By Marina lyashko & SvetLana Accenova.

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Egyptian Candidates

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  1. Egyptian Candidates Ahmed Faramawy T.A in ASU, Cairo, Egypt Hadeer ELHabashy TA in AUC, Cairo, Egypt Mostafa Abo ElsoudNational Research Center Supervised ByMarina lyashko & SvetLana Accenova

  2. The SOS response in Escerichia coli bacteria is a set of inducible physiological reactions that help a cell to servive after the treatment with various DNA-damaging agents, such as ultraviolet and ionizing radiation and some chemicals. • More than 40 genes are induced in response to DNA damage as part of the SOS regulon in Escherichia coli. • SOS repair may result in SOS mutagenesis due to the inhibition of the proofreading activity of the epsilon subunit of DNA Pol III.

  3. Lex A RecA SOS gene box Umuc, UmuD, DinI Pyrimidinephotodimers Mechanism of SOS repair system

  4. ssDNA+RecA+ATP Mechanism of SOS repair system RecA* DinI LexA UmuD UmuD’ . dinI umuC umuD . UmuDD’ UmuD2 UmuD’2 UmuC UmuD2C UmuD’2C UmuDD’C Pol V

  5. Mathematical Model of SOS-induced mutagenesis in bacteria Escherichia coli under ultraviolet irradiation By: Hadeer El Habashy

  6. Contents • Why?, Why?, Why? And why? 2. Developing Mathematical model

  7. Mathematical Model WHY? of SOS-induced mutagenesis WHY? in bacteria Escherichia coli under WHY? ultraviolet irradiation & WHY?

  8. Object for study • Escherichia coli bacteria – colibacillus cells – play an important role among the traditional biological objects used for studying the fundamental mechanisms of induced mutagenesis. • Using these cells as an object of study allows us to study the structural and functional organization of the genetic apparatus and the biochemical processes controlling the mutation process in details.

  9. Excision Repair SOS Repair T-T and T-C dimers: bases become cross-linked, T-T more prominent, caused by UV light (UV-C(<280 nm) and UV-B (280-320 nm

  10. The biological mechanism of SOS Reponce in E.Coli

  11. Developing the Mathematical model • Developing a system of Molecular Equations • Developing a system of Differential Equations • Developing a system of Normalized Differential Equations • Finding the constants

  12. 1. Developing a system of molecular equations

  13. 2.Developing the non-normalized differential equations The regulatory protein intracellular concentration the regulatory protein degradation rate. the regulatory accumulation protein rate.

  14. Equation for RecA protein

  15. Normalization process WHY? We non-dimensionalizethe model equations : 1. To facilitate analysis and solution correctly 2. To reduce the parameters in the problem (Aksenov1999 ) How? By dividing the parameters by constants that have the same dimensions

  16. 3. Developing a system of normalized differential equations

  17. Developing a system of Normalized Differential Equation for each protein of the SOS response LexA RecA UmuD

  18. The normalized( dimensionless) questions for each protein of the SOS response UmuC UmuD’

  19. UmuDD’ UmuDD’C DinI

  20. Finding the constants

  21. References • Aksenov, S.V., 1999. Dynamics of the inducing signal for the SOS regulatory system in Escherichia coli after ultraviolet irradiation. • Belov, O.V., 2007. Time dependence of the inducing signal of the E. coli SOS system under ultraviolet irradiation. Part. Nucl. Lett. 4, 519–523.

  22. MATHEMATICA What it can do for you ? Ahmed Faramawy(T.A in ASU, Cairo, Egypt )

  23. Stephen Wolfram: creator of Mathematica Background • Created by Stephen Wolfram and his team Wolfram Research. • Version 1.0 was released in 1988. • Latest version is Mathematica 8.0 – released last year.

  24. Q: What is Mathematica? A: An interactiveprogram with a vast range of uses: • Numerical calculations to required precision • Symbolic calculations/ simplification of algebraic expressions • Matrices and linear algebra • Graphics and data visualisation • Calculus • Equation solving (numeric and symbolic) • Optimization • Statistics • Polynomial algebra • Discrete mathematics • Number theory • Logic and Boolean algebra • Computational systems e.g. cellular automata

  25. Structure Composed of two parts: • Kernel: -interprets code, returns results, stores definitions (be careful) • Front end: - provides an interface for inputting Mathematica code and viewing output (including graphics and sound) called a notebook - contains a library of over one thousand functions - has tools such as a debugger and automatic syntax colouring

  26. More on notebooks • Notebooks are made up of cells. • There are different cell types e.g. “Title”, “Input”, “Output” with associated properties • To evaluate a cell, highlight it and then press shift-enter • To stop evaluation of code, in the tool bar click on Kernel, then Quit Kernel

  27. Language rules • ; is used at the end of the line from which no output is required • Built-in functions begin with a capital letter • [ ] are used to enclose function arguments • { } are used to enclose list elements • ( ) are used to indicate grouping of terms • expr/ .xymeans “replace x by y in expr” • expr/ .rulesmeans “apply rules to transform each subpart of expr” (also see Replace) • = assigns a value to a variable • == expresses equality • := defines a function • x_ denotes an arbitrary expression named x

  28. Language rules (2) • Any part of the code can be commented out by enclosing it in (* *). • Variable names can be almost anything, BUT - must not begin with a number or contain whitespace, as this means multiply (see later) - must not be protected e.g. the name of an internal function • BE CAREFUL - variable definitions remain until you reassign them or Clear them or quit the kernel (or end the session).

  29. Mathematica as a calculator • Contains mathematical and physical constants e.g. i(Imag),e (Exp) and p (Pi) • Addition + Subtraction - Multiplication * or blank space Division / Exponentiation ^ • Can do symbolic calculations and simplification of complicated algebraic expressions – see Simplify and FullSimplify.

  30. Calculus • See D to Differentiate. • Can do both definite and indefinite integrals – see Integrate • For a numeric approximation to an integral use NIntegrate.

  31. Equation solving • Use Solve to solve an equation with an exact solution, including a symbolic solution. • Use NSolve or FindRootto obtain a numerical approximation to the solution. • Use DSolve or NDSolve for differential equations. • To use solutions need to use expr / .xy.

  32. Creating your own functions Plot3D equation “as example”

  33. NDSolve equation “as example”

  34. Graphics • Mathematica allows the representation of data in many different formats: • 1D list plots, parametric plots • 3D scatter plots • 3D data reconstruction • Contour plots • Matrix plots • Pie charts, bar charts, histograms, statistical plots, vector fields (need to use special packages) • Numerous options are available to change the appearance of the graph. • Use Showto display combined graphics objects

  35. Taking it further • Mathematica has an excellent help menu (shift-F1) • Can get help within a notebook by typing? Function Name(e.g :NDSolve) • Website: http://www.wolfram.com/products/mathematica/index.html • To use Mathematica for parallel programming, look up Grid Mathematica.

  36. The Basic Of Mathematical Modeling The development of mathematical models of the genetic regulation and repair process in bacterial cells is caused by the necessity to study the structure and functioning of the genetic apparatus and biochemical mechanisms controlling the mutation process.

  37. Experimental data Reaction’s code Output Steps For Building Up The Model Sequence of Reactions Run Results

  38. All reactions were simulated using Mathematica software, using two approaches: • Stochastic approach • Deterministic approach • Outputs we obtained, characterized DNA repair steps as well as enzyme’s concentration changes.

  39. Results Lex A protein 3D plotting for Lex A 2D plotting for Lex A

  40. Rec A protein Rec A* protein 3D plotting for Rec A & Rec A*

  41. UmuD’2C protein (pol V) min 3D plotting for UmuD’2C min 2D plotting for UmuD’2C

  42. DinI protein 3D plotting for DinI min 2D plotting for DinI

  43. Conclusion • Using mathematical approaches • The model adequately describes the basic processes of the SOS response, • we consider how this model could be applied for the estimation of the mutagenic effect of UV irradiation and radiation, • A model of describing the dynamics of DinI- protein is developed,

  44. 4. The role of the DinI-proteins in the basic life processes of cells during the formation of mutations is studied, 5. Graphs were obtained, characterizing the concentration dynamic of DinI-proteins over time and depending on the dose of UV irradiation

  45. Acknowledgments • Dr. Oleg Belov, LRB, JINR • Marina lyashko, LRB, JINR • SvetLanaAksenova , LRB, JINR

  46. Thank You For Your Attention “спасибо” Дубна

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