Inclusion of the glucocorticoid receptor in a hypothalamic pituitary adrenal axis model reveals bistability

Background

This article deals with the theoretical size distribution (of number of sub-taxa) of a fossil taxon arising from a simple null model of macroevolution.

Model

New species arise through speciations occurring independently and at random at a fixed probability rate, while extinctions either occur independently and at random (background extinctions) or cataclysmically. In addition new genera are assumed to arise through speciations of a very radical nature, again assumed to occur independently and at random at a fixed probability rate.

Conclusion

The size distributions of the pioneering genus (following a cataclysm) and of derived genera are determined. Also the distribution of the number of genera is considered along with a comparison of the probability of a monospecific genus with that of a monogeneric family.     

A mechanism for the control of patch size in mammalian cell DNA excision repair

The hypothesis is suggested that size of the region excised in repair of UV-induced damage in mammalian cell is determined by the occurrence at random of a recognition sequence which terminates this excision process. The statistics of first occurrence times for a specific nucleotide sequence in a random chain are derived and shown to lead to an approximately random distribution of sizes around the average. The heterogeneity in sizes arising from a model are shown not to conflict with existing measurements. A sequence of length three or four is sufficient to account for the measured average size.     

A model explaining the size distribution of gene and protein families

This article deals with the theoretical size distribution of gene and protein families in complete genomes. A simple evolutionary model for the development of such families in which genes in a family are formed or selected against independently and at random, and in which new families are formed by the random splitting of existing families, is used to derive the resulting size distribution. Mathematically this turns out to be the distribution of the state of a homogeneous birth-and-death process after an exponentially distributed time, which it is shown will under certain conditions exhibit the power-law behaviour observed for gene and protein family sizes.     

Floristic and functional affiliations of woody plants with climate in western Amazonia

Aim To test whether a direct relationship exists between the relative abundance of woody plant genera and precipitation regime along the north–south climate gradient of the western Amazon. Location Lowland rain forests in the western Amazon. Methods Floristic data on 91 woody plant genera, from 39 0.1‐ha plots across the western Amazon, and precipitation data from a 0.5° global data set were used to test for correlations between plant relative abundance (defined as percentage number of stems ≥ 2.5 cm diameter at breast height for each woody plant genus per plot) and derived dry‐season variables. Moisture preference was then assessed in terms of pioneer and shade‐tolerant life‐history strategy. Results There were significant associations between the distribution of plant relative abundances and seasonal precipitation variables in 34% of genera analysed. Significant differences were identified in size‐class distribution between dry affiliates and generalists. Dry affiliates were not dominant in any size class in any plot type, whereas climate generalists dominated most of the size classes in the dry plots and the mid‐range size classes in the wet plots. Dry‐affiliate genera were a minority, even in dry forests. Wet‐affiliate genera were correlated with shade tolerance, whereas genera with no rainfall affiliation were often pioneers. Main conclusions The results suggest that moisture variable seasonality influences community composition in a manner that can be related to the life‐history trade‐off between shade tolerance and pioneer ranking. One possible reason for higher diversity in wetter forests is that high rainfall amplifies the niche space available to shade‐tolerant plants. Determining which plant groups are constrained by which environmental variables can contribute to our understanding of how forest composition may be changing now, and how it may change under future climate: if shade‐tolerant trees are also drought‐intolerant, community structure in wet forests may be more vulnerable to future increases in moisture stress.     

The Sizes of Spheres from Profiles in a Thin Slice II. Transparent Spheres

Formulae are derived for obtaining the size distribution of transparent spherical particles which are embedded in an opaque material. The data are the sizes of the circular profiles made by particles in a random thin slice of a specimen when it is viewed orthogonally. The formulae incorporate resolution constraints which cause various profile size ranges to be unobservable. Approximate solutions are obtained under specific resolution constraints when the slice is very thin. The corresponding case of opaque spheres in a transparent material was the subject of Part I (Coleman, 1982).     

Modeling the simple epidemic with deterministic differential equations and random initial conditions

In a simple epidemic the only transition in the population is from susceptible to infected and the total population size is fixed for all time. This paper investigates the effect of random initial conditions on the deterministic model for the simple epidemic. By assuming a Beta distribution on the initial proportion of susceptibles, we define a distribution that describes the proportion of susceptibles in a population at any time during an epidemic. The mean and variance for this distribution are derived as hypergeometric functions, and the behavior of these functions is investigated. Lastly, we define a distribution to describe the time until a given proportion of the population remains susceptible. A method for finding the quantiles of this distribution is developed and used to make confidence statements regarding the time until a given proportion of the population is susceptible.     

Character of Leaf Epidermis and Their Systematic Significance of Daphne and Wikstroemia (Thymelaeaceae)

Fifty six species (varieties) of Daphne, forty five species (varieties) of Wikstroemia and twelve species of outgroups from Thymelaeaceae, with ten phenotypic characters were selected, to study the leaf epidermal microfeatures by using light microscopy, Results reveal that Daphne and Wikstromia are consistent in most of leaf features. The epidermal cell are polygonal and irregular in shape. The patterns of anticlinal wall are straight, curved and U shape. The cell sizes range in 30-40μm × 10-20μm. Some species have singly hair on surface. Stomatal distribution is random, size range in 20-36μm × 17-25μm, most are broadly elliptical and narrowly elliptical, stomatal frequency are 100-250S/mm2, and the anomocytic stomatal type is dominate. It is apparently that many stomatal and epidermal features in Daphne and Wikstromia are crossed, and no distinguishable features are suitable for separating this two genera. Results from epidermal characters analysis don’t support monophyletic status of Daphne and Wikstroemia. Eriosolena should not be include in the genus Daphne as the special papillae only found in Eriosolena composita rather than in other genera of Thymeleaceae. In compare with other genera, Rhamnoneuron, Eriosolena, Stelleropsis, Daphnopsis and Edgeworthia in Thymelaeoideae, Daphne and Wikstroemia might be derived and originated latter based on the stomatal features.     

Exponential Size Distribution of von Willebrand Factor

Von Willebrand Factor (VWF) is a multimeric protein crucial for hemostasis. Under shear flow, it acts as a mechanosensor responding with a size-dependent globule-stretch transition to increasing shear rates. Here, we quantify for the first time, to our knowledge, the size distribution of recombinant VWF and VWF-eGFP using a multilateral approach that involves quantitative gel analysis, fluorescence correlation spectroscopy, and total internal reflection fluorescence microscopy. We find an exponentially decaying size distribution of multimers for recombinant VWF as well as for VWF derived from blood samples in accordance with the notion of a step-growth polymerization process during VWF biosynthesis. The distribution is solely described by the extent of polymerization, which was found to be reduced in the case of the pathologically relevant mutant VWF-IIC. The VWF-specific protease ADAMTS13 systematically shifts the VWF size distribution toward smaller sizes. This dynamic evolution is monitored using fluorescence correlation spectroscopy and compared to a computer simulation of a random cleavage process relating ADAMTS13 concentration to the degree of VWF breakdown. Quantitative assessment of VWF size distribution in terms of an exponential might prove to be useful both as a valuable biophysical characterization and as a possible disease indicator for clinical applications.     

Exponential Size Distribution of von Willebrand Factor

Von Willebrand Factor (VWF) is a multimeric protein crucial for hemostasis. Under shear flow, it acts as a mechanosensor responding with a size-dependent globule-stretch transition to increasing shear rates. Here, we quantify for the first time, to our knowledge, the size distribution of recombinant VWF and VWF-eGFP using a multilateral approach that involves quantitative gel analysis, fluorescence correlation spectroscopy, and total internal reflection fluorescence microscopy. We find an exponentially decaying size distribution of multimers for recombinant VWF as well as for VWF derived from blood samples in accordance with the notion of a step-growth polymerization process during VWF biosynthesis. The distribution is solely described by the extent of polymerization, which was found to be reduced in the case of the pathologically relevant mutant VWF-IIC. The VWF-specific protease ADAMTS13 systematically shifts the VWF size distribution toward smaller sizes. This dynamic evolution is monitored using fluorescence correlation spectroscopy and compared to a computer simulation of a random cleavage process relating ADAMTS13 concentration to the degree of VWF breakdown. Quantitative assessment of VWF size distribution in terms of an exponential might prove to be useful both as a valuable biophysical characterization and as a possible disease indicator for clinical applications.     

A Theoretical Analysis of Neuronal Variability

A simple neuronal model is assumed in which, after a refractory period, excitatory and inhibitory exponentially decaying inputs of constant size occur at random intervals and sum until a threshold is reached. The distribution of time intervals between successive neuronal firings (interresponse time histogram), the firing rate as a function of input frequency, the variability in the time course of depolarization from trial to trial, and the strength-duration curve are derived for this model. The predictions are compared with data from the literature and good qualitative agreement is found. All parameters are experimentally measurable and a direct test of the theory is possible with present techniques. The assumptions of the model are relaxed and the effects of such experimentally found phenomena as relative refractory and supernormal periods, adaptation, potentiation, and rhythmic slow potentials are discussed. Implications for gross behavior studies are considered briefly.     

Phylogenetic analysis of the Silurian Retiolitidae

A cladistic, phylogenetic analysis of the Retiolitidae, using 18 genera and parataxa and 23 characters, reveals that two distinct clades can be recognized within this family, as well as a primitive stem-group that includes the genus Pseudoretiolites . One of the derived clades includes Pseudo-plegmatograptus, Stomatograptus and Retiolites , which are assigned to the revised subfamily Retiolitinae. The other derived clade, the early part of which shows a paraphyletic relationship, includes the remaining known genera Rotaretiofites s.l., Paraplectograptus s.l., Sokolovograptus, Plectograptus, Agastograptus, Spinograptus, Gothograptus, Eisenackograptus, Neogothograptus, Semiplectograptus, Plectodinemagraptus and Holoretiolites . These genera are all included within an expanded Plectograptinae. The biostratigraphic distribution of these taxa suggests that these two clades diverged from a Pseudoretiolites-like ancestor in mid-Aeronian time.     

A general solution to the time interval omission problem applied to single channel analysis.

To obtain the open or closed time interval distributions of patch clamp signals, several workers have used a half-amplitude minimum time interval criterion. Within this framework, no transition between states of different conductance levels is considered to have taken place if it leads to a time interval smaller than a certain critical value. This procedure modifies substantially the open or closed time interval distribution of the random signal to be analyzed, since time intervals well above the time resolution of the recording system may be interrupted by short gaps that may or may not satisfy the minimum time interval criterion. We present here a general theoretical framework by means of which the effect of time interval omission on time interval distributions can be taken into account. Based on the mathematical formalism provided by the Kolmogorov forward equation, special matrix operators are first defined. The general solution to the time omission problem in its integral form is then derived. In view of the poor computational feasibility of the resulting solution, a first-order approximation is also presented. This approximation consists essentially in neglecting the contribution of the undetected gaps to the total length of the resulting time interval. The exact and approximate solutions are then applied to two special kinetic schemes commonly found in single-channel studies, namely the O-C and C-O-C models. The applicability of the proposed formalism to the time interval distribution problem of a damped random signal is finally discussed.     

Ewens' sampling formula and related formulae: combinatorial proofs, extensions to variable population size and applications to ages of alleles

Ewens' sampling formula, the probability distribution of a configuration of alleles in a sample of genes under the infinitely-many-alleles model of mutation, is proved by a direct combinatorial argument. The distribution is extended to a model where the population size may vary back in time. The distribution of age-ordered frequencies in the population is also derived in the model, extending the GEM distribution of age-ordered frequencies in a model with a constant-sized population. The genealogy of a rare allele is studied using a combinatorial approach. A connection is explored between the distribution of age-ordered frequencies and ladder indices and heights in a sequence of random variables. In a sample of n genes the connection is with ladder heights and indices in a sequence of draws from an urn containing balls labelled 1,2,...,n; and in the population the connection is with ladder heights and indices in a sequence of independent uniform random variables.     

Latitudinal diversity gradients for brachiopod genera during late Palaeozoic time: links between climate, biogeography and evolutionary rates

Aim The latitudinal diversity gradient, in which taxonomic richness is greatest at low latitudes and declines towards the poles, is a pervasive feature of the biota through geological time. This study utilizes fossil data to examine how the latitudinal diversity gradient and associated spatial patterns covaried through the major climate shifts at the onset and end of the late Palaeozoic ice age. Location Data were acquired from fossil localities from around the world. Methods Latitudinal patterns of diversity, mean geographical range size and macroevolutionary rates were constructed from a literature‐derived data base of occurrences of fossil brachiopod genera in space and time. The literature search resulted in a total of 18,596 occurrences for 991 genera from 2320 localities. Results Climate changes associated with the onset of the late Palaeozoic ice age (c. 327 Ma) altered the biogeographical structure of the brachiopod fauna by the preferential elimination of narrowly distributed, largely tropical genera when glaciation began. Because the oceans were left populated primarily with widespread genera, the slope of the diversity gradient became gentle at this time, and the gradient of average latitudinal range size weakened. In addition, because narrowly distributed genera had intrinsically high rates of origination and extinction, the gradients of both of these macroevolutionary rates were also reduced. These patterns were reversed when the ice age climate abated in early Permian time (c. 290 Ma): narrowly distributed genera rediversified at low latitudes, restoring steep gradients of diversity, average latitudinal range size and macroevolutionary rates. Main conclusions During late Palaeozoic time, these latitudinal gradients for brachiopods may have been linked by the increased magnitude of seasonality during the late Palaeozoic ice age. Pronounced seasonality would have prevented the existence of genera with narrow latitudinal ranges. These results for the late Palaeozoic ice age suggest a climatic basis for the present‐day latitudinal diversity gradient.     

Rank Diversity of Languages: Generic Behavior in Computational Linguistics

Statistical studies of languages have focused on the rank-frequency distribution of words. Instead, we introduce here a measure of how word ranks change in time and call this distribution rank diversity. We calculate this diversity for books published in six European languages since 1800, and find that it follows a universal lognormal distribution. Based on the mean and standard deviation associated with the lognormal distribution, we define three different word regimes of languages: “heads” consist of words which almost do not change their rank in time, “bodies” are words of general use, while “tails” are comprised by context-specific words and vary their rank considerably in time. The heads and bodies reflect the size of language cores identified by linguists for basic communication. We propose a Gaussian random walk model which reproduces the rank variation of words in time and thus the diversity. Rank diversity of words can be understood as the result of random variations in rank, where the size of the variation depends on the rank itself. We find that the core size is similar for all languages studied.     

Random disturbance and diversity of competitive systems

Population size distribution within a community of species with a competitive hierarchy, is studied. With the introduction of a stochastic model of invasion and extinction due to random environmental disturbance, the stationary population size distribution is derived as a function of the parameter, which denotes the ratio of rates of random extinction and invasion. From this result it is shown that the Shannon-type diversity takes the maximum value under the situation that 10 20 percent of habitat sites remain unoccupied, and the number of species also becomes maximum at intermediate levels of disturbance. The dynamical properties of a one-sided competitive system are also discussed by use of the Lotka-Volterra equations.     

Inbreeding reduces power-law scaling in the distribution of fluctuating asymmetry: an explanation of the basis of developmental instability

The study of fluctuating asymmetry has been controversial because of conflicting results found in much of the primary literature. It has been suggested that the source of this conflict is the fact that the basis of fluctuating asymmetry is poorly understood and that, as a consequence, methodology of fluctuating asymmetry studies may be flawed. A new model for the phenomenological basis of fluctuating asymmetry, that variation in fluctuating asymmetry is in large part due to the random exponential growth of cell populations (geometric Brownian motion) that are terminated randomly around a genetically programmed development time, is presented here. If termination of development has a genetic component, then scaling effects and kurtosis in the distribution of fluctuating asymmetry should increase with genetic redundancy of the population. This model prediction was tested by comparing the distribution of multivariate size and shape fluctuating asymmetry in large samples collected from both wild populations and four moderately inbred lines of Drosophila simulans. It was found that while wild populations were best described by a lognormal distribution with power-law scaled tails, the inbred lines derived from the wild stock were dramatically normalized (half-normal) in three of four cases. As predicted, the scaling exponent of the upper tail of the distribution of fluctuating asymmetry increased with inbreeding while the kurtosis and mean fluctuating asymmetry decreased with inbreeding. The model suggests an additional explanation of leptokurtosis in fluctuating asymmetry. Kurtosis and scaling of the statistical distribution of fluctuating asymmetry in a population is related directly to genetic differences between individuals and these differences affect their ability to buffer the process of development against random perturbations.     

Supramolecular photosystem II organization in grana thylakoid membranes: evidence for a structured arrangement

The distribution of photosystem (PS) II complexes in stacked grana thylakoids derived from electron microscopic images of freeze-fractured chloroplasts are examined for the first time using mathematical methods. These characterize the particle distribution in terms of a nearest neighbor distribution function and a pair correlation function. The data were compared with purely random distributions calculated by a Monte Carlo simulation. The analysis reveals that the PSII distribution in grana thylakoids does not correspond to a random protein mixture but that ordering forces lead to a structured arrangement on a supramolecular level. Neighboring photosystems are significantly more separated than would be the case in a purely random distribution. These results are explained by structural models, in which boundary lipids and light-harvesting complex (LHC) II trimers are arranged between neighboring PSII. Furthermore, the diffusion of PSII was analyzed by a Monte Carlo simulation with a protein density of 80% area occupation (determined for grana membranes). The mobility of the photosystems is severely reduced by the high protein density. From an estimate of the mean migration time of PSII from grana thylakoids to stroma lamellae, it becomes evident that this diffusion contributes significantly to the velocity of the repair cycle of photoinhibited PSII.     

A Markov Chain Model of Population Growth with an Application in Epidemiology

This paper is concerned with a class of population growth processes in discrete time; the simple epidemic process is considered as a specific example. A Markov chain model is constructed and standard Markov methods are used to study the main biological concepts. A simple and explicit formula is obtained for the transient distribution of the population size. Then, the cost of the process is defined and the joint probability generating function of its components is derived. Finally, the results are extended to the case where the inter-transition periods are bounded i.i.d. random variables.     

Qualitative behavior of a selectively neutral allelic model

A model of Fleming and Viot for describing frequency distributions for selectively neutral allelic populations and for multidimensional numerical genetic traits is studied, with specific attention given to two qualitative aspects that are derived: the coherence of the random wandering distribution and the tendency to cluster at microscopic scales. A new quantity, called the clustering or occupation index, is introduced to measure relative patchiness of the distribution in terms of a limiting subcell occupation frequency. Results of one- and two-dimensional computer-generated simulations are presented which provide an estimate of the theoretical expected distribution of allelic types. Evidence of the robustness of the model, in the sense that it arises from a variety of assumptions about the reproductive mechanism, is presented in the Appendix.