Reconstructing biochemical pathways from time course data

Time series data on biochemical reactions reveal transient behavior, away from chemical equilibrium, and contain information on the dynamic interactions among reacting components. However, this information can be difficult to extract using conventional analysis techniques. We present a new method to infer biochemical pathway mechanisms from time course data using a global nonlinear modeling technique to identify the elementary reaction steps which constitute the pathway. The method involves the generation of a complete dictionary of polynomial basis functions based on the law of mass action. Using these basis functions, there are two approaches to model construction, namely the general to specific and the specific to general approach. We demonstrate that our new methodology reconstructs the chemical reaction steps and connectivity of the glycolytic pathway of Lactococcus lactis from time course experimental data.     

Stimulus design for model selection and validation in cell signaling

Mechanism-based chemical kinetic models are increasingly being used to describe biological signaling. Such models serve to encapsulate current understanding of pathways and to enable insight into complex biological processes. One challenge in model development is that, with limited experimental data, multiple models can be consistent with known mechanisms and existing data. Here, we address the problem of model ambiguity by providing a method for designing dynamic stimuli that, in stimulus–response experiments, distinguish among parameterized models with different topologies, i.e., reaction mechanisms, in which only some of the species can be measured. We develop the approach by presenting two formulations of a model-based controller that is used to design the dynamic stimulus. In both formulations, an input signal is designed for each candidate model and parameterization so as to drive the model outputs through a target trajectory. The quality of a model is then assessed by the ability of the corresponding controller, informed by that model, to drive the experimental system. We evaluated our method on models of antibody–ligand binding, mitogen-activated protein kinase (MAPK) phosphorylation and de-phosphorylation, and larger models of the epidermal growth factor receptor (EGFR) pathway. For each of these systems, the controller informed by the correct model is the most successful at designing a stimulus to produce the desired behavior. Using these stimuli we were able to distinguish between models with subtle mechanistic differences or where input and outputs were multiple reactions removed from the model differences. An advantage of this method of model discrimination is that it does not require novel reagents, or altered measurement techniques; the only change to the experiment is the time course of stimulation. Taken together, these results provide a strong basis for using designed input stimuli as a tool for the development of cell signaling models.     

Circuit analysis of the oscillatory state in glycolysis

The oscillatory state of glycolysis in yeast extracts has been analysed by methods known from electronic circuit studies. The time course of the reactions are calculated by the method of least squares from experimentally determined sets of the concentrations of most of the metabolites. The dynamics of the glycolytic network of reactions can then be represented in terms of flow versus driving force (current versus voltage in the corresponding electronic circuit). The analysis of the dynamics leads to the conclusion that glycolysis is switched on and off in a pulsed manner during the oscillatory state. The resulting pulsed flow cannot only be measured with glycolytic end products, like carbon dioxide or ethanol, but can also readily be demonstrated by diagrams of reaction rates of single enzymic steps even in the initial stages of the glycolytic sequence. An analytic method widely applied to electronic circuits also proved to be useful in the study of the dynamics of a complex enzymic network.     

Calibration of dynamic models of biological systems with KInfer

Methods for parameter estimation that are robust to experimental uncertainties and to stochastic and biological noise and that require a minimum of a priori input knowledge are of key importance in computational systems biology. The new method presented in this paper aims to ensure an inference model that deduces the rate constants of a system of biochemical reactions from experimentally measured time courses of reactants. This new method was applied to some challenging parameter estimation problems of nonlinear dynamic biological systems and was tested both on synthetic and real data. The synthetic case studies are the 12-state model of the SERCA pump and a model of a genetic network containing feedback loops of interaction between regulator and effector genes. The real case studies consist of a model of the reaction between the inhibitor κB kinase enzyme and its substrate in the signal transduction pathway of NF-κB, and a stiff model of the fermentation pathway of Lactococcus lactis.     

Biochemical systems analysis of genome-wide expression data

MOTIVATION: Modern methods of genomics have produced an unprecedented amount of raw data. The interpretation and explanation of these data constitute a major, well-recognized challenge. RESULTS: Biochemical Systems Theory (BST) is the mathematical basis of a well-established methodological framework for analyzing networks of biochemical reactions. An existing BST model of yeast glycolysis is used here to explain and interpret the glycolytic gene expression pattern of heat shocked yeast. Our analysis demonstrates that the observed gene expression profile satisfies the primary goals of increased ATP, trehalose, and NADPH production, while maintaining intermediate metabolites at reasonable levels. Based on a systematic exploration of alternative, hypothetical expression profiles, we show that the observed profile outperforms other profiles. Conclusion: BST is a useful framework for combining DNA microarray data with enzymatic process information to yield new insights into metabolic pathway regulation. AVAILABILITY: All analyses were executed with the software PLAS(Copyright), which is freely available at http://correio.cc.fc.ul.pt/~aenf/plas.html for academic use. CONTACT: VoitEO@MUSC.edu     

Proteomics of skeletal muscle glycolysis

Glycolysis represents one of the best-understood and most ancient metabolic pathways. In skeletal muscle fibres, energy for contraction is supplied by adenosine triphosphate via anaerobic glycolysis, the phosphocreatine shuttle and oxidative phosphorylation. In this respect, the anaerobic glycolytic pathway supports short duration performances of contractile tissues of high intensity. The catalytic elements associated with glycolysis are altered during development, muscle differentiation, physiological adaptations and many pathological mechanisms, such as muscular dystrophy, diabetes mellitus and age-related muscle weakness. Although gel electrophoresis-based proteomics is afflicted with various biological and technical problems, it is an ideal analytical tool for studying the abundant and mostly soluble enzymes that constitute the glycolytic system. This review critically examines the proteomic findings of recent large-scale studies of glycolytic enzymes and associated components in normal, transforming and degenerating muscle tissues. In the long term, proteins belonging to the glycolytic pathway may be useful as biomarkers of muscle adaptations and pathophysiological mechanisms and can be employed to improve diagnostics and in the identification of novel therapeutic targets in neuromuscular disorders.     

Finding complex oscillatory phenomena in biochemical systems. An empirical approach

Starting with a model for a product-activated enzymatic reaction proposed for glycolytic oscillations, we show how more complex oscillatory phenomena may develop when the basic model is modified by addition of product recycling into substrate or by coupling in parallel or in series two autocatalytic enzyme reactions. Among the new modes of behavior are the coexistence between two stable types of oscillations (birhythmicity), bursting, and aperiodic oscillations (chaos). On the basis of these results, we outline an empirical method for finding complex oscillatory phenomena in autonomous biochemical systems, not subjected to forcing by a periodic input. This procedure relies on finding in parameter space two domains of instability of the steady state and bringing them close to each other until they merge. Complex phenomena occur in or near the region where the two domains overlap. The method applies to the search for birhythmicity, bursting and chaos in a model for the cAMP signalling system of Dictyostelium discoideum amoebae.     

Modeling Genome-Wide Dynamic Regulatory Network in Mouse Lungs with Influenza Infection Using High-Dimensional Ordinary Differential Equations

The immune response to viral infection is regulated by an intricate network of many genes and their products. The reverse engineering of gene regulatory networks (GRNs) using mathematical models from time course gene expression data collected after influenza infection is key to our understanding of the mechanisms involved in controlling influenza infection within a host. A five-step pipeline: detection of temporally differentially expressed genes, clustering genes into co-expressed modules, identification of network structure, parameter estimate refinement, and functional enrichment analysis, is developed for reconstructing high-dimensional dynamic GRNs from genome-wide time course gene expression data. Applying the pipeline to the time course gene expression data from influenza-infected mouse lungs, we have identified 20 distinct temporal expression patterns in the differentially expressed genes and constructed a module-based dynamic network using a linear ODE model. Both intra-module and inter-module annotations and regulatory relationships of our inferred network show some interesting findings and are highly consistent with existing knowledge about the immune response in mice after influenza infection. The proposed method is a computationally efficient, data-driven pipeline bridging experimental data, mathematical modeling, and statistical analysis. The application to the influenza infection data elucidates the potentials of our pipeline in providing valuable insights into systematic modeling of complicated biological processes.     

Extended CADLIVE: a novel graphical notation for design of biochemical network maps and computational pathway analysis

Biochemical network maps are helpful for understanding the mechanism of how a collection of biochemical reactions generate particular functions within a cell. We developed a new and computationally feasible notation that enables drawing a wide resolution map from the domain-level reactions to phenomenological events and implemented it as the extended GUI network constructor of CADLIVE (Computer-Aided Design of LIVing systEms). The new notation presents ‘Domain expansion’ for proteins and RNAs, ‘Virtual reaction and nodes’ that are responsible for illustrating domain-based interaction and ‘InnerLink’ that links real complex nodes to virtual nodes to illustrate the exact components of the real complex. A modular box is also presented that packs related reactions as a module or a subnetwork, which gives CADLIVE a capability to draw biochemical maps in a hierarchical modular architecture. Furthermore, we developed a pathway search module for virtual knockout mutants as a built-in application of CADLIVE. This module analyzes gene function in the same way as molecular genetics, which simulates a change in mutant phenotypes or confirms the validity of the network map. The extended CADLIVE with the newly proposed notation is demonstrated to be feasible for computational simulation and analysis.     

Continuous production of glutathione using immobilized microbial cells containing ATP generating system

Acetate kinase reaction in Escherichia coli cells and glycolytic pathway in Saccharomyces cerevisiae cells were utilized as ATP generation systems for glutathione synthetic processes. These two ATP generation systems were well coupled with glutathione synthetase reactions and glutathione was produced by coimmobilized E. coli cells with dextran-bound ATP or by immobilized S. cerevisiae cells. The glycolytic pathway in S. cerevisiae cells was further utilized for the biosynthetic processes of other useful compounds.     

Thermodynamics of enzyme-catalyzed reactions--a database for quantitative biochemistry

The Thermodynamics of Enzyme-catalyzed Reactions Database (TECRDB) is a comprehensive collection of thermodynamic data on enzyme-catalyzed reactions. The data, which consist of apparent equilibrium constants and calorimetrically determined molar enthalpies of reaction, are the primary experimental results obtained from thermodynamic studies of biochemical reactions. The results from approximately 1000 published papers containing data on approximately 400 different enzyme-catalyzed reactions constitute the essential information in the database. The information is managed using Oracle and is available on the Web. AVAILABILITY: http://xpdb.nist.gov/enzyme_thermodynamics/     

Validation of metabolic pathway databases based on chemical substructure search

Metabolic pathway databases such as KEGG contain information on thousands of biochemical reactions drawn from the biomedical literature. Ensuring consistency of such large metabolic pathways is essential to their proper use. In this paper, we present a new method to determine consistency of an important class of biochemical reactions. Our method exploits the knowledge of the atomic rearrangement pattern in biochemical reactions, to reduce the automatic atom mapping problem to a series of chemical substructure searches between the substrate and the product of a biochemical reaction. As an illustrative application, we describe the exhaustive validation of a substantial portion from the latest release of the KEGG LIGAND database.     

Analysis of the dynamics of relaxation type oscillation in glycolysis of yeast extracts.

In yeasts, the glycolysis may display oscillations of its metabolites while it is converting glucose. The dynamics of the oscillations has been investigated in cytoplasmic extracts of yeast under relaxation type conditions by determining the time course of some of the glycolytic metabolites. The compounds of the nucleotide pool have been identified as fast variables and the glucose derivatives as slow variables of the relaxation type. The period of oscillation has been subdivided into four phases which represent prominent parts of the limit cycle in the phase plane of a slow versus a fast variable. From the reaction processes in these phases, a dynamical picture of the mechanisms of oscillations is suggested. Accordingly, the oscillation results from an alternating activity of the fructose bisphosphate and the polysaccharide synthesis, both of which are coupled to glycolysis via the nucleotide pool. The processes in the phases are analyzed by calculating the rates of the reaction steps in the biochemical pathway.     

Spatial stochastic modelling of the phosphoenolpyruvate-dependent phosphotransferase (PTS) pathway in Escherichia coli

MOTIVATION: Many biochemical networks involve reactions localized on the cell membrane. This can give rise to spatial gradients of the concentration of cytosolic species. Moreover, the number of membrane molecules can be small and stochastic effects can become relevant. Pathways usually consist of a complex interaction network and are characterized by a large set of parameters. The inclusion of spatial and stochastic effects is a major challenge in developing quantitative and dynamic models of pathways. RESULTS: We have developed a particle-based spatial stochastic method (GMP) to simulate biochemical networks in space, including fluctuations from the diffusion of particles and reactions. Gradients emerging from membrane reactions can be resolved. As case studies for the GMP method we used a simple gene expression system and the phosphoenolpyruvate:glucose phosphotransferase system pathway. AVAILABILITY: The source code for the GMP method is available at http://www.science.uva.nl/research/scs/CellMath/GMP.     

Timescale analysis of rule-based biochemical reaction networks

The flow of information within a cell is governed by a series of protein–protein interactions that can be described as a reaction network. Mathematical models of biochemical reaction networks can be constructed by repetitively applying specific rules that define how reactants interact and what new species are formed on reaction. To aid in understanding the underlying biochemistry, timescale analysis is one method developed to prune the size of the reaction network. In this work, we extend the methods associated with timescale analysis to reaction rules instead of the species contained within the network. To illustrate this approach, we applied timescale analysis to a simple receptor–ligand binding model and a rule‐based model of interleukin‐12 (IL‐12) signaling in naïve CD4+ T cells. The IL‐12 signaling pathway includes multiple protein–protein interactions that collectively transmit information; however, the level of mechanistic detail sufficient to capture the observed dynamics has not been justified based on the available data. The analysis correctly predicted that reactions associated with Janus Kinase 2 and Tyrosine Kinase 2 binding to their corresponding receptor exist at a pseudo‐equilibrium. By contrast, reactions associated with ligand binding and receptor turnover regulate cellular response to IL‐12. An empirical Bayesian approach was used to estimate the uncertainty in the timescales. This approach complements existing rank‐ and flux‐based methods that can be used to interrogate complex reaction networks. Ultimately, timescale analysis of rule‐based models is a computational tool that can be used to reveal the biochemical steps that regulate signaling dynamics. © 2011 American Institute of Chemical Engineers Biotechnol. Prog., 2012     

Biochemical retrosynthesis of 2′-deoxyribonucleosides from glucose, acetaldehyde, and a nucleobase

2′-Deoxyribonucleosides are important as building blocks for the synthesis of antisense drugs, antiviral nucleosides, and 2′-deoxyribonucleotides for polymerase chain reaction. The microbial production of 2′-deoxyribonucleosides from simple materials, glucose, acetaldehyde, and a nucleobase, through the reverse reactions of 2′-deoxyribonucleoside degradation and the glycolytic pathway, was investigated. The glycolytic pathway of baker’s yeast yielded fructose 1,6-diphosphate from glucose using the energy of adenosine 5′-triphosphate generated from adenosine 5′-monophosphate through alcoholic fermentation with the yeast. Fructose 1,6-diphosphate was further transformed to 2-deoxyribose 5-phosphate in the presence of acetaldehyde by deoxyriboaldolase-expressing Escherichia coli cells via d-glyceraldehyde 3-phosphate. E. coli transformants expressing phosphopentomutase and nucleoside phosphorylase produced 2′-deoxyribonucleosides from 2-deoxyribose 5-phosphate and a nucleobase via 2-deoxyribose 1-phosphate through the reverse reactions of 2′-deoxyribonucleoside degradation. Coupling of the glycolytic pathway and deoxyriboaldolase-catalyzing reaction efficiently supplied 2-deoxyribose 5-phosphate, which is a key intermediate for 2′-deoxyribonucleoside synthesis. 2′-Deoxyinosine (9.9 mM) was produced from glucose, acetaldehyde, and adenine through three-step reactions via fructose 1,6-diphosphate and then 2-deoxyribose 5-phosphate, the molar yield as to glucose being 17.8%.