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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What are proteins?
for biological function
Amino Acids I
Amino Acids II
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-…
Waals interactions, …
Secondary Structure: Loops, -helices, -strands/sheets
backbone group and C=O (grey/red) backbone group
four residues earlier in sequence
amino acids per turn
to C=O (black/red) of another strand
aligned; side chains along single strand alternate
up and down
Backbonde Dihedral Angles
Ramachandran Plot: Determining Steric Clashes
4 atoms define dihedral angle:
< vdW radii
How can structures from PDB exist
outside Ramachadran bounds?
J. Mol. Biol. (1963) 7, 95-99
Side-Chain Dihedral Angles
4: Lys, Arg
Side chain: C-CH2-CH2-CH2-CH2-NH3
Use NCCCCCN to define 1, 2, 3,4
Your model is oversimplified
and has nothing to do with
Your model is too complicated
and has no predictive power!
Possible Strategies for Understanding Protein Folding
from atomic interactions within protein and protein-
solvent interactions; find conformation with lowest free
energy…e.g using all-atom molecular dynamics
Not possible?, limited time resolution
between residues and residues and solvent
General, but qualitative
Why do proteins fold (correctly & rapidly)??
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
universe ~ 1017 s
U, F =U-TS
Roughness of Energy Landscape
(Wolynes et. al. 1997)
Folding Phase Diagram
landscape roughness from sequence?
follows to its native state?
NP Hard Problem!
Digression---Number of Energy Minima for Sticky Spheres
Ns~exp(aNm); Np~exp(bNm) with b>a