Protein loops are often involved in important
biological functions such as
molecular recognition, signal transduction,
or enzymatic action. The
three dimensional structures of loops
can provide essential information for
understanding molecular mechanisms
behind protein functions. In this article,
we develop a novel method for
protein loop modeling, where the loop
conformations are generated by fragment
assembly and analytical loop closure.
The fragment assembly method
reduces the conformational space drastically,
and the analytical loop closure
method finds the geometrically consistent
loop conformations efficiently.
We also derive an analytic formula for
the gradient of any analytical function
of dihedral angles in the space of
closed loops. The gradient can be used
to optimize various restraints derived
from experiments or databases, for
example restraints for preferential
interactions between specific residues
or for preferred backbone angles. We
demonstrate that the current loop
modeling method outperforms previous
methods that employ residuebased
torsion angle maps or different
loop closure strategies when tested on
two sets of loop targets of lengths
ranging from 4 to 12.