1. Disulfide Bonds
Two cyteines in close proximity will form a covalent bond
Disulfide bond, disulfide bridge, or dicysteine bond.
Significantly stabilizes tertiary structure.
Protein Folding

2. Determining Protein Structure
There are O(100,000) distinct proteins in the human proteome.
3D structures have been determined for 14,000 proteins, from all organisms
Includes duplicates with different ligands bound, etc.
Coordinates are determined by X-ray crystallography
Protein Folding

3. X-Ray Crystallography
~0.5mm
The crystal is a mosaic of millions of copies of the protein.
As much as 70% is solvent (water)!
May take months (and a “green” thumb) to grow.
Protein Folding

4. X-Ray diffraction Image is averaged over: Space (many copies)
Time (of the diffraction experiment)
Protein Folding

5. Electron Density Maps
Resolution is dependent on the quality/regularity of the crystal
R-factor is a measure of “leftover” electron density
Solvent fitting
Refinement
Protein Folding

6. The Protein Data Bank http://www.rcsb.org/pdb/
ATOM N ALA E APR 213
ATOM CA ALA E APR 214
ATOM C ALA E APR 215
ATOM O ALA E APR 216
ATOM CB ALA E APR 217
ATOM N GLY E APR 218
ATOM CA GLY E APR 219
ATOM C GLY E APR 220
ATOM O GLY E APR 221
ATOM N VAL E APR 222
ATOM CA VAL E APR 223
ATOM C VAL E APR 224
ATOM O VAL E APR 225
ATOM CB VAL E APR 226
ATOM CG1 VAL E APR 227
ATOM CG2 VAL E APR 228
Protein Folding

7. A Peek at Protein Function
Serine proteases – cleave other proteins
Catalytic Triad: ASP, HIS, SER
Protein Folding

8. Cleaving the peptide bond
Protein Folding

9. Three Serine Proteases
Chymotrypsin – Cleaves the peptide bond on the carboxyl side of aromatic (ring) residues: Trp, Phe, Tyr; and large hydrophobic residues: Met.
Trypsin – Cleaves after Lys (K) or Arg (R)
Positive charge
Elastase – Cleaves after small residues: Gly, Ala, Ser, Cys
Protein Folding

10. Specificity Binding Pocket
Protein Folding

11. The Protein Folding Problem
Central question of molecular biology: “Given a particular sequence of amino acid residues (primary structure), what will the tertiary/quaternary structure of the resulting protein be?”
Input: AAVIKYGCAL… Output: 11, 22… = backbone conformation: (no side chains yet)
Protein Folding

12. Protein Folding – Biological perspective
“Central dogma”: Sequence specifies structure
Denature – to “unfold” a protein back to random coil configuration
-mercaptoethanol – breaks disulfide bonds
Urea or guanidine hydrochloride – denaturant
Also heat or pH
Anfinsen’s experiments
Denatured ribonuclease
Spontaneously regained enzymatic activity
Evidence that it re-folded to native conformation
Protein Folding

13. Folding intermediates
Levinthal’s paradox – Consider a 100 residue protein. If each residue can take only 3 positions, there are 3100 = 5  1047 possible conformations.
If it takes 10-13s to convert from 1 structure to another, exhaustive search would take 1.6  1027 years!
Folding must proceed by progressive stabilization of intermediates
Molten globules – most secondary structure formed, but much less compact than “native” conformation.
Protein Folding

14. Forces driving protein folding
It is believed that hydrophobic collapse is a key driving force for protein folding
Hydrophobic core
Polar surface interacting with solvent
Minimum volume (no cavities)
Disulfide bond formation stabilizes
Hydrogen bonds
Polar and electrostatic interactions
Protein Folding

15. Folding help Proteins are, in fact, only marginally stable
Native state is typically only 5 to 10 kcal/mole more stable than the unfolded form
Many proteins help in folding
Protein disulfide isomerase – catalyzes shuffling of disulfide bonds
Chaperones – break up aggregates and (in theory) unfold misfolded proteins
Protein Folding

16. The Hydrophobic Core
Hemoglobin A is the protein in red blood cells (erythrocytes) responsible for binding oxygen.
The mutation E6V in the  chain places a hydrophobic Val on the surface of hemoglobin
The resulting “sticky patch” causes hemoglobin S to agglutinate (stick together) and form fibers which deform the red blood cell and do not carry oxygen efficiently
Sickle cell anemia was the first identified molecular disease
Protein Folding

17. Sickle Cell Anemia
Sequestering hydrophobic residues in the protein core protects proteins from hydrophobic agglutination.
Protein Folding

18. Computational Problems in Protein Folding
Two key questions:
Evaluation – how can we tell a correctly-folded protein from an incorrectly folded protein?
H-bonds, electrostatics, hydrophobic effect, etc.
Derive a function, see how well it does on “real” proteins
Optimization – once we get an evaluation function, can we optimize it?
Simulated annealing/monte carlo EC
Heuristics
We’ll talk more about these methods later…
Protein Folding

19. Fold Optimization Simple lattice models (HP-models)
Two types of residues: hydrophobic and polar
2-D or 3-D lattice
The only force is hydrophobic collapse
Score = number of HH contacts
Protein Folding

20. Scoring Lattice Models
H/P model scoring: count noncovalent hydrophobic interactions.
Sometimes:
Penalize for buried polar or surface hydrophobic residues
Protein Folding

21. What can we do with lattice models?
For smaller polypeptides, exhaustive search can be used
Looking at the “best” fold, even in such a simple model, can teach us interesting things about the protein folding process
For larger chains, other optimization and search methods must be used
Greedy, branch and bound
Evolutionary computing, simulated annealing
Graph theoretical methods
Protein Folding

22. Learning from Lattice Models
The “hydrophobic zipper” effect:
Ken Dill ~ 1997
Protein Folding

23. Representing a lattice model
Absolute directions
UURRDLDRRU
Relative directions
LFRFRRLLFFL
Advantage, we can’t have UD or RL in absolute
Only three directions: LRF
What about bumps? LFRRR
Bad score
Use a better representation
Protein Folding

24. Preference-order representation
Each position has two “preferences”
If it can’t have either of the two, it will take the “least favorite” path if possible
Example: {LR},{FL},{RL}, {FR},{RL},{RL},{FR},{RF}
Can still cause bumps: {LF},{FR},{RL},{FL}, {RL},{FL},{RF},{RL}, {FL}
Protein Folding

25. “Decoding” the representation
The optimizer works on the representation, but to score, we have to “decode” into a structure that lets us check for bumps and score.
Example: How many bumps in: URDDLLDRURU?
We can do it on graph paper
Start at 0,0
Fill in the graph
In PERL we use a two-dimensional array
Protein Folding

26. A two-dimensional array in PERL
$configuration = “URDDLLDRURU”;
$sequence = “HPPHHPHPHHH”;
foreach $i (1..100) {
foreach $j (1..100) {
$grid[$i][$j] = “empty”; }
$x = 0;
$y = 0;
@moves = split(//,$configuration);
@residues = split(//,$sequence);
Protein Folding

27. Setting up the grid foreach $move (@moves) {
$residue =
if ($move = “U”) {
$y_position++; }
if ($move = “R”) {
$x_position++;
etc…
if ($grid[$x][$y] ne “empty”) {
BUMP!
} else {
$grid[$x][$y] = $residue;
Protein Folding

28. More realistic models Higher resolution lattices (45° lattice, etc.)
Off-lattice models
Local moves
Optimization/search methods and / representations
Greedy search
Branch and bound
EC, Monte Carlo, simulated annealing, etc.
Protein Folding

29. The Other Half of the Picture
Now that we have a more realistic off-lattice model, we need a better energy function to evaluate a conformation (fold).
Theoretical force field:
G = Gvan der Waals + Gh-bonds + Gsolvent + Gcoulomb
Empirical force fields
Start with a database
Look at neighboring residues – similar to known protein folds?
Protein Folding

30. Threading: Fold recognition
Given:
Sequence: IVACIVSTEYDVMKAAR…
A database of molecular coordinates
Map the sequence onto each fold
Evaluate
Objective 1: improve scoring function
Objective 2: folding
Protein Folding

31. Secondary Structure Prediction
AGVGTVPMTAYGNDIQYYGQVT…
A-VGIVPM-AYGQDIQY-GQVT…
AG-GIIP--AYGNELQ--GQVT…
AGVCTVPMTA---ELQYYG--T…
AGVGTVPMTAYGNDIQYYGQVT…
----hhhHHHHHHhhh--eeEE…
Protein Folding

32. Secondary Structure Prediction
Easier than folding
Current algorithms can prediction secondary structure with 70-80% accuracy
Chou, P.Y. & Fasman, G.D. (1974). Biochemistry, 13,
Based on frequencies of occurrence of residues in helices and sheets
PhD – Neural network based
Uses a multiple sequence alignment
Rost & Sander, Proteins, 1994 , 19, 55-72
Protein Folding

33. Chou-Fasman Parameters
Protein Folding

34. Chou-Fasman Algorithm
Identify -helices
4 out of 6 contiguous amino acids that have P(a) > 100
Extend the region until 4 amino acids with P(a) < 100 found
Compute P(a) and P(b); If the region is >5 residues and P(a) > P(b) identify as a helix
Repeat for -sheets [use P(b)]
If an  and a  region overlap, the overlapping region is predicted according to P(a) and P(b)
Protein Folding

35. Chou-Fasman, cont’d Identify hairpin turns: Accuracy  60-65%
P(t) = f(i) of the residue  f(i+1) of the next residue  f(i+2) of the following residue  f(i+3) of the residue at position (i+3)
Predict a hairpin turn starting at positions where:
P(t) >
The average P(turn) for the four residues > 100
P(a) < P(turn) > P(b) for the four residues
Accuracy  60-65%
Protein Folding

36. Chou-Fasman Example CAENKLDHVRGPTCILFMTWYNDGP
CAENKL – Potential helix (!C and !N)
Residues with P(a) < 100: RNCGPSTY
Extend: When we reach RGPT, we must stop
CAENKLDHV: P(a) = 972, P(b) = 843
Declare alpha helix
Identifying a hairpin turn
VRGP: P(t) =
Average P(turn) =
Avg P(a) = 79.5, Avg P(b) = 98.25
Protein Folding