PowerPoint Presentation - Undergraduate Research

Undergraduate ResearchNicholas CelmsUndergraduate BioMath Program, San Diego State UniversityNicholas Celms

Computer Science major, graduating after this semester.Involved with UBM for approx. 2 yearsUndergraduate Biomath Program @ SDSUResearch: College kids that dont care need not applyThe Need for ubmHistory on the relationship between mathematics and biology5HistoryThe interplay between mathematics and physics has, in recent years, become so profound that the lines have been blurred. The two disciplines, long complementary, have begun a deep and fundamental relationship... ~ Eric Zaslow56HistoryMathematics is biology's next microscope, only better; biology is mathematics' next physics, only better ~J.E. Cohen67The lack of real contact between mathematics and biology is either a tragedy, a scandal, or a challenge, it is hard to decide which ~ Gian-Carlo RotaHistory7Presentation OverviewProject ConceptWe organize multiple strainsCentral Dogma, Biology of sequenced genetic dataSequencing, BiologyInto a matrixMatrices, MathThen apply graph theoryGraph Theory, CSTo generate phylogenetic treesPhylogeny, BiologyKnown as splits trees, based on d-splitsSplits/d-splits, Math9Splits Graph of 45 Strains

22 strains of Escherichia, 15 strains of Salmonella, 8 strains of Shigella.910

Splits Graph of 3 Genuses SalmonellaShigella and Escherichia10Presentation OverviewI want all of you to understand my project, but I dont expect that to happen in one day, or in one presentation.

We will get as far as we can, but these conversations will continue this semester, so there is plenty of time for you to get it.

Please ask questions and slow me down as much as youd like, well get through it by December!Biology: Background

Biology: Background

Salmonella, viruses, etc Us, plants, etcBiology: BackgroundOrganismTypeBpBacteriophage MS2Virus3,569HIVVirus9,749E. coliBacteria4,600,000Drosophila melanogaster(fruit fly)Insect130,000,000HumansMammal3,200,000,000DNA

mRNA

ProteinReversetranscriptiontranscriptiontranslationBiology: Central dogma of biologyBiology: BackgroundEvery 3 base pairs of DNA encodes for one of the 20 amino acidsAmino Acids form proteins, which are structured groups of amino acids that operate as the building blocks of life.

Biology: Background

Shorter sequences longer sequencesMath: Graphs

Nodes/vertices are connected by paths/edgesThey are a central concept in computer science

Math: Graphs: CliquesA clique is a subset of a graph in which for every two vertices in the clique, there exists an edge connecting them.

Math: Graphs: CliquesA clique is a subset of a graph in which for every two vertices in the clique, there exists an edge connecting them.

For example, vertices 1, 2, and 5 form a cliqueMath: MatricesA Matrix is a rectangular array of numbers

Math: MatricesRows are strains, and columns are proteins in our matricesai,j = 1 if strain i contains protein j , and 0 otherwise.

Math: Matrices: Distance MatrixMath: Hamming Space: MetricsA metric defines distance between elements in a set.A metric for the set of US cities might define distance in miles, as the physical distance between the cities.In our case, we define a metric on a set of strains, and define distance as dissimilarity in proteins. For example, two identical strains have distance = 0.DataBacterial dataset and viral datasetEscherichia, shigella, and salmonellaBacterial datasetEscherichia

Shigella

Salmonella

Math: Graphs: CliquesA clique is a subset of a graph in which for every two vertices in the clique, there exists an edge connecting them.

For example, vertices 1, 2, and 5 form a cliqueFinding Cliques32Splits Graph of 45 Strains

22 strains of Escherichia, 15 strains of Salmonella, 8 strains of Shigella.3233

Splits Graph of 3 Genuses SalmonellaShigella and Escherichia33Applying This To Phages: What is a Phage?Short for bacteriophage, bacteria eaterViruses that infect bacteriaTypically have a head/capsid, tail, and a base plate (image next slide)Usually 24-200 nm longAttach to a bacteria, inject DNA, and either kill the cell, releasing hundreds of new phages (Lytic), or lay dormant in the bacteria, with the potential to become Lytic in the future (Lysogenic) (video will help!)Applying This To Phages: What is a Phage?

Applying This To Phages: What is a Phage?

Applying This To Phages: What is a Phage?

Applying This To Phages: Why is that hard?Horizontal Gene Transfer

Applying this to Phages: Early Results

Undergraduate ResearchNicholas CelmsUndergraduate BioMath Program, San Diego State University

Questions?