Dissipation and maintenance of stable states in an enzymatic system: analysis and simulation

The constraint-based analysis has emerged as a useful tool for analysis of biochemical networks. An essential assumption for constraint-based analysis is the formation of a stable steady state. This work investigates dissipation and maintenance of stable states in a simple reversible enzymatic reaction with substrate inhibition. Under mass-action kinetics, the conditions under which the reaction maintains a stable steady state are analytically derived and numerically confirmed. It is shown that, in order to maintain a steady state in the regulated reaction, maximal enzyme activity must be much higher than input rate. Moreover, it is revealed that requirements for large enzyme activity are due to substrate inhibition. It is suggested that high activities of enzymes may play a vital role in protecting a stable state from its catastrophic collapse, giving an additional explanation to an intriguing problem—why the activities of some enzymes greatly exceed the flux capacity of a pathway. In addition, dissipation of the enzymatic reaction is analysed. It is shown that the collapse of stable states is always associated with a point at which dissipation is the highest. Therefore, in order to maintain a stable state, dissipation of the reaction must be less than a critical value. Moreover, although external forcing may not change net mass flow, it may lead to collapse of stable states. Furthermore, when stable states collapse at a critical forcing amplitude and period, dissipation also reaches a highest value. It is concluded that collapse of stable steady state in the enzyme system with substrate inhibition always corresponds to critical points at which dissipation is highest, regardless if the reaction is forced or not. Therefore, for the substrate inhibited reaction, maintenance of stable states is intrinsically related to level of dissipation.     

Phenogenetic drift and the evolution of genotype-phenotype relationships

Maintenance of a stable two-locus polymorphism is analyzed statistically by fitting a logistic regression with a quadratic function of genotypic fitnesses to the probability for a fitness set to maintain a polymorphism. The regression is fitted using a data set containing information on stable equilibria maintained by 32,00 randomly generated fitness sets with three recombination values (0. 005, 0.05, 0.5). Fitted logistic regressions discriminate with 88 to 90% accuracy between fitness sets maintaining and not maintaining a stable internal equilibrium, which implies the existence of a fitness structure (balance of fitnesses) maintaining a two-locus polymorphism. Aspects of the balance of fitnesses revealed by logistic regressions are discussed. It is demonstrated that logistic regression also discriminates between types of a stable polymorphism: globally stable polymorphism, several simultaneously stable polymorphisms, and stable equilibria in addition to a polymorphic one, which implies that different balances of fitnesses are responsible for the maintenance of different types of polymorphism.     

On the number of stable equilibria and the simultaneous stability of fixation and polymorphism in two-locus models

It is shown that in simple symmetric two-locus, two-allele constant fitness models the bound of four simultaneously stable equilibria previously accepted for general two-locus, two-allele models is exceeded. Situations with five and six stable equilibria are exhibited. These involve four chromosomal fixations and either one or two polymorphic stable equilibria.     

Competition and body size

If being larger than competing conspecifics is important for fitness, then an unstable escalation of body size may result. In asexual populations, a cycling of sizes can occur but for sexual diploids, an irreversible size increase is more likely. Several factors can produce a stable distribution of sizes, but a single body size or even a narrow range of sizes cannot be stable. For example, enough environmental variance can produce stability without any genetic variability in the population. Or, with no environmental variance, a high cost of fighting between similar sizes or, for diploids, an increasing mortality with size may lead to a stable distribution of sizes. A game theory model is used to investigate the existence and form of a stable distribution of body sizes in a population.     

Role of bacteria in the oviposition behaviour and larval development of stable flies

Stable flies, Stomoxys calcitrans (L.), are the most important pests of cattle in the United States. However, adequate management strategies for stable flies, especially for pastured cattle, are lacking. Microbial/symbiont-based approaches offer novel venues for management of insect pests and/or vector-borne human and animal pathogens. Unfortunately, the fundamental knowledge of stable fly-microbial associations and their effect on stable fly biology is lacking. In this study, stable flies laid greater numbers of eggs on a substrate with an active microbial community (> 95% of total eggs oviposited) than on a sterilized substrate. In addition, stable fly larvae could not develop in a sterilized natural or artificial substrate/medium. Bacteria were isolated and identified from a natural stable fly oviposition/developmental habitat and their individual effect on stable fly oviposition response and larval development was evaluated in laboratory bioassays. Of nine bacterial strains evaluated in the oviposition bioassays, Citrobacter freundii stimulated oviposition to the greatest extent. C. freundii also sustained stable fly development, but to a lesser degree than Serratia fanticola. Serratia marcescens and Aeromonas spp. neither stimulated oviposition nor supported stable fly development. These results demonstrate a stable fly bacterial symbiosis; stable fly larval development depends on a live microbial community in the natural habitat, and stable fly females are capable of selecting an oviposition site based on the microbially derived stimuli that indicate the suitability of the substrate for larval development. This study shows a promising starting point for exploiting stable fly-bacterial associations for development of novel approaches for stable fly management.     

Discriminating between Light- and Heavy-Tailed Distributions with Limit Theorem

In this paper we propose an algorithm to distinguish between light- and heavy-tailed probability laws underlying random datasets. The idea of the algorithm, which is visual and easy to implement, is to check whether the underlying law belongs to the domain of attraction of the Gaussian or non-Gaussian stable distribution by examining its rate of convergence. The method allows to discriminate between stable and various non-stable distributions. The test allows to differentiate between distributions, which appear the same according to standard Kolmogorov–Smirnov test. In particular, it helps to distinguish between stable and Student’s t probability laws as well as between the stable and tempered stable, the cases which are considered in the literature as very cumbersome. Finally, we illustrate the procedure on plasma data to identify cases with so-called L-H transition.     

Experimental and clinical results of new advances in the treatment of facial trauma

Theoretical considerations and photoelastic and mechanical experiments showed us the progression from metal wires to metal plates in different systems. In the midface there is no question about stabilization by miniplate systems. For mandibular fracture treatment, there is a discussion going on at present about the use of stable maxisystems versus less stable minisystems. Our clinical experience of 15 years indicates that there is no further demand for strict stable fixation of mandibular fractures, and we were encouraged to use less stable systems with similar good results, as our follow-up and statistical evaluation showed. To continue the simplification of osteosynthesis methods we are performing experiments with resorbable materials. Early results show fracture healing comparable with that found with plate-and-screw systems. Our clinical experience has shown that there is no longer any question about the ability of stable fracture treatment by means of osteosynthesis. However, there still is the question of how functional such fracture treatment might be.     

Spatial patterns and ESS's

The classical idea of an evolutionarily stable strategy (ESS) does not involve any spatial dependence. An evolution equation for analyzing games in a region is suggested and the possibility of spatial patterns is investigated. It is shown that an ESS is so stable that it forbids any spatial dependence but that other equilibria may have patterns associated with them if the dispersion rates are suitably chosen.     

Absolute stability and transitions in ecosystems with a multiplicity of stable states and dispersal

The principle that for a large class of spatially extended dynamic systems with several locally stable states there exists at most one absolutely stable state is applied to population dynamical models with diffusive spatial dispersal. The basic concepts and methods to characterize absolute stability and its limits are presented. Some interesting results concerning the significance of dispersal ability in competing and mutualistic systems are found. The concepts appear of practical importance since only absolutely stable states are resilient against all localized fluctuations and disturbances.     

Multiple feedbacks and the prevalence of alternate stable states on coral reefs

The prevalence of alternate stable states on coral reefs has been disputed, although there is universal agreement that many reefs have experienced substantial losses of coral cover. Alternate stable states require a strong positive feedback that causes self-reinforcing runaway change when a threshold is passed. Here we use a simple model of the dynamics of corals, macroalgae and herbivores to illustrate that even weak positive feedbacks that individually cannot lead to alternate stable states can nonetheless do so if they act in concert and reinforce each other. Since the strength of feedbacks varies over time and space, our results imply that we should not reject or accept the general hypothesis that alternate stable states occur in coral reefs. Instead, it is plausible that shifts between alternate stable states can occur sporadically, or on some reefs but not others depending on local conditions. Therefore, we should aim at a better mechanistic understanding of when and why alternate stable states may occur. Our modelling results point to an urgent need to recognize, quantify, and understand feedbacks, and to reorient management interventions to focus more on the mechanisms that cause abrupt transitions between alternate states.     

Conformational studies on the gramicidin A transmembrane channel in lipid micelles and liposomes

The interaction of gramicidin A with lysolecithin micelles and with lecithin liposomes is demonstrated by circular dichroism to result in several metastable conformational states. A stable state can be obtained after extensive heating when the gramicidin A was added dry or in ethanol solution to the phospholipid dispersion but the stable state is readily obtained when gramicidin A is added in a trifluoroethanol solution. The circular dichroism of the stable conformational state is characterized by negative ellipticity below 205 nm and principally by a positive 220 nm band on which is superposed a weak 230 nm band (the latter likely arising from tryptophan side chains). The stable conformational state is considered to be that of the functional transmembrane channel primarily on the basis of extensive studies on its interaction with sodium ions.     

Protein structure, stability and solubility in water and other solvents

Proteins carry out the most difficult tasks in living cells. They do so by interacting specifically with other molecules. This requires that they fold to a unique, globular conformation that is only marginally more stable than the large ensemble of unfolded states. The folded state is stabilized mainly by the burial and tight packing of over 80% of the peptide groups and non-polar side chains. If life as we know it is to exist in a solvent other than water, the folded state must be stable and soluble in the new solvent. Our analysis suggests that proteins will be unstable in most polar solvents such as ethanol, extremely stable in non-polar solvents such as cyclohexane, and even more stable in a vacuum. Our solubility studies suggest that protein solubility will be markedly lower in polar solvents such as ethanol and that proteins will be essentially insoluble in non-polar solvents such as cyclohexane. For these and other reasons it seems unlikely that the life we know could exist in any solvent system other than water.     

Conformational studies on the gramicidin A transmembrane channel in lipid micelles and liposomes

The interaction of gramicidin A with lysolecithin micelles and with lecithin liposomes is demonstrated by circular dichroism to result in several metastable conformational states. A stable state can be obtained after extensive heating when the gramicidin A was added dry or in ethanol solution to the phospholipid dispersion but the stable state is readily obtained when gramicidin A is added in a trifluoroethanol solution. The circular dichroism of the stable conformational states is characterized by negative ellipticity below 205 nm and principally by a positive 220 nm band on which is superposed a weak 230 nm band (the latter likely arising from tryptophan side chains). The stable conformational state is considered to be that of the functional transmembrane channel primarily on the basis of extensive studies on its interaction with sodium ions.     

On evolution under symmetric and asymmetric competitions

This paper considers the coevolution of phenotypic traits in a community comprising two competitive species subject to strong Allee effects. Firstly, we investigate the ecological and evolutionary conditions that allow for continuously stable strategy under symmetric competition. Secondly, we find that evolutionary suicide is impossible when the two species undergo symmetric competition, however, evolutionary suicide can occur in an asymmetric competition model with strong Allee effects. Thirdly, it is found that evolutionary bistability is a likely outcome of the process under both symmetric and asymmetric competitions, which depends on the properties of symmetric and asymmetric competitions. Fourthly, under asymmetric competition, we find that evolutionary cycle is a likely outcome of the process, which depends on the properties of both intraspecific and interspecific competition. When interspecific and intraspecific asymmetries vary continuously, we also find that the evolutionary dynamics may admit a stable equilibrium and two limit cycles or two stable equilibria separated by an unstable limit cycle or a stable equilibrium and a stable limit cycle.     

Evolutionarily stable strategies and short-term selection in Mendelian populations re-visited

This note concerns a one locus, two allele, random mating diploid population, subject to frequency-dependent viability selection. It is already known that in such a population, any evolutionarily stable strategies (ESS), if only accessible by the genotype-to-phenotype mapping, is the phenotypic image of a stable genetic equilibrium (Eshel, I. 1982. Evolutionarily stable strategies and viability selection in Mendelian populations. Theor. Popul. Biol. 22(2), 204-217; Cressman et al. 1996. Evolutionary stability in strategic models of single-locus frequency-dependent viability selection. J. Math. Biol. 34, 707-733). The opposite is not true. We find necessary and sufficient parametric conditions for global convergence to the ESS, but we also demonstrate conditions under which, although a unique, genetically accessible ESS exists, there is another, "non-phenotypic" genetically stable equilibrium.     

Turnover of mammalian phospholipids. Stable and unstable components in neoplastic mast cells

1. Choline- and inositol-labelled phospholipids of exponentially growing or static neoplastic mast cells turn over by degradation and resynthesis of the entire molecule. Turnover follows a biphasic pattern, the unstable rapidly turning-over component accounting for 60–80% of labelled phospholipid. The residual stable component does not turn over any more than does protein or DNA. 2. Subcellular fractions and surface membranes of choline-labelled P815Y cells contain the same proportion of stable and unstable components as do whole cells. The unstable component is largely phosphatidylcholine; the stable component is relatively richer in sphingomyelin. 3. It is concluded that the phospholipids of neoplastic mast cells are of two classes, one of which is susceptible to continual enzymic degradation and resynthesis, and the other of which is metabolically stable.     

Stable isotopes in physiological ecology and food web research

Mention the word 'isotopes' and most people will think of short-lived radioactive isotopes. Yet far more abundant than the radioactive forms and perhaps much more useful for ecological studies are the stable isotopes. Early interest in stable isotope analyses developed in the geological sciences, and their application in environmental biology has developed slowly until recently. Over the past few years, innovative applications of stable isotope analyses to studies of biological processes have been expanding rapidly, and there is every indication that stable isotope approaches will lead to major advances over the next decade in our understanding of physiological processes and fluxes through ecological systems. Studies of plant and animal physiological ecology and food webs will benefit greatly.     

Synthesis and biological evaluation of bis and monocarbonate prodrugs of 10-hydroxycamptothecins

In an effort to improve the stability of labile lactone ring of camptothecins, the bis and mono-alkyl carbonate prodrugs of 10-hydroxycamptothecins were synthesized and their chemical and enzymatical stability as well as antitumor activity were studied. The in vitro evaluation of the stability of these carbonates indicates that the 10,20-biscarbonates are firstly hydrolyzed to afford the stable 20-monocarbonates. And the 10-carbonates are not stable in human plasma, mouse plasma and pH7.4 phosphate buffer, while the 20-carbonates are relatively stable in the three media and can be readily cleaved by porcine liver esterase. The overall toxicity of the tested carbonate against mice bearing S180 sarcoma is much lower when compared with the parent compound, and the antitumor activity is maintained.     

On the relation between the instability of ESS in discrete dynamics and segregation distortion

There is a simple correspondence between discrete dynamical systems associated with evolutionary game dynamics and general locus multiallele selection models with non-Mendelian segregation. When interpreted properly the payoff matrix has two components, a fitness matrix component and a segregation matrix component. The presence of segregation distortion which corresponds to a non-symmetric payoff matrix, is a source of instability. With non-symmetric payoff an ESS does not usually correspond to a stable equilibrium. It is always externally stable but does not necessarily have an internally stable equilibrium.     

生态系统的多稳态与突变

许多生态系统可能在短时间内发生难以预料的状态突变, 其中一些生态系统突变的机理可以用多稳态理论进行解释。近年来生态系统的多稳态和突变现象及其机理吸引了研究者和管理者的广泛关注。本文重点对生态系统多稳态的理论基础、识别方法及稳态转换发生的早期预警信号进行综述, 并基于典型生态系统过程对现实世界中可能观测到的稳态转换进行实例分析, 最后对多稳态概念框架和理论应用中的潜在争议进行讨论, 以期为非线性生态系统动态的理论研究、管理实践和生物多样性保护等提供参考。