Protein Conformation Prediction (Part I)

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Doug Raiford Lesson 17. Protein Conformation Prediction (Part I). Two folding models. Framework model Secondary structure first Assemble secondary structure segments Hydrophobic collapse Molten : compact but denatured Formation of secondary structure after: settles in
Doug RaifordLesson 17Protein Conformation Prediction (Part I)Two folding models
  • Framework model
  • Secondary structure first
  • Assemble secondary structure segments
  • Hydrophobic collapse
  • Molten: compact but denatured
  • Formation of secondary structure after: settles in
  • van der Waals forces and hydrogen bonds require close proximity
  • Protein Conformation Prediction (Part I)Experimentally determining
  • Isolate protein and crystalize
  • Time consuming process
  • Slowly evaporate
  • Many experiments in parallel
  • Different conditions
  • X-ray crystallography
  • Get XYZ spatial coordinates
  • Protein Conformation Prediction (Part I)PDBs
  • Store these XYZ coordinates in text files
  • PDB website
  • X Y Z Occu Temp ElementATOM 1 N THR A 5 23.200 72.500 13.648 1.00 51.07 N ATOM 2 CA THR A 5 23.930 72.550 12.350 1.00 51.27 C ATOM 3 C THR A 5 23.034 72.048 11.220 1.00 50.34 C ATOM 4 O THR A 5 22.819 72.747 10.228 1.00 51.19 O ATOM 5 CB THR A 5 25.221 71.703 12.416 1.00 51.94 C ATOM 6 OG1 THR A 5 26.159 72.326 13.305 1.00 53.51 O ATOM 7 CG2 THR A 5 25.849 71.583 11.046 1.00 53.33 CProtein Conformation Prediction (Part I)Modeling
  • To fully model the folding action of a polypeptide chain
  • Must know all the forces acting on each aa
  • Must be able to predict the motion of the aa’s given the forces
  • Protein Conformation Prediction (Part I)How to aa’s move?
  • Recall that proteins are able to fold because of the torsional rotation of the aa bonds
  • R almost always 180RProtein Conformation Prediction (Part I)In order to model folding…
  • Must be able to take phi and psi angles and transform into xyz coordinates of various atoms
  • Don’t forget about R groups
  • What places in space are occupied?
  • Bump checking
  • Protein Conformation Prediction (Part I)Anatomy of a carbon atom
  • Tetrahedron
  • Protein Conformation Prediction (Part I)Remember
  • Know distances
  • Each angle is 109.5
  • R almost always 180RProtein Conformation Prediction (Part I)The angles
  • 4 atoms on same plane
  • , , and ω all relative to R group (O in case of ω)
  • Protein Conformation Prediction (Part I)Torsion angles to xyz
  • One approach
  • Given xyz of last three, and next torsion angle…
  • Transform so that C is at origin, BC on new X, AB on plane of new Y
  • Then apply torsion
  • Start D on X
  • Swing out 70.5 (180-109.5; in the plane of Y)
  • Rotate by torsion angle
  • Protein Conformation Prediction (Part I)New vector space
  • To transform a vector space…
  • XCZYBAProtein Conformation Prediction (Part I)New vector space
  • To transform a vector space…
  • XCZYBNew X axisNew Z axisNew Y axisAProtein Conformation Prediction (Part I)New vector space
  • It’s all about projections
  • If target vector is a unit vector then simple dot product
  • ABProtein Conformation Prediction (Part I)New vector space
  • Dot product of a row with vector yields the projection of the vector onto the vector represented by the row
  • All three dot products yields all three components
  • XCZBYANew XNew ZNew YProtein Conformation Prediction (Part I)What is the new X?
  • The new X is BC (as a unit vector)
  • X’CZ’Y’BAProtein Conformation Prediction (Part I)But what is BC?
  • Remember, all we have is the last xyz coordinates
  • All vectors are assumed to originate at the origin
  • So BC is actually [XC,YC,ZC]-[XB,YB,ZB]
  • CBOriginProtein Conformation Prediction (Part I)And what is ||BC||?
  • Magnitude of BC
  • X’CZ’Y’BAProtein Conformation Prediction (Part I)New vector space
  • First row of transformation matrix
  • XCZBYANew XProtein Conformation Prediction (Part I)Second Row
  • AB in plane of new Y
  • so Z component is zero
  • XCZBYImportant piece: Y componentAProtein Conformation Prediction (Part I)New vector space
  • Second row of transformation matrix
  • XCZBYANew YProtein Conformation Prediction (Part I)New vector space
  • Third row of transformation matrix easy once have first two: Cross Product
  • XCZBYANew YProtein Conformation Prediction (Part I)The next point: it’s all trig
  • Know distance to next atom
  • Know angle is 70.5° (180-109.5)
  • X component = ||CD|| cos(70.5°)
  • Y component starts out at ||CD|| sin(70.5°)
  • This is the distance from X to the new D
  • XDCZYBAProtein Conformation Prediction (Part I)Final torsional rotationY
  • Z component is that distance times sinθ(torsion angle)
  • Y = ||CD|| sin(70.5°)*cos θ
  • Z = ||CD|| sin(70.5°)*sin θ
  • Dnewin plane of xy70.5°ZCXDfinalΘ (torsional angle)CDnewin plane of xyYProtein Conformation Prediction (Part I)Going from xyz to angles
  • Transform next xyz into new vector space coordinates (same as before
  • Determine ||CD||
  • XDCZYBAProtein Conformation Prediction (Part I)An example
  • XYZ coordinates for an amino acid
  • Build the linear transform matrix used to transform the original vector space into the space defined by the three atoms above.
  • Protein Conformation Prediction (Part I)Example
  • BC?
  • XCalculator makes life easier:[2.863,-15.219,-0.703] sto A[3.920,-14.209,-0.705] sto B[5.265,-14.836,-1.065] sto CunitV (C-B)unitV under “VECTR / MATH”[XC,YC,ZC]-[XB,YB,ZB][5.265 -14.836 -1.065]-[3.920 -14.209 -0.705][1.345 -0.627 -0.36]Magnitude of BC?CZdistance B to C: 1.527BNew X axis:[0.880 -0.410 -0.236]YAProtein Conformation Prediction (Part I)ExampleCalculatorA-C sto AB-C sto BC-C sto CB-Asto ABC-Bsto BCunitV BC (same answer)unitV under “VECTR / MATH”
  • Actually forgot a step
  • Need to translate all three points
  • Move in direction of negative C
  • Will place C and origin and keep A and B relative to C
  • XCZBYANo change to XProtein Conformation Prediction (Part I)Example
  • New Y?
  • XCalculatorunitV(AB-(dot(AB,BC)/(norm BC)2 * BC))Norm under “VECTR / MATH”CZBYANew Y axis:[0.440 0.894 0.088]Protein Conformation Prediction (Part I)ExampleCalculatorunitV BC entersto XunitV(AB-(dot(AB,BC)/(norm BC)2 * BC))entersto Ycross(X,Y)Cross under “VECTR / MATH”
  • New Z?
  • XCZBYANew Z axis:[0.174 -0.181 0.968]Protein Conformation Prediction (Part I)Two approaches
  • De novo
  • From first principles
  • Comparative/Homology Based
  • Sequence similarity
  • Protein Conformation Prediction (Part I)Protein Conformation Prediction (Part I)
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