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Nathan D Price

Publications and source records attributed to Nathan D Price.

At least 19 recordsLinked to original sources
PubMed2006

Matrix formalism to describe functional states of transcriptional regulatory systems.

Complex regulatory networks control the transcription state of a genome. These transcriptional regulatory networks (TRNs) have been mathematically described using a Boolean formalism, in which the state of a gene is represented as either transcribed or not transcribed in response to regulatory signals. The Boolean formalism results in a series of regulatory rules for the individual genes of a TRN that in turn can be used to link environmental cues to the transcription state of a genome, thereby forming a complete transcriptional regulatory system (TRS). Herein, we develop a formalism that represents such a set of regulatory rules in a matrix form. Matrix formalism allows for the systemic characterization of the properties of a TRS and facilitates the computation of the transcriptional state of the genome under any given set of environmental conditions. Additionally, it provides a means to incorporate mechanistic detail of a TRS as it becomes available. In this study, the regulatory network matrix, R, for a prototypic TRS is characterized and the fundamental subspaces of this matrix are described. We illustrate how the matrix representation of a TRS coupled with its environment (R*) allows for a sampling of all possible expression states of a given network, and furthermore, how the fundamental subspaces of the matrix provide a way to study key TRS features and may assist in experimental design.

Computational Biology↗
PubMed2006

Network-level analysis of metabolic regulation in the human red blood cell using random sampling and singular value decomposition.

BACKGROUND: Extreme pathways (ExPas) have been shown to be valuable for studying the functions and capabilities of metabolic networks through characterization of the null space of the stoichiometric matrix (S). Singular value decomposition (SVD) of the ExPa matrix P has previously been used to characterize the metabolic regulatory problem in the human red blood cell (hRBC) from a network perspective. The calculation of ExPas is NP-hard, and for genome-scale networks the computation of ExPas has proven to be infeasible. Therefore an alternative approach is needed to reveal regulatory properties of steady state solution spaces of genome-scale stoichiometric matrices. RESULTS: We show that the SVD of a matrix (W) formed of random samples from the steady-state solution space of the hRBC metabolic network gives similar insights into the regulatory properties of the network as was obtained with SVD of P. This new approach has two main advantages. First, it works with a direct representation of the shape of the metabolic solution space without the confounding factor of a non-uniform distribution of the extreme pathways and second, the SVD procedure can be applied to a very large number of samples, such as will be produced from genome-scale networks. CONCLUSION: These results show that we are now in a position to study the network aspects of the regulatory problem in genome-scale metabolic networks through the use of random sampling.

Algorithms↗
PubMed2006

Candidate states of Helicobacter pylori's genome-scale metabolic network upon application of "loop law" thermodynamic constraints.

Constraint-based modeling has proven to be a useful tool in the analysis of biochemical networks. To date, most studies in this field have focused on the use of linear constraints, resulting from mass balance and capacity constraints, which lead to the definition of convex solution spaces. One additional constraint arising out of thermodynamics is known as the "loop law" for reaction fluxes, which states that the net flux around a closed biochemical loop must be zero because no net thermodynamic driving force exists. The imposition of the loop-law can lead to nonconvex solution spaces making the analysis of the consequences of its imposition challenging. A four-step approach is developed here to apply the loop-law to study metabolic network properties: 1), determine linear equality constraints that are necessary (but not necessarily sufficient) for thermodynamic feasibility; 2), tighten V(max) and V(min) constraints to enclose the remaining nonconvex space; 3), uniformly sample the convex space that encloses the nonconvex space using standard Monte Carlo techniques; and 4), eliminate from the resulting set all solutions that violate the loop-law, leaving a subset of steady-state solutions. This subset of solutions represents a uniform random sample of the space that is defined by the additional imposition of the loop-law. This approach is used to evaluate the effect of imposing the loop-law on predicted candidate states of the genome-scale metabolic network of Helicobacter pylori.

Algorithms↗
PubMed2006

Metabolite coupling in genome-scale metabolic networks.

BACKGROUND: Biochemically detailed stoichiometric matrices have now been reconstructed for various bacteria, yeast, and for the human cardiac mitochondrion based on genomic and proteomic data. These networks have been manually curated based on legacy data and elementally and charge balanced. Comparative analysis of these well curated networks is now possible. Pairs of metabolites often appear together in several network reactions, linking them topologically. This co-occurrence of pairs of metabolites in metabolic reactions is termed herein "metabolite coupling." These metabolite pairs can be directly computed from the stoichiometric matrix, S. Metabolite coupling is derived from the matrix ŝŝT, whose off-diagonal elements indicate the number of reactions in which any two metabolites participate together, where ŝ is the binary form of S. RESULTS: Metabolite coupling in the studied networks was found to be dominated by a relatively small group of highly interacting pairs of metabolites. As would be expected, metabolites with high individual metabolite connectivity also tended to be those with the highest metabolite coupling, as the most connected metabolites couple more often. For metabolite pairs that are not highly coupled, we show that the number of reactions a pair of metabolites shares across a metabolic network closely approximates a line on a log-log scale. We also show that the preferential coupling of two metabolites with each other is spread across the spectrum of metabolites and is not unique to the most connected metabolites. We provide a measure for determining which metabolite pairs couple more often than would be expected based on their individual connectivity in the network and show that these metabolites often derive their principal biological functions from existing in pairs. Thus, analysis of metabolite coupling provides information beyond that which is found from studying the individual connectivity of individual metabolites. CONCLUSION: The coupling of metabolites is an important topological property of metabolic networks. By computing coupling quantitatively for the first time in genome-scale metabolic networks, we provide insight into the basic structure of these networks.

Chromosome Mapping↗
PubMed2006

Long-range periodic patterns in microbial genomes indicate significant multi-scale chromosomal organization.

Genome organization can be studied through analysis of chromosome position-dependent patterns in sequence-derived parameters. A comprehensive analysis of such patterns in prokaryotic sequences and genome-scale functional data has yet to be performed. We detected spatial patterns in sequence-derived parameters for 163 chromosomes occurring in 135 bacterial and 16 archaeal organisms using wavelet analysis. Pattern strength was found to correlate with organism-specific features such as genome size, overall GC content, and the occurrence of known motility and chromosomal binding proteins. Given additional functional data for Escherichia coli, we found significant correlations among chromosome position dependent patterns in numerous properties, some of which are consistent with previously experimentally identified chromosome macrodomains. These results demonstrate that the large-scale organization of most sequenced genomes is significantly nonrandom, and, moreover, that this organization is likely linked to genome size, nucleotide composition, and information transfer processes. Constraints on genome evolution and design are thus not solely dependent upon information content, but also upon an intricate multi-parameter, multi-length-scale organization of the chromosome.

Bacterial Proteins↗
PubMed2005

Expanded metabolic reconstruction of Helicobacter pylori (iIT341 GSM/GPR): an in silico genome-scale characterization of single- and double-deletion mutants.

Helicobacter pylori is a human gastric pathogen infecting almost half of the world population. Herein, we present an updated version of the metabolic reconstruction of H. pylori strain 26695 based on the revised genome annotation and new experimental data. This reconstruction, iIT341 GSM/GPR, represents a detailed review of the current literature about H. pylori as it integrates biochemical and genomic data in a comprehensive framework. In total, it accounts for 341 metabolic genes, 476 intracellular reactions, 78 exchange reactions, and 485 metabolites. Novel features of iIT341 GSM/GPR include (i) gene-protein-reaction associations, (ii) elementally and charge-balanced reactions, (iii) more accurate descriptions of isoprenoid and lipopolysaccharide metabolism, and (iv) quantitative assessments of the supporting data for each reaction. This metabolic reconstruction was used to carry out in silico deletion studies to identify essential and conditionally essential genes in H. pylori. A total of 128 essential and 75 conditionally essential metabolic genes were identified. Predicted growth phenotypes of single knockouts were validated using published experimental data. In addition, in silico double-deletion studies identified a total of 47 synthetic lethal mutants involving 67 different metabolic genes in rich medium.

Biotin↗
PubMed2004

Candidate metabolic network states in human mitochondria. Impact of diabetes, ischemia, and diet.

The human mitochondrial metabolic network was recently reconstructed based on proteomic and biochemical data. Linear programming and uniform random sampling were applied herein to identify candidate steady states of the metabolic network that were consistent with the imposed physico-chemical constraints and available experimental data. The activity of the mitochondrion was studied under four metabolic conditions: normal physiologic, diabetic, ischemic, and dietetic. Pairwise correlations between steady-state reaction fluxes were calculated in each condition to evaluate the dependence among the reactions in the network. Applying constraints on exchange fluxes resulted in predictions for intracellular fluxes that agreed with experimental data. Analyses of the steady-state flux distributions showed that the experimentally observed reduced activity of pyruvate dehydrogenase in vivo could be a result of stoichiometric constraints and therefore would not necessarily require enzymatic inhibition. The observed changes in the energy metabolism of the mitochondrion under diabetic conditions were used to evaluate the impact of previously suggested treatments. The results showed that neither normalized glucose uptake nor decreased ketone body uptake have a positive effect on the mitochondrial energy metabolism or network flexibility. Taken together, this study showed that sampling of the steady-state flux space is a powerful method to investigate network properties under different conditions and provides a basis for in silico evaluations of effects of potential disease treatments.

Adenosine Triphosphate↗
PubMed2004

Comparison of network-based pathway analysis methods.

Network-based definitions of biochemical pathways have emerged in recent years. These pathway definitions insist on the balanced use of a whole network of biochemical reactions. Two such related definitions, elementary modes and extreme pathways, have generated novel hypotheses regarding biochemical network function. The relationship between these two approaches can be illustrated by comparing and contrasting the elementary modes and extreme pathways of previously published metabolic reconstructions of the human red blood cell (RBC) and the human pathogen Helicobacter pylori. Descriptions of network properties generated by using these two approaches in the analysis of realistic metabolic networks need careful interpretation.

Algorithms↗
PubMed2004

Genome-scale models of microbial cells: evaluating the consequences of constraints.

Microbial cells operate under governing constraints that limit their range of possible functions. With the availability of annotated genome sequences, it has become possible to reconstruct genome-scale biochemical reaction networks for microorganisms. The imposition of governing constraints on a reconstructed biochemical network leads to the definition of achievable cellular functions. In recent years, a substantial and growing toolbox of computational analysis methods has been developed to study the characteristics and capabilities of microorganisms using a constraint-based reconstruction and analysis (COBRA) approach. This approach provides a biochemically and genetically consistent framework for the generation of hypotheses and the testing of functions of microbial cells.

Bacterial Physiological Phenomena↗
PubMed2004

In Silico Metabolic Model and Protein Expression of Haemophilus influenzae Strain Rd KW20 in Rich Medium.

The intermediary metabolism of Haemophilus influenzae strain Rd KW20 was studied by a combination of protein expression analysis using a recently developed direct proteomics approach, mutational analysis, and mathematical modeling. Special emphasis was placed on carbon utilization, sugar fermentation, TCA cycle, and electron transport of H. influenzae cells grown microaerobically and anaerobically in a rich medium. The data indicate that several H. influenzae metabolic proteins similar to Escherichia coli proteins, known to be regulated by low concentrations of oxygen, were well expressed in both growth conditions in H. influenzae. An in silico model of the H. influenzae metabolic network was used to study the effects of selective deletion of certain enzymatic steps. This allowed us to define proteins predicted to be essential or non-essential for cell growth and to address numerous unresolved questions about intermediary metabolism of H. influenzae. Comparison of data from in vivo protein expression with the protein list associated with a genome-scale metabolic model showed significant coverage of the known metabolic proteome. This study demonstrates the significance of an integrated approach to the characterization of H. influenzae metabolism.

Biochemistry↗
PubMed2004

Uniform sampling of steady-state flux spaces: means to design experiments and to interpret enzymopathies.

Reconstruction of genome-scale metabolic networks is now possible using multiple different data types. Constraint-based modeling is an approach to interrogate capabilities of reconstructed networks by constraining possible cellular behavior through the imposition of physicochemical laws. As a result, a steady-state flux space is defined that contains all possible functional states of the network. Uniform random sampling of the steady-state flux space allows for the unbiased appraisal of its contents. Monte Carlo sampling of the steady-state flux space of the reconstructed human red blood cell metabolic network under simulated physiologic conditions yielded the following key results: 1), probability distributions for the values of individual metabolic fluxes showed a wide variety of shapes that could not have been inferred without computation; 2), pairwise correlation coefficients were calculated between all fluxes, determining the level of independence between the measurement of any two fluxes, and identifying highly correlated reaction sets; and 3), the network-wide effects of the change in one (or a few) variables (i.e., a simulated enzymopathy or fixing a flux range based on measurements) were computed. Mathematical models provide the most compact and informative representation of a hypothesis of how a cell works. Thus, understanding model predictions clearly is vital to driving forward the iterative model-building procedure that is at the heart of systems biology. Taken together, the Monte Carlo sampling procedure provides a broadening of the constraint-based approach by allowing for the unbiased and detailed assessment of the impact of the applied physicochemical constraints on a reconstructed network.

Animals↗
PubMed2003

Network-based analysis of metabolic regulation in the human red blood cell.

Reconstruction of cell-scale metabolic networks is now possible. A description of allowable metabolic network functions can be obtained using extreme pathways, which are the convex basis vectors of the solution space containing all steady state flux distributions. However, only a portion of these allowable network functions are physiologically possible due to kinetic and regulatory constraints. Methods are now needed that enable us to take a defined metabolic network and deduce candidate regulatory structures that control the selection of these physiologically relevant states. One such approach is the singular value decomposition (SVD) of extreme pathway matrices (P), which allows for the characterization of steady state solution spaces. Eigenpathways, which are the left singular vectors from the SVD of P, can be described and categorized by their biochemical function. SVD of P for the human red blood cell showed that the first five eigenpathways, out of a total of 23, effectively characterize all the relevant physiological states of red blood cell metabolism calculated with a detailed kinetic model. Thus, with five degrees of freedom the magnitude and nature of the regulatory needs are defined. Additionally, the dominant features of these first five eigenpathways described key metabolic splits that are indeed regulated in the human red blood cell. The extreme pathway matrix is derived directly from network topology and only knowledge of Vmax values is needed to reach these conclusions. Thus, we have implemented a network-based analysis of regulation that complements the study of individual regulatory events. This topological approach may provide candidate regulatory structures for metabolic networks with known stoichiometry but poorly characterized regulation.

Erythrocytes↗
PubMed2003

Analysis of metabolic capabilities using singular value decomposition of extreme pathway matrices.

It is now possible to construct genome-scale metabolic networks for particular microorganisms. Extreme pathway analysis is a useful method for analyzing the phenotypic capabilities of these networks. Many extreme pathways are needed to fully describe the functional capabilities of genome-scale metabolic networks, and therefore, a need exists to develop methods to study these large sets of extreme pathways. Singular value decomposition (SVD) of matrices of extreme pathways was used to develop a conceptual framework for the interpretation of large sets of extreme pathways and the steady-state flux solution space they define. The key results of this study were: 1), convex steady-state solution cones describing the potential functions of biochemical networks can be studied using the modes generated by SVD; 2), Helicobacter pylori has a more rigid metabolic network (i.e., a lower dimensional solution space and a more dominant first singular value) than Haemophilus influenzae for the production of amino acids; and 3), SVD allows for direct comparison of different solution cones resulting from the production of different amino acids. SVD was used to identify key network branch points that may identify key control points for regulation. Therefore, SVD of matrices of extreme pathways has proved to be a useful method for analyzing the steady-state solution space of genome-scale metabolic networks.

Algorithms↗
PubMed2003

Genome-scale microbial in silico models: the constraints-based approach.

Genome sequencing and annotation has enabled the reconstruction of genome-scale metabolic networks. The phenotypic functions that these networks allow for can be defined and studied using constraints-based models and in silico simulation. Several useful predictions have been obtained from such in silico models, including substrate preference, consequences of gene deletions, optimal growth patterns, outcomes of adaptive evolution and shifts in expression profiles. The success rate of these predictions is typically in the order of 70-90% depending on the organism studied and the type of prediction being made. These results are useful as a basis for iterative model building and for several practical applications.

Animals↗
PubMed2003

Metabolic pathways in the post-genome era.

Metabolic pathways are a central paradigm in biology. Historically, they have been defined on the basis of their step-by-step discovery. However, the genome-scale metabolic networks now being reconstructed from annotation of genome sequences demand new network-based definitions of pathways to facilitate analysis of their capabilities and functions, such as metabolic versatility and robustness, and optimal growth rates. This demand has led to the development of a new mathematically based analysis of complex, metabolic networks that enumerates all their unique pathways that take into account all requirements for cofactors and byproducts. Applications include the design of engineered biological systems, the generation of testable hypotheses regarding network structure and function, and the elucidation of properties that can not be described by simple descriptions of individual components (such as product yield, network robustness, correlated reactions and predictions of minimal media). Recently, these properties have also been studied in genome-scale networks. Thus, network-based pathways are emerging as an important paradigm for analysis of biological systems.

Biochemistry↗
PubMed2002

The genome-scale metabolic extreme pathway structure in Haemophilus influenzae shows significant network redundancy.

Genome-scale metabolic networks can be characterized by a set of systemically independent and unique extreme pathways. These extreme pathways span a convex, high-dimensional space that circumscribes all potential steady-state flux distributions achievable by the defined metabolic network. Genome-scale extreme pathways associated with the production of non-essential amino acids in Haemophilus influenzae were computed. They offer valuable insight into the functioning of its metabolic network. Three key results were obtained. First, there were multiple internal flux maps corresponding to externally indistinguishable states. It was shown that there was an average of 37 internal states per unique exchange flux vector in H. influenzae when the network was used to produce a single amino acid while allowing carbon dioxide and acetate as carbon sinks. With the inclusion of succinate as an additional output, this ratio increased to 52, a 40% increase. Second, an analysis of the carbon fates illustrated that the extreme pathways were non-uniformly distributed across the carbon fate spectrum. In the detailed case study, 45% of the distinct carbon fate values associated with lysine production represented 85% of the extreme pathways. Third, this distribution fell between distinct systemic constraints. For lysine production, the carbon fate values that represented 85% of the pathways described above corresponded to only 2 distinct ratios of 1:1 and 4:1 between carbon dioxide and acetate. The present study analysed single outputs from one organism, and provides a start to genome-scale extreme pathways studies. These emergent system-level characterizations show the significance of metabolic extreme pathway analysis at the genome-scale.

Amino Acids↗