Elucidation and structural analysis of conserved pools for genome-scale metabolic reconstructions

In this article, we introduce metabolite concentration coupling analysis (MCCA) to study conservation relationships for metabolite concentrations in genome-scale metabolic networks. The analysis allows the global identification of subsets of metabolites whose concentrations are always coupled within common conserved pools. Also, the minimal conserved pool identification (MCPI) procedure is developed for elucidating conserved pools for targeted metabolites without computing the entire basis conservation relationships. The approaches are demonstrated on genome-scale metabolic reconstructions of Helicobacter pylori, Escherichia coli, and Saccharomyces cerevisiae. Despite significant differences in the size and complexity of the examined organism's models, we find that the concentrations of nearly all metabolites are coupled within a relatively small number of subsets. These correspond to the overall exchange of carbon molecules into and out of the networks, interconversion of energy and redox cofactors, and the transfer of nitrogen, sulfur, phosphate, coenzyme A, and acyl carrier protein moieties among metabolites. The presence of large conserved pools can be viewed as global biophysical barriers protecting cellular systems from stresses, maintaining coordinated interconversions between key metabolites, and providing an additional mode of global metabolic regulation. The developed approaches thus provide novel and versatile tools for elucidating coupling relationships between metabolite concentrations with implications in biotechnological and medical applications.     

Periodic coupling strength-dependent multiple coherence resonance by time delay in Newman–Watts neuronal networks

Recently, multiple coherence resonance induced by time delay has been observed in neuronal networks with constant coupling strength. In this paper, by employing Newman–Watts Hodgkin–Huxley neuron networks with time-periodic coupling strength, we study how the temporal coherence of spiking behavior and coherence resonance by time delay change when the frequency of periodic coupling strength is varied. It is found that delay induced coherence resonance is dependent on periodic coupling strength and increases when the frequency of periodic coupling strength increases. Periodic coupling strength can also induce multiple coherence resonance, and the coherence resonance occurs when the frequency of periodic coupling strength is approximately multiple of the spiking frequency. These results show that for periodic coupling strength time delay can more frequently optimize the temporal coherence of spiking activity, and periodic coupling strength can repetitively optimize the temporal coherence of spiking activity as well. Frequency locking may be the mechanism for multiple coherence resonance induced by periodic coupling strength. These findings imply that periodic coupling strength is more efficient for enhancing the temporal coherence of spiking activity of neuronal networks, and thus it could play a more important role in improving the time precision of information processing and transmission in neural networks.     

Estimation of secretory rates of hormones from the specific activities of metabolites which have multiple secreted precursors

The calculation of rates of entry of material into an open system of multiple pools in the steady state from the specific activities of end products, which may be derived from several pools, is described. This analysis may be applied to estimate the rates of secretion of steroid hormones from the specific activities of urinary metabolites which may have various hormones as common precursors. In a previous publication (Gurpideet al., 1963) formulae have been presented by which secretory rates could be calculated after a single injection of the tracers assuming that each of the urinary metabolites was uniquely derived from one of the pools in the system. In the present article similar formulae were derived without this assumption. Consequently, it is shown that, under certain circumstances, non-uniquely derived metabolites can be used to estimate secretory rates, and that it may be unnecessary to consider the pathways of conversion of the hormones to the metabolites or the sites where these conversion occur.     

Development and application of a differential method for reliable metabolome analysis in Escherichia coli

Quantitative metabolomics of microbial cultures requires well-designed sampling and quenching procedures. We successfully developed and applied a differential method to obtain a reliable set of metabolome data for Escherichia coli K12 MG1655 grown in steady-state, aerobic, glucose-limited chemostat cultures. From a rigorous analysis of the commonly applied quenching procedure based on cold aqueous methanol, it was concluded that it was not applicable because of release of a major part of the metabolites from the cells. No positive effect of buffering or increasing the ionic strength of the quenching solution was observed. Application of a differential method in principle requires metabolite measurements in total broth and filtrate for each measurement. Different methods for sampling of culture filtrate were examined, and it was found that direct filtration without cooling of the sample was the most appropriate. Analysis of culture filtrates revealed that most of the central metabolites and amino acids were present in significant amounts outside the cells. Because the turnover time of the pools of extracellular metabolites is much larger than that of the intracellular pools, the differential method should also be applicable to short-term pulse response experiments without requiring measurement of metabolites in the supernatant during the dynamic period.     

Estimation of secretory rates of hormones from the specific activities of metabolites which have multiple secreted precursors

The calculation of rates of entry of material into an open system of multiple pools in the steady state from the specific activities of end products, which may be derived from several pools, is described. This analysis may be applied to estimate the rates of secretion of steroid hormones from the specific activities of urinary metabolites which may have various hormones as common precursors. In a previous publication (Gurpideet al., 1963) formulae have been presented by which secretory rates could be calculated after a single injection of the tracers assuming that each of the urinary metabolites was uniquely derived from one of the pools in the system. In the present article similar formulae were derived without this assumption. Consequently, it is shown that, under certain circumstances, non-uniquely derived metabolites can be used to estimate secretory rates, and that it may be unnecessary to consider the pathways of conversion of the hormones to the metabolites or the sites where these conversion occur. This work was supported in part by Grant AM-00110 of the National Institutes of Health of the United States Public Health Service.     

Periodic coexistence of four species competing for three essential resources

We show the existence of a periodic solution in which four species coexist in competition for three essential resources in the standard model of resource competition. By assuming that species i is limited by resource i for each i near the positive equilibrium, and that the matrix of contents of resources in species is a combination of cyclic matrix and a symmetric matrix, we obtain an asymptotically stable periodic solution of three species on three resources via Hopf bifurcation. A simple bifurcation argument is then employed which allows us to add a fourth species. In principle, the argument can be continued to obtain a periodic solution adding one new species at a time so long as asymptotic stability can be assured at each step. Numerical simulations are provided to illustrate our analytical results. The results of this paper suggest that competition can generate coexistence of species in the form of periodic cycles, and that the number of coexisting species can exceed the number of resources in a constant and homogeneous environment.     

Influence of milking frequency on mammary gland dynamics

The effects of milking frequency on milk production is a key question for the dairy industry. Milk production is related to the number of active alveoli in the mammary gland and movement between active and quiescent alveolar pools is influenced by the milking frequency. In this paper, we analyse a mechanistic model based on known biological inputs that describes the effect of milking frequency on the alveolar composition of the mammary gland. It is shown that the model can qualitatively reproduce the correct alveolar dynamics. We also investigate the model robustness and parameter sensitivity. Additionally, by making the plausible assumption that the senescence rate of alveoli is proportional to the number of quiescent alveoli present, we obtain an analytical solution requiring periodic resetting.     

State-dependent impulsive models of integrated pest management (IPM) strategies and their dynamic consequences

A state-dependent impulsive model is proposed for integrated pest management (IPM). IPM involves combining biological, mechanical, and chemical tactics to reduce pest numbers to tolerable levels after a pest population has reached its economic threshold (ET). The complete expression of an orbitally asymptotically stable periodic solution to the model with a maximum value no larger than the given ET is presented, the existence of which implies that pests can be controlled at or below their ET levels. We also prove that there is no periodic solution with order larger than or equal to three, except for one special case, by using the properties of the LambertW function and Poincare map. Moreover, we show that the existence of an order two periodic solution implies the existence of an order one periodic solution. Various positive invariant sets and attractors of this impulsive semi-dynamical system are described and discussed. In particular, several horseshoe-like attractors, whose interiors can simultaneously contain stable order 1 periodic solutions and order 2 periodic solutions, are found and the interior structure of the horseshoe-like attractors is discussed. Finally, the largest invariant set and the sufficient conditions which guarantee the global orbital and asymptotic stability of the order 1 periodic solution in the meaningful domain for the system are given using the Lyapunov function. Our results show that, in theory, a pest can be controlled such that its population size is no larger than its ET by applying effects impulsively once, twice, or at most, a finite number of times, or according to a periodic regime. Moreover, our theoretical work suggests how IPM strategies could be used to alter the levels of the ET in the farmers' favour.     

Determination of pools of tricarboxylic acid cycle and related acids in bacteria.

Methods for sampling, extracting, and quantitating the metabolic pools of organic acids from bacteria have been developed. The concentration of these metabolites was determined by a new gas chromatographic method that can quantitatively determine the levels of lactate, pyruvate, fumarate, succinate, malate, alpha-ketoglutarate, and citrate. Values obtained were confirmed by fluorimetric analyses of five of the individual acids. In Escherichia coli, pools range from about 1 to 5 mumol/g of dry weight, with a variation in replicate samples of 5 to 15%. Under similar conditions, these pools in Bacillus licheniformis are in the same range, although the pyruvic acid pool is significantly larger.     

Determination of pools of tricarboxylic acid cycle and related acids in bacteria.

Methods for sampling, extracting, and quantitating the metabolic pools of organic acids from bacteria have been developed. The concentration of these metabolites was determined by a new gas chromatographic method that can quantitatively determine the levels of lactate, pyruvate, fumarate, succinate, malate, alpha-ketoglutarate, and citrate. Values obtained were confirmed by fluorimetric analyses of five of the individual acids. In Escherichia coli, pools range from about 1 to 5 mumol/g of dry weight, with a variation in replicate samples of 5 to 15%. Under similar conditions, these pools in Bacillus licheniformis are in the same range, although the pyruvic acid pool is significantly larger.     

Description and analysis of metabolic connectivity and dynamics in the human red blood cell

The human red blood cell (hRBC) metabolic network is relatively simple compared with other whole cell metabolic networks, yet too complicated to study without the aid of a computer model. Systems science techniques can be used to uncover the key dynamic features of hRBC metabolism. Herein, we have studied a full dynamic hRBC metabolic model and developed several approaches to identify metabolic pools of metabolites. In particular, we have used phase planes, temporal decomposition, and statistical analysis to show hRBC metabolism is characterized by the formation of pseudoequilibrium concentration states. Such equilibria identify metabolic "pools" or aggregates of concentration variables. We proceed to define physiologically meaningful pools, characterize them within the hRBC, and compare them with those derived from systems engineering techniques. In conclusion, systems science methods can decipher detailed information about individual enzymes and metabolites within metabolic networks and provide further understanding of complex biological networks.     

Evaluation of quenching methods for metabolite recovery in photoautotrophic Synechococcus sp. PCC 7002

The first step of many metabolomics studies is quenching, a technique vital for rapidly halting metabolism and ensuring that the metabolite profile remains unchanging during sample processing. The most widely used approach is to plunge the sample into prechilled cold methanol; however, this led to significant metabolite loss in Synecheococcus sp. PCC 7002. Here we describe our analysis of the impacts of cold methanol quenching on the model marine cyanobacterium Synechococcus sp. PCC 7002, as well as our brief investigation of alternative quenching methods. We tested several methods including cold methanol, cold saline, and two filtration approaches. Targeted central metabolites were extracted and metabolomic profiles were generated using liquid chromatography-tandem mass spectrometry (LC-MS/MS). The results indicate that cold methanol quenching induces dramatic metabolite leakage in Synechococcus, resulting in a majority of central metabolites being lost prior to extraction. Alternatively, usage of a chilled saline quenching solution mitigates metabolite leakage and improves sample recovery without sacrificing rapid quenching of cellular metabolism. Finally, we illustrate that metabolite leakage can be assessed, and subsequently accounted for, in order to determine absolute metabolite pool sizes; however, our results show that metabolite leakage is inconsistent across various metabolite pools and therefore must be determined for each individually measured metabolite.     

Effect of Slow Growth on Metabolism of Escherichia coli, as Revealed by Global Metabolite Pool (“Metabolome”) Analysis

Escherichia coli growing on glucose in minimal medium controls its metabolite pools in response to environmental conditions. The extent of pool changes was followed through two-dimensional thin-layer chromatography of all ¹⁴C-glucose labelled compounds extracted from bacteria. The patterns of metabolites and spot intensities detected by phosphorimaging were found to reproducibly differ depending on culture conditions. Clear trends were apparent in the pool sizes of several of the 70 most abundant metabolites extracted from bacteria growing in glucose-limited chemostats at different growth rates. The pools of glutamate, aspartate, trehalose, and adenosine as well as UDP-sugars and putrescine changed markedly. The data on pools observed by two-dimensional thin-layer chromatography were confirmed for amino acids by independent analysis. Other unidentified metabolites also displayed different spot intensities under various conditions, with four trend patterns depending on growth rate. As RpoS controls a number of metabolic genes in response to nutrient limitation, an rpoS mutant was also analyzed for metabolite pools. The mutant had altered metabolite profiles, but only some of the changes at slow growth rates were ascribable to the known control of metabolic genes by RpoS. These results indicate that total metabolite pool (“metabolome”) analysis offers a means of revealing novel aspects of cellular metabolism and global regulation.     

Seasonal dynamics of major cations in xylem sap and needles of Norway spruce (Picea abies L. Karst.) in stands with different soil solution chemistry

Soil solution, xylem sap and needles of mature trees were sampled in three spruce stands over one vegetation period and analysed for major cations. Investigations of nutrient distribution between these three pools and evaluations of seasonal dynamics give the following results: The highest nutrient concentrations in the xylem sap occur at the time of bud break and become gradually lower during the vegetation period. The trees show similar trends of xylem sap concentrations with time for potassium, calcium and magnesium regardless of the nutritional status of the plots. No coupling of xylem sap to soil solution composition can be observed in spite of a high variability of soil solution chemistry in time. The major cations in the current needles exhibit a significantly different trend with time. No time-based correlations for nutrient contents could be found for the needles from the previous year.Despite mobilisation of storage pools in the deficient stand, trees are not able to increase the Ca and Mg contents in the needles up to the level of the other stands. Potassium could be retranslocated in sufficient extent for nutrition of current needles. Due to seasonal variability and dependence upon internal processes, such as retranslocation and mobilisation of nutrients, xylem sap does not seem to be a good tool for the estimation of the nutritional status of forest sites.It was concluded that only minor transport into new foliage via xylem sap will proceed after nutrient flush during the bud break and the nutrient content in the new biomass will be governed by dilution due to biomass growth or by nutrient transport by other means than xylem sap.     

A sensitive and robust method for quantification of intracellular short-chain coenzyme A esters

A procedure for the analysis of short-chain intracellular coenzyme A (CoA) esters and adenine nucleotide pools in microbial cells is described. The simultaneous isolation of bacterial cells from media, quenching of their metabolism, and extraction of metabolites was accomplished by centrifugation of cells through a layer of silicone oil into a denser solution of trichloroacetic acid. The acid was neutralized by extraction into Freon containing tri-n-octylamine to provide a salt-free solution of cell metabolites. After high-performance liquid chromatography separation, CoA, CoA esters, and adenine-containing nucleotides were derivatized by postcolumn reaction with bromoacetaldehyde to form the fluorescent 1,N6-ethenoadenine adducts which were analyzed by a fluorescence detector at picomolar levels.     

Mass spectrometry for metabolic flux analysis

Mass spectrometry in combination with tracer experiments based on 13C substrates can serve as a powerful tool for the modeling and analysis of intracellular fluxes and the investigation of biochemical networks. The theoretical background for the application of mass spectrometry to metabolic flux analysis is discussed. Mass spectrometry methods are especially useful to determine mass distribution of metabolites. Additional information gained from fragmentation of metabolites, e.g., by electron impact ionization, allows further localization of labeling positions, up to complete resolution of isotopomer pools. To effectively handle mass distributions in simulation experiments, a matrix based general methodology is formulated. The natural isotope distribution of carbon, oxygen, hydrogen and nitrogen in the target metabolites is considered by introduction of correction matrices. It is shown by simulation results for the central carbon metabolism that neglecting natural isotope distributions causes significant errors in intracellular flux distributions. By varying relative fluxes into pentosephosphate pathway and pyruvate carboxylation reaction, marked changes in the mass distributions of metabolites result, which are illustrated for pyruvate, oxaloacetate, and alpha-ketoglutarate. In addition mass distributions of metabolites are significantly influenced over a broad range by the degree of reversibility of transaldolase and transketolase reactions in the pentosephosphate pathway. The mass distribution of metabolites is very sensitive towards intracellular flux patterns and can be measured with high accuracy by routine mass spectrometry methods. Copyright 1999 John Wiley & Sons, Inc.     

Almost periodic solution of non-autonomous Lotka-Volterra predator-prey dispersal system with delays

This paper studies a non-autonomous Lotka-Volterra almost periodic predator-prey dispersal system with discrete and continuous time delays which consists of n-patches, the prey species can disperse among n-patches, but the predator species is confined to one patch and cannot disperse. By using comparison theorem and delay differential equation basic theory, we prove the system is uniformly persistent under some appropriate conditions. Further, by constructing suitable Lyapunov functional, we show that the system is globally asymptotically stable under some appropriate conditions. By using almost periodic functional hull theory, we show that the almost periodic system has a unique globally asymptotical stable strictly positive almost periodic solution. The conditions for the permanence, global stability of system and the existence, uniqueness of positive almost periodic solution depend on delays, so, time delays are "profitless". Finally, conclusions and two particular cases are given. These results are basically an extension of the known results for non-autonomous Lotka-Volterra systems.     

A kinetic inhibition mechanism for maintenance

To fulfil their maintenance costs, most species use mobile pools of metabolites (reserve) in favourable conditions, but can also use less mobile pools (structure) under food-limiting conditions. While some empirical models always pay maintenance costs from structure, the presence of reserve inhibits the use of structure for maintenance purposes. The standard dynamic energy budgets (DEB) model captures this by simply supplementing all costs that could not be paid from reserve with structure. This is less realistic at the biochemical level, and involves a sudden use of structure that can complicate the analysis of the model properties. We here propose a new inhibition formulation for the preferential use of reserve above structure in maintenance that avoids sudden changes in the metabolites use. It is based on the application of the theory for synthesizing units, which can easily become rather complex for demand processes, such as the maintenance. We found, however, a simple explicit expression for the use of reserve and structure for maintenance purposes and compared the numerical behaviour with that of a classical model in oscillating conditions, by using parameters values from a fit of the models to data on yeasts in a batch culture. We conclude that our model can better handle variable environments. This new inhibition formulation has a wide applicability in modelling metabolic processes.     

Information coding and oscillatory activity in synfire neural networks with and without inhibitory coupling

When a population spike (pulse-packet) propagates through a feedforward network with random excitatory connections, it either evolves to a sustained stable level of synchronous activity or fades away (Diesmann et al. in Nature 402:529-533 1999; Cateau and Fukai Neur Netw 14:675-685 2001). Here I demonstrate that in the presence of noise, the probability of the survival of the pulse-packet (or, equivalently, the firing rate of output neurons) reflects the intensity of the input. Furthermore, inhibitory coupling between layers can result in quasi- periodic alternation between several levels of firing activity. These results are obtained by analyzing the evolution of pulse-packet activity as a Markov chain. For the Markov chain analysis, the output of the chain is a linear mapping of the input into a lower-dimensional space, and the eigenvalues and eigenvectors of the transition matrix determine the dynamics of the evolution. Synchronous propagation of firing activity in successive pools of neurons are simulated in networks of integrate-and-fire and compartmental model neurons, and, consistent with the discrete Markov process, the activation of each pool is observed to be predominantly dependent upon the number of cells that fired in the previous pool. Simulation results agree with the numerical solutions of the Markov model. When inhibitory coupling between layers are included in the Markov model, some eigenvalues become complex numbers, implying oscillatory dynamics. The quasiperiodic dynamics is validated with simulation with leaky integrate-and-fire neurons. The networks demonstrate different modes of quasiperiodic activity as the inhibition or excitation parameters of the network are varied.     

Pathways of arachidonic acid metabolism in human amnion cells at term

We have compared the metabolism of (3H) arachidonic acid by monolayers of human amnion, cells obtained prior to or following labor at term. Radiolabel was either added exogenously or previously incorporated into cellular phospholipid pools to compare metabolism of arachidonic acid from different substrate sources. Cells obtained both prior to and following labor synthesized metabolites co-chromatographing on HPLC with di- and mono-HETEs and also a metabolite with polarity corresponding to a epoxyeicosatrienoic acid. Both types of cells were able to synthesize PGE2 when (3H) arachidonic acid was added exogenously. However, only those cells obtained following labor synthesized PGE2 from (3H) arachidonic acid incorporated into intracellular pools. These findings suggest that the cyclooxygenase and PGE2 isomerase enzymes are present in amnion prior to delivery but that exogenous arachidonic acid would be required for PGE2 synthesis at that time as the enzymes do not appear to be linked to a source of endogenous arachidonic acid. At the time of parturition, there may be a switching on of an enzyme system to generate arachidonic acid from intracellular pools specifically for PGE2 synthesis or alternatively coupling of such a system to a cyclooxygenase-PGE2 isomerase system resulting in PGE2 synthesis. These findings raise intriguing new possibilities for the regulation of eicosanoid synthesis in amnion which may include membrane topography, substrate pool-enzyme linking and regulation of specific phospholipase enzymes.