egyptian candidates
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
Egyptian Candidates
Ahmed Faramawy T.A in ASU, Cairo, Egypt
Hadeer ELHabashyTA in AUC, Cairo, Egypt
Mostafa Abo ElsoudNational Research Center
Supervised ByMarina lyashko & SvetLana Accenova
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.
SOS gene boxUmuc, UmuD, DinI
Lex A
RecA
Pyrimidine photodimers
.
.umuC umuD
LexA
ssDNA+RecA+ATP
RecA*
dinI
UmuC
DinI
UmuD’
UmuD’2UmuD2 UmuDD’
UmuD2C UmuD’2C UmuDD’C
Pol V
UmuD
Mathematical Model of SOS-induced mutagenesis in bacteria Escherichia
coli under ultraviolet irradiation
By: Hadeer El Habashy
Contents 1.Why?, Why?, Why? And why? 2. Developing Mathematical model
Mathematical Model WHY?
of SOS-induced mutagenesis WHY?
in bacteria Escherichia coli under WHY?
ultraviolet irradiation & WHY?
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.
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
Excision Repair
SOS Repair
The biological mechanism of SOS Reponce in E.Coli
Developing the Mathematical model
1. Developing a system of Molecular Equations
2. Developing a system of Differential Equations
3. Developing a system of Normalized Differential Equations
4. Finding the constants
1. Developing a system of molecular equations
2.Developing the non-normalized differential equations
The regulatory protein intracellular concentration
the regulatory accumulation protein rate. the regulatory protein degradation rate.
Equation for RecA protein
Normalization process
WHY?We non-dimensionalize the model equations : 1. To facilitate analysis and solution correctly 2. To reduce the parameters in the problem (Aksenov 1999 )
How?By dividing the parameters by constants that havethe same dimensions
3. Developing a system of normalized differential equations
Developing a system of Normalized Differential Equation for each protein of the SOS response
LexA
RecA
UmuD
The normalized( dimensionless) questions for each protein of the SOS response
UmuC
UmuD’
UmuDD’
UmuDD’C
DinI
Finding the constants
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.
MATHEMATICA
What it can do for you ?
Ahmed Faramawy Ahmed Faramawy (T.A in ASU, Cairo, Egypt )
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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.
Stephen Wolfram: creator of Mathematica
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Q: What is Mathematica?A: An interactive program with a vast range of uses:- Numerical calculations to required precisionNumerical calculations to required precision- Symbolic calculations/ simplification of algebraic expressionsSymbolic calculations/ simplification of algebraic expressions- Matrices and linear algebraMatrices and linear algebra- Graphics and data visualisationGraphics and data visualisation- CalculusCalculus- Equation solving (numeric and symbolic)Equation solving (numeric and symbolic)- Optimization Optimization - StatisticsStatistics- Polynomial algebraPolynomial algebra- Discrete mathematicsDiscrete mathematics- Number theoryNumber theory- Logic and Boolean algebraLogic and Boolean algebra- Computational systems e.g. cellular automataComputational systems e.g. cellular automata
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StructureComposed 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
colouring28
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
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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/ .x y means “replace x by y in expr”• expr/ .rules means “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
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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).
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Mathematica as a calculator• Contains mathematical and physical constants e.g. i (Imag), e (Exp) and (Pi)• Addition + Subtraction - Multiplication * or blank space Division / Exponentiation ^• Can do symbolic calculations and simplification of complicated
algebraic expressions – see SimplifySimplify and FullSimplifyFullSimplify..
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Calculus
• See D to Differentiate.
• Can do both definite and indefinite integrals – see Integrate
• For a numeric approximation to an integral use NIntegrate.
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Equation solving
• Use Solve to solve an equation with an exact solution, including a symbolic solution.
• Use NSolve or FindRoot to obtain a numerical approximation to the solution.
• Use DSolve or NDSolve for differential equations.
• To use solutions need to use expr / .x y.
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Creating your own functions
Plot3D equation “as example”Plot3D equation “as example”
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Plot3DEvaluateX10 NA x1a1 t, Dz . sol1, t, 0, 150, Dz, 0.5, 100, PlotLabel Style"LexA", 16, ColorFunction "Aquamarine",
AxesLabel Style"мин.", 14, Black, Style"Дж м2", 14, Black, Style"N", 14, Black , LabelStyle DirectiveBlack Ticks 20,40,80,100, 0,20,40,60,80,100, 400,800,1300
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sol1 NDSolve Dx1t, Dz, t 1 k5^h1 1 k5 x1t, Dz ^h1 x1t, Dz 1 k6 x3t, Dz ,Dx2t, Dz, t 1 k7^h2 1 k7 x1t, Dz ^h2 x2t, Dz 1 k8 ODt, Dz k1 x3t, Dz,Dx3t, Dz, t k8 ODt, Dz x2t, Dz k1 x3t, Dz 1 x4t, Dz k9 x3t, Dz k1 x1t, Dz x3t, Dz,Dx4t, Dz, t k10 1 k11^h4 1 k11 x1t, Dz ^h4 x4t, Dz k12 x3t, Dz x4t, Dz k14 k13 x4t, Dz ^2,Dx5t, Dz, t k15 1 k16^h5 1 k16 x1t, Dz ^h5 k17 x7t, Dz x5t, Dz k18 x8t, Dz x5t, Dz k19 x9t, Dz x5t, Dz k20 x5t, Dz,Dx7t, Dz, t k24 x4t, Dz ^2 k25 x7t, Dz 0 k34 x5t, Dz x7t, Dz,Dx6t, Dz, t k12 x4t, Dz x3t, Dz k22 x6t, Dz ^2 k21 x8t, Dz x4t, Dz k23 x6t, Dz,Dx8t, Dz, t k22 x6t, Dz ^2 k21 x8t, Dz x4t, Dz k26 x8t, Dz 0 k35 x5t, Dz x8t, Dz,Dx9t, Dz, t k27 x4t, Dz x6t, Dz k21 x8t, Dz x4t, Dz k28 x9t, Dz 0 k36 x5t, Dz x9t, Dz, D x10t, Dz, t k29 x7t, Dz x5t, Dz k30 x10t, Dz,Dx11t, Dz, t k18 x8t, Dz x5t, Dz k31 x11t, Dz x4t, Dz k32 x11t, Dz, Dx12t, Dz, t k19 x9t, Dz x5t, Dz k31 x11t, Dz x4t, Dz k33 x12t, Dz,Dx13t, Dz, t k37 1 k39^h6 1 k39 x1t, Dz ^h6 x13t, Dz k38 x3t, Dz x13t, Dz k37, x10, Dz 1, x20, Dz 1, x30, Dz 0,
x40, Dz 1, x50, Dz 1, x70, Dz 1, x60, Dz 0, x80, Dz 0, x90, Dz 0, x100, Dz 1, x110, Dz 0, x120, Dz 0, x130, Dz 1, x1, x2, x3, x4, x5, x7, x6, x8, x9, x10, x11, x12, x13, t, 0, 20, Dz, 0.5, 100, MaxStepSize 0.8
NDSolve equation “as example”NDSolve equation “as example”
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 Show to display combined graphics objects
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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.
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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 apparatusand biochemical mechanisms controlling the mutation process.
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Experimental data
Sequence of Reactions
Reaction’s code
Run
Output
Results
Steps For Building Up The Model
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• All reactions were simulated using Mathematica software, using two approaches: 1. Stochastic approach
2. Deterministic approach
• Outputs we obtained, characterized DNA repair steps as well as enzyme’s concentration changes.
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Results
Lex A protein
2D plotting for Lex A
3D plotting for Lex A
0 5 0 1 0 0 1 5 0 2 0 0tim e m in
2 0 0
4 0 0
6 0 0
8 0 0
1 0 0 0
1 2 0 0
1 4 0 0N 1 04
lex A
Blue 1 J /m2
Pink 5 J /m2
yellow 20 J /m2
Green 100 J /m2
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Rec A protein
3D plotting for Rec A & Rec A*
Rec A* protein
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0 5 0 1 0 0 1 5 0 2 0 0tim e
1 0 0
2 0 0
3 0 0
4 0 0
5 0 0
NU m uD 2 'c
Blue 1 J /m2
Pink 5 J /m2
yellow 20 J /m2
Green 100 J /m2
min
min
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UmuD’2C protein (pol V)
3D plotting for UmuD’2C
2D plotting for UmuD’2C
DinI protein
2D plotting for DinI
min
3D plotting for DinI
0 5 0 1 0 0 1 5 0 2 0 0tim e
2 0 0
4 0 0
6 0 0
8 0 0N
D inI
Blue 1 J /m2
Pink 5 J /m2
yellow 20 J /m2
Green 100 J /m2
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ConclusionUsing mathematical approaches
1.The model adequately describes the basic processes of the SOS response,
2.we consider how this model could be applied for the estimation of the mutagenic effect of UV irradiation and radiation,
3.A model of describing the dynamics of DinI- protein is developed,
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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
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Acknowledgments
o Dr. Oleg Belov, LRB, JINRDr. Oleg Belov, LRB, JINRoMarina lyashko Marina lyashko , , LRB, JINRLRB, JINRoSvetLana AksenovaSvetLana Aksenova , , LRB, JINRLRB, JINR
Thank You For Your Attention
“ “спасибо”спасибо”
50ДубнаДубна