Doug Raiford Lesson 17

 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)

 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

 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 N ATOM 2 CA THR A C ATOM 3 C THR A C ATOM 4 O THR A O ATOM 5 CB THR A C ATOM 6 OG1 THR A O ATOM 7 CG2 THR A C

 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

 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 

 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

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

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

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

 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  ( ; in the plane of Y)  Rotate by torsion angle 11/8/201511Protein Conformation Prediction (Part I)

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

 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

 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

 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

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

 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

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

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

 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

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

 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

 Know distance to next atom  Know angle is 70.5° ( )  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

 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°

 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

 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 N CC C

 BC? 11/8/2015Protein Conformation Prediction (Part I)27 AtomXYZ A N B C  C C X Y Z A B C [X C,Y C,Z C ]-[X B,Y B,Z B ] [ ]-[ ] [ ] Magnitude of BC? distance B to C: New X axis: [ ] Calculator makes life easier: [2.863, ,-0.703] sto  A [3.920, ,-0.705] sto  B [5.265, ,-1.065] sto  C unitV (C-B) unitV under “VECTR / MATH” Calculator makes life easier: [2.863, ,-0.703] sto  A [3.920, ,-0.705] sto  B [5.265, ,-1.065] sto  C unitV (C-B) 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 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”

 New Y? 11/8/2015Protein Conformation Prediction (Part I)29 X Y Z A B C New Y axis: [ ] 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”

 New Z? 11/8/2015Protein Conformation Prediction (Part I)30 X Y Z A B C New Z axis: [ ] 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”

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

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