Team:UANL Mty-Mexico/Workshop Math1

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Math Modelling Course

This year, the iGEM UANL team decided to establish an introductory course called 'Mathematical Modeling in Systems Biology', with the idea of preparing our faculty students in the mathematical area of biology.

This course is made up of three phases, each one demanding a different knowledge level.

Phase I Has the intention of teaching the students theoretical and applicable aspects of differential and integral calculus as a fundamental part in solving and distinguishing differential equations.

Phase II Was designed with the aim of making the students able to understand the applications of linear transformation of vector spaces for the solution of differential equations that can be applied in systems biology.

Phase III. The objective of this part of the course is that students come to understand the general concepts of systems biology and become familiar with its theoretical basis, having as purpose increasing the student's critical awareness on this area.

1: DNA

Topics: -Miau Miau Miau.

2: Genes

Topics: -Genes as functional units of DNA -Organization and parts of a genes -How do the genes work? -Central dogma of molecular biology.  Activity: Puzzle with multiple options to explain gene function through the central Dogma. -Use of common examples.

3: Proteins

Topics: -Proteins as carriers of most biological processes -Types of proteins -Examples of  common proteins -The genetic code  Activity: Build a protein from DNA code (translation), Protein models.

4: Genetic Engineering

Topics: -Recombinant DNA technology -Restriction enzymes, ligase and vectors -Examples.  Activity: Build a recombinant DNA molecule with colored cables  and transform a cell.

5: Synthetic Biology

Topics: -Universality, modularity and abstraction of bioparts -Synbio as the application of engineering concepts to biology -Advancements in DNA synthesis and sequencing technologies. Activity:  Construct a genetic circuit on a board and estimate time and costs to build it.

6: Biobricks

Topics: -BioBricks as standard DNA parts - Parts of a BioBrick - Types of BioBricks. -Biobrick assembly -The Registry of Standard Biological Parts Activity: Put compatible bricks together.

7: Biological machine

Topics: -Imagine the possibilities -Addressing high impact problems through biomachines. -Metabolic load -Advantages of biomachines over robots. Activity: "Labyrinth of metabolism" so that the visitor knows that "parts" must be manipulated to make a organism perform certain function.

8: Applications of SynBio

Topics: -Impact of SynBio in a wide variety of areas - Examples of issues solved through SynBio (How do these projects work?)  Activity: The visitor must correlate a specific genetic circuit to its application area.

9: iGEM

Topics: iGEM as the biggest synthetic biology competition, rules, motivation, scope. - iGEM UANL 2011 and 2012 -CIDEB-UANL 2012  Activity: -Explain our 2011 project -Exhibition of the light-machine used in our project -Explain CIDEB's 2012 project

10: Ethics and Biosafety

Topics: -Ethics definition -Human quality of life -Good and ugly -Impact awareness -Acceptance of SynBio -Potential problems -Precautions taken to prevent them -Biosafety levels Activity: Dress with biosafety equipment  (lab coat, glasses, gloves…) as fast as possible!

Description Back to top

This program is based on the UNAM Genomic Sciences career's syllabus, which is an internationally-recognised career by many other universities and prestigious investigation centers in the world.

The first phase of the course was successfully imparted along June and July of this year by M.Sc. Jesús Botello González, professor of the Chemistry School of our University (UANL). It had a duration of 6 weeks and took place in our faculty; approximately 40 students enrolled this course.

M.Sc. Botello will impart phase II as well, but the program has still to be dated.

We think this course is a great step toward the learning of advanced knowledge in the field of molecular biology and genomics that has to be made use of, and it is really important for the UANL students, so that we are well-educated in this field.

The subjects that are included in the first phase (Phase I) of this course are:

1. Precalculus

1.1 Elementary algebra
1.2 Understanding of the behavior of functions through their graphs.
1.3 Functions, dependent and independent variables, domain and range.
1.4 Function composition
1.5 Inverse functions

2.1 Limits
2.2 Lateral limits
2.3 Infinite limits
2.4 Limits tending to infinite
2.5 Behavior of asymptotic rational functions applying limits
2.6 Continuity
2.7 Definition of derivatives
2.8 Derivation rules
2.9 Derivative of a composite function
2.10 Chain rule
2.11 Change rate in relation to time
2.12 Optimization
2.13 Function graphing using derivatives

3.1 Sigma notation
3.2 Riemann sums (Definite integral definition)
3.3 Calculation of the area under a curve with definite integrals
3.4 Integral calculus theorems, including the Fundamental Theorem of Calculus
3.5 Definition of indefinite integrals (anti-derivatives)
3.6 Polynomial function integration
3.7 Integration by substitution
3.8 Calculation of the area between functions
3.9 Calculation of volume by slices
3.10 Calculation of the volume of solids of revolution with discs and cylindric layers
3.11 Integration techniques