Biology Reference
In-Depth Information
The cubic grid representation is an essential element of the FFT correlation docking
algorithm published soon afterwards by Katchalski-Katzir et al. ( 1992 ) of the
Weizmann Institute in Israel. To start with, one picks an orientation of a protein rela-
tive to the other, and assigns appropriate weights to grid points of the surface and
the interior volume of the two molecules. The correlation between the two sets of
weights is used as a score. It may be written as a convolution product, and efficiently
computed for all translations at one time thanks to the Fast Fourier Transform (FFT)
algorithm. Then, the orientation is changed and the calculation repeated. The method
has been very successful, and it has benefited from many developments (Vakser and
A fl alo 1994 ; Gabb et al. 1997 ; Ritchie and Kemp 2000 ; Mandell et al. 2001 ; Heifetz
et al. 2002 ; Chen et al. 2003a ). Whereas the original formulation of the algorithm
assessed only the geometric complementarity, other molecular features can be
encoded as weights on a cubic grid; for instance, an electrostatic interaction energy
may be calculated by correlating the electric charges on one protein with the electric
field created by the other protein. Electrostatics, hydrophobicity, and a number of
other terms may be combined into a scoring function. Each of the Web sites listed
in Table 5.1 has its own scoring function, and its own way to calculate its terms as
FFT correlations.
5.3.3
Monte-Carlo and Related Docking Algorithms
Albeit “soft”, the FFT correlation and the geometric hashing algorithms explore
only the six degrees of freedom of rigid-body docking. Other algorithms devel-
oped afterwards handle other variable parameters, dihedral angles for instance, in
order to simulate side chain rotations and main chain conformation changes. They
take a heuristic approach to the problem, instead of performing an exhaustive
search. Monte-Carlo simulated annealing, the choice method in the 1990s, allowed
Totrov and Abagyan ( 1994 ) to adjust side chain conformations at the same time as
the docking search. These authors employed a detailed atomic model and a stan-
dard molecular mechanics force field, which was computationally very expensive.
Instead, all the later docking procedures based on simulated annealing or related
algorithms, proceed in two or more steps. The first step explores the rigid-body
parameter space with a simplified protein model and a coarse force field, the second
carries out a detailed refinement of the local minima (Fernández-Recio et al. 2002 ;
Zacharias 2003 ). The RosettaDock procedure (Gray et al. 2003 ) is a good exam-
ple: a first Monte-Carlo search is carried out on a low-resolution protein model
with residue-level potentials; it identifies many (a thousand or more) candidate
solutions, which are refined afterwards using a full-atom model and the Rosetta
force field. That force field, optimized on protein data, includes terms for desolva-
tion or rotamer preferences not present in standard force fields. It performs very
well in protein folding, its original application, and also in docking, at least
when the conformation changes are of limited amplitude (Schueler-Furman
et al. 2005 ) .
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