Introduction to Computational Biology Navraj S' Pannu Leiden University and Raimond Ravelli LUMC htt

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Introduction to Computational BiologyNavraj S.
Pannu Leiden UniversityandRaimond
RavelliLUMChttp//www.bfsc.leidenuniv.nl/teachin
g/icb/
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Objectives of course

• Understand the role of crystallography and
  electron microscopy in structural biology.
• Introduce the steps involved in obtaining a
  macromolecular crystal structure.
• Main goal To understand a scientific publication
  describing a crystal structure.

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Why structural biology?Motivation structural
biology and drug design
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Understanding and treating E. coli infections
Shiga-like toxins

• Produced by a certain strain of E. coli
• Infection by this strain
• From uncooked meat or tainted milk
• Initial signs are diarrhea
• But, may progress to kidney disease

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Shiga-like toxin subunitsPrevious biochemical
knowledge

• Consists of
• An enzymatic A subunit
• Inhibit protein synthesis
• B-pentamer reponsible for receptor binding
• Responsible for binding to cells
• Binds to a glycolipid Gb3

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Structure of the B-subunit in complex with Gb3

• Structure revealed 15 sugar binding sites 3 per
  monomer
• Mutagenesis studies confirmed observation and
  that sites 2 and 3 were strongest.

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Building an inhibitor

• Binding of protein to carbohydrates is generally
  weak.
• In collaboration with organic chemists, try to
  build an inhibitor that engages 5 or 10 sites at
  once to create a sub-nanomolar inhibitor

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Bridge-starfish molecule

• Bridge-starfish molecule designed to engage 10
  sites on one B-subunit simultaneously

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Stoichiometry 21 !
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Brief recap of complex arithmetic
a bi r ei? Addition and subtraction in
orthogonal coordinates z1 z2 (a1a2)
(b1b2)i
exp(i?) cos(?) i sin(?)
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Diffraction and Imaging
?

• Fourier transforms are used in
• crystallography - image analysis
• (NMR) spectroscopy - electron microscopy
• optics light-microscopy

A highly recommended site on Fourier transforms
is found at http//www.ysbl.york.ac.uk/cowtan
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Graphical representation of the Fourier synthesis
A unit cell (or any other signal)
A real function is represented as the summation
of cosine functions
A low resolution component
A higher resolution component
And even higher resolution
Summation / Integration
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Interference in the Fourier transform of a
lattice
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Effect of removing high resolution information
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Effect of removing low resolution information and
sections
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Properties of Fourier transforms
convolution
conv
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Convolution illustrated
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The convolution theorem
g is the Fourier transform of G h is the
Fourier transform of H
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G(f)H(f) is the Fourier transform of ?-?
g(t)h(?-t)dt
conv
x
Fourier transform