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.     

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

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

Metabolic networks evolve towards states of maximum entropy production

A metabolic network can be described by a set of elementary modes or pathways representing discrete metabolic states that support cell function. We have recently shown that in the most likely metabolic state the usage probability of individual elementary modes is distributed according to the Boltzmann distribution law while complying with the principle of maximum entropy production. To demonstrate that a metabolic network evolves towards such state we have carried out adaptive evolution experiments with Thermoanaerobacterium saccharolyticum operating with a reduced metabolic functionality based on a reduced set of elementary modes. In such reduced metabolic network metabolic fluxes can be conveniently computed from the measured metabolite secretion pattern. Over a time span of 300 generations the specific growth rate of the strain continuously increased together with a continuous increase in the rate of entropy production. We show that the rate of entropy production asymptotically approaches the maximum entropy production rate predicted from the state when the usage probability of individual elementary modes is distributed according to the Boltzmann distribution. Therefore, the outcome of evolution of a complex biological system can be predicted in highly quantitative terms using basic statistical mechanical principles.     

原核基因组的进化方向和癌／正常细胞的熵产生

本文评述了理论生物学的两个基础实验。一是用离子束辐照加速大肠杆菌进化的方法研究原核基因组的进化方向,证明进化中的缺失偏好性和编码信息量扩增律不矛盾。二是提出用导热法测量细胞的熵产生,比较研究了癌细胞和正常细胞的熵产生和外加电场的关系,证明在一定强度的电场作用下正常细胞的熵产生可以明显超过癌细胞,从而实现改变两类细胞间熵流方向的目的。     

Features of using the second principle of thermodynamics for describing brain function]

It has been shown that negative production of information entropy at the expense of its normalization change under the influence of neuromediators is specific for the nervous systems and brain. Chemical synapses are calculation elements with a diffusion input to control information entropy normalization. Reproduction stability of the nervous system and brain, and their functioning as well, are determined due to Lyapunov criteria by the maximum of entropy production in combination with minimum for the entropy itself. As far as information in nervous systems is connected with an element of energy normalization that is much greater than the scales of molecular energy of single atoms, physical and information self-organization can simultaneously either correlate or be sufficiently independent, because entropy corresponds to statically unstable point, with its output being natural in different ways. In particular, the brain potentialities are the more, the further it is advanced in its evolution in the sense of entropy increase of its structure, i.e. evolution perfection of mind results from the elementary meaning of the second principle of thermodynamics but in combination of the biochemical peculiarity--the growth of brain is controlled by adrenogens and because of this correlates with productivity.     

Game theory and evolution: finite size and absolute fitness measures

This article is concerned with the characterization and existence of evolutionarily stable strategies (ESS) in Games against Nature, a class of models described by finite size populations and absolute fitness measures. We address these problems in terms of a new formalism which revolves around the concept evolutionary entropy, a measure of the diversity of options associated with a strategy pure - strategies have zero entropy, mixed strategies positive entropy. We invoke this formalism to show that ESS are characterized by extremal states of entropy. We illustrate this characterization of ESS by an analysis of the evolution of the sex ratio and the evolution of seed size.     

Enzyme kinetics and the maximum entropy production principle

A general proof is derived that entropy production can be maximized with respect to rate constants in any enzymatic transition. This result is used to test the assumption that biological evolution of enzyme is accompanied with an increase of entropy production in its internal transitions and that such increase can serve to quantify the progress of enzyme evolution. The state of maximum entropy production would correspond to fully evolved enzyme. As an example the internal transition ES?EP in a generalized reversible Michaelis-Menten three state scheme is analyzed. A good agreement is found among experimentally determined values of the forward rate constant in internal transitions ES→EP for three types of β-Lactamase enzymes and their optimal values predicted by the maximum entropy production principle, which agrees with earlier observations that β-Lactamase enzymes are nearly fully evolved. The optimization of rate constants as the consequence of basic physical principle, which is the subject of this paper, is a completely different concept from a) net metabolic flux maximization or b) entropy production minimization (in the static head state), both also proposed to be tightly connected to biological evolution.     

A critique of directionality theory

Directionality theory suggests that demographic entropy, defined in a way analogous to thermodynamic entropy, is as important as the Malthusian parameter in determining life history evolution in an age-structured population. In particular, it suggests that entropy should increase in equilibrium species and decrease in opportunistic species. This theory has been applied to explain the evolution of body size and of senescence. It has been claimed recently that this theory has been validated by a simulation study, but it is argued here that this study reveals substantial flaws in directionality theory and that the Malthusian parameter rather than entropy is the appropriate tool in the study of life history evolution.     

生物多样性的熵值结构

多样性一般定义为生物进化过程中物种表现型的丰富程度。从广义上讲,生物进化与环境归类作用的结构复杂性对生物为多样性的解释是很有益处的。我们认为区域水平与样地水平上的气候归类型与植被归类型是最基本的划分因子,本文以中国东北部黑龙江省的山地植被为例,采用多等级熵值分配的方法来证明所使用的方法。我们得出气候归类型与植被归类型所占有的熵值成分要弱于物种表现型丰富度所占有的熵值成份。值得注意的是其相对的熵值贡献率对每一个因子的最大熵值的变化规律。分析结果表明气候归类型占有较低的熵值而植被归类型占有较高的熵值。因此仅仅以在区域气候型为主要指标所划分的物种生态位是不够的,而以小区域内的植被型为指标所产生的物种生态位具有较高利用价值。     

HIV-1 GP120 V3 conformational and informational entropies

In an attempt to analyze structure, function and evolution of HIV-1 GP120 V3, interactions among the Hartree–Fock energy, the conformational entropy and the Shannon entropy were determined for the 1NJ0 set of antibody-bound V3 loop conformers. The Hartree–Fock energy of each conformer was determined at the MINI level with GAMESS. The conformational entropy was determined per conformer and per residue from the mass-weighted covariance matrices. The Shannon entropy per residue was determined from sequence-substitution frequencies. Correlations were determined by linear regression analysis. There was a negative correlation between the Hartree–Fock energy and the conformational entropy (R=−0.4840, p=0.0078, df =28) that enhanced the negative Helmholtz-free-energy change for the binding of the GP120 ligand to target CD4. The Shannon entropy of V3 was a function of the conformational entropy variance (R=0.7225, p=0.00157, df=15) and of the V3 Hartree–Fock energy. Biological implications of this work are that (1) conformational entropy interacts with V3 Hartree–Fock energy to enhance GP120 binding to CD4 cell receptors and that (2) the Hartree–Fock energy of V3 interacts with the evolutionary system to participate in the regulation of V3 diversity.     

Relationship between local structural entropy and protein thermostability

We developed a technique to compute structural entropy directly from protein sequences. We explored the possibility of using structural entropy to identify residues involved in thermal stabilization of various protein families. Examples include methanococcal adenylate kinase, Ribonuclease HI and holocytochrome c(551). Our results show that the positions of the largest structural entropy differences between wild type and mutant usually coincide with the residues relevant to thermostability. We also observed a good linear relationship between the average structural entropy and the melting temperatures for adenylate kinase and its chimeric constructs. To validate this linear relationship, we compiled a large dataset comprised of 1153 sequences and found that most protein families still display similar linear relationships. Our results suggest that the multitude of interactions involved in thermal stabilization may be generalized into the tendency of proteins to maintain local structural conservation. The linear relationship between structural entropy and protein thermostability should be useful in the study of protein thermal stabilization.     

Competition between Homophily and Information Entropy Maximization in Social Networks

In social networks, it is conventionally thought that two individuals with more overlapped friends tend to establish a new friendship, which could be stated as homophily breeding new connections. While the recent hypothesis of maximum information entropy is presented as the possible origin of effective navigation in small-world networks. We find there exists a competition between information entropy maximization and homophily in local structure through both theoretical and experimental analysis. This competition suggests that a newly built relationship between two individuals with more common friends would lead to less information entropy gain for them. We demonstrate that in the evolution of the social network, both of the two assumptions coexist. The rule of maximum information entropy produces weak ties in the network, while the law of homophily makes the network highly clustered locally and the individuals would obtain strong and trust ties. A toy model is also presented to demonstrate the competition and evaluate the roles of different rules in the evolution of real networks. Our findings could shed light on the social network modeling from a new perspective.     

Entropy balances of microbial product formation

Considering the approach of Bermudez and Wagensberg (1986) devoted to the entropy balance of growing microorganisms some equations were developed which describe particularly the entropy balance of microbial product formation. The formula allows to determine the coefficients of resistance R(mn) and of coupling L(mn) according to rates of growth, product formation, maintenance metabolism and heat evolution assuming a linear relationship between thermodynamic fluxes and forces.In order to check the usefulness of the derived model appropriate experimental data of two microbial batch processes concerning production of L-lysine and the antibiotic nourseothricine were taken into account. The results showed similar courses of entropy balances despite different pathways of product formation which were characterized by an overshoot of entropy production at the beginning of biosynthesis of the primary and secondary metabolite. This fact was interpreted as a more general phenomenon for microorganisms under inbalanced nutritional conditions.     

基于生物适应进化原理论证生物进化的动力

文章从现有主流生物进化理论存在的问题入手, 以生物适应进化原理为认识基础, 讨论生物进化的动力, 以求对生物进化机制有一个新的认识。在薛定谔“生命赖负熵生存”观点的指导下, 提出了“负熵流”包括能量流、物质流和信息流, 以及负熵流是生命生存和发育的动力的观点。作者在原有生物适应进化原理基础上, 修改完善并提出了“DNA、RNA和蛋白质在环境作用下的生物适应进化调控系统”理论, 并根据系统发育是个体发育的“积分”的观点, 推论得出生物与环境的负熵差引起的负熵流也是生命进化的动力, 对生物进化机制作出了新的理解。基于这样的生物进化机制的认识, 提出了“进化是一个子系统在其上一等级系统中, 将自身全部或部分信息遗传给下一代子系统, 并在其适应上一等级系统过程中, 产生一些新质, 终止一些旧质, 从而在其上一等级系统中得以延续的变化过程”的概念, 并探讨了一些与进化有关的其他争议问题。     

Boltzmann Entropy: Generalization and Applications

The object of the paper is to generalize Boltzmann entropy to takeaccount of the subjective nature of a system. The generalized entropyor relative entropy so obtained has been applied to an ecologicalsystem leading to some interesting new results in violation ofexisting physical laws. The entropy was further developed to derive ageneralized macroscopic measure of relative entropy which plays asignificant role in the study of stability and evolution ofecological and chemical reaction systems.     

Constraints on HIV-1 diversity from protein structure

The high rate of HIV-1 evolution contributes to immune escape, enables the virus to escape drug therapy, and may underlie the difficulty of producing an effective vaccine. Identifying constraints on HIV evolution is therefore of prime importance. To investigate this problem, we examined the relationships between sequence diversity, selection, and protein structure. We found that while there was an increase in sequence diversity over time, this variation had a tendency to be limited to specific structural regions. When individual sites were analyzed, there was, in contrast, substantial and widespread evolutionary constraint over gag and env. This constraint was present even in the highly variable envelope proteins. The evolutionary significance of an individual site is indicated by the change in selection pressure along the time course: increasing entropy indicates that the site is evolving predominantly in a more "clock"-like manner, low entropy values with no increase indicate a high degree of constraint, and high entropy values indicate a lack of constraint. Few sites display high degrees of turnover. Mapping these sites onto the three-dimensional protein structure, we found a significant difference between evolutionary rates for regions buried in the core of the protein and those on the surface. This constraint did not change over the time period analyzed and was not subtype dependent, as similar results were found for subtypes B and C. This link between sequence and structure not only demonstrates the limits of recent HIV-1 evolution but also highlights the origins of evolutionary constraint on viral change.     

On the relationship between dissipation and the rate of spontaneous entropy production from linear irreversible thermodynamics

When systems are far from equilibrium, the temperature, the entropy and the thermodynamic entropy production are not defined and the Gibbs entropy does not provide useful information about the physical properties of a system. Furthermore, far from equilibrium, or if the dissipative field changes in time, the spontaneous entropy production of linear irreversible thermodynamics becomes irrelevant. In 2000 we introduced a definition for the dissipation function and showed that for systems of arbitrary size, arbitrarily near or far from equilibrium, the time integral of the ensemble average of this quantity can never decrease. In the low-field limit, its ensemble average becomes equal to the spontaneous entropy production of linear irreversible thermodynamics. We discuss how these quantities are related and why one should use dissipation rather than entropy or entropy production for non-equilibrium systems.     

Effects of ethanol and other alkanols on the kinetics and the activation parameters of thermal death in Saccharomyces cerevisiae

Ethanol, isopropanol, propanol, and butanol enhanced thermal death in Saccharomyces cerevisiae by increasing DeltaSdouble dagger, the entropy of activation of thermal death while DeltaHdouble dagger, the enthalpy of activation, was not significantly affected. The relation between DeltaSdouble dagger and alkanol concentration was linear with a different slope for each alkanol: DeltaS(double dagger) (X) = DeltaS(double dagger) (0) + C(A) (E)X, where X is the alkanol concentration and C(A) (E) the entropy coefficient for the aqueous phase defined as increase in entropy of activation per unit concentrations of the alkanol. C(A) (E) was correlated with the lipid-buffer partition coefficients of the alkanols while C(M) (E), the entropy coefficient for the lipid phase, was nearly identical for the four alkanol and averaged 37.6 entropy units per mole of alkanol per kilogram of membrane. As predicted by these results, the specific death rates (K(d)) at constant temperature were an exponential function of the alkanol concentration and behaved in agreement with the following equation: In K(X) (d) = In K(0) (d) + (C(A) (E)/R)X, where R is the gas constant. It was concluded that the alkanols enhanced thermal death through nonspecific action on membrane structure.     

Universal features of fluctuations in globular proteins

Using data from 2000 non‐homologous protein crystal structures, we show that the distribution of residue B factors of proteins collapses onto a single master curve. We show by maximum entropy arguments that this curve is a Gamma function whose order and dispersion are obtained from experimental data. The distribution for any given specific protein can be generated from the master curve by a linear transformation. Any perturbation of the B factor distribution of a protein, imposed at constant energy, causes a decrease in the entropy of the protein relative to that of the reference state. Proteins 2016; 84:721–725. © 2016 Wiley Periodicals, Inc.