1. Doug Raiford Lesson 17

2.  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 11/8/20152Protein Conformation Prediction (Part I)

3.  Isolate protein and crystalize  Time consuming process  Slowly evaporate  Many experiments in parallel  Different conditions  X-ray crystallography  Get XYZ spatial coordinates 11/8/2015Protein Conformation Prediction (Part I)3

4.  Store these XYZ coordinates in text files  PDB website 11/8/2015Protein Conformation Prediction (Part I)4 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

5.  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 11/8/2015Protein Conformation Prediction (Part I)5

6.  Recall that proteins are able to fold because of the torsional rotation of the aa bonds 11/8/2015Protein Conformation Prediction (Part I)6     almost always 180 

7.  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 11/8/2015Protein Conformation Prediction (Part I)7

8.  Tetrahedron 11/8/2015Protein Conformation Prediction (Part I)8

9. 11/8/20159Protein Conformation Prediction (Part I)     almost always 180   Know distances  Each angle is 109.5

10. 11/8/201510Protein Conformation Prediction (Part I)  4 atoms on same plane  , , and ω all relative to R group (O in case of ω)

11.  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 11/8/201511Protein Conformation Prediction (Part I)

12.  To transform a vector space… 11/8/2015Protein Conformation Prediction (Part I)12 X Y Z A B C

13.  To transform a vector space… 11/8/2015Protein Conformation Prediction (Part I)13 X Y Z A B C New X axis New Y axis New Z axis

14.  It’s all about projections  If target vector is a unit vector then simple dot product 11/8/2015Protein Conformation Prediction (Part I)14 A B

15.  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 11/8/2015Protein Conformation Prediction (Part I)15 X Y Z A B C New X New Y New Z

16.  The new X is BC (as a unit vector) 11/8/2015Protein Conformation Prediction (Part I)16 X’ Y’ Z’ A B C

17.  Remember, all we have is the last xyz coordinates  All vectors are assumed to originate at the origin  So BC is actually [X C,Y C,Z C ]-[X B,Y B,Z B ] 11/8/2015Protein Conformation Prediction (Part I)17 B C Origin

18.  Magnitude of BC 11/8/2015Protein Conformation Prediction (Part I)18 X’ Y’ Z’ A B C

19.  First row of transformation matrix 11/8/2015Protein Conformation Prediction (Part I)19 X Y Z A B C New X

20.  AB in plane of new Y  so Z component is zero 11/8/2015Protein Conformation Prediction (Part I)20 X Y Z A B C Important piece: Y component

21.  Second row of transformation matrix 11/8/2015Protein Conformation Prediction (Part I)21 X Y Z A B C New Y

22.  Third row of transformation matrix easy once have first two: Cross Product 11/8/2015Protein Conformation Prediction (Part I)22 X Y Z A B C New Y

23.  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 11/8/2015Protein Conformation Prediction (Part I)23 X Y Z A B C D

24.  Z component is that distance times sinθ (torsion angle)  Y = ||CD|| sin(70.5°)*cos θ  Z = ||CD|| sin(70.5°)*sin θ 11/8/2015Protein Conformation Prediction (Part I)24 Z Y C D new in plane of xy Y C X D final Θ (torsional angle) 70.5°

25.  Transform next xyz into new vector space coordinates (same as before  Determine ||CD|| 11/8/2015Protein Conformation Prediction (Part I)25 X Y Z A B C D

26.  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. 11/8/2015Protein Conformation Prediction (Part I)26 AtomXYZ N2.863-15.219-0.703 CC 3.920-14.209-0.705 C5.265-14.836-1.065

27.  BC? 11/8/2015Protein Conformation Prediction (Part I)27 AtomXYZ A N2.863-15.219-0.703 B C  3.920-14.209-0.705 C C5.265-14.836-1.065 X Y Z A B C [X C,Y C,Z C ]-[X B,Y B,Z B ] [5.265 -14.836 -1.065]-[3.920 -14.209 -0.705] [1.345 -0.627 -0.36] Magnitude of BC? distance B to C: 1.527 New X axis: [0.880 -0.410 -0.236] 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” 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”

28.  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 11/8/2015Protein Conformation Prediction (Part I)28 X Y Z A B C No change to X Calculator A-C sto  A B-C sto  B C-C sto  C B-A sto  AB C-B sto  BC unitV BC (same answer) unitV under “VECTR / MATH” Calculator A-C sto  A B-C sto  B C-C sto  C B-A sto  AB C-B sto  BC unitV BC (same answer) unitV under “VECTR / MATH”

29.  New Y? 11/8/2015Protein Conformation Prediction (Part I)29 X Y Z A B C New Y axis: [0.440 0.894 0.088] Calculator unitV(AB-(dot(AB,BC)/(norm BC) 2 * BC)) Norm under “VECTR / MATH” Calculator unitV(AB-(dot(AB,BC)/(norm BC) 2 * BC)) Norm under “VECTR / MATH”

30.  New Z? 11/8/2015Protein Conformation Prediction (Part I)30 X Y Z A B C New Z axis: [0.174 -0.181 0.968] Calculator unitV BC enter sto  X unitV(AB-(dot(AB,BC)/(norm BC) 2 * BC)) enter sto  Y cross(X,Y) Cross under “VECTR / MATH” Calculator unitV BC enter sto  X unitV(AB-(dot(AB,BC)/(norm BC) 2 * BC)) enter sto  Y cross(X,Y) Cross under “VECTR / MATH”

31.  De novo  From first principles  Comparative/Homology Based  Sequence similarity Structure prediction methods De novo Homology modeling 11/8/201531Protein Conformation Prediction (Part I)

32. 11/8/201532Protein Conformation Prediction (Part I)