FlexWeb

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FlexWeb
Nassim Sohaee
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Proteins

• The ability of proteins to change their
  conformation is important to their function as
  biological machines.

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Protein Structure

• Experimental methods cannot operate at the time
  scale necessary to record protein folding and
  motions.
• Traditional methods are just good for small
  peptide fragments.

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Protein Motion and Folding

• Understanding the folding process can give
  insight into how to develop better structure
  prediction algorithms.
• Some Diseases such as Alzheimers and Mad Cow
  disease are caused by misfolded proteins.
• Many biochemical process are regulated by protein
  switching from one shape to another shape.

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Classic Method

• Molecular Dynamic Simulation use energy function
  and solve Newtons equation of motions for the
  atoms in protein.
• Used in past 25 years.
• Computationally demanding (Many simulation
  steps.)
• Developing need to look at large proteins,
  protein complexes, viral capsids, etc.

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FIRST/FRODA

• The method is atom-led in the sense that the
  principal variables are the atomic positions
  rather than the dihedral angles.
• FIRST/FRODA is about 100 to 1000 times faster
  than previous methods, and treats all atoms
  equivalently, whether they are in rings or not,
  main-chain or side-chain.

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Review

• We consider a protein as a network in which all
  covalent bond lengths and angles are fixed
  (constrained), and the covalent double bonds are
  locked (constrained).
• Constraints are also assigned to hydrophobic
  interactions and hydrogen bonds, which are
  determined by using the local chemistry and
  geometry as input.

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Review

• Changes in the shape of the protein occur by
  changes in dihedral angles of rotatable bonds.
• Rigidity analysis, using the pebble game and
  FIRST, determines which dihedral angles are
  rotatable and which are locked.
• The rigidity of the three-dimensional folded
  protein is determined by the constraints
  introduced by hydrogen bonds and hydrophobic
  tethers (double bounds like CN are considered
  lock).

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Degree of Freedom

• Determining the rigidity of the protein is then a
  matter of balancing degrees of freedom against
  constraints.
• The pebble game is an algorithm for distributing
  the degrees of freedom belonging to the atoms
  (pebbles) over the bonds (constraints) so as to
  determine the rigidity.
• In FIRST/FRODA a protein is treated as a Body-Bar
  graph.

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Body-Bar Graph

• In the bodybar representation, rigid bodies,
  each having six degrees of freedom, define a set
  of vertices, and the set of generic bars that
  connect those bodies defines a network.

Example of Body-Bar graph.
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Body-Bar graph of Protein

• Each atomic site is a body with six degrees of
  freedom
• Hydrophobic tether reduce the degree of freedom
  by 2
• Single covalent bonds or Hydrogen bonds by 5
• Locked bonds (double, peptide) by 6

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Pebble Game
Rigid graph, check with Pebble game.
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FIRST

• The flexibility analysis performed by FIRST
  describes the rigidity of the protein based on a
  given set of hydrophobic and hydrogen bond
  constraint.
• Sections of protein that are not mutually rigid
  according to this analysis should be able to move
  relative to each other.

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Example of First
An example of a rigid cluster decomposition using
the pebble game in FIRST, showing the largest
rigid regions in solid colors (blue, green and
red).
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Not provided by FIRST

• flexibility and mobility are closely connected
  concepts, but not identical.
• The rigidity analysis does not determine the
  mobility or range of allowed motion that follows
  from the flexibility.

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FRODA

• Framework Rigidity Optimized Dynamic Algorithm
  is a form of geometric simulation which explores
  the allowed motion of the protein on the basis of
  rigidity analysis.
• In simulating the flexible motion of a protein,
  we constrain bond lengths and bond angles, while
  permitting some dihedral angles to vary.

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How FRODA works?

• A conformer of the protein must obey constraints
  on covalent bond length and angles, hydrogen-bond
  length and angles for those hydrogen bonds
  include in the rigidity analysis, and hydrophobic
  tether.
• FRODA finds new conformers by randomly displacing
  the atoms and then applying an interactive
  fitting process which enforce the constraints.

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WHATIF
By adding hydrogen atoms to the structure and
eliminated non-buried water molecules from the
structure, produce a structure suitable for
rigidity analysis and geometric simulation.
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In the result .pdb file remove the water
molecules.

• Add Protons to the Structure

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Upload the pdb file
Hydrogen bonds are identified with an energy
scale based on their geometry, with energies
ranging from 0 down to  - 10 (kcal/mol). A
user-defined energy cutoff determines which bonds
to include and which not, with the default being,
 - 1 (kcal/mol).
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Showing how the rigidity of the protein depends
on the cutoff, with a lower cutoff producing more
and smaller rigid clusters
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Results
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Plotting the mobility of each residue, showing
clearly that FRODA captures the main features of
the mobility of the protein, when compared with
the NMR data.
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