November 21, 2005: Seminar: ''A Parameterized Algorithm for Protein Structure Alignment''

Abstract:

I will present 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 several parameters, which usually can be treated as constants. In particular, to obtain an alignment with score at least $(1-\frac{1}{k})$ times optimal, the running time of the parameterized algorithm is $O(k^2poly(n)2^{tw\lg{\Delta}}/(\epsilon D_c)^6)$ where $poly(n)$ is a polynomial in the protein size $n$, $tw=O(k^2\frac {\max\{2D_c,D_u\}^3}{D_l^3})$, $\Delta=(1+\frac{2D_c} {D_l})^3$, $\epsilon$ is a small positive number, $D_u$ 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 inter-residue 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 polynomial-time approximation scheme for the non-sequential 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.

The same algorithm can also be used for the structure alignment in the case where the sequential order of alignment is enforced, although we do not have such a good time complexity. This result clearly demonstrates that the hardness of the contact-map 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 rigid-body transformation space. We have implemented our algorithm and the 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.

This is a joint work with Feng Jiao (Waterloo) and Bonnie Berger (MIT).

About the speaker:
Jinbo Xu received his Ph.D. from the University of Waterloo late in 2003. He spent one year following as a research assistant professor at the University of Waterloo and one year as a Postdoctoral Fellow in the Department of Mathematics and Computer Science and AI Laboratory at the Massachusetts Institute of Technology.

His primary research interest is computational biology and bioinformatics including homology search, protein structure prediction, and protein interaction prediction. He has developed several protein structure prediction tools, such as RAPTOR, ACE, and SCATD.

Hosts: Bhaskar DasGupta (CS) and Jie Liang (BioE)