Thermodynamic extremal principles in evolution

Summary An evolutionary ecosystem may be described in terms of a quasi autocatalytic model, i.e. in terms of a sequence of different autocatalytic systems. Such a sequence can exhibit considerable evolutionary change (for example, adjustment of various rate constants) even if the dissipation function remains essentially the same. Under these conditions the dissipation is always a monotonically increasing function of the concentration of catalyst (biomass) and certain rate constants (the catalytic capacity). Biomass and catalytic capacity are complementary in the sense that the quasi autocatalytic system always assumes a steady state by varying these quantities in the opposite direction (all other conditions remaining constant). This means that evolutionary systems cannot exhibit orthogenetic increases in both rate of operation and biomass, at least within any given evolutionary epoch. This has implications for the importance of spatial heterogeneity in stabilizing the behavior of evolutionary systems.     

Controlling light-use by Rhodobacter capsulatus continuous cultures in a flat-panel photobioreactor

The main bottleneck in scale-up of phototrophic fermentation is the low efficiency of light energy conversion to the desired product, which is caused by an excessive dissipation of light energy to heat. The photoheterotrophic formation of hydrogen from acetate and light energy by the microorganism Rhodobacter capsulatus NCIMB 11773 was chosen as a case study in this work. A light energy balance was set up, in which the total bacterial light energy absorption is split up and attributed to its destinations. These are biomass growth and maintenance, generation of hydrogen and photosynthetic heat dissipation. The constants defined in the light energy balance were determined experimentally using a flat-panel photobioreactor with a 3-cm optical path. An experimental method called D-stat was applied. Continuous cultures were kept in a so-called pseudo steady state, while the dilution rate was reduced slowly and smoothly. The biomass yield and maintenance coefficients of Rhodobacter capsulatus biomass on light energy were determined at 12.4 W/m(2) (400-950 nm) and amounted to 2.58 x 10(-8) +/- 0.04 x 10(-8) kg/J and 102 +/- 3.5 W/kg, respectively. The fraction of the absorbed light energy that was dissipated to heat at 473 W/m(2) depended on the biomass concentration in the reactor and varied between 0.80 and 0.88, as the biomass concentration was increased from 2.0 to 8.0 kg/m(3). The process conditions were estimated at which a 3.7% conversion efficiency of absorbed light energy to produced hydrogen energy should be attainable at 473 W/m(2).     

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.     

Kinetic Analysis of Self-Replicating Peptides: Possibility of Chiral Amplification in Open Systems

A simplified kinetic model scheme is presented that addresses the main reactions of two recently reported peptide self-replicators. Experimentally observed differences in the autocatalytic efficiency between these two systems-- caused by variations in the peptide sequences--and the possible effect of chiral amplification under heterochiral reaction conditions were evaluated. Our numerical simulations indicated that differences in the catalytic performance are exclusively due to pronounced variations in the rate parameters that control the reversible and hydrophobic interactions in the reaction system but neither to alterations in the underlying reaction network nor to changes in the stoichiometry of the involved aggregation processes. Model predictions further demonstrated the possible existence of chiral amplification if peptide self-replication is performed under heterochiral reaction conditions. Pointing into the direction of a possible cause for biomolecular homochirality, it was found that in open flow reactors, keeping the system under non-equilibrium conditions, a remarkable amplification of enantiomeric excess could be achieved. According to our modeling, this is due to a chiroselective autocatalytic effect and a meso-type separation process both of which are assumed to be intrinsic for the underlying dynamics of heterochiral peptide self-replication.     

A Mechanism of Energy Dissipation in Cyanobacteria

When grown under a variety of stress conditions, cyanobacteria express the isiA gene, which encodes the IsiA pigment-protein complex. Overexpression of the isiA gene under iron-depletion stress conditions leads to the formation of large IsiA aggregates, which display remarkably short fluorescence lifetimes and thus a strong capacity to dissipate energy. In this work we investigate the underlying molecular mechanism responsible for chlorophyll fluorescence quenching. Femtosecond transient absorption spectroscopy allowed us to follow the process of energy dissipation in real time. The light energy harvested by chlorophyll pigments migrated within the system and eventually reaches a quenching site where the energy is transferred to a carotenoid-excited state, which dissipates it by decaying to the ground state. We compare these findings with those obtained for the main light-harvesting complex in green plants (light-harvesting complex II) and artificial light-harvesting antennas, and conclude that all of these systems show the same mechanism of energy dissipation, i.e., one or more carotenoids act as energy dissipators by accepting energy via low-lying singlet-excited S₁ states and dissipating it as heat.     

A mathematical model for agitation-induced fragmentation of Penicillium chrysogenum

The morphology of filamentous organisms in submerged cultures varies between the pelleted and the dispersed forms depending on the strain of organism and the culture conditions. The dispersed form consists of branched and unbranched hyphae (freely dispersed form) and clumps (filamentous material in aggregates). In agitated systems, the choice of impeller geometry as well as the total power input determines the mechanical forces that might affect the morphology of filamentous species (e.g. by fragmentation) with simultaneous effects on their growth and productivity. To find out more about fragmentation of Penicillium chrysogenum caused by mechanical forces of different impeller types and agitation intensities, a population balance model has been developed. The projected area measured by image analysis was used to characterise the morphology (size) of the mycelia. In the model, the kinetics of mycelial fragmentation were expressed by a breakage rate constant K, which was assumed to be only dependent on the agitation conditions. The fragmentation rate was considered to follow a first order process in size (area) which was based on assumptions made for the mechanism of mycelial break-up, and work reported in the literature. Previously published mean and distributional data from off-line fragmentation experiments in ungassed vessels of sizes from 1.4 to 180?l were used to validate the model. For the first time a model has been found that is capable of fitting changes in mycelial morphology caused by mechanical forces generated by different impellers at various power inputs and scales. Besides the mean projected areas of the mycelia, the model allowed simulations of the projected area distributions, and changes in those distributions because of the agitation. At the small scale (1.4?l), the breakage rate constant K could be correlated well with either impeller tip speed or the “energy dissipation/circulation function”, which is based on mycelial circulation through the impeller region. The simpler but commonly used power input per unit tank volume did not correlate K adequately. The scale up data showed that only the “energy dissipation/circulation function” correlated mycelial fragmentation well. The dependence of K on biomass concentration, and its detailed dependence (if any) on the fermentation conditions at sampling, which might indicate likely breakage mechanisms, remain to be elucidated.     

A Simple Self-Maintaining Metabolic System: Robustness,Autocatalysis, Bistability

A living organism must not only organize itself from within; it must also maintain its organization in the face of changes in its environment and degradation of its components. We show here that a simple (M,R)-system consisting of three interlocking catalytic cycles, with every catalyst produced by the system itself, can both establish a non-trivial steady state and maintain this despite continuous loss of the catalysts by irreversible degradation. As long as at least one catalyst is present at a sufficient concentration in the initial state, the others can be produced and maintained. The system shows bistability, because if the amount of catalyst in the initial state is insufficient to reach the non-trivial steady state the system collapses to a trivial steady state in which all fluxes are zero. It is also robust, because if one catalyst is catastrophically lost when the system is in steady state it can recreate the same state. There are three elementary flux modes, but none of them is an enzyme-maintaining mode, the entire network being necessary to maintain the two catalysts.     

A density functional theory study of the decomposition mechanism of nitroglycerin

The detailed decomposition mechanism of nitroglycerin (NG) in the gas phase was studied by examining reaction pathways using density functional theory (DFT) and canonical variational transition state theory combined with a small-curvature tunneling correction (CVT/SCT). The mechanism of NG autocatalytic decomposition was investigated at the B3LYP/6-31G(d,p) level of theory. Five possible decomposition pathways involving NG were identified and the rate constants for the pathways at temperatures ranging from 200 to 1000 K were calculated using CVT/SCT. There was found to be a lower energy barrier to the β-H abstraction reaction than to the α-H abstraction reaction during the initial step in the autocatalytic decomposition of NG. The decomposition pathways for CHOCOCHONO₂ (a product obtained following the abstraction of three H atoms from NG by NO₂) include O–NO₂ cleavage or isomer production, meaning that the autocatalytic decomposition of NG has two reaction pathways, both of which are exothermic. The rate constants for these two reaction pathways are greater than the rate constants for the three pathways corresponding to unimolecular NG decomposition. The overall process of NG decomposition can be divided into two stages based on the NO₂ concentration, which affects the decomposition products and reactions. In the first stage, the reaction pathway corresponding to O–NO₂ cleavage is the main pathway, but the rates of the two autocatalytic decomposition pathways increase with increasing NO₂ concentration. However, when a threshold NO₂ concentration is reached, the NG decomposition process enters its second stage, with the two pathways for NG autocatalytic decomposition becoming the main and secondary reaction pathways.     

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.     

Dependence of mycelial morphology on impeller type and agitation intensity

The influence of the agitation conditions on the morphology of Penicillium chrysogenum (freely dispersed and aggregated forms) was examined using radial (Rushton turbines and paddles), axial (pitched blades, propeller, and Prochem Maxflow T), and counterflow impellers (Intermig). Culture broth was taken from a continuous fermentation at steady state and was agitated for 30 min in an ungassed vessel of 1.4-L working volume. The power inputs per unit volume of liquid in the tank, P/V(L), ranged from 0.6 to 6 kW/m(3). Image analysis was used to measure mycelial morphology. To characterize the intensity of the damage caused by different impellers, the mean total hyphal length (freely dispersed form) and the mean projected area (all dispersed types, i.e., also including aggregates) were used. [In this study, breakage of aggregates was taken into account quantitatively for the first time.]At 1.4-L scale and a given P/V(L), changes in the morphology depended significantly on the impeller geometry. However, the morphological data (obtained with different geometries and various P/V(L)) could be correlated on the basis of equal tip speed and two other, less simple, mixing parameters. One is based on the specific energy dissipation rate in the impeller region, which is simply related to P/V(L) and particular impeller geometrical parameters. The other which is developed in this study is based on a combination of the specific energy dissipation rate in the impeller swept volume and the frequency of mycelial circulation through that volume. For convenience, the function arising from this concept is called the "energy dissipation/circulation" function.To test the broader validity of these correlations, scale-up experiments were carried out in mixing tanks of 1.4, 20, and 180 L using a Rushton turbine and broth from a fed-batch fermentation. The energy dissipation/circulation function was a reasonable correlating parameter for hyphal damage over this range of scales, whereas tip speed, P/V(L), and specific energy dissipation rate in the impeller region were poor. Two forms of the energy dissipation/circulation function were considered, one of which additionally allowed for the numbers of vortices behind the blades of each impeller type. Although both forms were successful at correlating the data for the standard impeller designs considered here, there was preliminary evidence that allowing for the vortices would be valuable. (c) 1996 John Wiley & Sons, Inc.     

Feedforward non-Michaelis-Menten mechanism for CO(2) uptake by Rubisco: contribution of carbonic anhydrases and photorespiration to optimization of photosynthetic carbon assimilation

Rubisco, the most abundant protein serving as the primary engine generating organic biomass on Earth, is characterized by a low catalytic constant (in higher plants approx. 3s(-1)) and low specificity for CO(2) leading to photorespiration. We analyze here why this enzyme evolved as the main carbon fixation engine. The high concentration of Rubisco exceeding the concentration of its substrate CO(2) by 2-3 orders of magnitude makes application of Michaelis-Menten kinetics invalid and requires alternative kinetic approaches to describe photosynthetic CO(2) assimilation. Efficient operation of Rubisco is supported by a strong flux of CO(2) to the chloroplast stroma provided by fast equilibration of bicarbonate and CO(2) and forwarding the latter to Rubisco reaction centers. The main part of this feedforward mechanism is a thylakoidal carbonic anhydrase associated with photosystem II and pumping CO(2) from the thylakoid lumen in coordination with the rate of electron transport, water splitting and proton gradient across the thylakoid membrane. This steady flux of CO(2) limits photosynthesis at saturating CO(2) concentrations. At low ambient CO(2) and correspondingly limited capacity of the bicarbonate pool in the stroma, its depletion at the sites of Rubisco is relieved by utilizing O(2) instead of CO(2), i.e. by photorespiration, a process which supplies CO(2) back to Rubisco and buffers the redox state and energy level in the chloroplast. Thus, the regulation of Rubisco function aims to keep steady non-equilibrium levels of CO(2), NADPH/NADP and ATP/ADP in the chloroplast stroma and to optimize the condition of homeostatic photosynthetic flux of matter and energy.     

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.     

Ascorbic acid and copper in linoleate oxidation. II. Ascorbic acid and copper as oxidation catalysts

Both ascorbic acid and copper were strong prooxidants in the oxidation of linoleate in a buffered (pH 7.0) aqueous dispersion at 37 degrees C. Minimum concentrations at which catalytic activity was detected were 1.3 x 10(-7) m for copper and 1.8 x 10(-6) m for ascorbic acid. For concentrations up to 10(-3) m, the increase in rate of oxidation with increase in concentration of catalyst was greater for ascorbic acid than for copper. Ascorbic acid had maximum catalytic activity at 2.0 x 10(-3) m, but was still prooxidant at the highest concentration tested (5.0 x 10(-2) m). Dehydroascorbic acid was a weaker prooxidant than ascorbic acid. Further degradation products of ascorbic acid were not prooxidant. In early stages of the oxidation autocatalytic behavior was observed with copper, but not with ascorbic acid. Ascorbic acid functioned as a true catalyst, i.e., it accelerated the reaction but it was not oxidized simultaneously with the linoleate. It is proposed that the dehydroascorbic acid radical initiates the linoleate oxidation reaction.     

Relation between pristinamycins production by Streptomyces pristinaespiralis,power dissipation and volumetric gas–liquid mass transfer coefficient,kLa

During bioreactor cultures, microorganisms are submitted to non-optimal conditions such as nutritional and hydrodynamic stresses which may lead to modifications of the physiological cell response; this is especially true for filamentous microorganisms like Streptomycetes also subjected to significant morphological changes. In the present work, growth and production of pristinamycins by Streptomyces pristinaespiralis in shaking flasks have been related to power dissipation. The filamentous bacteria were grown in different flask conditions with various total and working volumes and at two agitation rates, to test the influence of power dissipation and gas–liquid mass transfer coefficient on growth and antibiotics production. As a first step, computational fluid dynamics–volume of fluid (CFD–VOF) calculations were shown to be able to predict power dissipations for the various operating conditions in Newtonian flow conditions. Then, in non-Newtonian flow conditions (biomass concentration superior to 14 g L⁻¹), the rheological model of Sisko was implemented in CFD simulations for the calculation of the fluid viscosity and then of power dissipation. Whereas microbial growth was correlated to k_La, the antibiotics production onset was linked to the volume mean power dissipation. Once a minimal cell concentration of 15 g L⁻¹ was reached, the concentration of antibiotics was correlated to power dissipation with an optimal range of production, between 5.5 and 8.5 kW m⁻³. Higher power dissipation entailed a drop in production which could be explained by hydrodynamic cell damages.     

南方红壤区3年生茶园土壤呼吸特征

为探讨南方红壤区茶园的土壤呼吸特征,采用LI-Cor8100开路式土壤碳通量测定系统观测3年生茶园系统的土壤呼吸速率,对茶园土壤呼吸速率的季节变化和在茶行尺度上的空间异质性进行了研究。结果表明,茶园土壤呼吸速率的月动态变化呈明显的单峰曲线特征,峰值出现在8月;茶园土壤呼吸速率的月动态变化与温度呈极显著相关(P<0.01),土壤10 cm的温度能够解释茶园不同观测区域土壤呼吸速率月动态变化的67.79%~88.52%;用指数方程计算的茶园不同观测区域土壤呼吸Q10值为1.58~1.86。在茶行尺度上,茶园土壤呼吸速率存在明显的空间异质性,土壤呼吸速率通常在距离茶树基部较近的位置较高;根系生物量能够解释茶园土壤呼吸速率在茶行尺度上空间变异的82.68%。因此,根系分布的空间差异是造成茶园土壤呼吸速率空间异质性的主要原因。     

A MODEL APPROACH FOR SIZE-SELECTIVE COMPETITION OF MARINE PHYTOPLANKTON FOR FLUCTUATING NITRATE AND AMMONIUM1

Phytoplankton size-selective competition for fluctuating nutrients was studied with the use of a numerical model, which describes nitrate and ammonium uptake, nitrate reduction to ammonium, and growth as a function of cell she under fluctuating nitrogen limitation. The only size-dependent parameter in the model was the cell nutrient quota. Related to this, the cell surface area per biomass was negatively correlated to cell volume, and the vacuole volume per biomass ratio was positively correlated to cell volume. Simulations showed an inverse correlation between the maximum specific growth rate and cell size under steady-state conditions. With nitrate as the limiting nitrogen source, nitrogen quotas were always higher than with ammonium at the same specific growth rate. Net passive transport of ammonium due to unspecific diffusion of ammonia across the plasma membrane decreased the affinity for ammonium, whereas the affinity for nitrate was not influenced. Transient state-specific ammonium uptake was not dependent on cell size. However, small algae always have the highest specific growth rate in ammonium-controlled systems according to our model. Transient state nitrate uptake rate was positively correlated to cell size because larger algae have a higher vacuole volume per biomass, in which nitrate can be stored. Despite their lower maximum growth rate, larger algae became dominant during simulations under fluctuating nitrate supply when amplitude of and the period between nitrate pulses were high enough. Results from model simulations were qualitatively validated by earlier observations that large diatoms become dominant under fluctuating conditions when nitrate is the main nitrogen source.     

On a certain model of cardiovascular system

A model of the arterial system is discussed which considers determination of the changes in density of energy dissipation of the pulse with the system entrance being the forcing of blood from the heart to the aorta. The effects of boundary conditions and branching upon dissipation density are analyzed on the basis of the model.     

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.