Thermodynamic efficiency of microbial growth is low but optimal for maximal growth rate

Flux balance analysis: a geometric perspective

Advances in the field of bioinformatics have led to reconstruction of genome-scale networks for a number of key organisms. The application of physicochemical constraints to these stoichiometric networks allows researchers, through methods such as flux balance analysis, to highlight key sets of reactions necessary to achieve particular objectives. The key benefits of constraint-based analysis lie in the minimal knowledge required to infer systemic properties. However, network degeneracy leads to a large number of flux distributions that satisfy any objective; moreover, these distributions may be dominated by biologically irrelevant internal cycles. By examining the geometry underlying the problem, we define two methods for finding a unique solution within the space of all possible flux distributions; such a solution contains no internal cycles, and is representative of the space as a whole. The first method draws on typical geometric knowledge, but cannot be applied to large networks because of the high computational complexity of the problem. Thus a second method, an iteration of linear programs which scales easily to the genome scale, is defined. The algorithm is run on four recent genome-scale models, and unique flux solutions are found. The algorithm set out here will allow researchers in flux balance analysis to exchange typical solutions to their models in a reproducible format. Moreover, having found a single solution, statistical analyses such as correlations may be performed.

Maximum power efficiency and criticality in random Boolean networks

Random Boolean networks are models of disordered causal systems that can occur in cells and the biosphere. These are open thermodynamic systems exhibiting a flow of energy that is dissipated at a finite rate. Life does work to acquire more energy, then uses the available energy it has gained to perform more work. It is plausible that natural selection has optimized many biological systems for power efficiency: useful power generated per unit fuel. In this Letter, we begin to investigate these questions for random Boolean networks using Landauer's erasure principle, which defines a minimum entropy cost for bit erasure. We show that critical Boolean networks maximize available power efficiency, which requires that the system have a finite displacement from equilibrium. Our initial results may extend to more realistic models for cells and ecosystems.

Bacterial physiology, regulation and mutational adaptation in a chemostat environment

The chemostat was devised over 50 years ago and rapidly adopted for studies of bacterial physiology and mutation. Despite the long history and earlier analyses, the complexity of events in continuous cultures is only now beginning to be resolved. The application of techniques for following regulatory and mutational changes and the identification of mutated genes in chemostat populations has provided new insights into bacterial behaviour. Inoculation of bacteria into a chemostat culture results in a population competing for a limiting amount of a particular resource. Any utilizable carbon source or ion can be a limiting nutrient and bacteria respond to limitation through a regulated nutrient-specific hunger response. In addition to transcriptional responses to nutrient limitation, a second regulatory influence in a chemostat culture is the reduced growth rate fixed by the dilution rate in individual experiments. Sub-maximal growth rates and hunger result in regulation involving sigma factors and alarmones like cAMP and ppGpp. Reduced growth rate also results in increased mutation frequencies. The combination of a strongly selective environment (where mutants able to compete for limiting nutrient have a major fitness advantage) and elevated mutation rates (both endogenous and through the secondary enrichment of mutators) results in a population that changes rapidly and persistently over many generations. Contrary to common belief, the chemostat environment is never in "steady state" with fixed bacterial characteristics usable for clean comparisons of physiological or regulatory states. Adding to the complexity, chemostat populations do not simply exhibit a succession of mutational sweeps leading to a dominant winner clone. Instead, within 100 generations large populations become heterogeneous and evolving bacteria adopt alternative, parallel fitness strategies. Transport physiology, metabolism and respiration, as well as growth yields, are highly diverse in chemostat-evolved bacteria. The rich assortment of changes in an evolving chemostat provides an excellent experimental system for understanding bacterial evolution. The adaptive radiation or divergence of populations into a collection of individuals with alternative solutions to the challenge of chemostat existence provides an ideal model system for testing evolutionary and ecological theories on adaptive radiations and the generation of bacterial diversity.

The energy spilling reactions of bacteria and other organisms

For many years it was assumed that living organisms always utilized ATP in a highly efficient manner, but simple growth studies with bacteria indicated that the efficiency of biomass production was often at least 3-fold lower than the amount that would be predicted from standard biosynthetic pathways. The utilization of energy for maintenance could only explain a small portion of this discrepancy particularly when the growth rate was high. These ideas and thermodynamic arguments indicated that cells might have another avenue of energy utilization. This phenomenon has also been called 'uncoupling', 'spillage' and 'overflow metabolism', but 'energy spilling' is probably the most descriptive term. It appears that many bacteria spill energy, and the few that do not can be killed (large and often rapid decrease in viability), if the growth medium is nitrogen-limited and the energy source is in 'excess'. The lactic acid bacterium, Streptococcus bovis, is an ideal bacterium for the study of energy spilling. Because it only uses substrate level phosphorylation to generate ATP, ATP generation can be calculated with a high degree of certainty. It does not store glucose as glycogen, and its cell membrane can be easily accessed. Comparative analysis of heat production, membrane voltage, ATP production and Ohm's law indicated that the energy spilling reaction of S. bovis is mediated by a futile cycle of protons through the cell membrane. Less is known about Escherichia coli, but in this bacterium energy spilling could be mediated by a futile cycle of potassium or ammonium ions. Energy spilling is not restricted to prokaryotes and appears to occur in yeasts and in higher organisms. In man, energy spilling may be related to cancer, ageing, ischemia and cardiac failure.

Something from nothing: bridging the gap between constraint-based and kinetic modelling

Two divergent modelling methodologies have been adopted to increase our understanding of metabolism and its regulation. Constraint-based modelling highlights the optimal path through a stoichiometric network within certain physicochemical constraints. Such an approach requires minimal biological data to make quantitative inferences about network behaviour; however, constraint-based modelling is unable to give an insight into cellular substrate concentrations. In contrast, kinetic modelling aims to characterize fully the mechanics of each enzymatic reaction. This approach suffers because parameterizing mechanistic models is both costly and time-consuming. In this paper, we outline a method for developing a kinetic model for a metabolic network, based solely on the knowledge of reaction stoichiometries. Fluxes through the system, estimated by flux balance analysis, are allowed to vary dynamically according to linlog kinetics. Elasticities are estimated from stoichiometric considerations. When compared to a popular branched model of yeast glycolysis, we observe an excellent agreement between the real and approximate models, despite the absence of (and indeed the requirement for) experimental data for kinetic constants. Moreover, using this particular methodology affords us analytical forms for steady state determination, stability analyses and studies of dynamical behaviour.

Switching between cooperation and competition in the use of extracellular glucose

This paper addresses some questions related to the evolution of cooperative behaviors, in the context of energetic metabolism. Glycolysis can perform either under a dissipative working regime suitable for rapid proliferation or under an efficient regime that entails a good modus operandi under conditions of glucose shortage. A cellular mechanism allowing switching between these two regimes may represent an evolutionary achievement. Thus, we have explored the conditions that might have favored the emergence of such an accommodative mechanism. Because of an inevitable conflict for resources between individual interests and the common good, rapid and inefficient use of glucose is always favored by natural selection in spatially homogeneous environment, regardless of the external conditions. In contrast, when the space is structured, the behavior of the system is determined by its free energy content. If the fuel is abundant, the dissipative strategy dominates the space. However, under famine conditions the efficient regime represents an evolutionary stable strategy in a Harmony game. Between these two extreme situations, both metabolic regimes are engaged in a Prisoner's Dilemma game, where the output depends on the extracellular free energy. The energy transition values that lead from one domain to another have been calculated. We conclude that an accommodative mechanism permitting alternation between dissipative and efficient regimes might have evolved in heterogeneous and highly fluctuating environments. Overall, the current work shows how evolutionary optimization and game-theoretical approaches can be complementary in providing useful insights into biochemical systems.

Divergence and redundancy of transport and metabolic rate-yield strategies in a single Escherichia coli population

The energetic efficiency of nutrient uptake and conversion into biomass is a key factor in the ecological behavior of microorganisms. The constraints shaping the metabolic rate-yield trade-off in bacteria are not well understood. To examine whether metabolic rate-yield settings and physiological strategies evolve toward a particular optimum in a constant environment, we studied multiple Escherichia coli isolates evolving in a glucose-limited chemostat population. A major divergence in transport and metabolic strategies was observed, and the isolates included inefficient rate strategists (polluters or cheaters) and yield strategists (conservationists), as well as various hybrid rate-yield strategists and alternative ecotypes (dropouts). Sugar transport assays, strain comparisons based on metabolomics, and Biolog profiling revealed variance to the point of individuality within an evolving population. Only 68 of 177 metabolites assayed were not affected in 10 clonally related strains. The parallel enrichment of rate and yield strategists and the divergence in metabolic phylogenies indicate that bacteria do not converge on a particular rate-yield balance or unique evolutionary solutions. Redundancies in transport and metabolic pathways are proposed to have laid the framework for the multiplicity of bacterial adaptations.

Physiology of Zymomonas mobilis: some unanswered questions

The ethanol-producing bacterium Zymomonas mobilis can serve as a model organism for the study of rapid catabolism and inefficient energy conversion in bacteria. Some basic aspects of its physiology still remain poorly understood. Here, the energy-spilling pathways during uncoupled growth, the structure and function of electron transport chain, and the possible reasons for the inefficient oxidative phosphorylation are analysed. Also, the interaction between ethanol synthesis and respiration is considered. The search for mechanisms of futile transmembrane proton cycling, as well as identification of respiratory electron transport complexes, like the energy-coupling NAD(P)H:quinone oxidoreductase and the cyanide-sensitive terminal oxidase(s), are outlined as the key problems for further research of Z. mobilis energy metabolism.

Growth yield homeostasis in respiring yeast is due to a strict mitochondrial content adjustment

In living cells, growth is the result of coupling between substrate catabolism and multiple metabolic processes taking place during net biomass formation and cell property maintenance. A crucial parameter for growth description is its yield, i.e. the efficiency of the transformation from substrate consumption to biomass formation. Using numerous yeast strains growing on different respiratory media, we have shown that the growth yield is identical regardless of the strain, growth phase, and respiratory substrate used. This homeostasis is the consequence of a strict linear relationship between growth and respiratory rates. Moreover, in all conditions tested, the oxygen consumption rate was strictly controlled by the cellular content of respiratory chain compounds in such a way that, in vivo, the steady state of oxidative phosphorylation was kept constant. Thus, the growth yield homeostasis depends on the tight adjustment of the cellular content of respiratory chain compounds to the growth rate. Any process leading to a defect in this adjustment allows an energy waste and consequently an energy yield decrease.

The multifarious short-term regulation of ammonium assimilation of Escherichia coli: dissection using an in silico replica

Ammonium assimilation in Escherichia coli is regulated through multiple mechanisms (metabolic, signal transduction leading to covalent modification, transcription, and translation), which (in-)directly affect the activities of its two ammonium-assimilating enzymes, i.e. glutamine synthetase (GS) and glutamate dehydrogenase (GDH). Much is known about the kinetic properties of the components of the regulatory network that these enzymes are part of, but the ways in which, and the extents to which the network leads to subtle and quasi-intelligent regulation are unappreciated. To determine whether our present knowledge of the interactions between and the kinetic properties of the components of this network is complete - to the extent that when integrated in a kinetic model it suffices to calculate observed physiological behaviour - we now construct a kinetic model of this network, based on all of the kinetic data on the components that is available in the literature. We use this model to analyse regulation of ammonium assimilation at various carbon statuses for cells that have adapted to low and high ammonium concentrations. We show how a sudden increase in ammonium availability brings about a rapid redirection of the ammonium assimilation flux from GS/glutamate synthase (GOGAT) to GDH. The extent of redistribution depends on the nitrogen and carbon status of the cell. We develop a method to quantify the relative importance of the various regulators in the network. We find the importance is shared among regulators. We confirm that the adenylylation state of GS is the major regulator but that a total of 40% of the regulation is mediated by ADP (22%), glutamate (10%), glutamine (7%) and ATP (1%). The total steady-state ammonium assimilation flux is remarkably robust against changes in the ammonium concentration, but the fluxes through GS and GDH are completely nonrobust. Gene expression of GOGAT above a threshold value makes expression of GS under ammonium-limited conditions, and of GDH under glucose-limited conditions, sufficient for ammonium assimilation.

The ATP paradox is the expression of an economizing fuel mechanism

The strong negative correlation between glycolytic flux and intracellular ATP concentration observed in yeast has long been an intriguing and counterintuitive phenomenon, which has been referred to as the ATP paradox. Herein, using principles of irreversible thermodynamics it was shown that if the ATP-consuming pathways are more sensitive to extracellular glucose than glycolysis, then upon glucose addition glycolysis performance can switch from an efficient working regime to a dissipative regime, and vice versa, depending on glucose availability. The efficient regime represents a good compromise between high output power and low dissipation, whereas the dissipative working regime offers a higher output power although at a high glucose cost. The physiological and evolutionary implications of this switch strategy are discussed.

Glutamine breakdown in rapidly dividing cells: waste or investment?

Tumours, and in general rapidly dividing cells, behave as dissipative devices that apparently waste glutamine, since its consumption seems to exceed both energetic and nitrogen needs. Although not conclusive, there is compelling evidence suggesting that the consumption of such large amounts of glutamine is essential to sustain high rates of cellular proliferation. Herein, I first review the experimental evidence linking proliferation with high rates of glutamine breakdown. Then, the current knowledge on the proteins and activities involved in this high glutamine consumption will be summarized. Finally, the significance of the apparent waste of glutamine will be discussed on bioenergetic grounds. The discussion leads to the hypothesis that glutamine breakdown might energize some endergonic processes, as well as accelerating other exergonic processes related to cellular proliferation.

Thermodynamics and bioenergetics

Bioenergetics is concerned with the energy conservation and conversion processes in a living cell, particularly in the inner membrane of the mitochondrion. This review summarizes the role of thermodynamics in understanding the coupling between the chemical reactions and the transport of substances in bioenergetics. Thermodynamics has the advantages of identifying possible pathways, providing a measure of the efficiency of energy conversion, and of the coupling between various processes without requiring a detailed knowledge of the underlying mechanisms. In the last five decades, various new approaches in thermodynamics, non-equilibrium thermodynamics and network thermodynamics have been developed to understand the transport and rate processes in physical and biological systems. For systems not far from equilibrium the theory of linear non-equilibrium thermodynamics is used, while extended non-equilibrium thermodynamics is used for systems far away from equilibrium. All these approaches are based on the irreversible character of flows and forces of an open system. Here, linear non-equilibrium thermodynamics is mostly discussed as it is the most advanced. We also review attempts to incorporate the mechanisms of a process into some formulations of non-equilibrium thermodynamics. The formulation of linear non-equilibrium thermodynamics for facilitated transport and active transport, which represent the key processes of coupled phenomena of transport and chemical reactions, is also presented. The purpose of this review is to present an overview of the application of non-equilibrium thermodynamics to bioenergetics, and introduce the basic methods and equations that are used. However, the reader will have to consult the literature reference to see the details of the specific applications.

The calorimetric-respirometric ratio is an on-line marker of enthalpy efficiency of yeast cells growing on a non-fermentable carbon source

Although on-line calorimetry has been widely used to detect transitions in global metabolic activity during the growth of microorganisms, the relationships between oxygen consumption flux and heat production are poorly documented. In this work, we developed a respirometric and calorimetric approach to determine the enthalpy efficiency of respiration-linked energy transformation of isolated yeast mitochondria and yeast cells under growing and resting conditions. On isolated mitochondria, the analysis of different phosphorylating and non-phosphorylating steady states clearly showed that the simultaneous measurements of heat production and oxygen consumption rates can lead to the determination of both the enthalpy efficiency and the ATP/O yield of oxidative phosphorylation. However, these determinations were made possible only when the net enthalpy change associated with the phosphorylating system was different from zero. On whole yeast cells, it is shown that the simultaneous steady state measurements of the heat production and oxygen consumption rates allow the enthalpy growth efficiency (i.e. the amount of energy conserved as biomass compared to the energy utilised for complete catabolism plus anabolism) to be assessed. This method is based on the comparison between the calorimetric-respirometric ratio (CR ratio) determined under growth versus resting conditions during a purely aerobic metabolism. Therefore, in contrast to the enthalpy balance approach, this method does not rely on the exhaustive and tedious determinations of the metabolites and elemental composition of biomass. Thus, experiments can be performed in the presence of non-limiting amounts of carbon substrate, an approach which has been successfully applied to slow growing cells such as yeast cells expressing wild-type or a mutant rat uncoupling protein-1.

Glucose and the ATP paradox in yeast

A sustained decrease in the intracellular ATP concentration has been observed when extra glucose was added to yeast cells growing aerobically under glucose limitation. Because glucose degradation is the main source of ATP-derived free energy, this is a counter-intuitive phenomenon, which cannot be attributed to transient ATP consumption in the initial steps of glycolysis. We present a core model for aerobic growth in which glucose supplies carbon, as well as free energy, for biosynthesis. With Metabolic Control Analysis and numerical simulations, we demonstrate that the decrease in the ATP concentration can be reproduced if the biosynthetic route is more strongly activated by carbon substrates than is the catabolic (ATP-producing) route.

Thermodynamic analysis of growth of methanobacterium thermoautotrophicum

Growth of Methanobacterium thermoautotrophicum, an anaerobic archaebacterium using methanogenesis as the catabolic pathway, is characterized by large heat production rates, up to 13 W g-1, and low biomass yields, in the order of 0.02 C-mol mol-1 H2 consumed. These values, indicating a possibly "inefficient" growth mechanism, warrant a thermodynamic analysis to obtain a better understanding of the growth process. The growth-associated heat production (DeltarHX0, min) and the growth-associated Gibbs energy dissipation per mol biomass formed (DeltarGXmin) were -3730 kJ C-mol-1 and -802 kJ C-mol-1, respectively. The Gibbs energy change found in this study is indeed unusually high as compared to aerobic methylotrophes, but not untypical for methanogens grown on CO2. It explains the low biomass yield. Based on the information available on the energetic metabolism and on an ATP balance, the biomass yield can be predicted to be approximately in the range of the experimentally determined value. The fact that the exothermicity exceeds vastly even the Gibbs energy change can be explained by a dramatic entropy decrease of the catabolic reaction. Microbial growth characterized by entropy reduction and correspondingly by unusually large heat production may be called entropy-retarded growth. Copyright 1999 John Wiley & Sons, Inc.

Energetics of bacterial growth: balance of anabolic and catabolic reactions

Biomass formation represents one of the most basic aspects of bacterial metabolism. While there is an abundance of information concerning individual reactions that result in cell duplication, there has been surprisingly little information on the bioenergetics of growth. For many years, it was assumed that biomass production (anabolism) was proportional to the amount of ATP which could be derived from energy-yielding pathways (catabolism), but later work showed that the ATP yield (YATP) was not necessarily a constant. Continuous-culture experiments indicated that bacteria utilized ATP for metabolic reactions that were not directly related to growth (maintenance functions). Mathematical derivations showed that maintenance energy appeared to be a growth rate-independent function of the cell mass and time. Later work, however, showed that maintenance energy alone could not account for all the variations in yield. Because only some of the discrepancy could be explained by the secretion of metabolites (overflow metabolism) or the diversion of catabolism to metabolic pathways which produced less ATP, it appeared that energy-excess cultures had mechanisms of spilling energy. Bacteria have the potential to spill excess ATP in futile enzyme cycles, but there has been little proof that such cycles are significant. Recent work indicated that bacteria can also use futile cycles of potassium, ammonia, and protons through the cell membrane to dissipate ATP either directly or indirectly. The utility of energy spilling in bacteria has been a curiosity. The deprivation of energy from potential competitors is at best a teleological explanation that cannot be easily supported by standard theories of natural selection. The priming of intracellular intermediates for future growth or protection of cells from potentially toxic end products (e.g., methylglyoxal) seems a more plausible explanation.

Energy flux and osmoregulation of Saccharomyces cerevisiae grown in chemostats under NaCl stress

The energetics and accumulation of solutes in Saccharomyces cerevisiae were investigated for cells grown aerobically in a chemostat under NaCl stress and glucose limitation. Changed energy requirements in relation to external salinity were examined by energy balance determinations performed by substrate and product analyses, with the latter including heat measurements by microcalorimetry. In both 0 and 0.9 M NaCl cultures, the catabolism was entirely respiratory at the lowest dilution rates tested but shifted to a mixed respiratory-fermentative metabolism at higher dilution rates. This shift occurred at a considerably lower dilution rate for salt-grown cells. The intracellular solute concentrations, as calculated on the basis of intracellular soluble space determinations, showed that the internal Na+ concentration increased from about 0.02 molal in basal medium to about 0.18 molal in 0.9 M NaCl medium, while intracellular K+ was maintained around 0.29 molal despite the variation in external salinity. The intracellular glycerol concentration increased from below 0.05 molal at low salinity to about 1.2 molal at 0.9 M NaCl. The concentrations of the internal solutes, however, changed insignificantly with growth rate and energy metabolism. The additional maintenance energy expenditure for growth at 0.9 M NaCl was, depending on the growth rate, 14 to 31% of the total energy requirement for growth at 0 M NaCl. Including the energy conserved in glycerol, the total additional energy demand for growth at 0.9 M NaCl corresponded to 28 to 51% of the energy required for growth at 0 M NaCl.

The relation of proton motive force, adenylate energy charge and phosphorylation potential to the specific growth rate and efficiency of energy transduction in Bacillus licheniformis under aerobic growth conditions

The magnitude of the proton motive force (delta p) and its constituents, the electrical (delta psi) and chemical potential (-Z delta pH), were established for chemostat cultures of a protease-producing, relaxed (rel-) variant and a not protease-producing, stringent (rel+) variant of an industrial strain of Bacillus licheniformis (respectively referred to as the A- and the B-type). For both types, an inverse relation of delta p with the specific growth rate mu was found. The calculated intracellular pH (pHin) was not constant but inversely related to mu. This change in pHin might be related to regulatory functions of metabolism but a regulatory role for pHin itself could not be envisaged. Measurement of the adenylate energy charge (EC) showed a direct relation with mu for glucose-limited chemostat cultures; in nitrogen-limited chemostat cultures, the EC showed an approximately constant value at low mu and an increased value at higher mu. For both limitations, the ATP/ADP ratio was directly related to mu. The phosphorylation potential (delta G'p) was invariant with mu. From the values for delta G'p and delta p, a variable -->H+/ATP-stoichiometry was inferred: -->H+/ATP = 1.83 +/- 0.52 mu, so that at a given -->H+/O-ratio of four (4), the apparent P/O-ratio (inferred from regression analysis) showed a decline of 2.16 to 1.87 for mu = 0 to mu max (we discuss how more than half of this decline will be independent of any change in internal cell-volume). We propose that the constancy of delta G'p and the decrease in the efficiency of energy-conservation (P/O-value) with increasing mu are a way in which the cells try to cope with an apparent less than perfect coordination between anabolism and catabolism to keep up the highest possible mu with a minimum loss of growth-efficiency. Protease production in nitrogen-limited cultures as compared to glucose-limited cultures, and the difference between the A- and B-type, could not be explained by a different energy-status of the cells.

Quantifying heterogeneity: flow cytometry of bacterial cultures

Flow cytometry is a technique which permits the characterisation of individual cells in populations, in terms of distributions in their properties such as DNA content, protein content, viability, enzyme activities and so on. We review the technique, and some of its recent applications to microbiological problems. It is concluded that cellular heterogeneity, in both batch and continuous axenic cultures, is far greater than is normally assumed. This has important implications for the quantitative analysis of microbial processes.

Quantitative approaches to the analysis of the control and regulation of microbial metabolism

Recently, a number of novel ways of considering the control, regulation and thermodynamics of microbial physiology have been developed and applied. We here present an overview of the new concepts involved, of their limitations and of the most recent attempts to deal with those limitations. We conclude that there no longer exist reasons of principle for vagueness in discussions of the control of microbial physiology and energetics. Further, the novel conceptual methods serve to remove part of the discordance between holistic and reductionistic views of microbial physiology.

A re-assessment of bacterial growth efficiency: the heat production and membrane potential of Streptococcus bovis in batch and continuous culture

Glucose-limited, continuous cultures (dilution rate 0.1 h-1) of Streptococcus bovis JB1 fermented glucose at a rate of 3.9 mumol mg protein-1 h-1 and produced acetate, formate and ethanol. Based on a maximum ATP yield of 32 cells/mol ATP (Stouthamer 1973) and 3 ATP/glucose, the theoretical glucose consumption for growth would have been 2.1 mumol mg protein-1 h-1. Because the maintenance energy requirement was 1.7 mumol/mg protein/h (Russell and Baldwin 1979), virtually all of the glucose consumption could be explained by growth and maintenance and the YATP was 30. Glucose-limited, continuous cultures produced heat at a rate of 0.29 mW/mg protein, and this value was similar to the enthalpy change of the fermentation (0.32 mW/mg protein). Batch cultures (specific growth rate 2.0 h-1) fermented glucose at a rate of 81 mumol mg protein-1 h-1, and produced only lactate. The heat production was in close agreement with the theoretical enthalpy change (1.72 versus 1.70 mW/mg protein), but only 80% of the glucose consumption could be accounted by growth and maintenance. The YATP of the batch cultures was 25. Nitrogen-limited, glucose-excess, non-growing cultures fermented glucose at a rate of 6.9 mumol mg protein-1 h-1, and virtually all of the enthalpy for this homolactic fermentation could be accounted as heat (0.17 mW/mg protein). The nitrogen-limited cultures had a membrane potential of 150 mV, and nearly all of the heat production could be explained by a futile cycle of protons through the cell membrane (watts = amperes X voltage where H+/ATP was 3).(ABSTRACT TRUNCATED AT 250 WORDS)

Effect of concentration of substrates and products on the growth of Klebsiella pneumoniae in chemostat cultures

Non-equilibrium thermodynamics (NET) can be used to describe microbial growth. In this description, the concentrations of products contribute to the driving forces of the metabolic processes (anabolism and catabolism). Thus, in contrast to the model of bacterial growth of Monod (Recherches sur la Croissance les Cultures Bactériennes (1942) Herman et Cie, Paris), it is predicted that the growth rate of a bacterial chemostat culture is, in principle, dependent on the concentration of the catabolic product (for instance HCO3-) during catabolite limitation and on the concentration of the anabolic product (for instance biomass) during anabolite limitation. In order to test this prediction, Klebsiella pneumoniae was grown in aerobic citrate-limited, glucose-limited or ammonia-limited chemostat cultures. Ammonia-limited cultures were considered to be essentially anabolite-limited, whereas citrate limitation was used as a representative for catabolite limitation. In ammonia-limited or in glucose-limited cultures it was found that the growth rate was independent of the biomass concentration present. In the NET description this means that the 'back' reaction (i.e., in the direction from biomass to substrates) is saturated with respect to biomass. On the other hand, in citrate-limited cultures, the steady-state concentration of citrate increased with the concentration of the catabolic product HCO3-. At relatively low concentrations of HCO3-, 'thermodynamic back-pressure' of growth (i.e., increase in product concentration was compensated by an increase in substrate concentration so that the driving force for growth remained almost constant) was demonstrated as predicted by the NET model. At concentrations above 40 mM, a kinetic (allosteric) effect of HCO3- was detected. This was concluded from a reduced growth yield on citrate, and from a significant decrease in the maximal growth rate and the maximal oxygen consumption rate after relief of the citrate limitation.

Energy coupling and Hill cycles in enzymatic processes

We review how Hill's work on enzyme catalysis has nurtured our understanding of the mechanism by which enzymes can couple downhill processes to uphill processes. More specifically, we discuss the following questions: (i) Does it make sense to distinguish the chemical potential of the bound ligand from that of the binding enzyme? (ii) To what extent can free-energy transduction be localized at some crucial step in the catalytic cycle? (iii) Need enzymes be optimized so as to even out the profile of basic free energy along the catalytic cycle? (iv) How do continuous models of conformational transitions relate to discrete state diagrams and their kinetic elaborations? We conclude that (1) only in very special cases is it useful to designate a portion of the free energy of the enzyme-ligand complex as the free energy of the bound ligand; (2) only for some mechanisms can free-energy transduction be localized within a part of the catalytic cycle; (3) only in special cases should one expect enzymes to be "optimized" so as to have smooth basic free-energy profiles; and (4) transition rate constants can often be related to conformational diffusion constants, although in certain situations the kinetic description of an enzyme as if jumping between discrete states is impracticable; a diffusion-type description may then be preferable.

Variation of efficiency with free-energy dissipation in models of biological energy transduction

For two models of biological free-energy transducers, it is investigated how free-energy dissipation and efficiency vary as (i) the demand for output free energy, (ii) the input free energy or (iii) the properties of the transducers themselves, are varied. One model is representative of near-equilibrium free-energy transducers in general, the other is a special case of far-from-equilibrium free-energy transduction, reminiscent of proton pumping by bacteriorhodopsin. It turns out that the relationship between efficiency and free-energy dissipation depends strongly on what varies. In some cases, free-energy dissipation increases as the efficiency increases. It is suggested that this is one reason why biological evolution has not resulted in high efficiencies and low rates of free-energy dissipation. For the near-equilibrium free-energy transducer, the free-energy dissipation at the static head steady state is minimal with respect to variations in the output force. For the far-from-equilibrium model (of bacteriorhodopsin), the static head does not correspond to such a minimum, if that free-energy transducer slips.

Heat production by ruminal bacteria in continuous culture and its relationship to maintenance energy

Selenomonas ruminantium HD4 and Bacteroides ruminicola B(1)4 were grown in continuous culture with glucose as the energy source, and heat production was measured continuously with a microcalorimeter. Because the bacteria were grown under steady-state conditions, it was possible to calculate complete energy balances for substrate utilization and product formation (cells, fermentation acids, and heat). As the dilution rate increased from 0.04 to 0.60 per h, the heat of fermentation declined from 19 to 2% and from 34 to 8% for S. ruminantium and B. ruminicola, respectively. At slow dilution rates the specific rate of heat production remained relatively constant (135 mW/g [dry weight] or 190 mW/g of protein for S. ruminantium and 247 mW/g [dry weight] or 467 mW/g of protein for B. ruminicola). Since the heat due to growth-related functions was small compared to maintenance expenditures, total heat production provided a reasonable estimate of maintenance under glucose-limiting conditions. As the dilution rate was increased, glucose eventually accumulated in the chemostat vessel and the specific rates of heat production increased more than twofold. Pulses of glucose added to glucose-limited cultures (0.167 per h) caused an immediate doubling of heat production and little increase in cell protein. These experiments indicate that bacterial maintenance energy is not necessarily a constant and that energy source accumulation was associated with an increase in heat production.

The protein burden of lac operon products

A new approach to measuring the slowing of growth due to the manufacture of proteins not needed by a bacterium is presented. An entire single colony of Escherichia coli was used to start a chemostat culture that was then given a selective pressure by the addition of phenylgalactoside (phi-gal). This enriched the population for constitutive mutants that produced beta-galactosidase without induction and could split phi-gal, consume the galactose, and grow faster. When the phi-gal was removed, the constitutives grew slower than the parental strain and were gradually lost. This procedure allows competition experiments to be carried out with minimum effects due to genetic drift. Experiments with both strains having wild-type and mutant permease genes were conducted. With the former the selective disadvantage was initially much greater than expected from the simplest hypothesis that extra unused proteins would slow growth in proportion to their fraction of the total protein synthesis. This phase was followed by a second phase where the selective disadvantage was smaller than predicted by this simple hypothesis. With a very slowly reverting permease negative strain the selective disadvantage, and therefore the protein burden, was found to be much smaller and not statistically different from zero. Thus, while one would expect under carbon and energy limitation in the chemostat the protein burden to be larger than under unlimited conditions, it is so small that even the refined technique used here could not measure it accurately. It is certainly less than the fraction of 'waste' protein synthesis; but it could be between zero and the fraction of the cells' energy and carbon budget spent on manufacture of the proteins of the lac operon.