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# Applied Mathematics & Statistics

AMS 534: Introduction to Systems Biology

A detailed introduction to essential concepts and computational skills for doing research in Systems Biology. The class will be centered upon two key programming languages: Matlab for modeling applications and the R language for statistical analysis and sequence manipulation. Examples will come from a broad range of biological applications ranging from theoretical population genetics, metabolic and gene network dynamics to analysis of high-throughput data. No prior knowledge of biology or mathematical/computational techniques is required.  Note: Crosslisted with BGE 534

Text:
"A First Course In Systems Biology" by Eberhard O. Voit, Garland Science; Publisher: Taylor, 2012, ISBN: 978-0815344674 (recommended/optional)

Spring Semester

Learning Outcomes:

1) Demonstrate amiliarity with essential concepts of quantitative Biology and the place of computational modeling in Systems Biology research.

2) Demonstrate competence in using basic Matlab functionality:
* Learn basic Matlab concepts such as matrix/vector manipulation and programming;
* Use matlab for solving systems of linear equations and performing regression.

3) Demonstrate a basic ability to model Ordinary Differential Equations using Matlab:
* Apply Matlab to modeling Mass action kinetics and the Michaelis-Menten rate law;
* Understand how ODEs are implemented in Matlab using callback functions.

4) Understand how to manage complexity in biochemical network modeling:
* Become familiar with the BioNetGen (BNGL) meta-language for modeling complexes;
* Be able to write simple BNGL scripts for generating Matlab code for complex systems.

5) Learn to analyze a simple Markov process. The case of genetic drift in a single-locus two-allele system in a finite population (Fisher-Wright model).

6) Learn basic programming in R and the differences between Matlab and R:
* Understand R programming concepts and data structures: lists, factors and data frame;
* Be able to use functional programming in R using apply, sapply, tapply, etc.;
* Learn data manipulation and visualization: input/output, reshaping data and plotting.

7) Be capable of using R for statistical hypothesis testing and model fitting:
* Understand random number generation and standard distributions;
* Be able to use difference of means tests to identify differential gene expression;
* Implement and compare linear models in R and apply to analysis of SNP data.

8) Elementary Bayesian Statistics using R:
* Understand the concepts of conditional probability and Bayes theorem;
* Be able to use R for Bayesian inference for binomial proportion.

9)  Manipulating and analyzing high-throughput sequence data:
* Learn to use key command-line tools: FastX-toolkit, bowtie and samtools;
* Understand the basic concepts in deep sequencing: RNA-Seq, ChIP-Seq, etc.;
* Learn to use R for genomic analysis, e.g. transcription factor binding sites;
* Be able to analyze differential methylation using Bayesian difference of proportions test. 