Holographic ART approach for Simulation of protein flexibility
1
Dupuis ,
2
Mousseau
Lilianne
Normand
(1) Département de biochimie, (2) Département de physique,
(1, 2) and Centre Robert-Cedergren, Université de Montréal, Montréal, Québec, Canada
ABSTRACT
We need to study protein flexibility for a better understanding of its function. Flexibility determines how a conformation changes when the protein enters in contact with a ligand for
enzymatic purposes or with other proteins during formation of complexes. In the protein organization, we can distinguish highly regular regions, or secondary structures, linked together by irregular loops.
In our approach, we compute secondary structure movement as elastic blocks. Complex movements are then reserved to the irregular parts. This allows us to avoid local changes when we travel in the
conformation space during the simulations. Secondary structures can easily be reevaluated on the fly between each event, allowing us to perform dynamical coarse graining. We use a real force field to
perform these moves, computing consensus block forces from atomic forces. Tests on a single set of pivots have established that the optimal pivot is not always near the border between the all-atom and
an elastic block or secondary structure. We get better results by performing a dynamic optimization of the pivot placement all along the simulation. This can be done by establishing a distinction between
coarse graining and ensemble move. In protein, a long-range move always implies a sensible change of the torsion angles  and  bordering one or several CA of the main chain. For each CA pivots in
the flexible areas, the entire protein part that is preceding it may swivel relatively to the entire protein part following it. We therefore reformulate the ART convergence method a holographic view of the
molecule forces for each free CA pivots viewpoint, enhancing the detection of the  and  angles modifications that serve the best interest of the whole molecule.
ART nouveau
(Activation Relaxation Technique) Computing
speed is one of our main goals. We use an activated method for the
simulation of conformation change events. ART is characterized by
its ability to seek for energetically favorable passages between
molecular conformations, each of them associated to a local
minima. It has been used with success for glasses and
proteins.(1,2). In this project, ART works with
positions and forces from several
representation levels.
1
OPEP scale
HOLOGRAPHIC Blocks
2
To ensure realistic swiveling of blocks, we
establish a distinction between block definition and long range moves. The
swiveling may around a CA of the flexible regions of the main chain, not always at
the block boundaries The entire protein part that is preceding a CA of the main
chain may rotate relatively to the entire protein part following it. We evaluate the
influence of those 2 parts on each other, by defining relative orthogonal basis from
the 2 peptidic planes bordering the CA. Because this may imply several
free CA pivots, we need an holographic evaluation of the protein
forces. That means multiple dichotomic force evaluations.
Secondary Structures Scale
Optimal Potential for Efficient peptide-structure Prediction
All atoms
OPEP atoms
The OPEP force field gives us a coarsegrained off-lattice representation. For each
amino acid, all the 5 atoms of the main
chain are represented. Each lateral chain
is approximated by a sphere, with specific
chemical properties. Water effect is implicit
in the force field.(3)
Inside this project, we use the
OPEP
representation
for
the
irregular region of the protein. We
also create our higher scale from
a reformulation of the OPEP atom
positions and forces
ACKOWLEDGEMENTS
Normand Mousseau and his group
Philippe Derreumaux
We have developed a higher scale
representation based on secondary
structures. They offer us a dynamic
coarse graining because we can
reevaluated
them
from
OPEP
positions
between
each
event
(passage though a transition state)..
We move each secondary structure as an elastic block using a
realistic force field. A secondary structure block may be moved
by translation, rotation, swiveling and with elasticity
When we evaluate a swiveling
f  r  (r  axis


movement for a block, we compute the f around_ axis 
r
torque contribution of each OPEP atom.
TESTS AND RESULTS

To test our high scale approach, we use
protein A, a 3 helix bundle. We work
near its native conformation, bending
the third helix. We observe that the third
helix move back successfully to its
native emplacement.
3
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3 orthogonal axes are computed for each peptidic
rCA 2  rCA1
plane using CAs and Oxygen positions:
a1 
rCA 2  rCA1
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Relative peptidic
planes position in
 conformation
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a2 
rOxyCA1  (rOxyCA1  a1 )
rOxyCA1  (rOxyCA1  a1 )
a3 
a1  a2
a1  a2
A long range motion implies swiveling of the main chain each sides of one or
several CA pivots, which may go from  to  conformation or vice-versa.



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Relative peptidic
planes position in
 conformation
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Tests on a more distant conformation,
With multi-scaling, protein A with 3 helices aligned, point
we need 10 to 60
out the need for a dynamic relocalization
events instead of 250 of block pivots. This is resolved by
to 400 events.
Holographic ART approach (above).
FUTUR WORK

We will test the method on protein A, EF-hand

We will study the loop flexibility of HPPK enzyme

Is the method able to detect sensitive parts of a protein?

We will adapt the method for 2 proteins interaction (or more)
REFERENCES 1) Barkema, G. and Mousseau, N., Event-based relaxation of continuous disordered systems, Phys. Rev. Lett. 1996, 77, 4358.
2) Malek, R. and Mousseau, N. Dynamics of Lennard-Jones clusters: A characterization of the activation-relaxation technique, Phys. Rev. 2000, E 62. 7723-7728.
3) Derreumaux, P. Generating ensemble averages for small proteins from extended conformations by Monte Carlo simulations. Phys. Rev.Lett. 2000, 85, 206-209.