A key aim of postgenomic biomedical research is to systematically catalogue all molecules and their interactions within a living cell. There is a clear need to understand how these molecules and the interactions between them determine the function of this enormously complex machinery, both in isolation and when surrounded by other cells. Rapid advances in network biology indicate that cellular networks are governed by universal laws and offer a new conceptual framework that could potentially revolutionize our view of biology and disease pathologies in the twenty-first century.

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Network biology: understanding the cell's functional organization

How different is local cortical circuitry from a random network? To answer this question, we probed synaptic connections with several hundred simultaneous quadruple whole-cell recordings from layer 5 pyramidal neurons in the rat visual cortex. Analysis of this dataset revealed several nonrandom features in synaptic connectivity. We confirmed previous reports that bidirectional connections are more common than expected in a random network. We found that several highly clustered three-neuron connectivity patterns are overrepresented, suggesting that connections tend to cluster together. We also analyzed synaptic connection strength as defined by the peak excitatory postsynaptic potential amplitude. We found that the distribution of synaptic connection strength differs significantly from the Poisson distribution and can be fitted by a lognormal distribution. Such a distribution has a heavier tail and implies that synaptic weight is concentrated among few synaptic connections. In addition, the strengths of synaptic connections sharing pre- or postsynaptic neurons are correlated, implying that strong connections are even more clustered than the weak ones. Therefore, the local cortical network structure can be viewed as a skeleton of stronger connections in a sea of weaker ones. Such a skeleton is likely to play an important role in network dynamics and should be investigated further.

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Highly nonrandom features of synaptic connectivity in local cortical circuits.

An important goal of whole-cell computational modeling is to integrate detailed biochemical information with biological intuition to produce testable predictions. Based on the premise that prokaryotes such as Escherichia coli have maximized their growth performance along evolution, flux balance analysis (FBA) predicts metabolic flux distributions at steady state by using linear programming. Corroborating earlier results, we show that recent intracellular flux data for wild-type E. coli JM101 display excellent agreement with FBA predictions. Although the assumption of optimality for a wild-type bacterium is justifiable, the same argument may not be valid for genetically engineered knockouts or other bacterial strains that were not exposed to long-term evolutionary pressure. We address this point by introducing the method of minimization of metabolic adjustment (MOMA), whereby we test the hypothesis that knockout metabolic fluxes undergo a minimal redistribution with respect to the flux configuration of the wild type. MOMA employs quadratic programming to identify a point in flux space, which is closest to the wild-type point, compatibly with the gene deletion constraint. Comparing MOMA and FBA predictions to experimental flux data for E. coli pyruvate kinase mutant PB25, we find that MOMA displays a significantly higher correlation than FBA. Our method is further supported by experimental data for E. coli knockout growth rates. It can therefore be used for predicting the behavior of perturbed metabolic networks, whose growth performance is in general suboptimal. MOMA and its possible future extensions may be useful in understanding the evolutionary optimization of metabolism.

/pdf/analysis-of-optimality-in-natural-and-perturbed-metabolic-47u78sdbxx.pdf

Analysis of optimality in natural and perturbed metabolic networks

The advent of genome-scale models of metabo- lism has laid the foundation for the development of computational procedures for suggesting genetic manipu- lations that lead to overproduction. In this work, the computational OptKnock framework is introduced for suggesting gene deletion strategies leading to the over- production of chemicals or biochemicals in E. coli. This is accomplished by ensuring that a drain towards growth resources (i.e., carbon, redox potential, and energy) must be accompanied, due to stoichiometry, by the production of a desired product. Computational results for gene de- letions for succinate, lactate, and 1,3-propanediol (PDO) production are in good agreement with mutant strains published in the literature. While some of the suggested deletion strategies are straightforward and involve elimi- nating competing reaction pathways, many others suggest complex and nonintuitive mechanisms of compensating for the removed functionalities. Finally, the OptKnock procedure, by coupling biomass formation with chemical production, hints at a growth selection/adaptation sys- tem for indirectly evolving overproducing mutants. B 2003 Wiley Periodicals. Biotechnol Bioeng 85: 000-000, 2003.

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OptKnock: A Bilevel Programming Framework for Identifying Gene Knockout Strategies for Microbial Strain Optimization

http://sansan.phy.ncu.edu.tw/~hclee/SB_course/Sterlling_CellRobust_Cell04.pdf

Robustness of cellular functions

The intracellular carbon flux distribution in wild-type and pyruvate kinase-deficient Escherichia coli was estimated using biosynthetically directed fractional 13C labeling experiments with [U-13C6]glucose in glucose- or ammonia-limited chemostats, two-dimensional nuclear magnetic resonance (NMR) spectroscopy of cellular amino acids, and a comprehensive isotopomer model. The general response to disruption of both pyruvate kinase isoenzymes in E. coli was a local flux rerouting via the combined reactions of phosphoenolpyruvate (PEP) carboxylase and malic enzyme. Responses in the pentose phosphate pathway and the tricarboxylic acid cycle were strongly dependent on the environmental conditions. In addition, high futile cycling activity via the gluconeogenic PEP carboxykinase was identified at a low dilution rate in glucose-limited chemostat culture of pyruvate kinase-deficient E. coli, with a turnover that is comparable to the specific glucose uptake rate. Furthermore, flux analysis in mutant cultures indicates that glucose uptake in E. coli is not catalyzed exclusively by the phosphotransferase system in glucose-limited cultures at a low dilution rate. Reliability of the flux estimates thus obtained was verified by statistical error analysis and by comparison to intracellular carbon flux ratios that were independently calculated from the same NMR data by metabolic flux ratio analysis.

http://www.nmr2.buffalo.edu/resources/GFT/szyperski_publications_1st_page/szyperski%2057.pdf

Metabolic Flux Responses to Pyruvate Kinase Knockout in Escherichia coli

Many attempts to engineer cellular metabolism have failed due to the complexity of cellular functions. Mathematical and computational methods are needed that can organize the available experimental information, and provide insight and guidance for successful metabolic engineering. Two such methods are reviewed here. Both methods employ a (log)linear kinetic model of metabolism that is constructed based on enzyme kinetics characteristics. The first method allows the description of the dynamic responses of metabolic systems subject to spatiotemporal variations in their parameters. The second method considers the product-oriented, constrained optimization of metabolic reaction networks using mixed-integer linear programming methods. The optimization framework is used in order to identify the combinations of the metabolic characteristics of the glycolytic enzymes from yeast and bacteria that will maximize ethanol production. The methods are also applied to the design of microbial ethanol production metabolism. The results of the calculations are in qualitative agreement with experimental data presented here. Experiments and calculations suggest that, in resting Escherichia coli cells, ethanol production and glucose uptake rates can be increased by 30% and 20%, respectively, by overexpression of a deregulated pyruvate kinase, while increase in phosphofructokinase expression levels has no effect on ethanol production and glucose uptake rates.

Application of mathematical tools for metabolic design of microbial ethanol production.

Glucose catabolism of Escherichia coli strains with increased activity and altered regulation of key glycolytic enzymes.

Glycolytic fluxes in resting Escherichia coli were enhanced by overexpression of heterologous pyruvate kinases (Pyk) from Bacillus stearothermophilus and Zymomonas mobilis, but not homologous Pyk. Compared to the control, an increase of 10% in specific glucose consumption and of 15% in specific ethanol production rates was found in anaerobic resting cells, expressing the heterologous Pyks, that were harvested from exponentially growing aerobic cultures. A further increase in glycolytic flux was achieved by simultaneous overexpression of E. coli phosphofructokinase (Pfk) and Pyk with specific glucose consumption and ethanol production rates of 25% and 35% greater, respectively, than the control. Fluxes to lactate were not significantly affected, contrary to previous observations with resting cells harvested from anaerobically growing cultures. To correlate the physiology of resting cells with the physiology of cells prior to harvest, we determined the relevant growth parameters from aerobic and anaerobic precultures. We conclude that glycolytic fluxes in E. coli with submaximal (aerobic) metabolic activity can be increased by overexpression of pyruvate kinases which do not require allosteric activation or co-overexpression with Pfk. However, such improvements require more extensive engineering in E. coli with near maximal (anaerobic) metabolic activity.

Marcel Emmerling

Papers

Metabolic Flux Responses to Pyruvate Kinase Knockout in Escherichia coli

Application of mathematical tools for metabolic design of microbial ethanol production.

Glucose catabolism of Escherichia coli strains with increased activity and altered regulation of key glycolytic enzymes.

Altered regulation of pyruvate kinase or co-overexpression of phosphofructokinase increases glycolytic fluxes in resting Escherichia coli.