By By Ahmed Faramawy Ahmed Faramawy (T.A in ASU, Cairo, Egypt ) Hadeer ElHabashy Hadeer ElHabashy (T.A in AUC, Cairo, Egypt ) Mostafa Abo Elsoud Mostafa Abo Elsoud (National Research Center) Under the supervision of: Marina lyashko & Marina lyashko & SvetLana SvetLana Aksenova Aksenova Laboratory of Radiation Biology, Joint Institute for Nuclear 1
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By Ahmed Faramawy Ahmed Faramawy (T.A in ASU, Cairo, Egypt ) Hadeer ElHabashy Hadeer ElHabashy (T.A in AUC, Cairo, Egypt ) Mostafa Abo Elsoud Mostafa Abo.
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ByByAhmed Faramawy Ahmed Faramawy (T.A in ASU, Cairo, Egypt )Hadeer ElHabashy Hadeer ElHabashy (T.A in AUC, Cairo, Egypt )Mostafa Abo Elsoud Mostafa Abo Elsoud (National Research Center)
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
- 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
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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.
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 )
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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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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Using mathematical approaches1.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