


A Parameterized Algorithm for Protein Structure Alignment.


Jinbo Xu, Feng Jiao and Bonnie Berger.




This paper proposes a parameterized algorithm for aligning two protein
structures, in the case where one protein structure is represented by a
contact map graph and the other by a contact map graph or a distance
matrix. If the sequential order of alignment is not required,
the time complexity is polynomial in the protein size and exponential
with respect to two parameters $\frac{D_u}{D_l}$ and $\frac{D_c}{D_l}$,
which usually can be treated as constants.
In particular, $D_u$ is the distance threshold determining if two
residues are in contact or not, $D_c$ is the maximally allowed distance
between two matched residues after two proteins are superimposed, and
$D_l$ is the minimum interresidue distance in a typical protein.
This result indicates that if both $\frac{D_u}{D_l}$ and
$\frac{D_c}{D_l}$ are small enough, then there is a polynomialtime
approximation scheme for the nonsequential protein structure alignment
problem. Empirically, both $\frac{D_u}{D_l}$ and $\frac{D_c}{D_l}$ are
very small and can be treated as constants. This result clearly
demonstrates that the hardness of the contactmap based protein
structure alignment problem is related not to protein size but to
several parameters, which depend on how the protein structure alignment
problem is modeled. The result is achieved by decomposing the protein
structure using tree decomposition and discretizing the rigidbody
transformation space. We have implemented our algorithm and preliminary
experimental results indicate that on a Linux PC, it takes from ten
minutes to one hour to align two proteins with approximately 100 residues.





