Lecture 2 - Matrices and Genomics - PDF

Lecture 2 September 3, 2024 Matrices 1 3 8 A= 1 2 6 0 1 2 m by n m is the number of row, n is the number of columns  Matrices 1 3 8 1 3...

Lecture 2 September 3, 2024 Matrices 1 3 8 A= 1 2 6 0 1 2 m by n m is the number of row, n is the number of columns  Matrices 1 3 8 1 3 1 0 2 A 1 2 6 1 2 CR 0 1 2 0 1 2 0 1 Rank Number of independent columns Is a column made up of all 0s? Is a column a multiple of another column? Is a column a combination of two other columns? Why matrices?  Represent systems of equations 𝑋1 + 3𝑋2 = 8 𝑋1 + 2𝑋2 = 6 𝑋2 = 2 Why matrices?  Represent systems of equations 𝑋1 + 3𝑋2 = 8 𝑋1 + 2𝑋2 = 6 𝑋2 = 2 1 3 8 1 2 6 0 1 2  0 1 1 0 0 Why matrices? 1 0 0 1 0 1 0 0 0 0  Represent Graphs 0 1 0 0 1 B 0 0 0 1 0 A D E C  0 1 1 0 0 Why matrices? 0 0 0 1 0 0 0 0 0 0  Represent Graphs 0 0 0 0 1 B 0 0 0 1 0 A D E C Why matrices? 0 1.5 5 0 0 0 0 0 0.25 0 0 0 0 0 0  Represent Graphs 0 0 0 0 2 B 0 0 0 2 0 A D E C Use of matrices in biology  Gene regulatory networks  Metabolic networks  Infectious disease models  Survival Analysis Genomics  Numerous genomes being sequenced  Genomes filled junk DNA?  Genes  Regulatory factors  Repetitive elements  Genes  Regulatory elements  Exons & Introns  Untranscribed elements Genomics  Variations within the genome  Large deletions  Large duplications  Translocations  Single Nucleotide Variations  Insertions  Deletions  Polymorphisms What can we do with this information?  Population/Ancestry structure  GWAS studies  Variant effects  Synonymous vs Non-Synonymous  Regulatory disruption Variant Call Format (VCF)  File format containing sequence information  Tab delimited file  Header region  Version info  Chromosome/Scaffold/Contig info  Details on content Variant Call Format (VCF)  Can contain info on one or more samples  General position info  Chromosome, position, Reference, Alternative(s)  Gene info  Total counts – Individual allele and overall  Sample specific info  Allele calls, site depth, number of counts per allele, quality  Can contain all sites or those with just variants Group Project  3 Groups  Form a testable hypothesis  Population analysis  Disease  Compile Genetic Information  Determine software necessary  Is it available or are you creating it?  Preliminary presentation and report  Run analysis on Biolinux machines  Final Write-up and Presentation