Application of macroscopic principles to microbial metabolism

General expressions for mass, elemental, energy, and entropy balances are derived and applied to microbial growth and product formation. The state of the art of the application of elemental balances to aerobic and heterotrophic growth is reviewed and extended somewhat to include the majority of the cases commonly encountered in biotechnology. The degree of reduction concept is extended to include nitrogen sources other than ammonia. The relationship between a number of accepted measures for the comparison of substrate yields is investigated. The theory is illustrated using a generalized correlation for oxygen yield data. The stoichiometry of anaerobic product formation is briefly treated, a limit to the maximum carbon conservation in product is derived, using the concept of elemental balance. In the treatment of growth energetics the correct statement of the second law of thermodynamics for growing organisms is emphasized. For aerobic heterotrophic growth the concept of thermodynamic efficiency is used to formulate a limit the substrate yield can never surpass. It is combined with a limit due to the fact that the maximum carbon conservation in biomass can obviously never surpass unity. It is shown that growth on substrates of a low degree of reduction is energy limited, for substrates of a high degree of reduction carbon limitation takes over. Based on a literature review concerning yield data some semiempirical notions useful for a preliminary evolution of aerobic heterotrophic growth are developed. The thermodynamic efficiency definition is completed by two other efficiency measures, which allow derivation of simple equations for oxygen consumption and heat production. The range of validity of the constancy of the rate of heat production to the rate of oxygen consumption is analyzed using these efficiency measures. The energetic of anaerobic growth are treated—it is shown that an approximate analysis in terms of an enthalpy balance is not valid for this case, the evaluation of the efficiency of growth has to be based on Gibbs free energy changes. A preliminary analysis shows the existence of regularities concerning the free energy conservation on anaerobic growth. The treatment is extended to include the effect of growth rate by the introduction of a linear relationship for substrate consumption. Aerobic and anaerobic growth are discussed using this relationship. A correlation useful in judging the potentialities for improvement in anaerobic product formation processes is derived. Finally the relevance of macroscopic principles to the modeling of bioengineering systems is discussed.     

Thermodynamics of Terrestrial Evolution

The causal element of biological evolution and development can be understood in terms of a potential function which is generalized from the variational principles of irreversible thermodynamics. This potential function is approximated by the rate of entropy production in a configuration space which admits of macroscopic excursions by fluctuation and regression as well as microscopic ones. Analogously to Onsager's dissipation function, the potential takes the form of a saddle surface in this configuration space. The path of evolution following from an initial high dissipation state within the fixed constraint provided by the invariant energy flux from the sun tends toward the stable saddle point by a series of spontaneous regressions which lower the entropy production rate and by an alternating series of spontaneous fluctuations which introduce new internal constraints and lead to a higher entropy production rate. The potential thus rationalizes the system's observed tendency toward "chemical imperialism" (high dissipation) while simultaneously accommodating the development of "dynamic efficiency" and complication (low dissipation).     

Are organisms committed to lower their rates of entropy production?: Possible relevance to evolution of the Prigogine theorem and the ergodic hypothesis

The physiology at limiting and stress conditions challenges the current view that the overall reaction of metabolic processes is always far from equilibrium and, therefore, that organisms are not committed to lower their rates of entropy production. Plausibly, critical steps of natural selection takes place at limiting conditions, near equilibrium, in the linear range response of entropy production, and consequently the trend to lower the rate of entropy production could be the fitness arrow of biological evolution. The evolutionary relevance of the Prigogine theorem is discussed in connection with the ergodic hypothesis of Boltzmann. The emergence of metabolic strategies to economise carbon/energy resources, of resource-waste systems like active transport and the irreversible increase in the complexity of organisms during evolution may be consequences of a more general trend of metabolic systems to lower the rates of entropy production.     

Statistical Mechanics of the Human Placenta: A Stationary State of a Near-Equilibrium System in a Linear Regime

All near-equilibrium systems under linear regime evolve to stationary states in which there is constant entropy production rate. In an open chemical system that exchanges matter and energy with the exterior, we can identify both the energy and entropy flows associated with the exchange of matter and energy. This can be achieved by applying statistical mechanics (SM), which links the microscopic properties of a system to its bulk properties. In the case of contractile tissues such as human placenta, Huxley’s equations offer a phenomenological formalism for applying SM. SM was investigated in human placental stem villi (PSV) (n = 40). PSV were stimulated by means of KCl exposure (n = 20) and tetanic electrical stimulation (n = 20). This made it possible to determine statistical entropy (S), internal energy (E), affinity (A), thermodynamic force (A / T) (T: temperature), thermodynamic flow (v) and entropy production rate (A / T x v). We found that PSV operated near equilibrium, i.e., A ≺≺ 2500 J/mol and in a stationary linear regime, i.e., (A / T) varied linearly with v. As v was dramatically low, entropy production rate which quantified irreversibility of chemical processes appeared to be the lowest ever observed in any contractile system.     

Thermodynamic approach to biomass distribution in ecological systems

In the derivation of the biomass distribution function for an ecological population critical use is made of an energetic constraint on the maximization of biomass diversity. The nature of this constraint is explored in detail using Kleiber's relation σ(m)=cm ^γ between animal metabolic rate σ(m) and body weightm in conjuction with the Prigogine-Wiame thermodynamic paradigm for specific entropy production in biological stationary states. These two inputs fix the energetic constraint on the maximization of biomass diversity to be the constancy of the mean metabolic rate of the ecosystem. The resulting biomass distribution function is tested against observational data.     

Efficiency of free energy transfer and entropy production in photosynthetic systems

The diagram method for the calculation of entropy production and efficiency associated with very first steps of photosynthetic mechanism is developed. By using one simple model for the bacteriorhodopsin light activated proton pump action, it is shown that in the steady state of biological interest, both entropy production and efficiency of transfer of light energy are maximal for the same optimal values of kinetic constants.     

Photosynthesis and negative entropy production

The widely held view that the maximum efficiency of a photosynthetic pigment system is given by the Carnot cycle expression (1-T/Tr) for energy transfer from a hot bath (radiation at temperature Tr) to a cold bath (pigment system at temperature T) is critically examined and demonstrated to be inaccurate when the entropy changes associated with the microscopic process of photon absorption and photochemistry at the level of single photosystems are considered. This is because entropy losses due to excited state generation and relaxation are extremely small (DeltaS < T/Tr) and are essentially associated with the absorption-fluorescence Stokes shift. Total entropy changes associated with primary photochemistry for single photosystems are shown to depend critically on the thermodynamic efficiency of the process. This principle is applied to the case of primary photochemistry of the isolated core of higher plant photosystem I and photosystem II, which are demonstrated to have maximal thermodynamic efficiencies of xi > 0.98 and xi > 0.92 respectively, and which, in principle, function with negative entropy production. It is demonstrated that for the case of xi > (1-T/Tr) entropy production is always negative and only becomes positive when xi < (1-T/Tr).     

Stationary-state distributions in membrane channels. I. Conservative flux systems.

The population distribution of cations at binding sites in membrane channels is determined for stationary states characterized by a net ion flux. For conservative systems, the net flux conserves the total intra-channel cation population for an ensemble of channels. The requisite matrix formalism is developed and illustrated for some homogeneous channels with N single-ion occupancy states with chemical and electrochemical transmembrane gradients. The lowest eigen-value approximation, which is used effectively for systems with no net cation flux, is applied to these stationary-state systems for comparison with the exact solutions. The stationary states are characterized by special thermodynamic functions for entropy, internal energy, and free energy defined by using information theory. The changes in these parameters for the transition from the equilibrium to the stationary state depend on the ratio of the next flux to the transition velocity for nearest-neighbor transitions within the channel. The free energy changes with the square of this ratio while the internal energy changes linearly.     

Does microbial life always feed on negative entropy? Thermodynamic analysis of microbial growth.

Schr?dinger stated in his landmark book, What is Life?, that life feeds on negative entropy. In this contribution, the validity of this statement is discussed through a careful thermodynamic analysis of microbial growth processes. In principle, both feeding on negative entropy, i.e. yielding products of higher entropy than the substrates, and generating heat can be used by microorganisms to rid themselves of internal entropy production resulting from maintenance and growth processes. Literature data are reviewed in order to compare these two mechanisms. It is shown that entropy-neutral, entropy-driven, and entropy-retarded growth exist. The analysis of some particularly interesting microorganisms shows that enthalpy-retarded microbial growth may also exist, which would signify a net uptake of heat during growth. However, the existence of endothermic life has never been demonstrated in a calorimeter. The internal entropy production in live cells also reflects itself in the Gibbs energy dissipation accompanying growth, which is related quantitatively to the biomass yield. An empirical correlation of the Gibbs energy dissipation in terms of the physico-chemical nature of the growth substrate has been proposed in the literature and can be used to predict the biomass yield approximately. The ratio of enthalpy change and Gibbs energy change can also be predicted since it is shown to be approximately equal to the same ratio of the relevant catabolic process alone.     

Filial cannibalism improves survival and development of beaugregory damselfish embryos

Cannibalism of small numbers of offspring by a parent has been proposed as an adaptive parental strategy, by providing energy to support parental care. However, there are few empirical studies to support this hypothesis. We conducted field and laboratory experiments to investigate partial filial cannibalism in Stegastes leucostictus, a coral reef fish with paternal care. Partial cannibalism was shown to be common, and males were found to remove developing embryos from throughout a clutch in a random pattern, rather than in the more aggregated pattern seen during embryo predation. Males that received a diet supplement grew faster than control males, but did not engage in less cannibalism. Also, males did not concentrate cannibalism on early embryonic stages with the highest energetic value. Experimental reduction of embryo densities was found to significantly increase embryo development rate and survival from egg deposition to hatching, and experimental reduction of oxygen levels significantly increased rates of partial filial cannibalism by males. Artificial spawning sites with low oxygen levels were avoided by spawning females, and cannibalism rates by males were higher. We propose that partial filial cannibalism serves as an adaptive parental strategy to low oxygen levels in S. leucostictus by increasing the hatching success of embryos.     

Entropy budgets of soybean and bur oak leaves at night

From energy budgets of soybean [ Glycine max (L.) Merr. cv. Chippewa] and bur oak ( Quercus macrocarpa ) leaves at night, entropy fluxes into or out of leaves are calculated. The absorbed entropy balances with the emitted entropy; this is not the case for leaves during the day and for an animal at night. On the assumption that the entropy in leaves is at steady state, entropy production in leaves becomes small and almost zero. Since entropy production is a measure of activity in organisms, the activity in leaves is small at night; this is in contrast to leaves during the day. Thus, a large portion of the activity in leaves is "on" in the daytime and "off" at night. Most of the activity in leaves may be triggered by solar radiation.     

Gradients of lipid storage, photosynthesis and plastid differentiation in developing soybean seeds

This study establishes a topographical framework for functional investigations on the regulation of lipid biosynthesis and its interaction with embryo photosynthesis in developing soybean seed. Structural observations, combined with molecular and functional parameters, revealed the gradual transformation of chloroplasts into storage organelles, starting from inner regions going outwards. This is evidenced by electron microscopy, confocal laser scanning microscopy, in situ hybridization and histochemical/biochemical data. As a consequence of plastid differentiation, photosynthesis becomes distributed along a gradient within the developing embryo. Electron transport rate, effective quantum yield and O2 production rate are maximal in the embryo periphery, as documented by imaging pulse-amplitude-modulated fluorescence and O2 release via microsensors. The gradual loss of photosynthetic capacity was accompanied by a similarly gradual accumulation of starch and lipids. Noninvasive nuclear magnetic resonance spectroscopy of mature seeds revealed steep gradients in lipid deposition, with the highest concentrations in inner regions. The inverse relationship between photosynthesis and lipid biosynthesis argues against a direct metabolic involvement of photosynthesis in lipid biosynthesis during the late storage stage, but points to a role for photosynthetic oxygen release. This hypothesis is verified in a companion paper.     

Effect of nutrition on endocrine parameters, ovarian physiology, and oocyte and embryo development

Reproductive efficiency in high yielding dairy cows has decreased over the past 50 years, despite significant gains in genetic selection for increased milk output. One possible reason for this decline has been a change in the nutritional intake to meet the increased energy and protein demands for higher milk production. Excess energy intake in sheep will lead to significant reductions in progesterone concentrations; the effects in cattle are not so clear. Nutrition, unless radically changed, will have little effect on gonadotropin concentrations in ruminants, and this is in contrast to the situation for pigs and for primates, where very short-term nutritional changes manifest themselves in altered gonadotropin secretion. Cattle with reduced energy intake have smaller dominant follicles and more three-wave cycles, compared with animals on higher feed intakes. One of the main areas where nutrition influences reproductive efficiency is at the level of embryo production. Several studies indicate that excess energy intake reduces the response to superovulation and also decrease the yield of embryos and alters expression of some gene constructs within the developing embryo. The mechanism of this effect is not clear but indications are that the quality of the oocytes may be compromised. Indeed recent data indicate that nutritional changes around the time of mating may have detrimental effects on the establishment of pregnancy in heifers. Thus, nutritional balancing is critical for high-yielding dairy cows, in particular. The challenge remains to modify nutritional and management strategies in such cows to maintain the levels of production made possible by genetic selection and still maintain an acceptable level of fertility.     

Error analysis of metabolic-rate measurements in mammalian-cell culture by carbon and nitrogen balances

The analysis of metabolic fluxes of large stoichiometric systems is sensitive to measurement errors in metabolic uptake and production rates. It is therefore desirable to independently test the consistency of measurement data, which is possible if at least two elemental balances can be closed. For mammalian-cell culture, closing the C balance has been hampered by problems in measuring the carbon-dioxide production rate. Here, it is shown for various sets of measurement data that the C balance can be closed by applying a method to correct for the bicarbonate buffer in the culture medium. The measurement data are subsequently subject to measurement-error analysis on the basis of the C and N balances. It is shown at 90% reliability that no gross measurement errors are present, neither in the measured production- and consumption rates, nor in the estimated in- and outgoing metabolic rates of te subnetwork, that contains the glycolysis, the pentose-phosphate, and the glutaminolysis pathways. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

Changes in the mitochondrial proteome of developing maize seed embryos

Mitochondria are required for seed development, but little information is available about their function and role during this process. We isolated the mitochondria from developing maize (Zea mays L. cv. Nongda 108) embryos and investigated the mitochondrial membrane integrity and respiration as well as the mitochondrial proteome using two proteomic methods, the two‐dimensional gel electrophoresis (2‐DE) and sequential windowed acquisition of all theoretical fragment ion mass spectra (SWATH). Mitochondrial membrane integrity and respiration were maintained at a high level up to 21 days after pollination (DAP) and decreased thereafter, while total mitochondrial number, cytochrome c oxidase activity and respiration per embryo exhibited a bell‐shaped change with peaks at 35–45 DAP. A total of 286 mitochondrial proteins changed in abundance during embryo development. During early stages of seed development (up to 21 DAP), proteins involved in energy production, basic metabolism, protein import and folding as well as removal of reactive oxygen species dominated, while during mid or late stages (35–70 DAP), some stress‐ and detoxification‐related proteins increased in abundance. Our study, for the first time, depicted a relatively comprehensive map of energy production by mitochondria during embryo development. The results revealed that mitochondria were very active during the early stages of maize embryo development, while at the late stages of development, the mitochondria became more quiescent, but well‐protected, presumably to ensure that the embryo passes through maturation, drying and long‐term storage. These results advance our understanding of seed development at the organelle level.     

Natural process--natural selection

Life is supported by a myriad of chemical reactions. To describe the overall process we have formulated entropy for an open system undergoing chemical reactions. The entropy formula allows us to recognize various ways for the system to move towards more probable states. These correspond to the basic processes of life i.e. proliferation, differentiation, expansion, energy intake, adaptation and maturation. We propose that the rate of entropy production by various mechanisms is the fitness criterion of natural selection. The quest for more probable states results in organization of matter in functional hierarchies.     

Patterns of Metabolism and Growth in Avian Embryos

Metabolic rates of embryos of precocial birds increase rapidlyuntil about 80% through incubation, then increase slowly remainconstant or even decline. In altricial species, embryo metabolicrates increase continuously and at an accelerating rate throughout incubation. Total energy cost of development is higher inprecocial than in altricial species. Growth patterns of altricialand precocial embryos differ in the same way as does metabolicrate. Embryo growth rates decline late in incubation in precocialspecies, but increase continuously in altricial species. Embryometabolic rate in cal/hr (P) is related to embryo mass in grams(M) and growth rate in grams/day (GR) by the equation P = 12.17GR+ 1.66M + 1.81. The energy cost of growth in avian embryos is292 cal/g. The energy cost of maintenance is 1.66 cal/g hr andappeals to be independent of embryo mass. Differences in growthpatterns account for the observed differences in metabolic ratesand total energy costs of development. High energy costs ofmaintenance account for high total developmental costs in piecocialspecies and in species that have unusually long incubation periods.     

The steady state kinetics of some biological systems: IV. Thermodynamic aspects

The investigation initiated in III is continued. The irreversible production of entropy and the rates of dissipation in diffusion fields and due to chemical reactions are discussed. The rates of change of free energy, entropy, etc. are indicated for type-systems of biological interest in which composition and reaction rates are a function of position. Some consequences of Onsager's generalization of Fick's Law are discussed in terms of maintenance of stationary, non-equilibrium concentration distributions, transport of a solute against a concentration gradient, and the dependence of these phenomena upon metabolism.     

Hydrobiological consequences of the addition of phosphate precipitants to inlet water of lakes

Summary In three model reservoirs (LUND, 1975) a method reducing bluegreen algal blooms in lakes was studied. Iron or aluminium were added to inlet waters for chemically binding the inflowing phosphorus.The research program, started in 1975, includes intensive monitoring of many chemical and hydrobiological variables, the determination of water and mass balances and since 1977 measurements or primary production rates with¹⁴C. In this paper only the results found in 1977 are discussed. An attempt is made to describe quantitatively how growth rates and changes in biomass are interconnected and how phosphorus precipitation changes these variables.In all reservoirs a large discrepancy was observed between the actual rate of increase in the algal population and the relative production rate. The latter appeared to be higher by one order of magnitude. The relative death rate due to grazing can account for the large difference between these growth rates only when selective grazing of zooplankton on phytoplankton is assumed.It can be concluded that treatment of inlet water with AVR, an aluminium salt, is unsuccessful in reducing algal development. Treatment with ironsulphate may be successful, but a reduction of the relative growth rates was not observed. The effects of grazing of zooplankton andDreissena polymorpha need further investigation.