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Molecular Dynamics simulation of 16-polyalanine in internal coordinates

Prof. Dr. G. Kneller, Centre de Biophysique Moleculaire, F-45071 Orleans

Here three Molecular Dynamics simulations of the polypeptide 16-polyalanine are shown. This molecule is just a model system consisting of 16 alanine aminoacids which folds into an alpha-helix. The goal of the simulations is to show the influence of geometrical constraints on the dynamics of polypeptide chains. We use a new approach for MD simulations of macromolecules where the molecule is considered as a chain of topologically linked rigid bodies. Two rigid bodies can be connected in common point or a common axis. A rigid body can have three moments of inertia or two, in case of a linear rigid body. The orientations of the rigid units are described by quaternions which are generalizations of complex numbers. This approach is well established in robot mechanics and has also been applied in MD simulations of molecular liquids consisting of completely rigid molecules. .

Reference simulation using only bond constraints ("SHAKE") (FileTypequicktime, 37 MB)

3.a) This is reference simulation using the well established SHAKE algorithm which works in Cartesian coordinates and serves to keep bond lengths fixed. This type of constraint is known not to influcence the essential dynamics of macromolecules. In principle the LRB-algorithm could do the same as SHAKE, but is not as efficient for this special purpose.

Frozen bonds and rigid peptide planes

(150 degrees of freedom) (FileTypequicktime, 37 MB)

3.b) Here the LRB-approach is used to keep all bonds and the peptide planes rigid. The peptide planes are planar structures in the backbone of proteins and peptides which can be well approximated as rigid planes. This type of constraint cannot be handled by existing methods. The forces are the same as in 3.a) where the computation of a subset of internal forces can be skipped due the rigidity of the peptide planes. The characteristics of the motion is still simular to the case 3.a), altough the amplitudes are somewhat larger. The rigid peptide planes force the molecule to perform stronger local motions to avoid 'bad contacts' between atoms. To avoid this the force field should have been reparametrized for the LRB model.

Simulation in (phi,psi)-angles

(38 degrees of freedom) (FileTypequicktime, 37 MB)

3.c) Here the peptide planes are kept rigid and also the tetrahedral binding geometry of the c-alpha-atoms which link the peptide planes. Now we are left with two rotational degrees of freedom per amino acid which are usually named phi and psi. It was often argued that these degrees of fredom would be sufficient to describe the essential dynamics of proteins and peptides. It is clearly seen from the video that this is not the case. Freezing the binding geometry of the c-alpha-atoms leeds effectively to an unwanted rigidification of the polypeptide. This has also been observed by some authors, with the comclusion that angles should not be frozen. As we see from 3.b) this is not true either. It matters which angles are frozen.

The movies were generated with molscript and raster3d.