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.     

Biological electron tunneling through native protein media

 Nature has engineered a universe of redox proteins to efficiently control the oxidation and reduction of substrates and to convert redox energy into a delocalized transmembrane proton gradient power source. Some rapid physiologically relevant electron transfers are rate limited by electron tunneling. Distance appears to be the principle means naturally selected to control the speed of electron tunneling; free energy and reorganization energy can play important auxiliary roles. Thus, an electron from a biological redox center can tunnel in any direction and is likely to reduce the closest redox center with a favorable free energy. Although it is clearly possible to facilitate electron tunneling by designing covalent bridges in the regions between donors and acceptors, this does not seem to be a strategy that evolution has used. Evolutionary mutagenic adjustment of a bridge-like quality of the amino acid medium may be difficult in the face of heavy selection on the folding, stability and other properties of the protein medium. Repositioning cofactors by even a few angstroms has more profound effects on promoting and retarding rates, independent of the structure of the amino acid medium. Received: 12 January 1997 / Accepted: 5 February 1997     

Role of epibiotic diatoms isolated from the barnacle shell in the cyprid metamorphosis of <Emphasis Type="Italic">Balanus amphitrite</Emphasis>

The mechanisms structuring aquatic communities across environmental gradients are often difficult to distinguish from one another and can produce similar patterns of species distributions. In freshwater systems, the amount of canopy cover from surrounding trees is often associated with transitions in local community structure. These community changes could be driven by habitat selection prior to colonization of the aquatic habitat and/or species-sorting post-colonization. To assess the contributions of pre- versus post-colonization processes in structuring larval dragonfly assemblages, we tested the impact of artificial and natural canopy cover on the selection of experimental aquatic mesocosms by adult dragonflies, and monitored the performance (i.e. growth and survival) of larval dragonflies that were placed in mesocosms under a gradient of natural canopy cover. We found that greater levels of canopy cover resulted in fewer adult visits to mesocosms, and more natural canopy cover decreased the species richness of visitors. There were no effects of canopy cover on the growth and survival of larvae added to the mesocosms. Our results suggest that adult habitat selection plays a dominant role in structuring larval dragonfly assemblages across a canopy cover gradient, and that canopy cover can be an important environmental filter on species distributions.     

Evolution in structured populations: beyond the kin versus group debate

Much of the literature on social evolution is pervaded by the old debate about the relative merits of kin and group selection. In this debate, the biological interpretation of processes occurring in real populations is often conflated with the mathematical methodology used to describe these processes. Here, we highlight the distinction between the two by placing this discussion within the broader context of evolution in structured populations. In this review we show that the current debate overlooks important aspects of the interplay between genetic and demographic structuring, and argue that a continued focus on the relative merits of kin versus group selection distracts attention from moving the field forward.     

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.     

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.     

GEOGRAPHICAL VARIATION IN THE RATE OF EVOLUTION: EFFECT OF AVAILABLE ENERGY OR FLUCTUATING ENVIRONMENT?

In a recent paper, Wright et al. (2003) argue for the hypothesis that greater biologically available energy elevates the rate of molecular evolution. However, their results are also consistent with alternative hypotheses that invoke either environmentally driven variation in effective population sizes, or natural selection, or both. The available energy gradient cited by Wright et al. is linearly correlated with temperature fluctuations, and the observed rate heterogeneity could be a consequence of this environmental variability. The distribution of phylogenetic branch lengths alone is insufficient to distinguish between the hypotheses, and complementary approaches are suggested.     

The proton flux through the bacterial flagellar motor

Bacterial flagella are driven by a rotary motor that utilizes the free energy stored in the electrochemical proton gradient across the cytoplasmic membrane to do mechanical work. The flux of protons coupled to motor rotation was measured in Streptococcus and found to be directly proportional to motor speed. This supports the hypothesis that the movement of protons through the motor is tightly coupled to the rotation of its flagellar filament. Under this assumption the efficiency of energy conversion is close to unity at the low speeds encountered in tethered cells but only a few percent at the high speeds encountered in swimming cells. This difference appears to be due to dissipation by processes internal to the motor. The efficiency at high speeds exhibits a steep temperature dependence and a sizable deuterium solvent isotope effect.     

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.     

Thermal energy dissipation and xanthophyll cycles beyond the Arabidopsis model

Thermal dissipation of excitation energy is a fundamental photoprotection mechanism in plants. Thermal energy dissipation is frequently estimated using the quenching of the chlorophyll fluorescence signal, termed non-photochemical quenching. Over the last two decades, great progress has been made in the understanding of the mechanism of thermal energy dissipation through the use of a few model plants, mainly Arabidopsis. Nonetheless, an emerging number of studies suggest that this model represents only one strategy among several different solutions for the environmental adjustment of thermal energy dissipation that have evolved among photosynthetic organisms in the course of evolution. In this review, a detailed analysis of three examples highlights the need to use models other than Arabidopsis: first, overwintering evergreens that develop a sustained form of thermal energy dissipation; second, desiccation tolerant plants that induce rapid thermal energy dissipation; and third, understorey plants in which a complementary lutein epoxide cycle modulates thermal energy dissipation. The three examples have in common a shift from a photosynthetically efficient state to a dissipative conformation, a strategy widely distributed among stress-tolerant evergreen perennials. Likewise, they show a distinct operation of the xanthophyll cycle. Expanding the list of model species beyond Arabidopsis will enhance our knowledge of these mechanisms and increase the synergy of the current studies now dispersed over a wide number of species.     

Heterogeneous selection promotes maintenance of polymorphism in host–parasite interactions

Polymorphism in loci affecting host resistance and parasite virulence is characteristic for nearly all species and this genetic variation is considered to have profound consequences for the patterns of disease incidence, prevalence and evolution. The gene-for-gene (GFG) system is a well-characterized genetic interaction of host recognition and parasite antigenic loci for a wide range of plant-parasite interactions. Long-term maintenance of polymorphism in GFG systems has remained puzzling for both theoreticians and empiricists. Traditionally this diversity has been explained by tradeoffs with other life-history traits closely linked with fitness, yet empirical evidence for such costs has remained mixed. Here we argue that incorporating simple ecological reality – spatial structuring and gradient of environmental conditions – into host–parasite research will help us understand how polymorphism is maintained. While environmental conditions (biotic and abiotic factors) have been studied in depth in plant pathology for their influence on disease severity and plant yield, they have been rarely set into an evolutionary framework. We briefly review recent data on natural plant–parasite metapopulations and theoretical models moving from single population models towards metapopulation theory to reveal in just how many ways spatial structuring may affect the coevolutionary process. We clarify also how spatially heterogeneous selection, through G×E (or G×G×E) interactions, may be particularly important for natural host–parasite interactions and suggest that this provides the unifying ground upon which future theoretical and empirical work should be build on.     

Novel strategies to study the role of mutation and nucleic acid structure in evolution

Natural selection processes tune genomes in the edge of the chaos imposed by mutation and drift, allowing an enduring exploration of fitter genetic networks within the constraints imposed by self-organization and the interactions of genotype and phenotype. Alternatively, evolution can be viewed from thermodynamic, kinetic or cybernetic perspectives. Regardless of insight, there is need to understand structure-function relationships at the molecular and holistic evolutionary levels. Strategies are here described that analyze genetic variation in time and trace the evolution of nucleic acid structure. Nucleic acid scanning techniques were used to measure sequence divergence and provide a direct inference of genome-wide mutation rate. This was tested for the first time in vegetatively propagating plants. The method is general and was also used in a study of mutational patterns in phytopathogenic fungi, showing there was a link between sequence and structural diversification of ribosomal gene spacers. In order to determine if this was a general phenomenon, the origin and diversification of nucleic acid secondary structure was traced using a cladistic method capable of producing rooted phylogenetic trees. Phylogenies reconstructed from primary and secondary RNA structure were congruent at all taxonomical levels, providing evidence of a strong link between phenotype and genotype favoring thermodynamic stability and dissipation of Gibbs free energy. Overall results suggest that thermodynamic principles are important driving forces of the evolutionary processes of the living world.     

Under what conditions signal transduction pathways are highly flexible in response to external forcing? A case study on calcium oscillations

Sensitivity and flexibility are typical properties of biological systems. These properties are here investigated in a model for simple and complex intracellular calcium oscillations. In particular, the influence of external periodic forcing is studied. The main point of the study is to compare responses of the system in a chaotic regime with those obtained in a regular periodic regime. We show that the response to external signals in terms of the range of synchronization is not significantly different in regular and chaotic Ca2+ oscillations. However, both types of oscillation are highly flexible in regimes with weak dissipation. Therefore, we conclude that dissipation of free energy is a suitable index characterizing flexibility. For biological systems this appears to be of special importance since for thermodynamic reasons, notably in view of low free energy consumption, dissipation should be minimized.     

CLINES IN CUTICULAR HYDROCARBONS IN TWO DROSOPHILA SPECIES WITH INDEPENDENT POPULATION HISTORIES

We took a comparative approach utilizing clines to investigate the extent to which natural selection may have shaped population divergence in cuticular hydrocarbons (CHCs) that are also under sexual selection in Drosophila. We detected the presence of CHC clines along a latitudinal gradient on the east coast of Australia in two fly species with independent phylogenetic and population histories, suggesting adaptation to shared abiotic factors. For both species, significant associations were detected between clinal variation in CHCs and temperature variation along the gradient, suggesting temperature maxima as a candidate abiotic factor shaping CHC variation among populations. However, rainfall and humidity correlated with CHC variation to differing extents in the two species, suggesting that response to these abiotic factors may vary in a species‐specific manner. Our results suggest that natural selection, in addition to sexual selection, plays a significant role in structuring among‐population variation in sexually selected traits in Drosophila.     

Large-scale patterns in morphological diversity and species assemblages in Neotropical Triatominae (Heteroptera: Reduviidae)

We analysed the spatial variation in morphological diversity (MDiv) and species richness (SR) for 91 species of Neotropical Triatominae to determine the ecological relationships between SR and MDiv and to explore the roles that climate, productivity, environmental heterogeneity and the presence of biomes and rivers may play in the structuring of species assemblages. For each 110 km x 110 km-cell on a grid map of America, we determined the number of species (SR) and estimated the mean Gower index (MDiv) based on 12 morphological attributes. We performed bootstrapping analyses of species assemblages to identify whether those assemblages were more similar or dissimilar in their morphology than expected by chance. We applied a multi-model selection procedure and spatial explicit analyses to account for the association of diversity-environment relationships. MDiv and SR both showed a latitudinal gradient, although each peaked at different locations and were thus not strictly spatially congruent. SR decreased with temperature variability and MDiv increased with mean temperature, suggesting a predominant role for ambient energy in determining Triatominae diversity. Species that were more similar than expected by chance co-occurred near the limits of the Triatominae distribution in association with changes in environmental variables. Environmental filtering may underlie the structuring of species assemblages near their distributional limits.     

Concentration polarization phenomenon in the case of mechanical pressure difference on the membrane

We analyzed the transport of KCl solutions through the bacterial cellulose membrane and concentration boundary layers (CBLs) near membrane with pressure differences on the membrane. The membrane was located in horizontal-plane between two chambers with different KCL solutions. The membrane was located in horizontal-plane between two chambers with different KCL solutions. As results from the elaborated model, gradient of KCL concentration in CBLs is maximal at membrane surfaces in the case when pressure difference on the membrane equals zero. The amplitude of this maximum decreases with time of CBLs buildup. Application of mechanical pressure gradient in the direction of gradient of osmotic pressure on the membrane causes a shift of this maximum into the chamber with lower concentration. In turn, application of mechanical pressure gradient directed opposite to the gradient of osmotic pressure causes the appearance of maximum of concentration gradient in chamber with higher concentration. Besides, the increase of time of CBLs buildup entails a decrease of peak height and shift of this peak further from the membrane. Similar behavior is observed for distribution of energy dissipation in CBLs but for pressure difference on the membrane equal to zero the maximum of energy dissipation is observed in the chamber with lower concentration. We also measured time characteristics of voltage in the membrane system with greater KCl concentrations over the membrane. We can state that mechanical pressure difference on the membrane can suppress or strengthen hydrodynamic instabilities visible as pulsations of measured voltage. Additionally, time of appearance of voltage pulsations, its amplitude, and frequency depend on mechanical pressure differences on the membrane and initial quotient of KCl concentrations in chambers.     

Thermodynamics of Ca2+ transport through sarcoplasmic reticulum membranes during the transient-state of simulated reactions

The kinetics of a chemical model of Ca2+ transport and coupled ATPase activity in sarcoplasmic reticulum membranes were solved for the transient-state of simulated reactions, using a numerical integration procedure. The simulation conditions reproduced in vitro experiments using either fragmented membranes or vesicles with Ca2+ accumulating ability. The results yielded the concentrations of all the ligands and intermediates of the enzymatic cycle as a function of the reaction time. These results were applied to calculations of several thermodynamic variables: (1) the step by step profile of the standard free energy change of the cycle. (2) The step by profile of the actual free energy change of the cycle, and its evolution with the reaction time. (3) The separate contributions of ATP hydrolysis and Ca2+ transport to the overall free energy change with the reaction. (4) The dependence of the velocity of the free energy change with the reaction time. (5) The efficiency of the transport system, and its change with the reaction time. (6) The separate contributions of the Ca2+ gradient and some enzymatic intermediates as free energy stores. The main findings are: (1) the step by step diagrams of the free energy change calculated from the results of the kinetic analysis better describe the thermodynamic profile of the cycle than previously reported diagrams of the standard free energy and basic free energy changes. The relative contribution of each partial step to the driving force of the whole reactions, as well as their changes upon the advancement of the reactions, are derived from the diagrams. (2) Free energy yielded by ATP hydrolysis is stored by the system, not only as a Ca2+ gradient, but also as enzymatic intermediates of the reaction. The progressive increase of both free energy pools upon the advancement of the reaction is quantitated.     

Photoprotection in an ecological context: the remarkable complexity of thermal energy dissipation

This review places photoprotection into the context of ecology and species diversity. The focus is on photoprotection via the safe removal - as thermal energy - of excess solar energy absorbed by the light collecting system, which counteracts the formation of reactive oxygen species. An update on the surprisingly complex, multiple variations of thermal energy dissipation is presented, placing these different forms into ecological and genetic contexts. Zeaxanthin-facilitated, flexible thermal dissipation associated with the PsbS protein and controlled by the trans-thylakoid pH gradient apparently occurs ubiquitously in plants, and can become sustained (and thus less flexible) at low temperatures. Long-lived, slow-growing plants with low intrinsic capacities for photosynthesis have greater capacities for this flexible dissipation than short-lived, fast-growing species. Furthermore, potent, but inflexible (zeaxanthin-facilitated) thermal dissipation, prominent in evergreen species under prolonged environmental stress, is characterized with respect to the involvement of photosystem II core rearrangement and/or degradation as well as the absence of control by trans-thylakoid pH and, possibly, PsbS. A role of PsbS-related proteins in photoprotection is discussed.     

Thermodynamical interpretation of evolutionary dynamics on a fitness landscape in an evolution reactor,II

In our previous report [Aita, T., Morinaga, S., Hosimi, Y., 2004. Thermodynamical interpretation of evolutionary dynamics on a fitness landscape in an evolution reactor I. Bull. Math. Biol. 66, 1371–1403], an analogy between thermodynamics and adaptive walks on a Mt. Fuji-type fitness landscape in an artificial selection system was presented. Introducing the ‘free fitness’ as the sum of a fitness term and an entropy term and ‘evolutionary force’ as the gradient of free fitness on a fitness coordinate, we demonstrated that the adaptive walk (=evolution) is driven by the evolutionary force in the direction in which free fitness increases. In this report, we examine the effect of various modifications of the original model on the properties of the adaptive walk. The modifications were as follows: first, mutation distance d was distributed obeying binomial distribution; second, the selection process obeyed the natural selection protocol; third, ruggedness was introduced to the landscape according to the NK model; fourth, a noise was included in the fitness measurement. The effect of each modification was described in the same theoretical framework as the original model by introducing ‘effective’ quantities such as the effective mutation distance or the effective screening size.     

Ecological succession as an energy dispersal process

Ecological succession is described by the 2nd law of thermodynamics. According to the universal law of the maximal energy dispersal, an ecosystem evolves toward a stationary state in its surroundings by consuming free energy via diverse mechanisms. Species are the mechanisms that conduct energy down along gradients between repositories of energy which consist of populations at various thermodynamic levels. The salient characteristics of succession, growing biomass production, increasing species richness and shifting distributions of species are found as consequences of the universal quest to diminish energy density differences in least time. The analysis reveals that during succession the ecosystem's energy transduction network, i.e., the food web organizes increasingly more effective in the free energy reduction by acquiring new, more effective and abandoning old, less effective species of energy transduction. The number of species does not necessarily peak at the climax state that corresponds to the maximum-entropy partition of species maximizing consumption of free energy. According to the theory of evolution by natural selection founded on statistical physics of open systems, ecological succession is one among many other evolutionary processes.