1 / 32

Protein Conformation Prediction (Part I)

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

nguyet
Télécharger la présentation

Protein Conformation Prediction (Part I)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Doug Raiford Lesson 17 Protein Conformation Prediction (Part I)

  2. 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)

  3. 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)

  4. PDBs • Store these XYZ coordinates in text files • PDB website X Y Z Occu Temp Element ATOM 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 C Protein Conformation Prediction (Part I)

  5. 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)

  6. 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    R Protein Conformation Prediction (Part I)

  7. 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)

  8. Anatomy of a carbon atom • Tetrahedron Protein Conformation Prediction (Part I)

  9. Remember • Know distances • Each angle is 109.5 R  almost always 180    R Protein Conformation Prediction (Part I)

  10. The angles • 4 atoms on same plane • , , and ω all relative to R group (O in case of ω) Protein Conformation Prediction (Part I)

  11. 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)

  12. New vector space • To transform a vector space… X C Z Y B A Protein Conformation Prediction (Part I)

  13. New vector space • To transform a vector space… X C Z Y B New X axis New Z axis New Y axis A Protein Conformation Prediction (Part I)

  14. New vector space • It’s all about projections • If target vector is a unit vector then simple dot product A B Protein Conformation Prediction (Part I)

  15. 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 X C Z B Y A New X New Z New Y Protein Conformation Prediction (Part I)

  16. What is the new X? • The new X is BC (as a unit vector) X’ C Z’ Y’ B A Protein Conformation Prediction (Part I)

  17. 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] C B Origin Protein Conformation Prediction (Part I)

  18. And what is ||BC||? • Magnitude of BC X’ C Z’ Y’ B A Protein Conformation Prediction (Part I)

  19. New vector space • First row of transformation matrix X C Z B Y A New X Protein Conformation Prediction (Part I)

  20. Second Row • AB in plane of new Y • so Z component is zero X C Z B Y Important piece: Y component A Protein Conformation Prediction (Part I)

  21. New vector space • Second row of transformation matrix X C Z B Y A New Y Protein Conformation Prediction (Part I)

  22. New vector space • Third row of transformation matrix easy once have first two: Cross Product X C Z B Y A New Y Protein Conformation Prediction (Part I)

  23. 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 X D C Z Y B A Protein Conformation Prediction (Part I)

  24. Final torsional rotation Y • 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 xy 70.5° Z C X Dfinal Θ (torsional angle) C Dnewin plane of xy Y Protein Conformation Prediction (Part I)

  25. Going from xyz to angles • Transform next xyz into new vector space coordinates (same as before • Determine ||CD|| X D C Z Y B A Protein Conformation Prediction (Part I)

  26. 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)

  27. Example • BC? X Calculator 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 C unitV (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? C Z distance B to C: 1.527 B New X axis: [0.880 -0.410 -0.236] Y A Protein Conformation Prediction (Part I)

  28. Example Calculator A-C sto A B-C sto B C-C sto C B-Asto AB C-Bsto BC unitV 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 X C Z B Y A No change to X Protein Conformation Prediction (Part I)

  29. Example • New Y? X Calculator unitV(AB-(dot(AB,BC)/(norm BC)2 * BC)) Norm under “VECTR / MATH” C Z B Y A New Y axis: [0.440 0.894 0.088] Protein Conformation Prediction (Part I)

  30. Example Calculator unitV BC entersto X unitV(AB-(dot(AB,BC)/(norm BC)2 * BC))entersto Y cross(X,Y) Cross under “VECTR / MATH” • New Z? X C Z B Y A New Z axis: [0.174 -0.181 0.968] Protein Conformation Prediction (Part I)

  31. Two approaches • De novo • From first principles • Comparative/Homology Based • Sequence similarity Protein Conformation Prediction (Part I)

  32. Protein Conformation Prediction (Part I)

More Related