Math of DNA Project Suggestions
  • 1. Implement the transvection algorithm for virtual trackball controlled three-dimensional rotations in Labview, Java, Matlab, C++. You may base your implementation on my Flash/Actionscript version for Platonic Solids.
    Transvection Demo
    Algorithm code
    Perspective figures
    Perspective code
  • 2. Generate data for three-dimensional visualization of strands of DNA winding into double helices and unwinding to random coils from time varying curvature and torsion. You might include sequence dependent features.
    Space curves
    Curvature and torsion
  • 3. Convert a set of related computer programs (or any other evolving information) into DNA sequences of ACGTs and perform hierarchical clustering on them without multiple alignment, and with some different forms of multiple alignment first. You may use the Clustal programs to do this.
    Clustal W homepage
    Clustal X homepage
  • 4. Solve the DNA Melting Curve Model ODE with prescribed thermodynamic parameters calculated from a given sequence in Labview using the built in Runge-Kutta solver .vi and the thermodynamic parameter calculator.
    Melting curves
    Melting curve ODEs
    SantaLucia papers
  • 5. Obtain the genomic data for the SNPs on a chromosome, and find examples of every SNP type having frequencies within a desired range for homozygous, heterozygous, and wild-type forms.
    NCBI Homepage
  • 6. Investigate the dependence of the background fluorescence vs. temperature amplitude and decay behavior on the properties of the single-stranded oligonucleotides present (e.g. their length, GC content, sequence, etc.)
    Melting curves program
  • 7. How many classes does a dendrogram represent?
    Clustering
  • 8. Systematic organization of tetrads with mismatchs for DNA with one mismatch, DNA-RNA, dangling ends, etc.
    SantaLucia papers
  • 9. Investigate simulate the advantages/disadvantages of different thermodynamic parameter inversion methods - Fit vs. Local, Which linear system, etc., and different molecules (sequences) for determining parameters.
    SantaLucia papers
    Melting curve theory
    Melting curve theory