Glycolytic oscillations in a model of a lactic acid bacterium metabolism

Dynamic fluctuations in a bacterial metabolic network

The operation of the central metabolism is typically assumed to be deterministic, but dynamics and high connectivity of the metabolic network make it potentially prone to generating fluctuations. However, time-resolved measurements of metabolite levels in individual cells that are required to characterize such fluctuations remained a challenge, particularly in small bacterial cells. Here we use single-cell metabolite measurements based on Förster resonance energy transfer, combined with computer simulations, to explore the real-time dynamics of the metabolic network of Escherichia coli. We observe that steplike exposure of starved E. coli to glycolytic carbon sources elicits large periodic fluctuations in the intracellular concentration of pyruvate in individual cells. These fluctuations are consistent with predicted oscillatory dynamics of E. coli metabolic network, and they are primarily controlled by biochemical reactions around the pyruvate node. Our results further indicate that fluctuations in glycolysis propagate to other cellular processes, possibly leading to temporal heterogeneity of cellular states within a population.

Observability analysis and state reconstruction for networks of nonlinear systems

We address the problem of retrieving the full state of a network of Rössler systems from the knowledge of the actual state of a limited set of nodes. The selection of nodes where sensors are placed is carried out in a hierarchical way through a procedure based on graphical and symbolic observability approaches applied to pairs of coupled dynamical systems. By using a map directly obtained from governing equations, we design a nonlinear network reconstructor that is able to unfold the state of non-measured nodes with working accuracy. For sparse networks, the number of sensor scales with half the network size and node reconstruction errors are lower in networks with heterogeneous degree distributions. The method performs well even in the presence of parameter mismatch and non-coherent dynamics and for dynamical systems with completely different algebraic structures like the Hindmarsch-Rose; therefore, we expect it to be useful for designing robust network control laws.

Synchronisation of glycolytic activity in yeast cells

Glycolysis is the central metabolic pathway of almost every cell and organism. Under appropriate conditions, glycolytic oscillations may occur in individual cells as well as in entire cell populations or tissues. In many biological systems, glycolytic oscillations drive coherent oscillations of other metabolites, for instance in cardiomyocytes near anorexia, or in pancreas where they lead to a pulsatile release of insulin. Oscillations at the population or tissue level require the cells to synchronize their metabolism. We review the progress achieved in studying a model organism for glycolytic oscillations, namely yeast. Oscillations may occur on the level of individual cells as well as on the level of the cell population. In yeast, the cell-to-cell interaction is realized by diffusion-mediated intercellular communication via a messenger molecule. The present mini-review focuses on the synchronisation of glycolytic oscillations in yeast. Synchronisation is a quorum-sensing phenomenon because the collective oscillatory behaviour of a yeast cell population ceases when the cell density falls below a threshold. We review the question, under which conditions individual cells in a sparse population continue or cease to oscillate. Furthermore, we provide an overview of the pathway leading to the onset of synchronized oscillations. We also address the effects of spatial inhomogeneities (e.g., the formation of spatial clusters) on the collective dynamics, and also review the emergence of travelling waves of glycolytic activity. Finally, we briefly review the approaches used in numerical modelling of synchronized cell populations.

Clb3-centered regulations are recurrent across distinct parameter regions in minimal autonomous cell cycle oscillator designs

Some biological networks exhibit oscillations in their components to convert stimuli to time-dependent responses. The eukaryotic cell cycle is such a case, being governed by waves of cyclin-dependent kinase (cyclin/Cdk) activities that rise and fall with specific timing and guarantee its timely occurrence. Disruption of cyclin/Cdk oscillations could result in dysfunction through reduced cell division. Therefore, it is of interest to capture properties of network designs that exhibit robust oscillations. Here we show that a minimal yeast cell cycle network is able to oscillate autonomously, and that cyclin/Cdk-mediated positive feedback loops (PFLs) and Clb3-centered regulations sustain cyclin/Cdk oscillations, in known and hypothetical network designs. We propose that Clb3-mediated coordination of cyclin/Cdk waves reconciles checkpoint and oscillatory cell cycle models. Considering the evolutionary conservation of the cyclin/Cdk network across eukaryotes, we hypothesize that functional ("healthy") phenotypes require the capacity to oscillate autonomously whereas dysfunctional (potentially "diseased") phenotypes may lack this capacity.

Analysis of Raw Biofluids by Mass Spectrometry Using Microfluidic Diffusion-Based Separation

Elucidation and monitoring of biomarkers continues to expand because of their medical value and potential to reduce healthcare costs. For example, biomarkers are used extensively to track physiology associated with drug addiction, disease progression, aging, and industrial processes. While longitudinal analyses are of great value from a biological or healthcare perspective, the cost associated with replicate analyses is preventing the expansion of frequent routine testing. Frequent testing could deepen our understanding of disease emergence and aid adoption of personalized healthcare. To address this need, we have developed a system for measuring metabolite abundance from raw biofluids. Using a metabolite extraction chip (MEC), based upon diffusive extraction of small molecules and metabolites from biofluids using microfluidics, we show that biologically relevant markers can be measured in blood and urine. Previously it was shown that the MEC could be used to track metabolic changes in real-time. We now demonstrate that the device can be adapted to high-throughput screening using standard liquid chromatography mass spectrometry instrumentation (LCMS). The results provide insight into the sensitivity of the system and its application for the analysis of human biofluids. Quantitative analysis of clinical predictors including nicotine, caffeine, and glutathione are described.

Real-time digitization of metabolomics patterns from a living system using mass spectrometry

The real-time quantification of changes in intracellular metabolic activities has the potential to vastly improve upon traditional transcriptomics and metabolomics assays for the prediction of current and future cellular phenotypes. This is in part because intracellular processes reveal themselves as specific temporal patterns of variation in metabolite abundance that can be detected with existing signal processing algorithms. Although metabolite abundance levels can be quantified by mass spectrometry (MS), large-scale real-time monitoring of metabolite abundance has yet to be realized because of technological limitations for fast extraction of metabolites from cells and biological fluids. To address this issue, we have designed a microfluidic-based inline small molecule extraction system, which allows for continuous metabolomic analysis of living systems using MS. The system requires minimal supervision, and has been successful at real-time monitoring of bacteria and blood. Feature-based pattern analysis of Escherichia coli growth and stress revealed cyclic patterns and forecastable metabolic trajectories. Using these trajectories, future phenotypes could be inferred as they exhibit predictable transitions in both growth and stress related changes. Herein, we describe an interface for tracking metabolic changes directly from blood or cell suspension in real-time.

Optimizing metabolite production using periodic oscillations

Methods for improving microbial strains for metabolite production remain the subject of constant research. Traditionally, metabolic tuning has been mostly limited to knockouts or overexpression of pathway genes and regulators. In this paper, we establish a new method to control metabolism by inducing optimally tuned time-oscillations in the levels of selected clusters of enzymes, as an alternative strategy to increase the production of a desired metabolite. Using an established kinetic model of the central carbon metabolism of Escherichia coli, we formulate this concept as a dynamic optimization problem over an extended, but finite time horizon. Total production of a metabolite of interest (in this case, phosphoenolpyruvate, PEP) is established as the objective function and time-varying concentrations of the cellular enzymes are used as decision variables. We observe that by varying, in an optimal fashion, levels of key enzymes in time, PEP production increases significantly compared to the unoptimized system. We demonstrate that oscillations can improve metabolic output in experimentally feasible synthetic circuits.

A model reduction method for biochemical reaction networks

BACKGROUND

In this paper we propose a model reduction method for biochemical reaction networks governed by a variety of reversible and irreversible enzyme kinetic rate laws, including reversible Michaelis-Menten and Hill kinetics. The method proceeds by a stepwise reduction in the number of complexes, defined as the left and right-hand sides of the reactions in the network. It is based on the Kron reduction of the weighted Laplacian matrix, which describes the graph structure of the complexes and reactions in the network. It does not rely on prior knowledge of the dynamic behaviour of the network and hence can be automated, as we demonstrate. The reduced network has fewer complexes, reactions, variables and parameters as compared to the original network, and yet the behaviour of a preselected set of significant metabolites in the reduced network resembles that of the original network. Moreover the reduced network largely retains the structure and kinetics of the original model.

RESULTS

We apply our method to a yeast glycolysis model and a rat liver fatty acid beta-oxidation model. When the number of state variables in the yeast model is reduced from 12 to 7, the difference between metabolite concentrations in the reduced and the full model, averaged over time and species, is only 8%. Likewise, when the number of state variables in the rat-liver beta-oxidation model is reduced from 42 to 29, the difference between the reduced model and the full model is 7.5%.

CONCLUSIONS

The method has improved our understanding of the dynamics of the two networks. We found that, contrary to the general disposition, the first few metabolites which were deleted from the network during our stepwise reduction approach, are not those with the shortest convergence times. It shows that our reduction approach performs differently from other approaches that are based on time-scale separation. The method can be used to facilitate fitting of the parameters or to embed a detailed model of interest in a more coarse-grained yet realistic environment.