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Biomathematics seminar

Biomathematics seminar. Application of Fourier to Bioinformatics. Girolamo Giudice. Background.  −1 + 3 i  and −1 − 3 i ,. Background.  Z = −1 + 3 i. Complex plane. Periodic and aperiodic function. Periodic function. Aperiodic function. Sine (or cosine) wave.

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Biomathematics seminar

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  1. Biomathematics seminar Application of Fourier to Bioinformatics Girolamo Giudice

  2. Background  −1 + 3i and −1 − 3i,

  3. Background  Z = −1 + 3i Complex plane

  4. Periodic and aperiodic function Periodic function Aperiodic function

  5. Sine (or cosine) wave • A the amplitude, is the peak deviation of the function from zero. • F the frequency, is the number of oscillations (cycles) that occur each second of time. • ω = 2πf, the angular frequency , how many cycles occur in a second • φ the phase , specifies (in radians) where in its cycle the oscillation is at t = 0.

  6. Harmonic analysis and Fouries series It is possible to express periodic function into the sum of a (possibly infinite) set sinesand cosines (or, equivalently, complex exponentials). Quadrature Fourier Series Euler Formula Complex Fourier series

  7. Spectrum Fourier Series Spectrum

  8. Example A=5 0

  9. Take home message

  10. Fourier transform Continuous Domain Discrete domain Complex Fourier series Inverse Fourier Transform

  11. RelationshipbetweenFourier series and transform

  12. Application of Fourier to Bioinformatics

  13. Binary Indicator Sequences Any three of the four indicator sequences completely characterize the full DNA character string. Indicator sequences can be analyzed to identify in the structure of a DNA string.

  14. Period-3 property PS of a protein coding region PS of a non-coding region

  15. Identify Protein-Coding Regions

  16. Resonant Recognition Model • The energy of delocalized electrons in amino acids produce the strongest impact on the electronic distribution of the whole protein because produce electromagnetic irradiation or absorption with spectral characteristics corresponding to energy distribution along the protein

  17. Repetita Permit to find periodicities hidden along the sequence.

  18. Repetita

  19. MSA with Fourier - MAFFT

  20. MSA with Fourier - MAFFT Homologous regions are quickly identified by converting amino acid residues to vectors of volume and polarity is If are the volume component of the nth site 

  21. Recursive Splicing

  22. Recursive Splicing Intron Exon Intron Exon Exon Pre-mRNA motifs RNA Binding protein

  23. Take home message Fourier transform and Fourier series have the same purpose: decompose a signal in sum of waves. It was possible: • Detect hidden signal (period-3 property) • Filtering noise (identify Protein-Coding Regions) • Detect periodicity (Repetita) • Detect common structure and sequence similarities (Resonant recognition model, MAFFT) • Denoising and reconstructing signals( Recursive splicing) • Reduce computational time ( MAFFT)

  24. Thank you

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