Biomedical Engineering Reference
In-Depth Information
protein design. RAAFF has borrowed much from classical molecular-
mechanics force-fields (MMFF)
35
but also contains important differences.
As in MMFFs, energies are computed as sums over interactions between a
relatively small set of different atom types, a Lennard-Jones potential describes
van der Waals interactions between atoms. Similar to the NMR hybrid force-
fields (see above), a stiffer representation of the covalent structure than in
MMFFs is chosen, bond lengths and angles are kept rigid, and side-chains are
tethered to one of the rotameric states.
36
Instead of modelling the hydrogen
bond by the Coulomb interaction of adjusted partial charges as in MMFFs,
the orientation dependence of the hydrogen bond arising from its partially
covalent character is treated explicitly.
Parameters are derived from experimental high-resolution structural data of
proteins by direct inversion of probability distributions of structural
parameters. This procedure can involve considerable double-counting of
interactions, which was resolved by subtracting ROSETTA-generated
distributions from their experimental counterparts in an iterative force-field
refinement procedure.
37
The resulting energy function, encoding the basic
physics of molecular interactions, is necessarily approximate. For example, the
explicit structure of solvent, long-range electrostatics, and residual dynamics in
the molecule have been ignored. Another striking omission is the massive
entropy change of the molecule upon attaining an ordered structure; one
assumes, to a first approximation, that the conformational entropies of
different well-packed protein conformations are similar. Despite these
omissions, RAAFF fares remarkably well in structure prediction and protein
design.
38-42
In the following, the individual energy terms in RAAFF are listed:
parameters for bond lengths, bond angles and atom radii are taken from
CHARMM. Attractive and repulsive forces are modelled with the popular
Lennard-Jones potential with its r
212
and r
26
terms, where r is the atomic
distance (fa_atr, fa_rep). The cost of desolvation of polar atoms and the
hydrophobic effect are approximated by the Lazaridis--Karplus solvation
model (fa_sol). Side-chain configurations are assigned to the closest rotameric
state and scored according to the backbone w/y-dependent probability of the
assigned rotameric state and a harmonic penalty for deviations from this
rotameric state (fa_dun).
36
The rama and p_aa_pp terms are two-dimensional
(w/y) energy-landscapes parameterised for every amino acid type. The omega
term tethers the omega backbone torsion angle to either 0 or 180u, respectively,
and the pro_close term improves the proline geometry. Hydrogen bond terms
are split into short- and long-range for intra-backbone bonds, and into side-
chain-side-chain or side-chain-backbone bonds (hbond_sr_bb, hbond_lr_bb,
hbond_sc, hbond_bb_sc). A small set of hydrogen-bond types parameterise the
h-bond energy via the geometry of the hydrogen acceptor and donor.
43
To
capture further interactions that are not explicitly accounted for yet, as for
example electrostatic effects, a pairwise term has been derived from PDB-
statistics (fa_pair).
