Kinetic modeling and fitting software for interconnected reaction schemes: VisKin

Reaction kinetics for complex, highly interconnected kinetic schemes are modeled using analytical solutions to a system of ordinary differential equations. The algorithm employs standard linear algebra methods that are implemented using MatLab functions in a Visual Basic interface. A graphical user interface for simple entry of reaction schemes facilitates comparison of a variety of reaction schemes. To ensure microscopic balance, graph theory algorithms are used to determine violations of thermodynamic cycle constraints. Analytical solutions based on linear differential equations result in fast comparisons of first order kinetic rates and amplitudes as a function of changing ligand concentrations. For analysis of higher order kinetics, we also implemented a solution using numerical integration. To determine rate constants from experimental data, fitting algorithms that adjust rate constants to fit the model to imported data were implemented using the Levenberg-Marquardt algorithm or using Broyden-Fletcher-Goldfarb-Shanno methods. We have included the ability to carry out global fitting of data sets obtained at varying ligand concentrations. These tools are combined in a single package, which we have dubbed VisKin, to guide and analyze kinetic experiments. The software is available online for use on PCs.     

Theory of metabolism regulation: a complete system of equations for regulation coefficients

Basic quantitative parameters of control in a metabolic system are considered: control coefficients of enzymes with respect to metabolic fluxes and concentrations, and in the case when there are conservation laws, the response coefficients of metabolic fluxes and concentrations to changes in the conserved sums of metabolite concentrations (e. g. conserved moieties). Relationships are obtained which generalize the well known connectivity relations for the case of metabolites binding by conservation laws. Additional relationships are obtained which complement the set of connectivity relations up to the complete system of equations for determining all the control coefficients. The control coefficients are expressed through the enzyme elasticity coefficients, steady state metabolic fluxes and concentrations. Formulas are derived which express response coefficients of flux and concentrations through the enzyme control and elasticity coefficients and metabolite concentrations.     

The regulatory principles of glycolysis in erythrocytes in vivo and in vitro. A minimal comprehensive model describing steady states, quasi-steady states and time-dependent processes.

A simple mathematical model for glycolysis in erythrocytes is presented which takes into account ATP synthesis and consumption. The system is described by four ordinary differential equations. Conditions in vivo are described by a stable steady state. The model predicts correctly the metabolite concentrations found in vivo. The parameters involved are in agreement with data on the separate steps. The metabolite changes found in pyruvate kinase-deficient erythrocytes and the species variations among erythrocytes from different animals are described satisfactorily. The roles of the enzymes in the control of metabolites and glycolytic flux are expressed in the form of a control matrix and control strengths [R. Heinrich & T.A. Rapoport (1974) Eur. J. Biochem. 42, 89-95] respectively. Erythrocytes from various species are shown to be adapted to a maximal ATP-consumption rate. The calculated eigenvalues reveal the pronounced time-hierarchy of the glycolytic reactions. Owing to the slowness of the 2,3-bisphospho-glycerate phosphatase reaction, quasi-steady states occur during the time-interval of about 0.5-2h incubation, which are defined by perturbed 2,3-bisphosphoglycerate concentrations. The theoretical predictions agree with experimental data. In the quasi-steady state the flux control is exerted almost entirely by the hexokinase-phosphofructokinase system. The model describes satisfactorily the time-dependent changes after addition of glucose to starved erythrocytes. The theoretical consequences are discussed of the conditions in vitro with lactate accumulation and the existence of a time-independent conservation quantity for the oxidized metabolites. Even in this closed system quasi-steady states occur which are characterized by approximately constant concentrations of all glycolytic metabolites except for the accumulation of lactate, fructose 1,6-bisphosphate and triose phosphate.     

Identifying and quantifying metabolites by scoring peaks of GC-MS data

Background

Metabolomics is one of most recent omics technologies. It has been applied on fields such as food science, nutrition, drug discovery and systems biology. For this, gas chromatography-mass spectrometry (GC-MS) has been largely applied and many computational tools have been developed to support the analysis of metabolomics data. Among them, AMDIS is perhaps the most used tool for identifying and quantifying metabolites. However, AMDIS generates a high number of false-positives and does not have an interface amenable for high-throughput data analysis. Although additional computational tools have been developed for processing AMDIS results and to perform normalisations and statistical analysis of metabolomics data, there is not yet a single free software or package able to reliably identify and quantify metabolites analysed by GC-MS.

Results

Here we introduce a new algorithm, PScore, able to score peaks according to their likelihood of representing metabolites defined in a mass spectral library. We implemented PScore in a R package called MetaBox and evaluated the applicability and potential of MetaBox by comparing its performance against AMDIS results when analysing volatile organic compounds (VOC) from standard mixtures of metabolites and from female and male mice faecal samples. MetaBox reported lower percentages of false positives and false negatives, and was able to report a higher number of potential biomarkers associated to the metabolism of female and male mice.

Conclusions

Identification and quantification of metabolites is among the most critical and time-consuming steps in GC-MS metabolome analysis. Here we present an algorithm implemented in a R package, which allows users to construct flexible pipelines and analyse metabolomics data in a high-throughput manner.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-014-0374-2) contains supplementary material, which is available to authorized users.     

Identification of a Metabolic Reaction Network from Time-Series Data of Metabolite Concentrations

Recent development of high-throughput analytical techniques has made it possible to qualitatively identify a number of metabolites simultaneously. Correlation and multivariate analyses such as principal component analysis have been widely used to analyse those data and evaluate correlations among the metabolic profiles. However, these analyses cannot simultaneously carry out identification of metabolic reaction networks and prediction of dynamic behaviour of metabolites in the networks. The present study, therefore, proposes a new approach consisting of a combination of statistical technique and mathematical modelling approach to identify and predict a probable metabolic reaction network from time-series data of metabolite concentrations and simultaneously construct its mathematical model. Firstly, regression functions are fitted to experimental data by the locally estimated scatter plot smoothing method. Secondly, the fitted result is analysed by the bivariate Granger causality test to determine which metabolites cause the change in other metabolite concentrations and remove less related metabolites. Thirdly, S-system equations are formed by using the remaining metabolites within the framework of biochemical systems theory. Finally, parameters including rate constants and kinetic orders are estimated by the Levenberg–Marquardt algorithm. The estimation is iterated by setting insignificant kinetic orders at zero, i.e., removing insignificant metabolites. Consequently, a reaction network structure is identified and its mathematical model is obtained. Our approach is validated using a generic inhibition and activation model and its practical application is tested using a simplified model of the glycolysis of Lactococcus lactis MG1363, for which actual time-series data of metabolite concentrations are available. The results indicate the usefulness of our approach and suggest a probable pathway for the production of lactate and acetate. The results also indicate that the approach pinpoints a probable strong inhibition of lactate on the glycolysis pathway.     

Relationship between soluble carbohydrate level and tolerance of meadow fescue callus to Bipolaris sorokiniana (Sacc.) Shoem. and Drechslera dictyoides (Drechsl.) Shoem. metabolites

The aim of the presented work was the search for the relationship between the level of soluble carbohydrates in callus tissues of eight meadow fescue (Festuca pratensis Huds.) cultivars and their growth ability on media containing Bipolaris sorokiniana and Drechslera dictyoides metabolites. Calli were induced from mature grains using the method previously described (Płażek 1994). Callus obtained from single caryopsis was cut into three pieces which were weighted and put on the media with or without pathogen metabolites. Tissue selection was performed by means of “double-layer culture” technique (Lepoivre et al. 1986). After two-week culture in the darkness at temp. of 25°C the calli were weighted again. The sugar level in tissue was measured by means of colorimetric method of Klein & Weissman according to Snell (1961). Fresh mass decrease of calli developing on the media with fungus metabolites was observed by all studied object. The tolerance of calli of the tested cultivars to metabolites of both pathogens was significantly different. However, significant similarity between the tolerance of calli of particular varietes to both fungi was noted. The soluble carbohydrate contents in control tissue of all studied cultivars were similar and their values ranged between 2.4 and 3 % of fresh mass. B. sorokiniana metabolites caused a significant decrease of the sugar content in calli, while D. dictyoides metabolites did not decrease the sugar level.     

Characterization of the biochemical variability of bovine milk using metabolomics

Bovine milk contains a complex mixture of metabolites, which were identified by liquid and gas chromatography mass spectrometry methods. With the aid of new software methods, spectral assignment was carried out, enabling the identification of 223 metabolites. Those included amino acids, lipids, carbohydrates, nucleotides, energy metabolites, vitamins, cofactors and short peptides. Metabolite concentrations were compared between 10 bovine milk varieties, differing in brand, fat content, expiry date, package type and farming method. Principal components analysis showed a clear separation of the different milk varieties. Whole milk could be distinguished from reduced fat and fat free milk by higher lipid metabolites like free fatty acids, cholesterol and 1,2-dipalmitoylglycerol. But also, the reduced fat varieties had lower levels of vitamin E. In comparing organic to conventional milk, 14 named metabolites were statistically different between the two farming methods. This shows the potential of identifying farming-method-specific biomarkers upon analysis and validation of a larger sample size. Finally, high biochemical variability was shown in conventional whole milk derived from different producers. The distinct biochemical profiles of milk varieties shows the utility of metabolic profiling for authentication of milk varieties, and for deriving potential markers that can serve as signatures for a particular milk.     

A new method for the analysis of the dynamics of the molecular genetic control systems. I. Description of the method of generalized threshold models.

In the molecular system of coding polymers and metabolites a control subsystem has been singled out that forms controlling variables showing the action of regulatory molecules and a controlled subsystem where, depending on the values of controlling variables controlled variables are formed, i.e. concentrations of DNA, m-RNA, proteins and metabolites. Relationships have been obtained which enable controlling variables to be found. Equations showing the dynamics of molecular genetic control systems' components have been obtained. A method of generalized threshold models that enables kinetic curves to be obtained by pure mathematical means for macromolecular components (DNA, RNA, proteins) of molecular genetic control systems of varying complexity is suggested.     

Study of leucine-enkephalin in rat brain by a new high-performance liquid chromatographic method

A specific method is presented for the assay of leucine-enkephalin (Leu-Enk) and its metabolites by reversed-phase high-performance liquid chromatography on a μBondapak C₁₅ column with a mobile phase of methanol—water and 0.005M tetrabutylammonium phosphate. The four substances are resolved by a linear program from 8 to 70% methanol in 25 min. Detection is achieved by monitoring the absorbance at 280 nm. Time of analysis can be reduced by means of a new high-speed liquid chromatography package.

This method allows the study of the effect of Phe-Ala on the cerebral metabolism of Leu-Enk. For this purpose, membrane preparations from rat striatum were incubated in the presence of [³H]Leu-Enk with different concentrations of Phe-Ala from 10⁻⁷ to 10⁻³M during 1 h at 37°C. Collected eluates were counted by liquid scintillation. The results suggest the presence of three membrane enzymes which generate the three metabolites, Tyr, Tyr-Gly-Gly and Tyr-Gly, in order of abundance. Maximum inhibition of [³H]Leu-Enk degradation is obtained at a concentration of 10⁻³M Phe-Ala.     

Stochastic modeling of nonlinear epidemiology

The objectives of this paper to analyse, model and simulate the spread of an infectious disease by resorting to modern stochastic algorithms. The approach renders it possible to circumvent the simplifying assumption of linearity imposed in the majority of the past works on stochastic analysis of epidemic processes. Infectious diseases are often transmitted through contacts of those infected with those susceptible; hence the processes are inherently nonlinear. According to the classical model of Kermack and McKendrick, or the SIR model, three classes of populations are involved in two types of processes: conversion of susceptibles (S) to infectives (I) and conversion of infectives to removed (R). The master equations of the SIR process have been formulated through the probabilistic population balance around a particular state by considering the mutually exclusive events. The efficacy of the present methodology is mainly attributable to its ability to derive the governing equations for the means, variances and covariance of the random variables by the method of system-size expansion of the nonlinear master equations. Solving these equations simultaneously along with rates associated influenza epidemic data yields information concerning not only the means of the three populations but also the minimal uncertainties of these populations inherent in the epidemic. The stochastic pathways of the three different classes of populations during an epidemic, i.e. their means and the fluctuations around these means, have also been numerically simulated independently by the algorithm derived from the master equations, as well as by an event-driven Monte Carlo algorithm. The master equation and Monte Carlo algorithms have given rise to the identical results.     

EXPERFARM: a new package in BASIC for teaching genetics

We have developed two interactive computer programs (togetherreferred to as EXPERFARM), which enable simulation of a greatvariety of genetic situations. This package is designed forteaching basic genetics as well as quantitative and populationgenetics. The main advantages of EXPERFARM are its great versatility,as different situations can be simulated by simply changingthe inputs, and the small amount of training necessary for theusers. Received on August 15, 1985; accepted on February 3, 1986     

Control in channelled pathways. A matrix method calculating the enzyme control coefficients

The usual equations expressing the enzyme control coefficients (quantitative indicators of 'global' control properties of a pathway) via the elasticity coefficients (reflecting local kinetic properties of an enzyme reaction), cannot be applied to a variety of 'non-ideal' pathways, in particular to pathways with metabolic channelling. Here we show that the relationship between the control and elasticity coefficients can be obtained by considering such a metabolic pathway as a network of elemental chemical conversions (steps). To calculate the control coefficients of enzymes one should first determine the elasticity coefficients of such elemental steps and then take their appropriate combinations. Although the method is illustrated for a channelled pathway it can be used for any non-ideal pathway including those with high enzyme concentrations where the sequestration of metabolites by enzymes cannot be neglected.     

Conversion of 3,4-Dihydroxyphenylalanine and Deuterated 3,4-Dihydroxyphenylalanine to Alcoholic Metabolites of Catecholamines in Rat Brain

Abstract: We have investigated the effects of 3,4-dihydroxyphenylalanine l -DOPA) and its deuterated analogue on the concentrations of alcoholic metabolites of catecholamines in rat brain by means of gas chromatography/mass spectrometry with selected-ion monitoring. Whole brain concentrations of the two neutral norepinephrine metabolites, 3-methoxy-4-hydroxyphenylethylene-glycol (MHPG) and 3,4-dihydroxyphenylethyleneglycol (DHPG), were significantly increased in a dose-dependent manner by a single intraperitoneal injection of l -DOPA. Both MHPG and DHPG, as well as the corresponding dopamine metabolites, reached a maximum 1 h after injection. Brain MHPG and DHPG concentrations were elevated by 78 and 134%, respectively, 1 h after injection of 150 mg/kg l -DOPA. Analyses of discrete brain regions revealed that concentrations of the norepinephrine metabolites were elevated uniformly in all regions, except that MHPG showed a greater increase in the cerebellum than in other regions. The latter result appeared to be explained by the finding that 52% of the total MHPG in the cerebellum was unconjugated (compared to 15% in the whole brain). l -DOPA caused a proportionately greater increase in free MHPG than in total MHPG in the cerebellum and brain stem. By using deuterated l -DOPA in place of l -DOPA and measuring both the deuterated and nondeuterated norepinephrine metabolites, we demonstrated that virtually all of the increases in MHPG and DHPG were due to the conversion of the exogenous l -DOPA to norepinephrine. Thus, the effects of norepinephrine metabolism need to be considered in attempts to understand clinical and behavioral effects of l -DOPA.     

Purine metabolites in serum of higher primates,including man

Using a new method for simultaneous quantification of hypoxanthine, xanthine, uric acid, and allantoin by means of high-pressure liquid chromatography, purine metabolites of 18 species of higher primates, including man, have been determined. The data thus produced indicate that the serum concentrations of purine metabolites in primates are influenced by nutrition, sexual hormones, and the procedures used in catching the animals for venipuncture. In the Callitrichidae examined, serum concentrations of purines differ significantly from species to species. The results of a nutritional test show that Callithrix jacchus possesses an efficient system for degradation of dietary purines.     

Steady-state modelling of metabolic pathways: A guide for the prospective simulator

Steady-state modelling and control analysis by means of computersimulation provides valuable insight into the behaviour of metabolicpathways. This review, which is aimed at the newcomer to thisfield, discusses the objectives of steady-state modelling andthe steady-state properties of the four basic metabolic structures,namely linear and branched chains, loops and cycles It is shownhow the model definition in terms of stoichiometric reactionsand rate equations leads to a set of balance equations fromwhich the conservation constraints and flux relationships canbe deduced, either informally or through a rigourous analysisof the stoichiometnc matrix The initial analysis of a steady-statemetabolic model is summarized in an algorithm. Key referencesto the literature on metabolic modelling are given.     

Climate-driven changes on phytoplankton–zooplankton coupling and nutrient availability in high mountain lakes of Southern Europe

1. The effect of climate variability on phytoplankton and zooplankton dynamics and nutrient availability was studied in two high mountain fishless lakes (La Caldera and Río Seco) of contrasting morphology, hydrology and dissolved inorganic nitrogen : soluble reactive phosphate (DIN : SRP) ratios during 1986 and after a 10‐year‐long drought in 1996 and 1997. 2. Thaw was delayed and water temperatures were lower in both lakes in 1996 than in 1986 and 1997. However, the lake‐specific DIN : SRP ratio was maintained in the 3 years studied, reflecting its local control. 3. On other hand, the presumptive limiting nutrient in each lake, P in La Caldera and N in Río Seco, showed higher concentrations in 1996 versus 1986 and 1997. Significant positive correlations between temperature and chlorophyll a were found in both lakes in 1996 but these relationships were negative or not significant in 1986 and 1997. Zooplankton biomass showed lower values in 1996 than in 1986 or 1997. 4. These findings can be explained by a decoupling of the phytoplankton–zooplankton interaction because of a constraint on zooplankton growth by low temperatures in the coldest year studied. This observation furnishes evidence that regional climatic control on the phytoplankton–zooplankton link can modulate the overall demand for nutrients.     

Temporal changes in metabolites of prostanoids in milk of heifers after intramammary infusion of Escherichia coli organisms

A study was conducted to characterize the changes in the concentrations of three metabolites of prostanoids in the milk of a) heifers (n = 14; control) inoculated with Escherichia coli (E. coli) organisms into the udder and b) in heifers (n = 10; treatment) vaccinated with E. coli bacterin and treated similar to control heifers. Milk samples were obtained from the challenged quarter and analyzed for the concentrations of stable metabolites of thromboxane A2 (TXB2), prostacyclin (PCM) and prostaglandin E2 (PGEM) using radioimmunoassays. In control heifers milk TXB2 concentrations were significantly higher (P = 0.03) compared to treated heifers. Milk PCM concentrations increased significantly (P = 0.02) in control and treated heifers after the respective treatments, however, differences between the two groups were not significant. Milk PGEM concentrations also increased significantly (P = 0.02) in control and treated heifers after the respective treatments, and there were no differences between the two groups. Results of the present study suggest that, the prostanoids have a role in the pathophysiologic process of coliform mastitis.