Doug RaifordLesson 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

04/21/23 2Protein Conformation Prediction (Part I)

Isolate protein and crystalize Time consuming process Slowly evaporate Many experiments in parallel Different conditions

X-ray crystallographyGet XYZ spatial coordinates

04/21/23 Protein Conformation Prediction (Part I) 3

Store these XYZ coordinates in text files

PDB website

04/21/23 Protein Conformation Prediction (Part I) 4

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 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

04/21/23 Protein Conformation Prediction (Part I) 5

Recall that proteins are able to fold because of the torsional rotation of the aa bonds

04/21/23 Protein 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 groupsWhat places in space are occupied?

Bump checking

04/21/23 Protein Conformation Prediction (Part I) 7

Tetrahedron

04/21/23 Protein Conformation Prediction (Part I) 8

04/21/23 9Protein Conformation Prediction (Part I)

almost always 180

Know distancesEach angle is 109.5

04/21/23 10Protein 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

(180-109.5; in the plane of Y)

Rotate by torsion angle04/21/23 11Protein Conformation Prediction (Part I)

To transform a vector space…

04/21/23 Protein Conformation Prediction (Part I) 12

X

Y

Z

A

B

C

To transform a vector space…

04/21/23 Protein Conformation Prediction (Part I) 13

X

Y

Z

A

B

C

New X axisNew Y axis

New Z axis

It’s all about projections If target vector is a unit vector then

simple dot product

04/21/23 Protein 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

04/21/23 Protein Conformation Prediction (Part I) 15

X

Y

Z

A

B

C

New XNew Y

New Z

The new X is BC (as a unit vector)

04/21/23 Protein 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 [XC,YC,ZC]-[XB,YB,ZB]

04/21/23 Protein Conformation Prediction (Part I) 17

B

C

Origin

Magnitude of BC

04/21/23 Protein Conformation Prediction (Part I) 18

X’

Y’

Z’

A

B

C

First row of transformation matrix

04/21/23 Protein Conformation Prediction (Part I) 19

X

Y

Z

A

B

C

New X

AB in plane of new Y so Z component is zero

04/21/23 Protein Conformation Prediction (Part I) 20

X

Y

Z

A

B

C

Important piece: Y component

Second row of transformation matrix

04/21/23 Protein 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

04/21/23 Protein Conformation Prediction (Part I) 22

X

Y

Z

A

B

C

New Y

Know distance to next atomKnow 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

04/21/23 Protein 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

04/21/23 Protein Conformation Prediction (Part I) 24

Z

Y

C

Dnew in plane of xy

YC Dnew in

plane of xy

X

Dfinal

Θ (torsional angle)

70.5°

Transform next xyz into new vector space coordinates (same as before

Determine ||CD||

04/21/23 Protein 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.

04/21/23 Protein Conformation Prediction (Part I) 26

Atom X Y ZN 2.863 -15.219 -0.703C 3.920 -14.209 -0.705C 5.265 -14.836 -1.065

BC?

04/21/23 Protein Conformation Prediction (Part I) 27

Atom X Y Z A N 2.863 -15.219 -0.703 B C 3.920 -14.209 -0.705 C C 5.265 -14.836 -1.065

X

Y

Z

A

B

C

[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?

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 CunitV (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 CunitV (C-B)

unitV under “VECTR / MATH”

Actually forgot a stepNeed to translate all three pointsMove in direction of negative CWill place C and origin and

keep A and B relative to C

04/21/23 Protein Conformation Prediction (Part I) 28

X

Y

Z

A

B

C

No change to X

CalculatorA-C sto AB-C sto BC-C sto CB-A sto ABC-B sto BC

unitV BC (same answer)

unitV under “VECTR / MATH”

CalculatorA-C sto AB-C sto BC-C sto CB-A sto ABC-B sto BC

unitV BC (same answer)

unitV under “VECTR / MATH”

New Y?

04/21/23 Protein 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”

New Z?

04/21/23 Protein Conformation Prediction (Part I) 30

X

Y

Z

A

B

C

New Z axis:[0.174 -0.181 0.968]

CalculatorunitV BC enter sto XunitV(AB-(dot(AB,BC)/(norm BC)2 * BC)) enter sto Ycross(X,Y)

Cross under “VECTR / MATH”

CalculatorunitV BC enter sto XunitV(AB-(dot(AB,BC)/(norm BC)2 * BC)) enter sto Ycross(X,Y)

Cross under “VECTR / MATH”

De novo From first principles

Comparative/Homology Based Sequence similarity

04/21/23 31Protein Conformation Prediction (Part I)

04/21/23 32Protein Conformation Prediction (Part I)