Biomedical subjects

Jens Gramm

Publications and source records attributed to Jens Gramm.

3 recordsLinked to original sources

PubMed2005

Multiplexing schemes for generic SNP genotyping assays.

Association studies in populations relate genomic variation among individuals with medical condition. Key to these studies is the development of efficient and affordable genotyping techniques. Generic genotyping assays are independent of the target SNPs and offer great flexibility in the genotyping process. Efficient use of such assays calls for identifying sets of SNPs that can be interrogated in parallel under constraints imposed by the genotyping technology. In this paper, we study problems arising in the design of genotyping experiments using generic assays. Our problem formulation deals with two main factors that affect the genotyping cost: the number of assays used and the number of PCR reactions required for sample preparation. We prove that the resulting computational problems are hard, but provide approximate and heuristic solutions to these problems. Our algorithmic approach is based on recasting the multiplexing problems as partitioning and packing problems on a bipartite graph. We tested our algorithmic approaches on an extensive collection of synthetic data and on data that was simulated using real SNP sequences. Our results show that the algorithms achieve near-optimal designs in many cases and demonstrate the applicability of generic assays to SNP genotyping.

Algorithms↗

PubMed2002

Breakpoint medians and breakpoint phylogenies: a fixed-parameter approach.

With breakpoint distance, the genome rearrangement field delivered one of the currently most popular measures in phylogenetic studies for related species. Here, BREAKPOINT MEDIAN, which is NP-complete already for three given species (whose genomes are represented as signed orderings), is the core basic problem. For the important special case of three species, approximation (ratio 7/6) and exact heuristic algorithms were developed. Here, we provide an exact, fixed-parameter algorithm with provable performance bounds. For instance, a breakpoint median for three signed orderings over nelements that causes at most d breakpoints can be computed in time O((2.15)(d).n). We show the algorithm's practical usefulness through experimental studies. In particular, we demonstrate that a simple implementation of our algorithm combined with a new tree construction heuristic allows for a new approach to breakpoint phylogeny, yielding evolutionary trees that are competitive in comparison with known results developed in a recent series of papers that use clever algorithm engineering methods.

Algorithms↗

PubMedDate not supplied

A polynomial-time algorithm for the matching of crossing contact-map patterns.

Contact maps are a model to capture the core information in the structure of biological molecules, e.g., proteins. A contact map consists of an ordered set S of elements (representing a protein's sequence of amino acids), and a set A of element pairs of S, called arcs (representing amino acids which are closely neighbored in the structure). Given two contact maps (S, A) and (Sp, Ap) with /A/ > or = /Ap/, the CONTACT MAP PATTERN MATCHING (CMPM) problem asks whether the "pattern" (Sp, A,) "occurs" in (S, A), i.e., informally stated, whether there is a subset of /Ap/ arcs in A whose arc structure coincides with Ap. CMPM captures the biological question of finding structural motifs in protein structures. In general, CMPM is NP-hard. In this paper, we show that CMPM is solvable in O(/A/6/Ap/2) time when the pattern is {precedes, crosses}-structured, i.e., when each two arcs in the pattern are disjoint or crossing. Our algorithm extends to other closely related models. In particular, it answers an open question raised by Vialette that, rephrased in terms of contact maps, asked whether CMPM for {precedes, crosses}-structured patterns is NP-hard or solvable in polynomial time. Our result stands in sharp contrast to the NP-hardness of closely related problems. We provide experimental results which show that contact maps derived from real protein structures can be processed efficiently.

Algorithms↗