Bioinformatics Advance Access originally published online on March 7, 2007
Bioinformatics 2007 23(10):1258-1264; doi:10.1093/bioinformatics/btm082
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Metabolic systems cost-benefit analysis for interpreting network structure and regulation
Department of Chemical and Biological Engineering, Center for Biofilm Engineering, Montana State University, Bozeman, MT 59717, USA
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ABSTRACT |
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 TOP ABSTRACT 1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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Motivation: Interpretation of bioinformatics data in terms of cellular function is a major challenge facing systems biology. This question is complicated by robust metabolic networks filled with structural features like parallel pathways and isozymes. Under conditions of nutrient sufficiency, metabolic networks are well known to be regulated for thermodynamic efficiency however; efficient biochemical pathways are anabolically expensive to construct. While parameters like thermodynamic efficiency have been extensively studied, a systems-based analysis of anabolic proteome synthesis ‘costs’ and the cellular function implications of these costs has not been reported.
Results: A cost-benefit analysis of an in silico Escherichia coli network revealed the relationship between metabolic pathway proteome synthesis requirements, DNA-coding sequence length, thermodynamic efficiency and substrate affinity. The results highlight basic metabolic network design principles. Pathway proteome synthesis requirements appear to have shaped biochemical network structure and regulation. Under conditions of nutrient scarcity and other general stresses, E.coli expresses pathways with relatively inexpensive proteome synthesis requirements instead of more efficient but also anabolically more expensive pathways. This evolutionary strategy provides a cellular function-based explanation for common network motifs like isozymes and parallel pathways and possibly explains ‘overflow’ metabolisms observed during nutrient scarcity.
Contact: alicia{at}iastate.edu
Supplementary information: Supplementary data are available at Bioinformatics online.
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1 INTRODUCTION |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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Metabolic network structure is a reflection of ancient environments. A formal understanding of network design principles like the cellular function of parallel pathways and isozymes requires knowledge of evolutionary stresses and the competitive basis of the organism's adaptive response. The elemental composition of life is vastly different than the elemental composition of the Earth (Sterner and Elser, 2002). Scarce elemental resources, competition from other organisms and geochemical cycles are thought to have influenced the elemental make-up of microbes (Baudouin-Cornu et al., 2001; Bragg and Hyder, 2004; Giovanni et al., 2005). Evolutionary success necessitates competitive elemental investment strategies. For instance, E.coli DNA and amino acid sequences are reported to have been influenced by sulfur, nitrogen and energy scarcity (Akashi and Gojobori, 2002; Baudouin-Cornu et al., 2001, 2004; Bragg and Hyder, 2004).
During conditions of nutrient sufficiency, the role of thermodynamic efficiency on metabolic regulation has been well established both theoretically and experimentally (Carlson and Srienc, 2004a; Lehninger, 1975; Varma and Palsson, 1993; Varma et al., 1993). Under conditions of nutrient excess and nutrient scarcity, ‘overflow’ metabolisms, which deviate from maximum cellular thermodynamic efficiency, have been described (El-Mansi and Holms, 1989; Majewski and Domach, 1990; Neijssel et al., 1996; Teixeira de Mattos and Neijssel, 1997). It has been suggested that overflow metabolisms during conditions of nutrient excess are the result of loose substrate uptake control, limited citric acid cycle flux capacity or limited respiratory chain capacity (Holms, 1996). The cellular function of an overflow metabolism during times of nutrient starvation or environmental stress has been largely overlooked. While maintenance energy requirements are well known to lower cellular yields at low growth rates, the metabolic shift to enzymes with lowered thermodynamic efficiency has been a paradox (Neijssel et al., 1996; Teixeira de Mattos and Neijssel, 1997). This mystery highlights a major practical problem facing post-genomic biology, which is the lack of a formal understanding of network design principles (Huang, 2000).
Here, a cost-benefit analysis based on process design principles demonstrates that the E.coli metabolic network structure and function are a result of evolutionary pressures for strategic proteomic investment of scarce anabolic resources as well as for thermodynamic efficiency. The significance of investment costs, which here are defined as the elemental requirements to construct a functional metabolic pathway, has not been previously identified as an important selection pressure. Earlier network studies of E.coli growth focused only parameters like thermodynamic efficiency (for instance: Carlson and Srienc 2004a; Varma and Palsson, 1993). This study explicitly elucidates the relationships between metabolic pathway proteome synthesis requirements, pathway thermodynamic efficiency, enzyme-substrate affinity and DNA-coding sequence length for a network comprised of tens of millions of unique, mathematically defined pathways.
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2 METHODS |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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2.1 Economic analysis of metabolic pathways
The trade-off between capital investment costs and operating costs is a classic factory design challenge. As a polarized example, a factory assembly line can be constructed with expensive, automated, energy efficient equipment representing a ‘high investment cost-low operating cost’ strategy or an assembly line can be constructed with cheap, labor intensive, energy inefficient equipment representing a ‘low investment cost-high operating cost’ strategy. Optimal resolution of these trade-offs is typically determined through a multidimensional analysis of location-specific parameters like regional tax laws, labor costs and energy prices (Peters and Timmerhaus, 1980). Robust biochemical networks with numerous parallel pathways and isozymes represent an array of investment opportunities. Analogous to factory assembly lines, metabolic pathways can be constructed using different combinations of enzymes resulting in pathways with very different properties. It is hypothesized that the optimal resolution of the metabolic trade-off between pathway investment costs, which are equivalent to proteome synthesis requirements, and pathway operating costs, which reflect thermodynamic efficiency, can be resolved through multidimensional analysis of parameters like growth rate and the availability of anabolic and catabolic resources.
The E.coli central metabolism model is presented in Table S1 (Supplementary Material). The reaction stoichiometry, protein assignment for each reaction, enzyme subunit stoichiometry, and the carbon, nitrogen, sulfur, amino acid count and DNA-coding sequence requirements for each protein are listed. Enzyme assignments and subunit stoichiometries are based on data from EcoCyc, EcoGene and current literature (Kesseler et al., 2005; Rudd, 2000).
The metabolism model considers glucose as the sole energy source while glucose and CO2 are potential carbon sources. Seven different E.coli biomass compositions are considered. The biomass stoichiometries are listed in Table S2. The macromolecular composition can be found in Carlson and Srienc (2004a). The presented biomass compositions are used to test the robustness of the analysis to different cellular compositions. The biomass synthesis expression is based on the theory of Neidhardt et al. (1990) and considers the metabolite drain off the central metabolism. The individual enzymes involved in these biosynthetic reactions are not considered. The seven biomass expressions are normalized with respect to the ATP requirements so each doubling, time-dependent expression represents a different number of biomass Cmoles as listed in Table S2. These expressions only consider biosynthesis and do not include maintenance energy expenditures.
The in silico representation of the E.coli central metabolism was decomposed into its simplest, biologically relevant reaction sequences using elementary flux mode analysis (Schuster et al., 1994, 2000; Stelling et al., 2002). The elementary flux modes were identified using FluxAnalyzer (version 5.2) (Klamt et al., 2003). A flux mode is a mathematically defined biochemical pathway. A typical flux mode connects the conversion of substrates into products while balancing system carbon, redox and ATP fluxes. Considering a single growth rate and therefore a single biomass composition, 
3.4 million unique, flux modes were identified.
Flux modes are comprised of a series of metabolite membrane transport steps and chemical reactions. Each enzyme-catalyzed event requires an investment of anabolic resources for enzyme synthesis. The flux mode investment costs were calculated by translating the modes, which synthesize either biomass or ATP as a product, into sets of utilized enzymes. Investment costs were not calculated for other flux modes including futile cycles. These enzymes sets represent theoretical proteomes. Five different investment costs were calculated for each enzyme set. The atomic carbon, nitrogen and sulfur as well as the total number of amino acids required to synthesize each enzyme set were tabulated using proteomic databases (see Supplementary Material). The total number of amino acids is considered in addition to the three elements because this parameter can be correlated to cellular phosphorus requirements and energy charge (see Supplementary Material). The fifth tabulated cost was the number of DNA nucleotides required to code each enzyme set.
The atomic carbon, nitrogen, sulfur and amino acid investment costs considered enzyme expression levels. Pathway velocity was assumed to follow saturation-type kinetics analogous to enzymatic Michaelis–Menten kinetics and cellular Monod kinetics (Teixeira de Mattos and Neijssel, 1997). For low and high substrate concentrations, the kinetic expression can be simplified with either the first order or the zeroth order approximation, respectively. The presented study considers only environmental conditions that can be described by the first order kinetic approximation ([S] << Km) where 0 < µ << µmax. See Supplementary Material for a formal treatment of investment cost assumptions. The case for transporter substrate affinity is discussed in a later section. The zeroth order kinetics case will be presented elsewhere.
Flux mode operating costs were defined as the expenditure of substrate, either glucose or oxygen, to synthesize either one Cmole of biomass or one mole of ATP. Glucose was the sole considered energy source, so all flux modes that synthesized either biomass or ATP as a product consumed glucose. Operating costs were not calculated for futile cycles or pathways that did not produce either biomass or ATP. The operating costs were determined for the appropriate flux modes using a MATLAB subroutine which calculated the ratio of the Cmoles of substrate consumed to either the Cmoles of biomass produced or the moles of ATP produced. The biomass operating cost is equivalent to the inverse biomass yield and reflects the thermodynamic efficiency of the pathway (Carlson and Srienc, 2004a).
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3 RESULTS |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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3.1 Multidimensional costs analysis
The investment and operating costs for each flux mode were plotted as coordinates in a multidimensional space. The coordinate magnitudes reflect fundamental flux mode properties. For instance, Figure 1a illustrates the multidimensional relationship between nitrogen investment cost, glucose operating cost and oxygen operating cost for flux modes synthesizing biomass. Each sphere represents the coordinates of a unique flux mode producing 1 Cmole of biomass. Earlier network studies of E.coli growth analyzed oxygen and glucose fluxes that maximized thermodynamic efficiency (for instance: Carlson and Srienc, 2004a; Varma and Palsson, 1993). Figure 1a graphically illustrates how the current study adds additional dimensions of data to the previous work. Figure 1b–d highlights regions of interest in the 2-dimensional glucose operating cost/nitrogen investment cost plane. The data is broken into three separate plots, each with a different scale, to avoid compression of the high investment cost data points. If factory design principles are relevant to evolutionary design strategies, low costs are desirable. Flux modes with coordinates lying near the axes represent low-cost strategies. Considering Figure 1b, the flux modes labeled ‘1’ and ‘2’ lie nearest the ordinate and have the smallest glucose operating costs and therefore convert glucose into biomass with the highest efficiency. In Figure 1d, the flux mode labeled ‘12’ lies closest to the abscissa and has the smallest nitrogen investment cost. Between the minimal operating cost and the minimal investment cost strategies is a continuous set of strategies defined by a line segment envelope that minimizes the combined operating and investment costs. For the presented example, 12 unique flux modes are required to most economically span the possibilities between the minimal operating cost and the minimal investment cost strategies (see Table S5 in the Supplementary Material for an explicit listing of the 12 flux modes along the minimization envelope). The continuous ‘minimization envelope’ is explicitly defined by non-negative linear combinations of the flux modes labeled 1–12. Flux modes with coordinates above the minimization envelope have higher investment or higher operating costs than the strategies on the minimization envelope (Carlson and Srienc, 2004a). Additional orthogonal, 2-dimensional projections can be found in the Supplementary Material.
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Figure 2 highlights shifts in enzyme usage as a function of biomass composition, four investment costs and glucose operating costs. Isozymes and parallel pathway enzymes are of special interest. The enzyme patterns are from flux modes lying on their respective minimization envelope. The twelve flux modes which define the minimization envelope in Figure 1b–d are labeled in the nitrogen investment cost section for a 200-min doubling time. Each rectangle represents a single flux mode along the minimization envelope. The same minimization envelope flux modes are analyzed for usage of five different enzyme groupings. Data from seven biomass compositions are presented. The total number of flux modes along each minimization envelope varies between some biomass compositions. This was often due to a linear combination of flux modes which have equal and opposite fluxes in the pentose phosphate pathway reactions. When these flux modes are combined, the reaction flux sums to zero creating a situation where the associated enzyme is not required, creating a unique flux mode (Vijayasankaran et al., 2005). The pentose phosphate pathway fluxes vary depending on the biomass composition.
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–KGDc), the glyoxylate shunt isocitrate lyase enzyme (AceA), the oxidative branch of the pentose phosphate pathway (Zwf) and the Entner–Doudoroff pathway (Eda).Flux modes which minimize operating costs typically utilize enzymes with high thermodynamic efficiencies but also require relatively high anabolic resource investments. Flux modes in Figure 2 minimizing operating costs utilize the PEP-dependent PTS glucose transporter, the Embden–Meyerhof–Parnas glycolysis pathway, the pyruvate dehydrogenase complex (PDHc), cyclic TCA cycle fluxes including the resource intensive alpha–ketoglutarate dehydrogenase complex, the soluble transhydrogenase enzyme (UdhA) and the high yielding Nuo-cytochrome o electron transport chain. These modes do not secrete any partially oxidized by-products. The majority of the high investment cost-low operating cost strategy predictions have been experimentally established with nutrient sufficient chemostat growth (Alexeeva et al., 2000; Carlson and Srienc, 2004b; Iuchi and Lin, 1991; Sauer et al., 2004; Varma et al., 1993). When substrate uptake is limited to a constant rate, like in a chemostat, maximizing yields, which is equivalent to minimizing operating costs, has been recognized as a competitive strategy (Menlendez-Hevia et al., 1997).
Enzymes associated with minimal investment cost strategies typically have relatively low thermodynamic yields but the enzymes also have relatively small anabolic resource investment requirements. These flux modes utilize the galactose permease/glucose kinase (GalP/GlK) glucose transport and phosphorylation system, the Entner–Doudoroff pathway, the pyruvate formate lyase enzyme (Pfl), branched oxidative and reductive TCA cycle fluxes, the membrane-bound transhydrogenase (PntAB), and the lower proton motive force yielding Ndh-cytochrome d electron transport chain. These flux modes secrete partially oxidized products like formate and acetate. The majority of these enzyme usage patterns have been reported for experimental conditions with low anabolic resource availability or during nutrient starvation (Fischer and Sauer, 2003; Murray and Conway, 2005; Nyström and Gustavsson, 1998; Nyström and Neidhardt, 1993; Nyström et al., 1996). Another common experimental observation consistent with the low investment cost predictions is the reduced substrate yields reported during anabolic resource limitation (Teixeira de Mattos and Neijssel, 1997). Under conditions of resource scarcity, construction of a functional, inexpensive pathway seems to take precedence over thermodynamic efficiency. The inexpensive, less efficient pathways have properties analogous to the observed ‘overflow’ metabolism. In addition to permitting higher fluxes, the ‘overflow’ metabolism requires less resources to synthesize the associated pathway enzymes (Teixeira de Mattos and Neijssel, 1997). Additional references for proteomic studies supporting the predictions can be found in the Supplementary Material.
From the minimal operating cost scenario to the minimal investment cost scenario, the glucose operating costs increase by a factor of about 10 while the atomic investment costs decrease by a factor of 3.
3.2 General stress responses
The investment cost scenarios in Figure 2 predict general nutrient stress responses. Enzyme usage patterns for the four investment costs are all very similar. Escherichia coli possesses a family of general stress regulator proteins known as the universal stress proteins. The universal stress proteins are expressed during starvation for carbon, nitrogen, sulfate, phosphate and amino acids as well as during exposure to heat, oxidants, metals, ethanol, antibiotics and other stresses (Nachin et al., 2005). The enzymatic patterns of the low investment cost-high operating cost strategies are consistent with the reported universal stress protein mediated enzyme usage (Nachin et al., 2005; Nyström and Gustavsson, 1998; Nyström and Neidhardt, 1993; Nyström et al., 1996). Many bacteria are considered homeostatically regulated. The biomass carbon to nitrogen ratio (C:N) is nearly constant regardless of substrate C:N ratio (Sterner and Elser, 2002). Therefore, a limitation of either carbon or nitrogen requires a subsequent down shift in the investment of the other element. This is consistent with the present study. The flux mode enzyme C:N ratio as well as the C:S ratio for the minimization envelope are relatively constant regardless of a minimal operating cost or a minimal investment cost strategy (see Supplementary Material).
3.3 Evolutionary trade-off values
Nutrient-specific stress responses often involve expression of high affinity enzymes (Teixeira de Mattos and Neijssel, 1997). The high affinity E.coli glucose transporter (Mgl) and ammonia assimilation pathway (GOGAT) are two examples. These enzymes have both higher investment costs and higher operating costs than comparable parallel pathways and therefore are not predicted with the presented methodology. However, competitive evolutionary pressures have selected the use of these enzymes suggesting that under some circumstances, the added investment and operating costs are off-set by advantages of high substrate affinity. The relationship between investment costs, operating costs and enzyme affinity was analyzed to quantify the advantage of high substrate affinity in terms of investment costs. The operating cost and investment cost differences between the three glucose uptake systems are shown in Figure 3a. The investment cost difference (ordinate-axis) between the lower affinity GalP system and the higher affinity Mgl system increases as the flux mode carbon investment is minimized. The GalP system has a Km of 10 µM while the Mgl system Km is estimated to be less than 1 µM (Gosset, 2005; Manche et al., 1999). Increasing glucose affinity by an order of magnitude can translate into an investment cost of an additional 15 000 carbon atoms per flux mode. As a comparison, the PtsG system has a Km of 5 µM (Gosset, 2005). Ammonia assimilation affinity was also examined (Fig. 3b). The glutamate dehydrogenase (Gdh) ammonia assimilation path has a Km of 3 mM while the glutamine synthetase-glutamate synthase (GOGAT) ammonia assimilation system has a Km of <0.2 mM (Helling, 1994). Improving the ammonia affinity by approximately one order of magnitude can translate into an additional investment cost of 7500 nitrogen atoms per flux mode. High affinity enzymes, would in theory, permit higher metabolite fluxes than low affinity enzymes under the same low substrate concentration conditions which may justify the additional investment and operating costs.
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4 DISCUSSION |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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Thermodynamically efficient metabolic pathways require more resources to construct than less efficient pathways. The difference in metabolic pathway construction requirements seems to have resulted in regulation patterns that favor less expensive metabolic pathways during nutrient scarcity. A functional, inexpensive pathway seems to take precedence over thermodynamic efficiency during nutrient stress resulting in a lower yielding energy metabolism with properties analogous to an ‘overflow’ metabolism.
The current study supports the widely held view that E.coli evolved under nutrient feast and famine conditions (Koch, 1971). Escherichia coli can toggle between parallel pathways with high protein investment cost-low operating cost strategies or low protein investment cost-high operating cost strategies with minimal enzyme regulation to adapt to catabolic or anabolic nutrient ‘feasts or famines’. Velicer and Lenski (1999) studied E.coli fitness after consecutive rounds of nutrient abundance and nutrient scarcity. Strain fitness under nutrient abundance did not preclude its fitness under nutrient scarcity and vice versa. Evolutionary pressures have created an organism that carries the resource burden of numerous genetic instructions and numerous regulatory systems but has the advantage of being able to compete under a wide variety of nutritional environments.
Previous proteomic studies of central metabolism adaptations to starvation conditions suggest the responses are regulated at the protein synthesis level (Nyström and Gustavsson, 1998). Two major regulators in this starvation metabolic shift are the universal stress protein UspA and ArcA. ArcA is a well-studied regulator associated with the absence of an external electron acceptor and explains the numerous similarities between starvation and anaerobiosis enzyme usage patterns (Alexeeva et al., 2000; Nyström and Gustavsson, 1998; Nyström and Neidhardt, 1993). The presented, theoretical study also suggests that the nutrient scarcity response would be regulated at the level of protein translation and not necessarily enzyme activity. Synthesizing a protein that is inactive would represent a non-performing investment of resources. While there are cases of non-functioning protein subunits being synthesized, likely as an investment which prepares the cell for rapid changes in environmental conditions, these protein subunits are likely expressed at low levels especially during starvation conditions (Alexeeva et al., 2000).
There is much interest in minimal genome size, the minimal number of genes required for life, and the optimization of industrial organisms (Giovanni et al., 2005; Glass et al., 2006). Minimal genomes are not likely to carry many, if any, isozymes or parallel pathways. A theoretical minimal genome would only carry instructions for a limited number of metabolic strategies and a limited number of regulatory systems. In the present study, pathways that minimize investment costs require 66% fewer amino acids as compared to the minimal operating cost strategies. Not surprising, minimizing the number of amino acids also reduces the size of the DNA-coding sequences (Fig. S1 in Supplementary Material). However, there is not a simple linear correlation between the number of flux mode amino acids and the coding sequence length due to multimeric enzyme structure. The minimal amino acid investment strategy requires around 33% fewer DNA-coding nucleotides than the minimal operating cost scenario. Minimizing genomes raises an interesting evolutionary consideration. Primitive life likely started with a single metabolic strategy and only evolved additional strategies with time. The central metabolic portal of the E.coli minimal investment cost strategies is the Entner–Doudoroff pathway (Fig. 2). This pathway along with features like the branched use of the TCA cycle enzymes, the lack of oxidative phosphorylation, and absence of the PTS glucose transport system have all been cited as examples of a primitive paleometabolism (Menlendez-Hevia et al., 1997; Romano and Saier, 1992). This could suggest that E.coli has evolved toward strategies that minimize operating costs, however, at least key portions of primitive metabolic pathways have been retained because they offer competitive advantages during famines or other environmental stresses.
The current study considers 134 E.coli genes. For a single biomass composition, these genes can be arranged into 3.4 + million unique, mathematically defined biochemical pathways. Genome scale analysis will require improved computer memory architecture like a 64-bit system or more efficient software algorithms. The presented methodology applies cellular function to a metabolic network and then identifies the corresponding patterns of enzyme/gene usage. The approach provides a theoretical basis for studying critical network properties like the possible function of isozymes and parallel pathways. A comparison of low investment cost strategies, where proteome investment is minimized, with oxygen-limited, low operating cost strategies, where thermodynamic yield is maximized for the available oxygen, illustrates how different environmental stresses can have similar enzymatic usage patterns. For instance, competitive strategies for both environmental conditions utilize branched TCA cycle fluxes, the pyruvate formate-lyase enzyme, and both secrete partially oxidized by-products like acetate and formate (Carlson and Srienc, 2004b). However, the current study suggests there are metabolic adaptation differences between the two stresses. The Entner–Doudoroff pathway is used with low investment cost strategies instead of the Embden–Meyerhof–Parnas glycolysis pathway which is used with oxygen-limited, low operating cost strategies. This slight difference highlights the challenges facing approaches that first generate experimental patterns of enzyme/gene usage and then try to identify cellular function.
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ACKNOWLEDGEMENTS |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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The author would like to thank R. Hunt for plotting the data in Figure 1a, N. Vijayasankaran, D.A. Fell, P.S. Stewart and an anonymous reviewer for helpful manuscript suggestions, the Montana State University EPSCoR program, the College of Engineering, Vice President for Research, the Department of Chemical and Biological Engineering and the Center for Biofilm Engineering for their generous funding.
Conflict of Interest: none declared.
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FOOTNOTES |
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Associate Editor: Limsoon Wong
Received on November 2, 2006; revised on February 27, 2007; accepted on February 27, 2007
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