BACKGROUND: A structure alignment method based on a local geometric property is presented and its performance is tested in pairwise and multiple structure alignments. In this approach, the writhing number, a quantity originating from integral formulas of Vassiliev knot invariants, is used as a local geometric measure. This measure is used in a sliding window to calculate the local writhe down the length of the protein chain. By encoding the distribution of writhing numbers across all the structures in the protein databank (PDB), protein geometries are represented in a 20-letter alphabet. This encoding transforms the structure alignment problem into a sequence alignment problem and allows the well-established algorithms of sequence alignment to be employed. Such geometric alignments offer distinct advantages over structural alignments in Cartesian coordinates as it better handles structural subtleties associated with slight twists and bends that distort one structure relative to another. RESULTS: The performance of programs for pairwise local alignment (TLOCAL) and multiple alignment (TCLUSTALW) are readily adapted from existing code for Smith-Waterman pairwise alignment and for multiple sequence alignment using CLUSTALW. The alignment algorithms employed a blocked scoring matrix (TBLOSUM) generated using the frequency of changes in the geometric alphabet of a block of protein structures. TLOCAL was tested on a set of 10 difficult proteins and found to give high quality alignments that compare favorably to those generated by existing pairwise alignment programs. A set of protein comparison involving hinged structures was also analyzed and TLOCAL was seen to compare favorably to other alignment methods. TCLUSTALW was tested on a family of protein kinases and reveal conserved regions similar to those previously identified by a hand alignment. CONCLUSION: These results show that the encoding of the writhing number as a geometric measure allow high quality structure alignments to be generated using standard algorithms of sequence alignment. This approach provides computationally efficient algorithms that allow fast database searching and multiple structure alignment. Because the geometric measure can employ different window sizes, the method allows the exploration of alignments on different, well-defined length scales.

MOTIVATION: There has been considerable interest in developing computational techniques for inferring genetic regulatory networks from whole-genome expression profiles. When expression time series data sets are available, dynamic models can, in principle, be used to infer correlative relationships between gene expression levels, which may be causal. However, because of the range of detectable expression levels and the current quality of the data, the predictive nature of such inferred, quantitative models is questionable. Network models derived from simple rate laws offer an intermediate level analysis, going beyond simple statistical analysis, but falling short of a fully quantitative description. This work shows how such network models can be constructed and describes the global properties of the networks derived from such a model. These global properties are statistically robust and provide insights into the design of the underlying network. RESULTS: Several whole-genome expression time series data sets from yeast microarray experiments were analyzed using a Markov-modeling method (Dewey and Galas, FUNC: Integr. Genomics, 1, 269-278, 2001) to infer an approximation to the underlying genetic network. We found that the global statistical properties of all the resulting networks are similar. The overall structure of these biological networks is distinctly different from that of other recently studied networks such as the Internet or social networks. These biological networks show hierarchical, hub-like structures that have some properties similar to a class of graphs known as small world graphs. Small world networks exhibit local cliquishness while exhibiting strong global connectivity. In addition to the small world properties, the biological networks show a power law or scale free distribution of connectivities. An inverse power law, N(k) approximately k(-3/2), for the number of vertices (genes) with k connections was observed for three different data sets from yeast. We propose network growth models based on gene duplication events. Simulations of these models yield networks with the same combination of global graphical properties that we inferred from the expression data.