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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 Folding1. Understanding the folding process can

give insight into how to develop better structure prediction algorithms.

2. Some Diseases such as Alzheimer’s and Mad Cow disease are caused by misfolded proteins.

3. 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 Newton’s 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 C=N 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 body–bar 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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•Add Protons to the Structure

In the result .pdb file remove the water molecules.

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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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