Protein folding Simplified models

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Protein folding Simplified models

• Charlotte Deane

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The protein folding problem
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Protein Folding

• Levinthals paradox
• If for each residue there are only two degrees of
  freedom (?,?).
• Assume each can have only 3 stable values.
• This leads to 32n possible conformations.
• If a protein can explore 1013 conformation per
  second. (10 per picosecond).
• Still requires an astronomical amount of time to
  fold a protein.
• This is impossible. So protein must fold in a
  way that does not randomly explore each possible
  conformations.

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The energy landscape

• Many intermediates that lead to the same fold -
  energy well

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Forces acting on Proteins

• Hydrogen Bonding
• Van der Waals interactions
• Ion pairing
• Disulfide bonds
• Intrinsic properties
• (conformational preference)
• Hydrophobic Effect the dominant
• force in protein folding (Dill, 1990)

Hydro (water) philic (loving) phobic (fearing)
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The Hydrophobic Effect
Each molecule of water in the solid state is
engaged in 4.0 hydrogen bonds. (accepting two and
donating two) Each molecule of water in the
liquid state is engaged in approximately 3.0 -
3.5 hydrogen bonds. What happens when a
hydrophobic molecule is added to the water?
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The Hydrophobic Effect
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The Hydrophobic Effect
In the example of n-butane in water at 25c the
equation breaks down as follows ?G ?H - T?S
24.5kJ/mol ?H -4.3kJ/mol -T?S
28.7kJ/mol It is actually enthalpically
favorable to place n-butane in water, but it is
very unfavorable from an entropic
perspective. Water forms, on average, more
hydrogen bonds but also must become more
organized.
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The Hydrophobic Effect
Based on the above, what causes the hydrophobic
effect (the apparent attraction between two or
more hydrophobic molecules)?
This is not an intermolecular force, but rather
the effect of the important and peculiar solvent,
water.
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Reduced models

• Proteins
• Multiple complex energy terms
• Many degrees of freedom
• Purpose
• Lowering degrees of freedom
• Use
• Investigate general protein structure folding
• Protein structure prediction

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Example HP lattice models

• 2 monomer types
• hydrophobic (H), hydrophilic (P).
• Two residues are said to be in contact if they
  are adjacent in space but not in sequence
• H H contact -1
• All other contacts are 0

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HP models

• Used as simple systems to demonstrate protein
  behaviour
• Commonly used to describe properties of protein
  folding
• Shown to have protein secondary structure
• In particular HP sequences of length 16 or 24

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Lattice Energy

• Red hydrophobic, Blue hydrophilic
• If Red is near another Red E E-1
• If Blue is near another Blue E E0
• If Blue is near Red E E0

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A Simple 2D Lattice
3.5Å
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Lattice Folding
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Example

• H-P-P-P-P-H-P-P-P-H-P-H-P-P-H-H
• On a 2d square lattice
• Find some minimal energy conformations
• Try for a global minimum

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H-P-P-P-P-H-P-P-P-H-P-H-P-P-H-H
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Another example

• H-P-H-P-P-H-H-P-P-H-P-P-H-P-H-H

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H-P-H-P-P-H-H-P-P-H-P-P-H-P-H-H
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Place the H or P monomers on a lattice

• 2D
• Square lattice
• Triangular lattice
• 3D
• Square lattice
• Triangular lattice
• Face-Centered-Cubic lattice

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3D Lattices
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Complex 3D lattices
Simple lattices made give idea about how proteins
fold More complex lattices are needed for
Simulation of an individual protein
fold Protein structure prediction
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Reduced models Protein structure prediction

• Discriminating the space of possible conformation
  for optimization
• Necessary to predict folding in large proteins
• Use multiple levels of resolution
• Use statistical information from PDB
• Mixing some different models to satisfy both
  accuracy and time saving

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Tasser Protein structure prediction
Schematic representation of a piece of
polypeptide chain on and off-lattice Each
residue is described by its C and sidechain
center of mass (SG). Whereas C values (white)
of unaligned residues are confined to the
underlying cubic lattice system C values
(yellow) of aligned residues are excised from
templates and traced off-lattice. SG values
(red) are always off-lattice and determined by
using a two-rotamer approximation
Proc. Natl. Acad. Sci. USA 2004 101 7594-7599
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Lattice Methods
Advantages
Disadvantages

• Easiest and quickest way to build a polypeptide
• Implicitly includes excluded volume
• More complex lattices allow reasonably accurate
  representation
• You can use MC (Monte Carlo method) to simulate
  ensemble averaging.

• At best, only an approximation to the real thing
• Does not allow accurate constructs
• Complex lattices are as costly as the real
  thing
• Oversimplified model can not give valuable
  results.
• The size of lattice can limit use in some models
• Conformational search is NP complete problem

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Summary

• Protein folding is a minimization of Gibbs free
  energy that is marginally stable.
• There is a spectrum of models varying in accuracy
  and time/money.
• Oversimplified model such as simple lattice to
• sophisticated model such as all atom model
• Lattice models
• Simple models for principles in protein folding
• Complex models can be used in protein structure
  prediction

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Co-translational folding

• Charlotte Deane

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Ribosome

• Proteins are manufactured in the ribosome
• Folding rates gt translation rates
• Protein folds as it comes off the ribosome

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Do we know co-translational folding happens?

• Many Biological Examples
• Semliki forest virus capsid protein becomes
  biologically active before full length
  polypeptide is produced
• Folding space is restricted by the ribosome

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Co-translational folding
C
Have k residues extruded from the ribosome Fold
but do not go over energy barriers gt d Extrude
up to s more monomers Repeat Until k n Is
this conformation different than starting
from all n residues out and folding?
N
C
N
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Energy Profile
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HP lattice models - again

• 2 monomer types
• hydrophobic (H), hydrophilic (P).
• Two residues are said to be in contact if they
  are adjacent in space but not in sequence
• H H contact -1
• All other contacts are 0

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Example

• H-P-P-P-P-H-P-P-P-H-P-H-P-P-H-H
• On a 2d square lattice
• Find some minimal energy conformations
• Sequential minimum
• Cant go over energy barriers greater than 0

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H-P-P-P-P-H-P-P-P-H-P-H-P-P-H-H
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Another example

• H-P-H-P-P-H-H-P-P-H-P-P-H-P-H-H

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H-P-H-P-P-H-H-P-P-H-P-P-H-P-H-H