A transition probability model for amino acid substitutions from blocks.

Substitution matrices have been useful for sequence alignment and protein sequence comparisons. The BLOSUM series of matrices, which had been derived from a database of alignments of protein blocks, improved the accuracy of alignments previously obtained from the PAM-type matrices estimated from only closely related sequences. Although BLOSUM matrices are scoring matrices now widely used for protein sequence alignments, they do not describe an evolutionary model. BLOSUM matrices do not permit the estimation of the actual number of amino acid substitutions between sequences by correcting for multiple hits. The method presented here uses the Blocks database of protein alignments, along with the additivity of evolutionary distances, to approximate the amino acid substitution probabilities as a function of actual evolutionary distance. The PMB (Probability Matrix from Blocks) defines a new evolutionary model for protein evolution that can be used for evolutionary analyses of protein sequences. Our model is directly derived from, and thus compatible with, the BLOSUM matrices. The model has the additional advantage of being easily implemented.     

森林种群径阶转移模型中转移概率的估算方法

基于统计分析理论和微分方程理论,给出了森林种群径阶转移模型中估算转移概率的方法：第一种是在有两次样地观测数据,不考虑林分环境因子等因素的条件下估算转移概率;第二种是在已知林分环境因子条件下,不需要对样地有两次观测数据来估算转移概率．实例验证结果表明,两种估算转移概率的方法具有计算简单和实用性强的特点,对森林经营与管理有一定的理论指导和实际应用价值．     

Cell cycle variability: The oscillator model of the cell cycle yields transition probability alpha and beta type curves

The limit cycle concept of cell replication attributes cell cycle variability to continuous random modulation of the rates of reactions forming the intracellular control system believed to be responsible for replication processes. It is shown that this model can yield frequency histograms and both alpha and beta type accumulative distribution curves (with respect to generation times and also to cycle phases) which are of the various forms seen experimentally. The results thus provide additional support for this concept.     

Family tree analysis of a transformed cell line and the transition probability model for the cell cycle

Variation in intermitotic time between individual cells in culture can be ascribed to the occurrence of random transitions in the cell cycle. We have analysed a family tree of mouse neuroblastoma cells, and observed that variation in difference in intermitotic time between sister cells is smaller than between cousin cells, and this difference is again smaller than between second-cousin and unrelated cells. This observation is incompatible with all transition probability models presented so far. We propose a model for the cell cycle with a single random transition, but with the additional assumption that the (two) system parameters may show variability within the population such that the closer cells are in their relation to each other, the closer their values of the system parameters will be. This model describes correctly the behaviour of the family tree of the cell line and in addition is able to explain why differences in intermitotic time between sister cells are exponentially distributed, while intermitotic times themselves are more or less normally distributed. Methods have been described to quantify the various system parameters.     

A re-investigation and re-interpretation of the cumacean photoreceptor

Evidence for and against the view that the singular eye in Diastylis rathkei (Cumacea) represents a regressed compound eye is summarised and supplemented with new ultrastructural observations. Neither in the adult nor in the larval manca stage are even traces of a facetation found. The eye consists of two closely apposed eye halves and the four lenticular complexes in each appear to increase in size with age along an isometric growth curve. Each lenticular complex consists of a lens rich in glycogen-like particles and a rhabdom made up of regularly aligned microvilli 0.075 μ m in diameter. No more than three retinula cells contribute to each lenticular compkx. Retinula cells contain presumed carotenoid bodies 0.4–0.5 μm in diameter and clusters of electron-opaque glycogen matcrial near the proximally-located nuclei. The bulk of the eye is occupied by cells crowded with reflecting vesicles of approximately 0.8 μ m diameter. Though it appears too early to offer a final and decisive conclusion as to the nature and origin of the eye of D. rathkei , comparisons with compound eyes of other peracaridan crustaceans and anatomical parallels to isopod and other malacostracan ocelli make clear that the long-held view that the cumacean photoreceuptor represents a regressed compound eye is not necessarily the correct one.     

The relationship between the transition matrix model and the diffusion model

The diffusion equation model and the Lefkovitch matrix model have been employed independently in plant population ecology in order to analyze the dynamics of growth and size structure. The two models describe the dynamics of size structure in biological populations, and thus there must be some relationship between them. In the present paper, we examine the theoretical relationship between these two models. We demonstrate, on a certain assumption, that the one-step Lefkovitch matrix model corresponds to a difference equation of the diffusion equation and that the two- and three-step Lefkovitch matrix model correspond to difference equations of the 4th- and 6th-order Kramers-Moyal expansions, respectively. It is also shown that 2n moments (the first to the 2n-th moments) of growth rate are necessary and sufficient to rewrite uniquely the n-step Lefkovitch matrix model in terms of the linear combination of the moments. We finally discuss the relationship between the species characteristics of census data and the appropriate types of the Lefkovitch matrix.     

A re-interpretation of the Fabroniaceae,III: Anacamptodon and Fabronidium revisited,Mamillariella, Helicodontiadelphus and Bryobartlettia gen. nov.

Anacamptodon is shown by SEM to have a typically formed diplolepideous exostome.Fabronidium is transferred to the Leskeaceae nearSchwetschkea, with a single species,F. guatemaliensis (C. Müll.) comb. nov.Mamillariella is redescribed and illustrated from authentic material and is placed in the Leskeaceae nearLindbergia. The monotypicHelicodontiadelphus is described and illustrated from the type and only known collection.Helicodontiadelphus australiensis Dix. is synonymized withEriodon cylindritheca (Dix.) Dix. & Sainsb. of the Brachytheciaceae.Bryobartlettia costata gen. et sp. nov. is described from New Zealand and is placed in the Leskeaceae nearIwatsukiella. A summary of the generic changes in the Fabroniaceae is provided in chart form.     

The neuronal transition probability (NTP) model for the dynamic progression of non-REM sleep EEG: the role of the suprachiasmatic nucleus

Little attention has gone into linking to its neuronal substrates the dynamic structure of non-rapid-eye-movement (NREM) sleep, defined as the pattern of time-course power in all frequency bands across an entire episode. Using the spectral power time-courses in the sleep electroencephalogram (EEG), we showed in the typical first episode, several moves towards-and-away from deep sleep, each having an identical pattern linking the major frequency bands beta, sigma and delta. The neuronal transition probability model (NTP)--in fitting the data well--successfully explained the pattern as resulting from stochastic transitions of the firing-rates of the thalamically-projecting brainstem-activating neurons, alternating between two steady dynamic-states (towards-and-away from deep sleep) each initiated by a so-far unidentified flip-flop. The aims here are to identify this flip-flop and to demonstrate that the model fits well all NREM episodes, not just the first. Using published data on suprachiasmatic nucleus (SCN) activity we show that the SCN has the information required to provide a threshold-triggered flip-flop for TIMING the towards-and-away alternations, information provided by sleep-relevant feedback to the SCN. NTP then determines the PATTERN of spectral power within each dynamic-state. NTP was fitted to individual NREM episodes 1-4, using data from 30 healthy subjects aged 20-30 years, and the quality of fit for each NREM measured. We show that the model fits well all NREM episodes and the best-fit probability-set is found to be effectively the same in fitting all subject data. The significant model-data agreement, the constant probability parameter and the proposed role of the SCN add considerable strength to the model. With it we link for the first time findings at cellular level and detailed time-course data at EEG level, to give a coherent picture of NREM dynamics over the entire night and over hierarchic brain levels all the way from the SCN to the EEG.     

Temperature response of the cell cycle of Haplopappus gracilis in suspension culture and its significance to the G1 transition probability model

The effects of temperature on the cell cycle of Haplopappus gracilis suspension cultures were analysed by the fraction of labelled mitoses method. Sphase in these cultures shows a different temperature optimum as compared to optima derived for G₂ and mitosis. G₁ phase has a much lower Q₁₀ than the other cell cycle phases and shows no temperature optimum between 22 and 34° C. These results are discussed in relation to a transition probability model of the cell cycle proposed by Smith and Martin (Proc. Natl. Acad. Sci. USA 70, 1263–1267, 1973), in which each cell has a time independent probability of initiating the transition into another round of DNA replication and division. The implications of such a model for cell cycle analysis are discussed and a tentative model for a probabilistic transition trigger is advanced.Abbreviations FLM Fraction of labelled mitoses - T_B Total B-phase     

On the probability model for asthma attacks

In environmental epidemiology, the impact of environmental agents on symptoms or health status is of interest. This influence is described quantitatively in the theory of Whittemore & Keller (1979). They formulated a logistic model for individuals that is useful in evaluation of panel studies in which each participant protocols whether he does or does not have a certain symptom each day. In the present paper an equation for the prevalence of symptoms in the study population that is defined as the fraction of symptomatic subjects is deduced from the model for individuals. The model for the aggregated quantity depends on the individuals' parameters in a nonlinear manner. The relationship between the individual-based model and the corresponding population-based model is illustrated by means of a simulated panel. Bayesian estimates of the parameters are calculated and compared for both approaches. Bayesian inference enables to apply the prevalence model to a population of non-identical individuals. For such a heterogeneous population, we observe an attenuation of environmental effects on the aggregated symptom prevalence in comparison to the individual-based approach. The presented theory is applicable not only to panel studies but also in time-series analysis of prevalences and incidences.     

The basic reproduction number and the probability of extinction for a dynamic epidemic model

We consider the spread of an epidemic through a population divided into n sub-populations, in which individuals move between populations according to a Markov transition matrix Σ and infectives can only make infectious contacts with members of their current population. Expressions for the basic reproduction number, R₀, and the probability of extinction of the epidemic are derived. It is shown that in contrast to contact distribution models, the distribution of the infectious period effects both the basic reproduction number and the probability of extinction of the epidemic in the limit as the total population size N → ∞. The interactions between the infectious period distribution and the transition matrix Σ mean that it is not possible to draw general conclusions about the effects on R₀ and the probability of extinction. However, it is shown that for n = 2, the basic reproduction number, R₀, is maximised by a constant length infectious period and is decreasing in ?, the speed of movement between the two populations.     

The relationship between the transition probability and oscillator concepts of the cell cycle and the nature of the commitment to replication

The oscillator concept of the cell cycle predicts the existence of threshold conditions within the cell which must be exceeded before replication is initiated. It is shown (a) that if the conditions are subthreshold, random disturbances can trigger a cycle of the oscillation (round of replication) and (b) that the probability of this occurring increases as the state of the system approaches the threshold. It is concluded that the oscillator concept explains the data on which the transition probability model is based. It also accounts for the ability of cells to replicate even when the mitogen is present for a limited period only.     

The stretched intermediate model of B-Z DNA transition

There have been numerous attempts to describe the mechanism of B-Z transition. Our simulations based on the stochastic difference equation with length algorithm show that a short DNA oligomer will tend to unwind and overstretch during the transition. The overstretching of DNA is then understood from the Zhou, Zhang, and Ou-Yang model. Unlike the Harvey model, the stretched intermediate model does not pose any steric dilemma; we are able to show that the chain sense reversal progresses spontaneously using the stretched intermediate model. A nonlinear DNA model is used to describe the origins and mechanism of base rotation in the stretched intermediate state of DNA. We also propose an experiment that can verify the existence of a stretched intermediate state during B-Z transition, thus opening up fresh grounds for experimentation in this field.     

The probability of causation under a stochastic model for individual risk

In this paper we offer a mathematical definition for the probability of causation that formalizes the legal and ordinary-language meaning of the term. We show that, under this definition, even the average probability of causation among exposed cases is not identifiable from epidemiologic data. This is because the probability of causation depends both on the unknown mechanisms by which exposure affects disease risk and competing risks, and on the unknown degree of heterogeneity in the background disease risk of the exposed population. We derive the maximum and minimum values for the probability of causation consistent with the observable population quantities. We also derive the relationship of the "assigned share" (excess incidence rate as a proportion of total incidence rate) to the probability of causation.     

HLA and the probability of paternity.

In cases of disputed paternity, blood tests are often used to obtain an estimate of the probability that the accused male is the true father. The interpretation of the genetic data is usually based upon a statistic called the paternity index. This paper shows that the paternity index method cannot be applied to data from compound loci in the absence of information on linkage phase. Since phenotypic data from compound loci, such as HLA, MNSs, and Rh, are often useful in disputed paternity proceedings, they should be analyzed with available alternative statistics.     

The two-pathway model for the catch-slip transition in biological adhesion

Some recently studied biological noncovalent bonds have shown increased lifetime when stretched by mechanical force. In each case these counterintuitive "catch-bonds" have transitioned into ordinary "slip-bonds" that become increasingly shorter lived as the tensile force on the bond is further increased. We describe analytically how these results are supported by a physical model whereby the ligand escapes the receptor binding site via two alternative routes, a catch-pathway that is opposed by the applied force and a slip-pathway that is promoted by force. The model predicts under what conditions and at what critical force the catch-to-slip transition would be observed, as well as the degree to which the bond lifetime is enhanced at the critical force. The model is applied to four experimentally studied systems taken from the literature, involving the binding of P- and L-selectins to sialyl Lewis(X) oligosaccharide-containing ligands. Good quantitative fit to the experimental data is obtained, both for experiments with a constant force and for experiments where the force increases linearly with time.