In our effort to elucidate the systems biology of the model organism, Escherichia coli, we have developed a mathematical model that simulates the allosteric regulation for threonine biosynthesis pathway starting from aspartate. To achieve this goal, we used kMech, a Cellerator language extension that describes enzyme mechanisms for the mathematical modeling of metabolic pathways. These mechanisms are converted by Cellerator into ordinary differential equations (ODEs) solvable by Mathematica. In this paper, we describe a more flexible model in Cellerator, which generalizes the Monod, Wyman, Changeux (MWC) model for enzyme allosteric regulation to allow for multiple substrate, activator and inhibitor binding sites. Furthermore, we have developed a model that describes the behavior of the bifunctional allosteric enzyme aspartate Kinase I-Homoserine Dehydrogenase I (AKI-HDHI). This model predicts the partition of enzyme activities in the steady state which paves a way for a more generalized prediction of the behavior of bifunctional enzymes.
We study the parsimony approach to haplotype inference, which calls for finding a set of haplotypes of minimum cardinality that explains an input set of genotypes. We prove that the problem is APX-hard even in very restricted cases. On the positive side, we identify islands of tractability for the problem, by focusing on instances with specific structure of haplotype sharing among the input genotypes. We exploit the structure of those instance to give polynomial and constant-approximation algorithms to the problem. We also show that the general parsimony haplotyping problem is fixed parameter tractable.
LTR retrotransposons constitute one of the most abundant classes of repetitive elements in eukaryotic genomes. In this paper, we present a new algorithm for detection of full-length LTR retrotransposons in genomic sequences. The algorithm identifies regions in a genomic sequence that show structural characteristics of LTR retrotransposons. Three key components distinguish our algorithm from that of current software — (i) a novel method that preprocesses the entire genomic sequence in linear time and produces high quality pairs of LTR candidates in run-time that is constant per pair, (ii) a thorough alignment-based evaluation of candidate pairs to ensure high quality prediction, and (iii) a robust parameter set encompassing both structural constraints and quality controls providing users with a high degree of flexibility. We implemented our algorithm into a software program called LTR_par, which can be run on both serial and parallel computers. Validation of our software against the yeast genome indicates superior results in both quality and performance when compared to existing software. Additional validations are presented on rice BACs and chimpanzee genome.
A linear programming algorithm is presented to constructively compute thermodynamically feasible fluxes and change in chemical potentials of reactions for a metabolic network. It is based on physical laws of mass conservation and the second law of thermodynamics that all chemical reactions should satisfy. As a demonstration, the algorithm has been applied to the core metabolic pathway of E.coli.
We present TreeRefiner, a tool for refining multiple alignments of biological sequences. Given a multiple alignment, a phylogenetic tree, and scoring parameters as input, TreeRefiner optimizes the sum-of-pairs function in a restricted three-dimensional space around the alignment. At each internal node of the unrooted tree, the multiple alignment is projected to the sub-alignments corresponding to the three neighboring nodes, and three-dimensional dynamic programming is performed within a user-specified radius r around the original alignment. We test TreeRefiner on simulated sequences aligned by several popular tools, and demonstrate substantial improvements in the percentage of correctly aligned positions.
