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Bioinformatics: Practical Application of Simulation and Data Mining Protein Folding I. Prof. Corey O’Hern Department of Mechanical Engineering Department of Physics Yale University. Statistical Mechanics. Protein Folding. Biochemistry. What are proteins?. Linear polymer. Folded state.

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bioinformatics practical application of simulation and data mining protein folding i
Bioinformatics: Practical Application of Simulation and Data MiningProtein Folding I
  • Prof. Corey O’Hern
  • Department of Mechanical Engineering
  • Department of Physics
  • Yale University
slide2

Statistical

Mechanics

Protein

Folding

Biochemistry

slide3

What are proteins?

Linear polymer

Folded state

  • Proteins are important; e.g. for catalyzing and regulating biochemical reactions,
  • transporting molecules, …
  • Linear polymer chain composed of tens (peptides) to thousands (proteins) of monomers
  • Monomers are 20 naturally occurring amino acids
  • Different proteins have different amino acid sequences
  • Structureless, extended unfolded state
  • Compact, ‘unique’ native folded state (with secondary and tertiary structure) required

for biological function

  • Sequence determines protein structure (or lack thereof)
  • Proteins unfold or denature with increasing temperature or chemical denaturants
slide4

Amino Acids I

N-terminal

C-terminal

C

peptide

bonds

R

variable

side chain

  • Side chains differentiate amino acid repeat units
  • Peptide bonds link residues into polypeptides
the protein folding problem
The Protein Folding Problem:

What is ‘unique’ folded 3D structure of a protein based on its amino acid

sequence? Sequence  Structure

Lys-Asn-Val-Arg-Ser-Lys-Val-Gly-Ser-Thr-Glu-Asn-Ile-Lys- His-Gln-Pro- Gly-Gly-Gly-…

slide7

Driving Forces

  • Folding: hydrophobicity, hydrogen bonding, van der

Waals interactions, …

  • Unfolding: increase in conformational entropy,

electric charge…

Hydrophobicity index

inside

H (hydrophobic)

outside

P (polar)

slide9

Secondary Structure: Loops, -helices, -strands/sheets

-helix

-strand

-sheet

  • Right-handed; three turns
  • Vertical hydrogen bonds between NH2 (teal/white)

backbone group and C=O (grey/red) backbone group

four residues earlier in sequence

  • Side chains (R) on outside; point upwards toward NH2
  • Each amino acid corresponds to 100, 1.5Å, 3.6

amino acids per turn

  • (,)=(-60,-45)
  • -helix propensities: Met, Ala, Leu, Glu
  • 5-10 residues; peptide backbones fully extended
  • NH (blue/white) of one strand hydrogen-bonded

to C=O (black/red) of another strand

  • C ,side chains (yellow) on adjacent strands

aligned; side chains along single strand alternate

up and down

  • (,)=(-135,-135)
  • -strand propensities: Val, Thr, Tyr, Trp,

Phe, Ile

slide11

Ramachandran Plot: Determining Steric Clashes

Gly

Non-Gly

Backbone

dihedral angles

theory

4 atoms define dihedral angle:

PDB

CCNC

=0,180

CN CC

N CCN

vdW radii

backbone

flexibility

< vdW radii

slide12

How can structures from PDB exist

outside Ramachadran bounds?

  • Studies were performed on alanine dipeptide
  • Fixed bond angle (=110) [105,115]

J. Mol. Biol. (1963) 7, 95-99

slide13

Side-Chain Dihedral Angles

4: Lys, Arg

5: Arg

Side chain: C-CH2-CH2-CH2-CH2-NH3

Use NCCCCCN to define 1, 2, 3,4

slide14

Your model is oversimplified

and has nothing to do with

biology!

Your model is too complicated

and has no predictive power!

Molecular biologist

Biological Physicist

slide15

Possible Strategies for Understanding Protein Folding

  • For all possible conformations, compute free energy

from atomic interactions within protein and protein-

solvent interactions; find conformation with lowest free

energy…e.g using all-atom molecular dynamics

simulations

Not possible?, limited time resolution

  • Use coarse-grained models with effective interactions

between residues and residues and solvent

General, but qualitative

slide16

Why do proteins fold (correctly & rapidly)??

Levinthal’s paradox:

For a protein with N amino acids, number of backbone conformations/minima

 = # allowed dihedral angles

How does a protein find the global optimum w/o

global search? Proteins fold much faster.

Nc~ 3200 ~1095

fold ~ Nc sample ~1083 s

fold ~ 10-6-10-3 s

vs

universe ~ 1017 s

slide17

Energy Landscape

U, F =U-TS

S12

S23

S-1

M2

M3

M1

minimum

all atomic

coordinates;

dihedral angles

saddle point

maximum

slide18

Roughness of Energy Landscape

smooth, funneled

rough

(Wolynes et. al. 1997)

slide19

Folding Pathways

dead

end

similarity to

native state

slide21

Open Questions

  • What differentiates the native state from other low-lying energy minima?
  • How many low-lying energy minima are there? Can we calculate

landscape roughness from sequence?

  • What determines whether protein will fold to the native state or become
  • trapped in another minimum?
  • What are the pathways in the energy landscape that a given protein

follows to its native state?

NP Hard Problem!

slide22

Digression---Number of Energy Minima for Sticky Spheres

Nm

Ns

Np

4

1

1

sphere

packings

1

5

6

6

2

50

7

5

486

8

13

5500

polymer

packings

9

52

49029

10

-

-

Ns~exp(aNm); Np~exp(bNm) with b>a

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