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Motif recognition is a challenging problem in bioinformatics due to the diversity of protein motifs. Many existing algorithms identify motifs of a given length, thus being either not applicable or not efficient when searching simultaneously for motifs of various lengths. Searching for gapped motifs, although very important, is a highly time-consuming task due to the combinatorial explosion of possible combinations implied by the consideration of long gaps. We introduce a new graph theoretical approach to identify motifs of various lengths, both with and without gaps. We compare our approach with two widely used methods: MEME and GLAM2 analyzing both the quality of the results and the required computational time. Our method provides results of a slightly higher level of quality than MEME but at a much faster rate, i.e., one eighth of MEME's query time. By using similarity indexing, we drop the query times down to an average of approximately one sixth of the ones required by GLAM2, while achieving a slightly higher level of quality of the results. More precisely, for sequence collections smaller than 50,000 bytes GLAM2 is 13 times slower, while being at least as fast as our method on larger ones. The source code of our C++ implementation is freely available in GitHub: https://github.com/hirvolt1/debruijn-motif. [ABSTRACT FROM PUBLISHER]

In vitro assembly of intermediate filaments from tetrameric vimentin consists of a very rapid phase of tetramers laterally associating into unit-length filaments and a slow phase of filament elongation. We focus in this paper on a systematic quantitative investigation of two molecular models for filament assembly, recently proposed in (Kirmse et al. J. Biol. Chem. 282, 52 (2007), 18563-18572), through mathematical modeling, model fitting, and model validation. We analyze the quantitative contribution of each filament elongation strategy: with tetramers, with unit-length filaments, with longer filaments, or combinations thereof. In each case, we discuss the numerical fitting of the model with respect to one set of data, and its separate validation with respect to a second, different set of data. We introduce a high-resolution model for vimentin filament self-assembly, able to capture the detailed dynamics of filaments of arbitrary length. This provides much more predictive power for the model, in comparison to previous models where only the mean length of all filaments in the solution could be analyzed. We show how kinetic observations on low-resolution models can be extrapolated to the high-resolution model and used for lowering its complexity. [ABSTRACT FROM PUBLISHER]