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.

Holographic ART approach for Simulation of protein flexibilityLilianne Dupuis1, Normand Mousseau2 (1) Département de biochimie, (2) Département de physique,

(1, 2) and Centre Robert-Cedergren, Université de Montréal, Montréal, Québec, Canada

QuickTime™ et undécompresseur TIFF (non compressé)

sont requis pour visionner cette image.

QuickTime™ et undécompresseur TIFF (non compressé)

sont requis pour visionner cette image.

QuickTime™ et undécompresseur TIFF (non compressé)

sont requis pour visionner cette image.

QuickTime™ et undécompresseur TIFF (non compressé)

sont requis pour visionner cette image.

QuickTime™ et undécompresseur TIFF (non compressé)

sont requis pour visionner cette image.

QuickTime™ et undécompresseur TIFF (non compressé)

sont requis pour visionner cette image.

QuickTime™ et undécompresseur TIFF (non compressé)

sont requis pour visionner cette image.

QuickTime™ et undécompresseur TIFF (non compressé)

sont requis pour visionner cette image.

3Secondary Structures Scale

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.

OPEP scale

ACKOWLEDGEMENTSNormand Mousseau and his groupPhilippe Derreumaux

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.

1

FUTUR WORKWe will test the method on protein A, EF-handWe will study the loop flexibility of HPPK enzymeIs the method able to detect sensitive parts of a protein?We will adapt the method for 2 proteins interaction (or more)

The OPEP force field gives us a coarse-grained 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

Optimal Potential for Efficient peptide-structure Prediction

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)..

When we evaluate a swiveling movement for a block, we compute the torque contribution of each OPEP atom.

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

All atoms OPEP atoms

€

faround_axis=v f ∧v r −(v r ⋅axis( )( )∑ v r ∑

2

TESTS AND RESULTSTo 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.

With multi-scaling, we need 10 to 60 events instead of 250 to 400 events.

Tests on a more distant conformation, protein A with 3 helices aligned, point out the need for a dynamic relocalization of block pivots. This is resolved by Holographic ART approach (above).

Relative peptidic planes position in conformation

Relative peptidic planes position in conformation

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.

HOLOGRAPHIC Blocks 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.

3 orthogonal axes are computed for each peptidic plane using CAs and Oxygen positions:

€

va 1=v r CA2−v r CA1v r CA2−v r CA1

€

va 2=v r Oxy−CA1−(v r Oxy−CA1⋅v a 1)v r Oxy−CA1−(v r Oxy−CA1⋅v a 1)

€

va 3=v a 1×v a 2v a 1×v a 2