Bioinformatics. My work focuses on theoretical as well as practical aspects of biological sequence analysis. While the more theoretical face of my research has considerable overlap with computational statistics, the applied side of it has more of a data driven discovery flavor. The following couple of examples of projects I am working on with my students Patrick Ng and Niranjan Nagarajan (now at U. Maryland) will give you a better idea what I mean.
Motif Finding - The identification of transcription factor binding sites is an important step in understanding the regulation of gene expression. To address this need, many motif-finding tools (or finders) have been described that can find short sequence motifs given only an input set of sequences. The motifs returned by these tools are evaluated and ranked according to some measure of statistical over-representation, the most popular of which is based on the information content, or entropy. Our approach to motif finding focuses on analyzing the problem from two perspectives. First, we seek to characterize twilight-zone motif finding: when the “real” motifs are barely significant statistically when compared to top scoring random motifs. Delineation of this zone is important for understanding how far our current finders are from being optimal. We invest considerable more effort into our second goal of analyzing the statistical significance of a finder's output. This important area has lagged considerably behind the extensive development of the finders. Our main interest is to design a reliable and usable significance analysis. Nevertheless, we also show how such analysis can be leveraged to improve the actual motif finding process.
Study of Replication Origins - DNA replication is a fundamental process essential for cell proliferation. While the proteins involved in initiating DNA replication are essentially conserved from yeast to humans, the implicated sequence motifs that these conserved factors interact with are poorly understood outside of S. cerevisiae (baker's yeast). Moreover, even for S. cerevisiae the replication initiation process is not completely understood. For example, it is known that the roughly 400 replication origins in cerevisiae, called ARSs (Autonomously Replicating Sequences), differ in several important aspects from one another: at which times and frequencies do they initiate replication, and how do they respond to mutations in proteins that are known to be involved in forming the pre-replication complex. Still, much of this variability is yet to be explained. We are collaborating with Cornell molecular biologist Bik Tye on gaining a better characterization of replication origins in Saccharomyces species. In particular we are interested in characterizing the sequence elements that account for the variability among replication origins in cerevisiae as well as in detecting and analyzing new replication origins in related Saccharomyces species.
Computational Statistics - Our search for an efficient and accurate computation of motif significance led us to develop a new approach for exact tests (exact tests are ones where the significance of the test is evaluated directly from the underlying distribution rather than using an approximation). Borrowing ideas from large-deviation theory, the underlying mechanism of our approach is the exact numerical calculation of the exponentially shifted characteristic function of the test statistic. We use this approach so far to develop faster exact algorithms for the classical multinomial goodness-of-fit test and the Mann-Whitney test.
CS 280 - Discrete Structures:
CS 4520 (aka CS 426) - Introduction to Bioinformatics: Fall 05, Spring 07, Spring 08, Fall 08
CS 628 - Biological Sequence Analysis: Fall 04 Spring 06, Fall 07,
CS 726 - Problems and perspective in computational molecular biology: Fall 03, Spring 04, Spring 05
Sequence Analysis Journal Club (run with Tomas Vinar and Brona Brejova): Fall 06, Spring 07 Fall 07
ENGRG 150 - Engineering Seminar: Fall 06
GIMSAN – a novel tool for de novo motif finding that includes a reliable significance analysis
SADMAMA – computational tool for detection of significant variation in binding affinity across two sets of sequences
The FAST package – Fourier transform based Algorithms for Significance Testing of ungapped multiple alignments
csFFT/sFFT – computing the p-value of the information content (entropy score) of a sequence motif
BagFFT – computing the exact p-value of the llr statistic for multinomial goodness-of-fit test
GibbsILR – a Gibbs sampler based motif finder
Ph.D. in Mathematics, Courant Institute, New York
Thesis title: Stationary Approximations to Non-Stationary Stochastic Processes.
Advisor: Prof. H . P. McKean
M.Sc. in Mathematics, Department of Mathematics, Technion -
Israel Institute of Technology
Thesis title: A Generalization of the "Ahlswede Daykin Inequality".
Advisor: Prof. R. Aharoni
B.Sc. in Computer Science and Mathematics, Hebrew University of Jerusalem
NSF CAREER Award No. 0644136, 7/2007-1/2012.
Ng P., Keich U. Factoring local sequence composition in motif significance analysis. GIW 2008, In Press.
Keich U., Gao H., Garretson JS., Bhaskar A., Liachko I., Donato J., Tye B. Computational detection of significant variation in binding affinity across two sets of sequences with application to the analysis of replication origins in yeast. BMC Bioinformatics, 9:372, 2008. (paper).
Ng P., Keich U. GIMSAN: a Gibbs motif finder with significance analysis. Bioinformatics, In Press.
Keich U., Ng P. A conservative parametric approach to motif significance analysis. Genome Informatics, 19:61-72, 2007. (preprint)
Nagarajan N., Keich U. FAST: Fourier transform based Algorithms for Significance Testing of ungapped multiple alignments. Bioinformatics, 24(4):577-8, 2008.
Ng P., Nagarajan N., Jones N., and Keich U. Apples to apples: improving the performance of motif finders and their significance analysis in the Twilight Zone. Bioinformatics, 22(14):e393-401, ISMB 2006. (preprint)
Nagarajan N., Ng P., Keich U. Refining motif finders with E-value calculations. Proceedings of the 3rd RECOMB Satellite Workshop on Regulatory Genomics, Singapore 2006. (preprint)
Keich U., Nagarajan N. A fast and numerically robust method for exact multinomial goodness-of-fit test. Journal of Computational and Graphical Statistics, , 15(4):779-802, 2006. (preprint)
Nagarajan N., Jones N., and Keich U. Computing the p-value of the information content from an alignment of multiple sequences. Bioinformatics, Vol. 21, Suppl 1, ISMB 2005, i311-i318. (preprint)
Buhler J., Keich U., Sun Y. Designing Seeds for Similarity Search in Genomic DNA. Journal of Computer and System Sciences, Volume 70, Issue 3, May 2005, Pages 342-363. (preprint)
Keich U., and Nagarajan N. A Faster Reliable Algorithm to Estimate the p-Value of the Multinomial llr Statistic. Proceedings of the 4th International Workshop on Algorithms in Bioinformatic (WABI 2004), September 2004, Bergen, Norway. (preprint)
Keich U. sFFT: a faster accurate computation of the p-value of the entropy score. Journal of Computational Biology, Volume 12, Number 4, May 2005, Pages 416-430. (preprint)
Zhi D., Keich U., Pevzner P., Heber S., and Tang H. Checking for base-calling errors in repeats. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 4(1):54-64, (2007). (preprint)
Keich U., Li M., Ma B., and Tromp J. On Spaced Seeds for Similarity Search. Discrete Applied Mathematics, 138(3):253--263. 2004. (preprint)
Buhler J., Keich U., Sun Y. Designing Seeds for Similarity Search in Genomic DNA. Proceedings of the Seventh Annual International Conference on Research in Computational Molecular Biology (RECOMB-2003), April 2003, Berlin, Germany. (preprint)
Eskin E., Keich U., Gelfand M.S., Pevzner P.A. Genome-Wide Analysis of Bacterial Promoter Regions. Proceedings of the Pacific Symposium on Biocomputing (PSB-2003), January 2003, Kaua'i, Hawaii. (preprint)
Keich U., and Pevzner, P.A. Finding motifs in the twilight zone. Bioinformatics, Vol. 18 (2002), Issue 10, 1374-1381. (preprint)
Keich U., and Pevzner P.A. Subtle motifs: defining the limits of motif finding algorithms. Bioinformatics, Vol. 18 (2002), Issue 10, 1382-1390. (preprint)
Keich U. and Pevzner P.A. Finding motifs in the twilight zone. Proceedings of the Sixth Annual International Conference on Research in Computational Molecular Biology (RECOMB-2002), April 2002, Washington DC, USA, ACM Press. (preprint)
Keich U., A Stationary Tangent - the Discrete and Non-smooth Cases. Journal of Time Series Analysis, March 2003, vol. 24, no. 2, pp. 173-192(20). (preprint)
Cwikel M. and Keich U., Optimal decompositions for the K-functional for a couple of Banach lattices. Arkiv för Matematik, 39 (2001), No. 1, 27-64. (preprint)
Keich U., A Possible Definition of A Stationary Tangent. Stochastic Processes and Their Applications, 88 (2000), No. 1, 1-36. (preprint)
Keich U., Krein's Strings, the Symmetric Moment Problem, and Extending a Real Positive Definite Function., Communications on Pure and Applied Mathematics, 52 (1999), no. 10, 1315-1334. (preprint)
Keich U., On Lp Bounds for Kakeya Maximal Functions and the Minkowski Dimension in R2., Bulletin of the London Mathematical Society, 31 (1999), 213-221. (preprint)
Keich U., Absolute Continuity Between the Wiener and Stationary Gaussian Measures., Pacific Journal of Mathematics, Vol. 88 (1999), No. 1, 95-108. (preprint)
Keich U., The Entropy Distance Between the Wiener and Stationary Gaussian Measures., Pacific Journal of Mathematics, Vol. 88 (1999), No. 1, 109-128. (preprint)
Aharoni R. and Keich U, A Generalization of the Ahlswede Daykin
Inequality., Discrete Mathematics , 152 (1996), 1-12.