Relative von Neumann entropy for evaluating amino acid conservation

The Shannon entropy is a common way of measuring conservation of sites in multiple sequence alignments, and has also been extended with the relative Shannon entropy to account for background frequencies. The von Neumann entropy is another extension of the Shannon entropy, adapted from quantum mechanics in order to account for amino acid similarities. However, there is yet no relative von Neumann entropy defined for sequence analysis. We introduce a new definition of the von Neumann entropy for use in sequence analysis, which we found to perform better than the previous definition. We also introduce the relative von Neumann entropy and a way of parametrizing this in order to obtain the Shannon entropy, the relative Shannon entropy and the von Neumann entropy at special parameter values. We performed an exhaustive search of this parameter space and found better predictions of catalytic sites compared to any of the previously used entropies.     

最大信息熵原理与群体遗传平衡

建立了用最大信息熵原理推导群体遗传平衡定律的统一数学模型,并给出了模型的统一解,此解正是Hardy-Weinberg定律所给出的平衡群体的基因型频率,说明当群体信息熵达到最大时,群体基因型频率不再变化,即达到“平衡”。这证明了最大熵分布就是Hardy-Weinberg平衡分布。Hardy-Weinberg平衡定律与最大信息熵原理的内在一致性说明,杂交和随机交配是一个不可逆过程,使群体基因型信息熵增大,无序性增,是选择和近亲交配使群体的信息熵降低,有序性增加,育种过程实际就是调节群体信息熵的过程。过程信息熵的含义是表示一个概率分布的不确定性,最大熵原理意味着在一定的约束条件,选择具有最大不确定性的分布,从而其分布是最为随机的。最大熵原理在信息,工程,天文,地理,图像处理,模式识别等自然科学和社会科学领域都有广泛的成功应用,本文从群体遗传学角度证明了这一原理具有普遍适用性。熵是描述系统状态的函数,而最大熵原理则表明了系统发展变化的趋势,系统的最终状态必然是熵增加至最大值的状态,对于任何系统都是如此。因此,群体遗传系统的平衡定律可以统一用最大熵原理进行判定和描述;任意群体的基因型信息熵在随机交配世代传递时有不断增加的趋势;在一定约束条件下基因型信息熵达到最大值时,就称之为达到遗传平衡。本文将信息论原理应用于群体遗传学研究,揭示了基因信息熵的生物学意义,并表明可以用信息学和控制论的原理和方法来研究群体遗传学问题。     

Entropy flow and entropy production in the human body in basal conditions

Entropy inflow and outflow for the naked human body in basal conditions in the respiration calorimeter due to infrared radiation, convection, evaporation of water and mass-flow are calculated by use of the energetic data obtained by Hardy & Du Bois. Also, the change of entropy content in the body is estimated. The entropy production in the human body is obtained as the change of entropy content minus the net entropy flow into the body. The entropy production thus calculated becomes positive. The magnitude of entropy production per effective radiating surface area does not show any significant variation with subjects. The entropy production is nearly constant at the calorimeter temperatures of 26-32 degrees C; the average in this temperature range is 0.172 J m-2 sec-1 K-1. The forced air currents around the human body and also clothing have almost no effect in changing the entropy production. Thus, the entropy production of the naked human body in basal conditions does not depend on its environmental factors.     

一个基于熵的指数精细定位人类复杂性状位点

近来,一个基于熵的指数被提出用来对人类复杂性状位点进行连锁不平衡定位．这个熵指数比较了患病个体与正常个体或极端样本之间标记基因频率的熵和条件熵．本文基于熵理论,提出了另一个备选指数．这个新的指数比较患病个体与正常个体之间标记基因型频率的熵和条件熵．计算机模拟结果表明本文提出的新指数平行于之前的熵指数．而基于遗传性血色病（hereditary haemochromatosis,HH）数据的分析表明了这个新指数能有效对人类复杂性状位点进行精细定位．     

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.     

Kauzmann's paradox and the glass transition

Kauzmann showed that the entropy of a liquid decreases rapidly on cooling towards the kinetic glass transition temperature and extrapolates to unreasonable values at lower temperature. The temperature where the extrapolated liquid entropy meets the crystal entropy is now called the Kauzmann temperature. Thermodynamics, with Planck's statement of the third law, shows that the entropy of a liquid cannot be less than the entropy of a glass with the same enthalpy. This is the thermodynamic condition violated by the Kauzmann extrapolation and it suggests a thermodynamic glass transition. Simulations show that, for the simple models studied and regardless of how the liquid entropy is extrapolated, the Kauzmann temperature cannot be reached because the entropy of glasses with the same enthalpy as the liquid is greater than that of the crystal.     

Entropy calculations on the molten globule state of a protein: side-chain entropies of alpha-lactalbumin.

We present entropy estimates based on molecular dynamics simulations of models of the molten globule state of the protein alpha-lactalbumin at low pH. The entropy calculations use the covariance matrix of atom-positional fluctuations and yield the complete configurational entropy. The configurational entropy of the entire protein and of each of its side chains is calculated. Exposed side chains show a larger entropy compared to buried side chains. A comparison to data from rotamer counting is made and significant differences are found.     

Entropy principle for human development, growth and aging

Entropy productions within nude subjects in respiration calorimeters are calculated from the corresponding energetic data obtained by Du Bois et al. (1952, J. Nutr. 48, 257-293.). The entropy production for men is constant at environmental temperatures from 24-34 degrees C. The metabolic entropy production comprises 98.6% of the total entropy production. The entropy production for women shows a minimum at 30 degrees C (the middle of the neutral zone), a small rise in the cold zone and a trend toward a rise in the warm zone; the average entropy production for women is 8.7% smaller than that for men. The entropy production rises from 0-2 years of age, and decreases rapidly from 2-25 years of age and then gradually to 85 years of age. The entropy production does not seem to achieve a minimum or a level in the lives of men and women. Based on these results, a three-stage hypothesis of entropy production in human life is proposed.     

Effects of exercise and chills on entropy production in human body

Entropy flows and changes of entropy content for naked subjects in the respiration calorimeter in exercise and chills are calculated from the energetic data given by Hardy et al. (1938, J. Nutr. 16, 477) and Du Bois (1939, Bull. N.Y. Acad. Med. 15, 143). By use of these values, entropy productions in the human body in exercise and chills are estimated. The entropy production in mild exercise is 1.5-2.4 times as great as that in basal conditions. The entropy production in violent exercise is six to eight times as great as that before exercise. The entropy production in chills in cold environments is about twice as large as that in basal conditions. The entropy production in a malarial chill is about four times of that in normal subjects. These increases in entropy production will be due to the increase in heat production within the body. It seems that there is a parallel between energy and entropy viewpoints for human physiology.     

Entropy and convergence in dynamics and demography

Demographic dynamics is formally equivalent to the dynamics of a Markov chain, as is true of some nonlinear dynamical systems. Convergence to demographic equilibrium can be studied in terms of convergence in the Markov chain. Tuljapurkar (1982) showed that population entropy (Kolmogorov-Sinai entropy) provides information on the rate of this convergence. This paper begins by considering finite state Markov chains, providing elementary proofs of the relationship between convergence rate and entropy, and discusses in detail the uses and limitations of entropy as a convergence measure; these results also apply to Markovian dynamical systems. Next, new qualitative and quantitative arguments are used to discuss the demographic meaning of entropy. An exact relationship is established giving population entropy in terms of the eigenvalues of the Leslie matrix characteristic equation. Finally, the significance of imprimitive and periodic limits is discussed in relation to population entropy.     

基于Agent模型的生态公平指数构建与模拟

伴随着社会经济的发展,社会公平逐渐成为热点话题。社会公平问题不但体现在社会现象上,还对生态系统起着重要的影响。通过构建资本交换自主体模型,模拟社会财富分配动态过程,可观测资本交换熵指数变化情况,从而解释熵增原理。除此以外,不同系统的最终状态能达到的最大熵指数不同,用熵增原理与本文构建的最大熵指数模型可以对系统的生态公平进行纵向或横向评价。构建的资本交换熵模型也可以证明最大熵原理,同时,财富集中的现象将会使生态环境的选择权完全交予富人群体,影响可持续发展。     

Entropy balance of white-tailed deer during a winter night

The entropy budget of a white-tailed deer (50kg) on a maintenance diet and a full-feed diet in a standing posture in an open field under clear nocturnal skies with an air temperature of −20°C is investigated based on the energetics given by Moen. Entropy inflow into a white-tailed deer due to infra-red radiation and entropy outflows from a deer due to infra-red radiation, convection, evaporation of water and conduction to ingested food are calculated. Also the entropy production due to metabolic heat production is estimated. Net entropy flow into a deer from its environment becomes negative. On the assumption that a white-tailed deer is in a steady state in entropy, the total entropy production in a deer on a maintenance diet becomes +0.46 J/sec/K. Positiveness of the entropy production shows that the Second Law of Thermodynamics certainly holds in a white-tailed deer. The entropy production per effective radiating surface area of a deer on a maintenance diet is 0.32×10⁻⁴ J/cm²/sec/K. On the other hand, the entropy production in a deer on a full-feed diet is 0.59 J/sec/K and that per effective surface area is 0.41×10⁻⁴ J/cm²/sec/K. Uptake of 1 g of food produces 22 J/K of entropy within the body of a white-tailed deer. Comparison is made with the results for entropy production in a lizard and in plant leaves.     

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.     

Natural Selection and Age-Structured Populations

This paper studies the properties of a new class of demographic parameters for age-structured populations and analyzes the effect of natural selection on these parameters. Two new demographic variables are introduced: the entropy of a population and the reproductive potential. The entropy of a population measures the variability of the contribution of the different age classes to the stationary population. The reproductive potential measures the mean of the contribution of the different age classes to the Malthusian parameter. The Malthusian parameter is precisely the difference between the entropy and the reproductive potential. The effect of these demographic variables on changes in gene frequency is discussed. The concept of entropy of a genotype is introduced and it is shown that in a random mating population in Hardy-Weinberg equilibrium and under slow selection, the rate of change of entropy is equal to the genetic variance in entropy minus the covariance in entropy and reproductive potential. This result is an information theoretic analog of Fisher''s fundamental theorem of natural selection.     

Configurational entropy change of netropsin and distamycin upon DNA minor-groove binding

Binding of a small molecule to a macromolecular target reduces its conformational freedom, resulting in a negative entropy change that opposes the binding. The goal of this study is to estimate the configurational entropy change of two minor-groove-binding ligands, netropsin and distamycin, upon binding to the DNA duplex d(CGCGAAAAACGCG).d(CGCGTTTTTCGCG). Configurational entropy upper bounds based on 10-ns molecular dynamics simulations of netropsin and distamycin in solution and in complex with DNA in solution were estimated using the covariance matrix of atom-positional fluctuations. The results suggest that netropsin and distamycin lose a significant amount of configurational entropy upon binding to the DNA minor groove. The estimated changes in configurational entropy for netropsin and distamycin are -127 J K(-1) mol(-1) and -104 J K(-1) mol(-1), respectively. Estimates of the configurational entropy contributions of parts of the ligands are presented, showing that the loss of configurational entropy is comparatively more pronounced for the flexible tails than for the relatively rigid central body.     

Low HRV entropy is strongly associated with myocardial infarction.

Heart rate variability (HRV) is a marker of autonomous activity in the heart. An important application of HRV measures is the stratification of mortality risk after myocardial infarction. Our hypothesis is that the information entropy of HRV, a non-linear approach, is a suitable measure for this assessment. As a first step, to evaluate the effect of myocardial infarction on the entropy, we compared the entropy to standard HRV parameters. The entropy was estimated by compressing the tachogram with Bzip2. For univariate comparison, statistical tests were used. Multivariate analysis was carried out using automatically generated decision trees. The classification rate and the simplicity of the decision trees were the two evaluation criteria. The findings support our hypothesis. The meanNN-normalized entropy is reduced in patients with myocardial infarction with very high significance. One entropy parameter alone exceeds the discrimination strength of multivariate standards-based trees.     

Entropy-Based Financial Asset Pricing

We investigate entropy as a financial risk measure. Entropy explains the equity premium of securities and portfolios in a simpler way and, at the same time, with higher explanatory power than the beta parameter of the capital asset pricing model. For asset pricing we define the continuous entropy as an alternative measure of risk. Our results show that entropy decreases in the function of the number of securities involved in a portfolio in a similar way to the standard deviation, and that efficient portfolios are situated on a hyperbola in the expected return – entropy system. For empirical investigation we use daily returns of 150 randomly selected securities for a period of 27 years. Our regression results show that entropy has a higher explanatory power for the expected return than the capital asset pricing model beta. Furthermore we show the time varying behavior of the beta along with entropy.     

Entropy budgets of soybean and bur oak leaves at night

From energy budgets of soybean [ Glycine max (L.) Merr. cv. Chippewa] and bur oak ( Quercus macrocarpa ) leaves at night, entropy fluxes into or out of leaves are calculated. The absorbed entropy balances with the emitted entropy; this is not the case for leaves during the day and for an animal at night. On the assumption that the entropy in leaves is at steady state, entropy production in leaves becomes small and almost zero. Since entropy production is a measure of activity in organisms, the activity in leaves is small at night; this is in contrast to leaves during the day. Thus, a large portion of the activity in leaves is "on" in the daytime and "off" at night. Most of the activity in leaves may be triggered by solar radiation.