Free energy distributions in proteins.

Protein molecules in solution have a broad distribution of enthalpy states. A good approximation to the distribution function for enthalpy states can be calculated, using the maximum-entropy method, from the moments of the distribution that, in turn, are obtained from the experimental temperature dependence of the heat capacity. In the present paper, we show that the enthalpy probability distribution can then be formulated in terms of a free energy function that gives the free energy of the protein corresponding to a particular value of the enthalpy. By the location of the minima in this function, the free energy distribution graphically indicates the most probable values of the enthalpy for the protein. We find that the behavior of the free energy functions for proteins falls somewhere between two different cases: a two-state like function with two minima, the relative levels of the two states changing with temperature; and, a single-minimum function where the position of the minimum shifts to higher enthalpy values as the temperature is increased. We show that the temperature dependence of the free energy function can be expressed in terms of a central free energy distribution for a given, fixed temperature (which is most conveniently chosen as the temperature of the maximum in the heat capacity). The nature of this central free energy function for a given protein thus yields all of the thermodynamic behavior of that protein over the temperature range of the denaturation process.     

梭梭种群不同发育阶段的空间格局与关联性分析

运用点格局法中的Ripley'sK(r)函数的变形L(r)函数和g(r)函数,对古尔班通古特沙漠不同生境下不同发育阶段梭梭种群的空间格局及关联性进行了研究。结果表明:L(r)函数显示梭梭种群格局倾向于聚集分布,且集中分布在0-25m尺度范围内,而g(r)函数分析在小于3m的尺度上呈聚集分布,大于3m的尺度后波动较小,最大聚集尺度表现在0-10m范围内;梭梭在不同发育阶段过程中,L(r)和g(r)函数都显示由幼苗、幼树的聚集分布变为成年树的随机分布,甚至在某些尺度上变为均匀分布,同时幼苗幼树向成年树过渡过程中,梭梭的聚集强度呈逐渐减弱趋势。在关联性分析中,L(r)函数分析中正关联维持的尺度范围较g(r)函数大。L(r)函数分析幼苗与幼树、成年树在0-15m尺度内呈现正关联,g(r)函数在0-5m范围内表现为正关联,而幼树与成年树在0-10m尺度内多呈负关联,且两个大小级的形体大小差异越大,它们的正关联关系越弱,甚至表现为负关联或无关联。幼苗幼树的聚集分布和正关联是梭梭种子的传播和密度制约的一个平衡,对梭梭种群的生存和发展是有利的。另外,梭梭种群分布格局的强度在不同地形也存在差异,奎屯平地比五家渠的聚集强度和关联性大,缓坡差异较小,这说明地形对各种资源的再分配间接地影响了梭梭的格局。总体上看,同时应用L(r)和g(r)函数进行梭梭空间格局与关联性分析时结果不尽相同。L(r)函数的最大值可以反映典型的聚集尺度,而g(r)函数中出现的第1个最大值可以表示植株间典型距离。在小尺度下两种函数分析所得空间格局是一致的,而在大尺度上有较大差异。g(r)函数在小尺度范围内的分析结果更接近实际情况,有利于揭示出梭梭空间格局与生态过程有联系的"关键尺度",说明梭梭为了适应恶劣环境往往表现为聚集分布,这种聚集生长现象有利于个体的生存与繁衍。因此,联合使用L(r)函数和g(r)函数更有利于揭示植物个体间的关系。     

Demography in stochastic environments. I. Exact distributions of age structure

The steady state distribution of age structure is studied for populations with two age classes and stochastic vital rates. For a serially uncorrelated dichotomic vital rate the distribution of age structure is found analytically to be a singular steplike function; outside a specific region of vital rate values the singular function crosses a threshold to a smooth function. For a vital rate following a correlated two state Markov process the joint distributions of age structure and environment are found analytically to be singular steplike functions; again a threshold marks a transition to a smooth function. For fecundities which are serially uncorrelated but continuously distributed the age structure distribution is obtained as a smooth analytic function for all parameter values. These explicit results have applications to studies of age structure and average growth rate.     

Fluctuation analysis in small chemically reacting systems

A theory of noise fluctuations is developed which is applicable to systems of any size in which unimolecular or bimolecular reactions are occurring. The main difference between small and large reacting systems is that in the former the probability of finding a particle in a particular state does not obey a Gaussian distribution, but satisfies a distribution which reflects the mechanism of the chemical reaction. This difference is reflected in the main result of the theory: an autocorrelation function that is expressible as a sum of exponentials, the amplitudes of which are explicit functions of the moments of the distribution. Thus, by using small systems, the autocorrelation function,in principle, allows the elucidation of reaction mechanisms. Numerical simulations indicate that for reacting systems having ten or fewer particles, the deviation of the autocorrelation function from a single exponential should be easily detectable, and that estimates of the first four moments of the distribution should be possible. Accurate inference of the distribution, however, will require further mathematical and experimental advances.     

Ion velocity distribution in a plasma with low-intensity ion acoustic turbulence

The quasi-steady ion distribution in a plasma with a single ion species and with low-intensity ion acoustic turbulence is found. Conditions are determined under which the stimulated scattering of ion acoustic waves by ions leads to the formation of a superthermal ion distribution function that decreases with increasing velocity more gradually than does a Maxwellian distribution function. It is found that the plasma conductivity increases as a result of a decrease in the turbulence level due to an enhancement of the Cherenkov damping of ion acoustic waves by resonant ions, whose number increases because of the formation of a gradually decreasing distribution of superthermal ions.     

Diffuse and constricted modes of a dc discharge in neon: Simulation of the hysteresis transition

Results are presented from theoretical studies of high-pressure (～100 Torr) dc discharges in neon. The diffuse and constricted discharge modes are studied using a model including the equation of balance for charged and excited particles, heat conduction equations for the neutral gas and plasma electrons, and Poisson’s equation for the radial electric field at a fixed total discharge current. A specific feature of the constricted mode in the investigated range of low fields and high degrees of ionization is that the excitation and ionization rates in the center of the discharge tube and at the periphery differ by several orders of magnitude. This implies that, in the constricted mode, the region where the electron energy distribution function is Maxwellian due to electron-electron collisions may adjoin the region (beyond the constriction zone) where the high-energy part of the distribution function is depleted. The hysteresis transition between the diffuse and constricted modes is analyzed. A transition from the constricted to the diffuse mode can be regarded as a manifestation of the nonlocal character of the formation of the electron distribution function, specifically, the diffusion of high-energy electrons capable of producing gas ionization from the central (constricted) region toward the periphery. The nonlocal formation of the distribution function is described by a nonlocal kinetic equation accounting for electron-electron collisions and electron transport along the radius of the discharge tube. Since only high-energy electrons produce gas ionization, the effect of the nonlocal formation of the electron distribution function is taken into account by introducing the effective temperature of the high-energy part of the distribution function and solving the equation for the radial profile of the high-energy part of the distribution function. This approach allows one to approximately take into account the nonlocal character of the electron distribution function without substantial expenditure of computer resources. The nonlocal model makes it possible to numerically simulate the hysteresis transition between the diffuse and constricted modes, which is impossible in the local approximation.     

传递函数在生物组织光传输问题中的应用

本文将传递函数的概念引入生物组织光传输问题,并将传递函数理论用于面光源照射下生物组织内特定深度层面上光场强度分布的理论计算。结合Monte Carlo模拟获取脉冲相应函数,我们分析了不同面光源照射下层状组织样品透射面上的光场强度分布。理论计算结果与实验测试结果的一致性较好,这充分说明了本文建立的基于Monte Carlo模拟的传递函数方法是一种处理面光源照射下生物组织内光场空间的直接而有效的手段。     

Ligand binding distributions in nucleic acids

We illustrate a new method for the determination of the complete binding polynomial for nucleic acids based on experimental titration data with respect to ligand concentration. From the binding polynomial, one can then calculate the distribution function for the number of ligands bound at any ligand concentration. The method is based on the use of a finite set of moments of the binding distribution function, which are obtained from the titration curve. Using the maximum-entropy method, the moments are then used to construct good approximations to the binding distribution function. Given the distribution functions at different ligand concentrations, one can calculate all of the coefficients in the binding polynomial no matter how many binding sites a molecule has. Knowledge of the complete binding polynomial in turn yields the thermodynamics of binding. This method gives all of the information that can be obtained from binding isotherms without the assumption of any specific molecular model for the nature of the binding. Examples are given for the binding of Mn(2+) and Mg(2+) to t-RNA and for the binding of Mg(2+) and I(6) to poly-C using literature data.     

Charging of dust grains in a nonequilibrium plasma of a stratified glow discharge

A theoretical model is presented that describes the charging of dust grains in the positive plasma column of a stratified glow dc discharge in argon. A one-dimensional self-consistent model is used to obtain axial profiles of the electric field, as well as the electron energy distribution function along the axis of the discharge tube. Radial profiles of the electric field are determined in the ambipolar diffusion approximation. It is assumed that, in the radial direction, the electron distribution function depends only on the total electron energy. Two-dimensional distributions of the discharge plasma parameters are calculated and used to determine the potential and charge of a test dust grain at a certain point within the discharge and the electrostatic forces acting on it. It is shown that the grain charge distribution depends strongly on the nonequilibrium electron distribution function and on the nonuniform distribution of the electric field in a stratified glow discharge. A discussion is presented on the suspension of dust grains, the separation of grains by size in the discharge striations, and a possible mechanism for the onset of vortex dust motion at the edge of a dust cloud.     

Long-range correlations in the helix free energy distribution in DNA

In this paper we explore the free energy distribution in the helical form of DNA using the genome of the virus Rickettsia prowazekii Madrid E as an example. The genome of this organism has been determined by Andersson et al. (Nature 396 (1998) 133) and is available on the World Wide Web (www.tigr.org). Using the helix statistical weights based on nearest-neighbor base pairs of SantaLucia (Proc. Natl. Acad. Sci. USA 95 (1998) 1460), we calculate the free energy in consecutive blocks of m base pairs in the DNA sequence and then construct the free energy distribution for these values. Using the maximum-entropy method we can fit the distribution curves with a function based on the moments of the distribution. For blocks containing 10-20 base pairs the distribution is slightly skewed and we require four moments to accurately fit the function. For blocks containing 100 base pairs or more, the distribution is well approximated by a Gaussian function based on the first two moments of the distribution. We find that the free energy distribution for m=20 can be reproduced using random sequences that have the local (singlet, doublet or triplet) statistics of Rickettsia. However, for much larger blocks, for example m=500, the width of the free energy distribution based on the actual Rickettsia genome is broader by almost a factor of 3 than the distributions based on random local statistics. We find that the distribution functions for the C or G content in blocks of m base pairs have almost the same behavior as a function of block size as do the free energy distributions. In order to duplicate the width of the distribution functions based on the actual Rickettsia sequence, we need to introduce tables (matrices) that correlate the states of consecutive blocks hundreds of base pairs long. This indicates that correlations on the order of the number of base pairs contained in the average gene are required to give the actual widths for either the C or G content or the helix free energy distributions. Above a certain m value, the distributions for larger m can be accurately expressed in terms of the distribution functions for smaller m. Thus, for example, the distribution for m=5000 can be expressed in terms of the generating function for m=1000.     

Counterion diffusion in heparin solutions

The physiological importance of heparin is due to its strong interaction with bivalent counterions, especially Ca2+. A diffusional approach of this property is presented in this article: the observable is the self-diffusion coefficient of the counterions, as a function of the ratio of the polyelectrolyte over the added salt concentrations. All the results are in agreement with a simple "quasi-chemical model" in which two different states are assumed for the counterions: "free" or "bound." The proportions of these two types of ions are calculated according to the distribution function of the counterions around the polyion. We assume that those of counterions located at a distance closer than a, the characteristic distance, are bound; the others are free. The ionic distribution function is evaluated by a numerical integration of a cell model Poisson-Boltzmann equation. Finally, this model leads to a very good agreement with the experimental results, if the radius of heparin polyion is assumed to be 6 and 10 A.     

The role of abnormal mitochondrial dynamics in the pathogenesis of Alzheimer's disease

Mitochondria play critical roles in neuronal function and almost all aspects of mitochondrial function are altered in Alzheimer neurons. Emerging evidence shows that mitochondria are dynamic organelles that undergo continuous fission and fusion, the balance of which not only controls mitochondrial morphology and number, but also regulates mitochondrial function and distribution. In this review, after a brief overview of the basic mechanisms involved in the regulation of mitochondrial fission and fusion and how mitochondrial dynamics affects mitochondrial function, we will discuss in detail our and others' recent work demonstrating abnormal mitochondrial morphology and distribution in Alzheimer's disease (AD) models and how these abnormalities may contribute to mitochondrial and synaptic dysfunction in AD. We propose that abnormal mitochondrial dynamics plays a key role in causing the dysfunction of mitochondria that ultimately damage AD neurons.     

Thyroid gland in dwarf mice

Stereological methods were used to compare thyroids of dwarf mice and of their heterozygote littermates. In the thyroid of dwarf mice unorganized cellular masses, adipous tissue and ultimobranchial cysts are abundant. Follicles are small and their distribution function is unimodal. The number of cells per follicle is considerably lowered if compared with the normal. In control mice the distribution function of thyroid follicles is bimodal. These data show that the origin of the thyroid anomaly in dwarf mice is due to a drastic diminution of cell divisions, probably resulting from the lack of growth hormone.     

城市中的伴人植物

伴人植物分布于城市中的许多地方,常被视为杂草而清除。本文论述了城市伴人植物的特点、分布,及其在城市环境保护及美化中的作用,最后列出了北方城市中一些常见伴人植物的名称。     

Nonlocal nature of the electron energy spectrum in a glow discharge in pure O2: I. Nonlocal character of the electron distribution function

Abstrac A study is made of the nonlocal nature of the electron energy distribution function in the positive column of a glow discharge in a tube filled with pure oxygen. The distribution function and the axial (E _z) and radial (E _r) electric fields as functions of radius are measured using an array of mobile probes. The experimentally obtained spatial profiles of the distribution function are used to test the applicability of the two-term approximation to the distribution function of the electrons with a nonlocal energy spectrum. The distribution function in a specified electric field E=E _z +E _r (where E _z ⊥ E _r) is calculated by solving the coordinate-dependent Boltzmann equation in the two-term approximation and by directly integrating the equations of electron motion using the Monte Carlo method. A comparison between the experimental data and the results of simulations carried out for a broad parameter range shows that, in the case of a highly nonlocal electron energy spectrum, the two-term approximation makes it possible to calculate the electron distribution function with a fairly good accuracy, in which case, however, in imposing the boundary conditions, the electron losses at the plasma surface should be treated in the kinetic approximation. It is shown that using the reflection coefficient of the plasma surface for electrons instead of the loss cone in space makes it possible to accurately calculate the electron energy distribution function over the entire parameter range under consideration, including the transient region in which the electron-energy relaxation length is comparable to the characteristic plasma dimension. __________ Translated from Fizika Plazmy, Vol. 26, No. 11, 2000, pp. 1038–1045. Original Russian Text Copyright ? 2000 by Ivanov, Klopovskii, Lopaev, Rakhimov, Rakhimova.     

Survival and aging in the wild via residual demography

Information about the age distribution and survival of wild populations is of much interest in ecology and biodemography, but is hard to obtain. Established schemes such as capture-recapture often are not feasible. In the proposed residual demography paradigm, individuals are randomly sampled from the wild population at unknown ages and the resulting captive cohort is reared out in the laboratory until death. Under some basic assumptions one obtains a demographic convolution equation that involves the unknown age distribution of the wild population, the observed survival function of the captive cohort, and the observed survival function of a reference cohort that is independently raised in the laboratory from birth. We adopt a statistical penalized least squares method for the deconvolution of this equation, aiming at extracting the age distribution of the wild population under suitable constraints. Under stationarity of the population, the age density is proportional to the survival function of the wild population and can thus be inferred. Several extensions are discussed. Residual demography is demonstrated for data on fruit flies Bactrocera oleae.     

Measurements and calculations of the electron distribution function in the electronegative plasma of a hollow-cathode discharge in N<Subscript>2</Subscript>: SF<Subscript>6</Subscript> mixtures

Results are presented from measurements and numerical calculations of the electron energy distribution function in the plasma of a hollow-cathode glow discharge in N₂: SF₆ mixtures. It is shown that, when a small amount of SF₆ is added to nitrogen, the number of electrons in the inverse region of the distribution function (2–6 eV) increases by about one order of magnitude. As the electric field in plasma increases to ≈0.5 V/cm, the dip in the distribution function disappears and the inversion region vanishes.     

基于土地利用变化的贵州坝子土地利用功能演变研究

贵州省为典型喀斯特山区,强烈的人类活动主要分布在坝地地区,研究坝子土地利用功能演变对土地可持续利用具有重要价值。基于土地利用变化,根据三生功能理论构建土地利用功能分类体系,以贵州省1990年、2000年、2010年和2016年四期遥感影像为数据源,借助ArcGIS10.2软件平台构建土地利用功能转移矩阵和坝子功能冷热点分布图。研究表明:(1)贵州省坝子土地利用功能已由以传统农业生产功能为主转为以传统农业生产功能-农村居住生活功能为主,坝子土地利用由单一功能向多功能转变;(2)1990—2016年,坝子的功能类型增加10种类型,其中8类是复合类型,坝子功能向多样性转变;(3)单一功能与复合功能坝子比例变化曲线呈"X"型,到2016年,复合功能坝子比例大于单一功能坝子;(4)1990—2000年,坝子土地利用功能变化缓慢,2000年以后坝子土地利用功能变化强烈;(5)传统农业生产功能转移最为强烈,主要转移为城镇居住生活功能、农村居住生活功能、工业生产功能及与之相关的复合功能和自然生态功能;(6)各种功能类型坝子冷热点的空间分布变化复杂,从总体上看各功能的空间分布由集聚变为分散。     

Jaw biomechanics and the evolution of biting performance in theropod dinosaurs

Despite the great diversity in theropod craniomandibular morphology, the presence and distribution of biting function types across Theropoda has rarely been assessed. A novel method of biomechanical profiling using mechanical advantage computed for each biting position along the entirety of the tooth row was applied to 41 extinct theropod taxa. Multivariate ordination on the polynomial coefficients of the profiles reveals the distribution of theropod biting performance in function space. In particular, coelophysoids are found to occupy a unique region of function space, while tetanurans have a wide but continuous function space distribution. Further, the underlying phylogenetic structure and evolution of biting performance were investigated using phylogenetic comparative methods. There is a strong phylogenetic signal in theropod biomechanical profiles, indicating that evolution of biting performance does not depart from Brownian motion evolution. Reconstructions of ancestral function space occupation conform to this pattern, but phylogenetically unexpected major shifts in function space occupation can be observed at the origins of some clades. However, uncertainties surround ancestor estimates in some of these internal nodes, so inferences on the nature of these evolutionary changes must be viewed with caution.     

Robust modeling in screening studies: estimation of sensitivity and preclinical sojourn time distribution

In early-detection clinical trials, quantities such as the sensitivity of the screening modality and the preclinical duration of the disease are important to describe the natural history of the disease and its interaction with a screening program. Assume that the schedule of a screening program is periodic and that the sojourn time in the preclinical state has a piecewise density function. Modeling the preclinical sojourn time distribution as a piecewise density function results in robust estimation of the distribution function. Our aim is to estimate the piecewise density function and the examination sensitivity using both generalized least squares and maximum likelihood methods. We carried out extensive simulations to evaluate the performance of the methods of estimation. The different estimation methods provide complimentary tools to obtain the unknown parameters. The methods are applied to three breast cancer early-detection trials.