Thermodynamic correlates of evolution

At any given time the ecosystem is roughly describable as an autocatalytic collection of substances in the steady state. The evolutionary behavior of such a system may be studied by making a thermodynamic analysis of the autocatalytic model. our main assumptions are: the energy input is constant; the dissipation is a function of the concentration of catalyst and the rate constants which characterize the reaction (the catalytic capacity); the dissipation function is time independent. Our main result is: the concentration of catalyst and catalytic capacity are complementary. This means that biomass and rate cannot both increase in the course of evolution. The stationary state which fulfills this complementarity condition is stable and unique, in the sense that the dissipation function along with the catalytic capacity is sufficient to determine the quantity of catalyst. Under quite general conditions changes in the catalytic capacity are positively correlated to changes in the turnover frequency of matter and energy and negatively correlated to changes in the free energy of the system. The spatial heterogeneity of the system plays an important role in determining the applicability of these conditions. Spatial heterogeneity stabilizes the catalytic capacity and biomass since it allows for net movements of catalyst which always oppose changes in these quantities.     

The coupling of biogeochemical cycles of nutrients

For any element which is incorporated into biomass, the biogeochemical cycle of that element in a given ecosystem will be coupled to that of any other element similarly incorporated. The mutual interaction of two such cycles is examined using a simple model in which each cycle is constrained into four compartments. In each cycle the assimilation rate (primary productivity) is related in a non-linear fashion to the two nutrients and to biomass. The interactions are represented by combining a hyperbolic dependence for each nutrient (involving a "Michaelis constant") with a logistic equation governing the dependence of rate on biomass (involving a "carrying capacity"). The response of the model to perturbation (e.g. mobilization of an abiotic reserve) is strongly governed by the values assigned to these constants. The coupled cycles can exhibit positive feed-back with anomalous responses of the steady state and time-dependent solutions may exhibit complex oscillatory behaviour. Both the steady-state sensitivity and the kinetic behaviour of such coupled systems are simplified if the range of atomic ratios permitted by the assimilation process is restricted. It will therefore be of importance to determine under what conditions the assimilation rates for different elements are governed by mass-action effects (Liebig's Law) or by stoichiometric constraints (Redfield ratios).     

Modelling, steady state analysis and optimization of the catalytic efficiency of the triosephosphate isomerase

In the present work we have modelled and optimized the reaction mechanism of the triose phosphate isomerase (TIM) enzyme (E.C. 5.3.1.1). For this purpose we have used an approach that combines the S-system representation within the power law formalism and linear programming techniques. By this means we have explored those rate constants whose alterations are likely to improve the catalytic efficiency of the enzyme and investigated the available room for optimization in different metabolic conditions. The role and plausibility of the different types of mutations on the evolution of this enzyme have also been considered. Steady state sensitivity analysis was carried out and a new set of aggregated logarithmic gains was defined in order to quantify the responses of the system to changes in groups of rate constants that could be explained in terms of mutations affecting the catalytic properties of the enzyme. Evaluation of these logarithmic gains at different levels of saturation and disequilibrium ratios enabled us to reach conclusions about the meaning and role of the diffusion limitation terms. The catalytic efficiency of the monoenzymatic system was optimized through changes in the kinetic rate constants within different sets of restrictions ranging from thermodynamic or kinetic to evolutionary ones. Results showed that, at very different conditions, there is still room for improvement in the TIM enzyme. Thus, in a wide range of metabolically significant values of the disequilibrium ratio there is a minimal variation in the optimal profile that yields 2.1 times the velocity of the basal states. Though most of this increase is accounted for by the increase of the second order constants (that could have already reached a theoretical maximum) significant increases (10%) in catalytic efficiencies are obtained by changes of the internal steps only. Besides these new findings our optimization approach has been able to reproduce results obtained with other approaches.     

One fold with many functions: the evolutionary relationships between TIM barrel families based on their sequences,structures and functions

The eightfold (betaalpha) barrel structure, first observed in triose-phosphate isomerase, occurs ubiquitously in nature. It is nearly always an enzyme and most often involved in molecular or energy metabolism within the cell. In this review we bring together data on the sequence, structure and function of the proteins known to adopt this fold. We highlight the sequence and functional diversity in the 21 homologous superfamilies, which include 76 different sequence families. In many structures, the barrels are "mixed and matched" with other domains generating additional variety. Global and local structure-based alignments are used to explore the distribution of the associated functional residues on this common structural scaffold. Many of the substrates/co-factors include a phosphate moiety, which is usually but not always bound towards the C-terminal end of the sequence. Some, but not all, of these structures, exhibit a structurally conserved "phosphate binding motif". In contrast metal-ligating residues and catalytic residues are distributed along the sequence. However, we also found striking structural superposition of some of these residues. Lastly we consider the possible evolutionary relationships between these proteins, whose sequences are so diverse that even the most powerful approaches find few relationships, yet whose active sites all cluster at one end of the barrel. This extreme example of the "one fold-many functions" paradigm illustrates the difficulty of assigning function through a structural genomics approach for some folds.     

Evolution of regulatory enzymes towards functional simplicity

The potential kinetic complexity of polymeric regulatory enzymes does not seem to be often expressed in nature. Most of these enzymes exhibit in fact a rather simple kinetic behaviour. This functional simplicity is probably the consequence of constraints between rate constants or of blocking of some reaction steps. Functional simplicity is believed to have emerged in the course of neo-Darwinian evolution as a consequence of a trend towards an improved functional efficiency. Functional efficiency may be reached, in polymeric regulatory enzymes, when either of the two sets of conditions are met. The first set of conditions implies the occurrence of the unicity of enzyme conformation in any transition state, a loose coupling between subunits and an exact balance of the driving forces exerted by the enzyme in the forward and backward directions of the catalytic step. This situation results in constraints between rate constants which allow degenerescence of the steady state rate equation. The second set of conditions involves again the unicity of enzyme conformation in any of the transition states, associated with a tight coupling of subunits, and a driving force exerted by the enzyme much strongly in the forward than in the backward direction of the catalytic step. These conditions imply blocking of some reaction steps and again degenerescence of the corresponding rate equation. The most frequent types of quaternary structure and subunit interactions, namely loose coupling between subunits, and tight coupling associated with conservation of at least one symmetry axis, have probably emerged as molecular organizations, which precisely allow both functional efficiency and simplicity to occur. Indeed these situations probably represent the term of two different evolutionary trends. Therefore enzymes that have not reached this state usually exhibit more complex kinetic behaviour. Wavy curves, “bumps” and turning points may be considered as manifestations of the ancestral character of an enzyme.     

Elementary vectors and autocatalytic sets for resource allocation in next-generation models of cellular growth

Traditional (genome-scale) metabolic models of cellular growth involve an approximate biomass “reaction”, which specifies biomass composition in terms of precursor metabolites (such as amino acids and nucleotides). On the one hand, biomass composition is often not known exactly and may vary drastically between conditions and strains. On the other hand, the predictions of computational models crucially depend on biomass. Also elementary flux modes (EFMs), which generate the flux cone, depend on the biomass reaction. To better understand cellular phenotypes across growth conditions, we introduce and analyze new classes of elementary vectors for comprehensive (next-generation) metabolic models, involving explicit synthesis reactions for all macromolecules. Elementary growth modes (EGMs) are given by stoichiometry and generate the growth cone. Unlike EFMs, they are not support-minimal, in general, but cannot be decomposed “without cancellations”. In models with additional (capacity) constraints, elementary growth vectors (EGVs) generate a growth polyhedron and depend also on growth rate. However, EGMs/EGVs do not depend on the biomass composition. In fact, they cover all possible biomass compositions and can be seen as unbiased versions of elementary flux modes/vectors (EFMs/EFVs) used in traditional models. To relate the new concepts to other branches of theory, we consider autocatalytic sets of reactions. Further, we illustrate our results in a small model of a self-fabricating cell, involving glucose and ammonium uptake, amino acid and lipid synthesis, and the expression of all enzymes and the ribosome itself. In particular, we study the variation of biomass composition as a function of growth rate. In agreement with experimental data, low nitrogen uptake correlates with high carbon (lipid) storage.     

Thermodynamics of microbial growth and metabolism: an analysis of the current situation

This paper attempts to review in how far thermodynamic analysis can be used to understand and predict the performance of microorganisms with respect to growth and bio-product synthesis. In the first part, a simple thermodynamic model of microbial growth is developed which explains the relationship between the driving force for growth in terms of Gibbs energy dissipation and biomass yield. From the currently available literature, it appears that the Gibbs energy dissipation per C-mol of biomass grown, which represents the driving force for chemotrophic growth, may have been adapted by evolutionary processes to strike a reasonable compromise between metabolic rate and growth efficiency. Based on empirical correlations of the C-molar Gibbs energy dissipation, the wide variety of biomass yields observed in nature can be explained and roughly predicted. This type of analysis may be highly useful in environmental applications, where such wide variations occur. It is however not able to predict biomass yields in very complex systems such as mammalian cells nor is it able to predict or to assess bio-product or recombinant protein yields. For this purpose, a much more sophisticated treatment that accounts for individual metabolic pathways separately is required. Based on glycolysis as a test example, it is shown in the last part that simple thermodynamic analysis leads to erroneous conclusions even in well-known, simple cases. Potential sources for errors have been analyzed and can be used to identify the most important needs for future research.     

Effects of primary sequence differences on the global structure and function of an enzyme: a study of pyruvate kinase isozymes

Pyruvate kinase is an important glycolytic enzyme which is expressed differentially as four distinct isozymes whose catalytic activity is regulated in a tissue-specific manner. The kidney isozyme is known to exhibit sigmoidal kinetics, whereas the muscle isozyme exhibits hyperbolic kinetic properties. By integration of the crystallographic [Stuart, D. I., Levine, M., Muirhead, H., & Stammers, D.K. (1979) J. Mol. Biol. 134, 109-142] and primary sequence data [Noguchi, T., Inoue, H., & Tanaka, T. (1986) J. Biol. Chem. 261, 13807], it was shown that the primary sequence for the C alpha 1 and C alpha 2 regions may constitute the allosteric switching site. To provide insights into the effects of the localized sequence change on the global structural and functional behavior of the enzyme, kinetic studies under a wide spectrum of conditions were conducted for both the muscle and kidney isozymes. These conditions include measurements of enzyme activity as a function of substrate concentrations with different concentrations of allosteric inhibitors or activators. These results showed that both isozymes exhibit the same regulatory properties although quantitatively the distribution of active and inactive forms and the various dissociation constants which govern the binding of substrate and allosteric effectors with the enzyme are different. For such a majority of equilibrium constants to be altered, the localized primary sequence change must confer global perturbations which are manifested as differences in the various equilibrium constants. Structural information about these two isozymes was provided by phase-modulation measurement of the fluorescence lifetime of tryptophan residues under a variety of experimental conditions.(ABSTRACT TRUNCATED AT 250 WORDS)     

Dynamic analysis of differential scanning calorimetry data

The apparent heat capacity function measured by high-sensitivity differential scanning calorimetry contains dynamic components of two different origins: (1) an intrinsic component arising from the finite instrument time response; and (2) a sample component arising from the kinetics of the thermal transition under study. The intrinsic instrumental component is always present and its effect on the shape of the experimental curve depends on the magnitude of the calorimeter response time. Usually, high-sensitivity instruments exhibit characteristic time constants varying from 10 to 100 s. This slow response introduces distortions in the shape of the heat capacity function especially at fast scanning rates. In addition to this instrumental component, dynamic effects due to sample relaxation processes also contribute to the shape of the experimental heat capacity profile. Since the nature and magnitude of these effects are a function of the kinetic parameters of the transition, they can be used to obtain kinetic information. This communication presents a dynamic deconvolution technique directed to remove artificial distortions in the shape of the heat capacity function measured at any scanning rate, and to obtain a kinetic characterization of a thermally induced transition. The kinetic characterization obtained by this method allows the researcher to obtain transition relaxation times as a continuous function of temperature. This technique has been applied to the thermal unfolding of ribonuclease A and the pretransition of dipalmitoylphosphatidylcholine (DPPC). In both systems the transition relaxation times are temperature dependent. For the protein system the relaxation time is very slow below the transition temperature (approximately 30 s) and very fast above Tm (less than 1 s) in agreement with direct kinetic measurements. For the pretransition of DPPC, the relaxation time is maximal at the transition midpoint and of the order of approx. 40 s.     

In search of a thermodynamic description of biomass yields for the chemotrophic growth of microorganisms

Correlations for the prediction of biomass yields are valuable, and many proposals based on a number of parameters (Y(ATP), Y(Ave), eta(o), Y(c), Gibbs energy efficiencies, and enthalpy efficiencies) have been published. This article critically examines the properties of the proposed parameters with respect to the general applicability to chemotrophic growth systems, a clear relation to the Second Law of Thermodynamics, the absence of intrinsic problems, and a requirement of only black box information. It appears that none of the proposed parameters satisfies all these requirements. Particularly, the various energetic efficiency parameters suffer from major intrinsic problems. However, this article will show that the Gibbs energy dissipation per amount of produced biomass (kJ/C-mod) is a parameter which satisfies the requirements without having intrinsic problems. A simple correlation is found which provides the Gibbs energy dissipation/C-mol biomass as a function of the nature of the C-source (expressed as the carbon chain length and the degree of reduction). This dissipation appears to be nearly independent of the nature of the electron acceptor (e.g., O(2), No(3) (-), fermentation). Hence, a single correlation can describe a very wide range of microbial growth systems. In this respect, Gibbs energy dissipation is much more useful than heat production/C-mol biomass, which is strongly dependent on the electron acceptor used. Evidence is presented that even a net heat-uptake can occur in certain growth systems.The correlation of Gibbs energy dissipation thus obtained shows that dissipation/C-mol biomass increases for C-sources with smaller chain length (C(6) --> C(1)), and increases for both higher and lower degrees of reduction than 4. It appears that the dissipation/C-mol biomass can be regarded as a simple thermodynamic measure of the amount of biochemical "work" required to convert the carbon source into biomass by the proper irreversible carbon-carbon coupling and oxidation/reduction reactions. This is supported by the good correlation between the theoretical ATP requirement for biomass formation on different C-sources and the dissipation values (kJ/C-mol biomass) found. The established correlation for the Gibbs energy dissipation allows the prediction of the chemotrophic biomass yield on substrate with an error of 13% in the yield range 0.01 to 0.80 C-mol biomass/(C)-mol substrate for aerobic/anaerobic/denitrifying growth systems.     

The evolution of the protein synthesis system

An evolutionary picture of the early protein synthesis was presented in relation to the problem of the origin and the evolution of life. A model of an autocatalytic system was studied in this connection. The system in this model included a template nucleotide and two activated amino acid polymerases with or without a nucleotide polymerase. Variables defining the system were: (1) Catalytic activity of the polymerases, (2) Number of amino acid residues at the activity site of the polymerases, (3) Number of amino acid residues at the selectivity site of the polymerases, (4) Number of the polymerases, (5) Accuracy of polymerization and activity of the polymerases, (6) Number of evolutionary improvements, and (7) The probability of an occurrence of beneficial mutations. The population changes of the systems were obtained by computer calculations. The simulation results indicated that even a very small enzymic activity and specificity of the polymerases could eventually lead the system to the most accurate protein synthesis, as far as transitions to systems with higher accuracy were allowed. The model study would encourage further quantiative investigations on catalytic activities of synthetic peptides, and on interactions between nucleotides and amino acids, and constructions of autocatalytic systems from a chemical evolutionary point of view.This is a part of a dissertation of HM to be presented to the Graduate School of the University of Maryland in partial fulfilment of the requirements for the Ph.D.     

The Promise and Peril of Continuous In Vitro Evolution

Experimental evolution methods can be used to address and illuminate issues central to the understanding of evolutionary theory. One of the most powerful of these methods involves the in vitro evolution of nucleic acid enzymes, taking advantage of the direct relationship between the genotype of a nucleic acid sequence and the phenotype of its associated catalytic function. This review and commentary focuses on the past, present, and future potential of systems for the continuous in vitro evolution of nucleic acid enzymes as tools for modeling evolutionary processes in biology. It offers a candid appraisal of both the strengths and the limitations of these systems.     

Evolutionary optimization of the catalytic efficiency of enzymes.

1. The rate equation for a generalized Michaelian type of enzymic reaction mechanism has been analyzed in order to establish how the mechanism should be kinetically designed in order to optimize the catalytic efficiency of the enzyme for a given average magnitude of true and apparent first-order rate constants in the mechanism at given concentrations of enzyme, substrate and product. 2. As long as on-velocity constants for substrate and product binding to the enzyme have not reached the limiting value for a diffusion-controlled association process, the optimal state of enzyme operation will be characterized by forward (true and apparent) first-order rate constants of equal magnitude and reverse rate constants of equal magnitude. The drop in free energy driving the catalysed reaction will occur to an equal extent for each reaction step in the mechanism. All internal equilibrium constants will be of equal magnitude and reflect only the closeness of the catalysed reaction to equilibrium conditions. 3. When magnitudes of on-velocity constants for substrate and product binding have reached their upper limits, the optimal kinetic design of the reaction mechanism becomes more complex and has to be established by numerical methods. Numerical solutions, calculated for triosephosphate isomerase, indicate that this particular enzyme may or may not be considered to exhibit close to maximal efficiency, depending on what value is assigned to the upper limit for a ligand association rate constant. 4. Arguments are presented to show that no useful information on the evolutionary optimization of the catalytic efficiency of enzymes can be obtained by previously taken approaches that are based on the application of linear free-energy relationships for rate and equilibrium constants in the reaction mechanism.     

Influence of Product Addition on the Oxidation of D-Sorbitol to L-Sorbose by the Strain Acetobacter suboxydans

The kinetics of the D-sorbitol to L-sorbose biotransformation catalysed by the strain Acetobacter suboxydans is studied. The product inhibits the bacterial growth but the transformation is an autocatalytic process. However, higher initial concentrations of sorbose lead to a considerable decrease of the rate constant of the reaction, although the autocatalytic process takes place too. The addition of sorbose in the exponential phase of bacterial growth, or in the stationary phase, leads to a considerable shortening of the process duration, compared to the traditional fermentation.

The rate constants calculated from the kinetic curves are dependent on the initial dry substances concentration and there is a correlation between these levels and the biomass concentration in the stationary phase.     

Coenzyme binding ability of homologs of M4-lactate dehydrogenase in temperature adaptation

Temperature effects on dissociation constants (Kd), binding enthalpies and apparent Michaelis constants (Km) for NADH, plus Arrhenius activation energies (Ea), substrate turnover numbers (kcat), and NADH 'on' constants (k1) were measured or calculated for M4-lactate dehydrogenase homologs from deep-sea, midwater, shallow-water temperate, and shallow-water tropical teleost fishes, and a mammal. At any single measurement temperature, Km and kcat values were significantly higher for groups adapted to lower temperatures. This pattern of Km values and temperature illustrates a strong evolutionary conservation of Km of NADH. When determined at the average body temperature of each species, the Km values are very similar, resulting in the preservation of the catalytic capacity and regulatory properties of these enzyme homologs at their in situ temperatures. In contrast, Kd values, while varying considerably among species, are not significantly different among the different groups at any one temperature. The ratio of Km to Kd tends to follow a phylogenetic pattern rather than a pattern of environmental adaptation. Thus, evolutionary adjustments in Km are not directly the result of changes in cofactor binding. All the rate constants involved in determining the Km and Kd of NADH (kcat, k1 and k-1) can be modified.     

Non-catalytic Binding Sites Induce Weaker Long-Range Evolutionary Rate Gradients than Catalytic Sites in Enzymes

Enzymes exhibit a strong long-range evolutionary constraint that extends from their catalytic site and affects even distant sites, where site-specific evolutionary rate increases monotonically with distance. While protein–protein sites in enzymes were previously shown to induce only a weak conservation gradient, a comprehensive relationship between different types of functional sites in proteins and the magnitude of evolutionary rate gradients they induce has yet to be established. Here, we systematically calculate the evolutionary rate (dN/dS) of sites as a function of distance from different types of binding sites in enzymes and other proteins: catalytic sites, non-catalytic ligand binding sites, allosteric binding sites, and protein–protein interaction sites. We show that catalytic sites indeed induce significantly stronger evolutionary rate gradient than all other types of non-catalytic binding sites. In addition, catalytic sites in enzymes with no known allosteric function still induce strong long-range conservation gradients. Notably, the weak long-range conservation gradients induced by non-catalytic binding sites in enzymes is nearly identical in magnitude to those induced by ligand binding sites in non-enzymes. Finally, we show that structural determinants such as local solvent exposure of sites cannot explain the observed difference between catalytic and non-catalytic functional sites. Our results suggest that enzymes and non-enzymes share similar evolutionary constraints only when examined from the perspective of non-catalytic functional sites. Hence, the unique evolutionary rate gradient from catalytic sites in enzymes is likely driven by the optimization of catalysis rather than ligand binding and allosteric functions.     

Functional Constraints on Insect Immune System Components Govern Their Evolutionary Trajectories

Roles of constraints in shaping evolutionary outcomes are often considered in the contexts of developmental biology and population genetics, in terms of capacities to generate new variants and how selection limits or promotes consequent phenotypic changes. Comparative genomics also recognizes the role of constraints, in terms of shaping evolution of gene and genome architectures, sequence evolutionary rates, and gene gains or losses, as well as on molecular phenotypes. Characterizing patterns of genomic change where putative functions and interactions of system components are relatively well described offers opportunities to explore whether genes with similar roles exhibit similar evolutionary trajectories. Using insect immunity as our test case system, we hypothesize that characterizing gene evolutionary histories can define distinct dynamics associated with different functional roles. We develop metrics that quantify gene evolutionary histories, employ these to characterize evolutionary features of immune gene repertoires, and explore relationships between gene family evolutionary profiles and their roles in immunity to understand how different constraints may relate to distinct dynamics. We identified three main axes of evolutionary trajectories characterized by gene duplication and synteny, maintenance/stability and sequence conservation, and loss and sequence divergence, highlighting similar and contrasting patterns across these axes amongst subsets of immune genes. Our results suggest that where and how genes participate in immune responses limit the range of possible evolutionary scenarios they exhibit. The test case study system of insect immunity highlights the potential of applying comparative genomics approaches to characterize how functional constraints on different components of biological systems govern their evolutionary trajectories.     

Effect of agitation intensities on fungal morphology of submerged fermentation

Both parallel fermentations with Aspergillus awamori (CBS 115.52) and a literature study on several fungi have been carried out to determine a relation between fungal morphology and agitation intensity. The studied parameters include hyphal length, pellet size, surface structure or so-called hairy length of pellets, and dry mass per-wet-pellet volume at different specific energy dissipation rates. The literature data from different strains, different fermenters, and different cultivation conditions can be summarized to say that the main mean hyphal length is proportional to the specific energy dissipation rate according to a power function with an exponent of -0.25 +/- 0.08. Fermentations with identical inocula showed that pellet size was also a function of the specific energy dissipation rate and proportional to the specific energy dissipation rate to an exponent of -0.16 +/- 0.03. Based on the experimental observations, we propose the following mechanism of pellet damage during submerged cultivation in stirred fermenters. Interaction between mechanical forces and pellets results in the hyphal chip-off from the pellet outer zone instead of the breakup of pellets. By this mechanism, the extension of the hyphae or hair from pellets is restricted so that the size of pellets is related to the specific energy dissipation rate. Hyphae chipped off from pellets contribute free filamentous mycelia and reseed their growth. So the fraction of filamentous mycelial mass in the total biomass is related to the specific energy dissipation rate as well.To describe the surface morphology of pellets, the hyphal length in the outer zone of pellets or the so-called hairy length was measured in this study. A theoretical relation of the hairy length with the specific energy dissipation rate was derived. This relation matched the measured data well. It was found that the porosity of pellets showed an inverse relationship with the specific energy dissipation rate and that the dry biomass per-wet-pellet volume increased with the specific energy dissipation rates. This means that the tensile strength of pellets increased with the increase of specific energy dissipation rate. The assumption of a constant tensile strength, which is often used in literature, is then not valid for the derivation of the relation between pellet size and specific energy dissipation rate. The fraction of free filamentous mycelia in the total biomass appeared to be a function of the specific energy dissipation in stirred bioreactors. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 715-726, 1997.     

Role of hemoglobin in proton transfer to the active site of carbonic anhydrase.

The binding of bovine oxyhemoglobin to bovine carbonic anhydrase with a dissociation constant between 10(-5) and 10(-7) M has been determined by countercurrent distribution using aqueous, biphasic polymer systems. This result provides an explanation for the very efficient proton transfer between hemoglobin and carbonic anhydrase, a transfer which enhances the catalytic activity of carbonic anhydrase as measured by 18O exchange between bicarbonate and water at chemical equilibrium (Silverman, D. N., Tu, C. K., and Wynns, G. C. (1978) J. Biol. Chem, 253, 2563-2567). Two rate constants describing 18O exchange activity of carbonic anhydrase at pH 7.5 show saturation behavior when plotted against hemoglobin concentration consistent with a dissociation constant of 2.5 X 10(-6) M between bovine hemoglobin and carbonic anhydrase. Interpretation of these rate constants in terms of a two-step model for 18O exchange indicates that hemoglobin enhances the rate of exchange from carbonic anhydrase of water containing the oxygen abstracted from bicarbonate, but does not affect the catalytic interconversion of CO2 and HCO3- at chemical equilibrium.     

The strategy of ecosystem development: specific dissipation as an indicator of ecosystem maturity

The ratio of entropy generation rate to entropy embodied in structures relatively to the surroundings can be considered as an indicator of the ability of a self-organizing dissipative system to maintain itself far from equilibrium by pumping out entropy. The higher the ratio (which may be called the specific entropy production or the specific dissipation of a system), the lower the capacity of a system to convert the incoming low-entropy energy into internal organization. It appears that the ratio attains special significance for interpreting the evolution of biological systems, as the maximum expression of self-organizing systems, from the sub-cellular to the ecosystem scale. This paper proposes specific dissipation, written as the ratio of biological entropy production to exergy stored in the living biomass, as a thermodynamic orientor as well as an indicator of the development state of ecological systems. After having presented a method for estimating the specific dissipation in lakes, the adequacy of the proposed indicator is discussed and also tested by comparing its response to those of some classical ecological attributes (successional sequences of species, biodiversity, individual body size, structural organization and generation time of organisms) throughout the seasonal progression of the plankton community in Lake Trasimeno (Umbria, Italy). The results support the hypothesis that the minimization of specific dissipation is a primary criterion of evolution of ecological systems and also sustain the use of specific dissipation as an indicator of ecological maturity.