John D Kececioglu

PMID: 2734293;PMCID: PMC287279;Abstract:

Multiple sequence alignment can be a useful technique for studying molecular evolution and analyzing sequence-structure relationships. Until recently, it has been impractical to apply dynamic programming, the most widely accepted method for producing pairwise alignments, to comparisons of more than three sequences. We describe the design and application of a tool for multiple alignment of amino acid sequences that implements a new algorithm that greatly reduces the computational demands of dynamic programming. This tool is able to align in reasonable time as many as eight sequences the length of an average protein.

Abstract:

We introduce a new combinatorial formulation of chromosome physical-mapping by the sampling-without-replacement protocol. In this protocol, which is simple, inexpensive, and has been used to successfully map several organisms, equal-length clones are hybridized against a subset of the clones called probes, which are designed to form a maximal nonoverlapping clone-subset. The output of the protocol is the clone-probe hybridization matrix H. The problem of finding a maximum-likelihood reconstruction of the order of the probes along the chromosome in the presence of false positive and negative hybridization error is equivalent to finding the minimum number of entries of H to change to zeros so that the resulting matrix has at most 2 ones per row, and the consecutive-ones property across rows. This combinatorial problem, which we call 2-Consecutive-Ones Mapping, has a concise integer linear-programming formulation, to which we apply techniques from polyhedral combinatorics. The formulation is unique in that it does not explicitly represent the probe permutation, and in contrast to prior linear-programming approaches, the number of variables is small: in practice, linear in the number of clones. We derive a large class of facet-defining inequalities for the 2-consecutive-ones polytope that we call the augmented k-degree inequalities, and we show that the basic k-degree class can be efficiently separated using bipartite matchings. Computational results with an implementation of the resulting branch-and-cut algorithm applied to both simulated and real data from the complete genome of Aspergillus nidulans show that we can solve many problems to provable optimality and find maps of higher quality than previously possible.

PMID: 22536398;PMCID: PMC3334995;Abstract:

Automatic design of synthetic gene circuits poses a significant challenge to synthetic biology, primarily due to the complexity of biological systems, and the lack of rigorous optimization methods that can cope with the combinatorial explosion as the number of biological parts increases. Current optimization methods for synthetic gene design rely on heuristic algorithms that are usually not deterministic, deliver sub-optimal solutions, and provide no guaranties on convergence or error bounds. Here, we introduce an optimization framework for the problem of part selection in synthetic gene circuits that is based on mixed integer non-linear programming (MINLP), which is a deterministic method that finds the globally optimal solution and guarantees convergence in finite time. Given a synthetic gene circuit, a library of characterized parts, and user-defined constraints, our method can find the optimal selection of parts that satisfy the constraints and best approximates the objective function given by the user. We evaluated the proposed method in the design of three synthetic circuits (a toggle switch, a transcriptional cascade, and a band detector), with both experimentally constructed and synthetic promoter libraries. Scalability and robustness analysis shows that the proposed framework scales well with the library size and the solution space. The work described here is a step towards a unifying, realistic framework for the automated design of biological circuits. © 2012 Huynh et al.

PMID: 20377464;Abstract:

Accurately aligning distant protein sequences is notoriously difficult. Since the amino acid sequence alone often does not provide enough information to obtain accurate alignments under the standard alignment scoring functions, a recent approach to improving alignment accuracy is to use additional information such as secondary structure. We make several advances in alignment of protein sequences annotated with predicted secondary structure: (1) more accurate models for scoring alignments, (2) efficient algorithms for optimal alignment under these models, and (3) improved learning criteria for setting model parameters through inverse alignment, as well as (4) in-depth experiments evaluating model variants on benchmark alignments. More specifically, the new models use secondary structure predictions and their confidences to modify the scoring of both substitutions and gaps. All models have efficient algorithms for optimal pairwise alignment that run in near-quadratic time. These models have many parameters, which are rigorously learned using inverse alignment under a new criterion that carefully balances score error and recovery error. We then evaluate these models by studying how accurately an optimal alignment under the model recovers benchmark reference alignments that are based on the known three-dimensional structures of the proteins. The experiments show that these new models provide a significant boost in accuracy over the standard model for distant sequences. The improvement for pairwise alignment is as much as 15% for sequences with less than 25% identity, while for multiple alignment the improvement is more than 20% for difficult benchmarks whose accuracy under standard tools is at most 40%. © Copyright 2010, Mary Ann Liebert, Inc.

Abstract:

One of the classic problems in computational biology is the reconstruction of evolutionary histories. A recent trend is toward increasing the explanatory power of the models by incorporating higher-order evolutionary events that more accurately reflect the full range of mutation at the molecular level. In this paper, we take a step in this direction by considering the problem of reconstructing an evolutionary history for a set of genetic sequences that have evolved by recombination. Recombination produces a new sequence by crossing two parent sequences, and is among the most important mechanisms of higher-order molecular mutation.