A stochastic model of a cell population with quiescence

A cell population in which cells are allowed to enter a quiescent (nonproliferating) phase is analyzed using a stochastic approach. A general branching process is used to model the population which, under very mild conditions, exhibits balanced exponential growth. A formula is given for the asymptotic fraction of quiescent cells, and a numerical example illustrates how convergence toward the asymptotic fraction exhibits a typical oscillatory pattern. The model is compared with deterministic models based on semigroup analysis of systems of differential equations.     

On a two-phase size-structured population model with infinite states-at-birth and distributed delay in birth process

In this paper we study the two-phase size-structured population model with infinite states-at-birth and distributed delay in birth process. The model distinguishes individuals by two different status: the ‘reproductive’ stage and the ‘nonreproductive’ stage. We establish the well-posedness for this model and show that the solution of this model exhibits asynchronous exponential growth by means of semigroups. We also consider a special case in which the individuals in the ‘reproductive’ stage and the ‘nonreproductive’ stage have the same growth rates and give a comparison between this two-phase model with the classical one-phase model.     

An algorithm for molecular dissection of tumor progression

The volumetric growth of tumor cells as a function of time is most often likely to be a complex trait, controlled by the combined influences of multiple genes and environmental influences. Genetic mapping has proven to be a powerful tool for detecting and identifying specific genes affecting complex traits, i.e., quantitative trait loci (QTL), based on polymorphic markers. In this article, we present a novel statistical model for genetic mapping of QTL governing tumor growth trajectories in humans. In principle, this model is a combination of functional mapping proposed to map function-valued traits and linkage disequilibrium mapping designed to provide high resolution mapping of QTL by making use of recombination events created at a historic time. We implement an EM-simplex hybrid algorithm for parameter estimation, in which a closed-form solution for the EM algorithm is derived to estimate the population genetic parameters of QTL including the allele frequencies and the coefficient of linkage disequilibrium, and the simplex algorithm incorporated to estimate the curve parameters describing the dynamic changes of cancer cells for different QTL genotypes. Extensive simulations are performed to investigate the statistical properties of our model. Through a number of hypothesis tests, our model allows for cutting-edge studies aimed to decipher the genetic mechanisms underlying cancer growth, development and differentiation. The implications of our model in gene therapy for cancer research are discussed.     

Asymptotic behavior of nonlinear semigroup describing a model of selective cell growth regulation

A new scheme of regulation of cell population growth is considered, called the selective growth regulation. The principle is that cells are withdrawn from proliferation depending on their contents of certain biochemical species. The dynamics of the cell population structured by the contents of this species is described by the functional integral equation model, previously introduced by the authors. The solutions of the model equations generate a semigroup of nonlinear positive operators. The main problem solved in this paper concerns stability of the equilibria of the model. This requires stating and proving of an original abstract result on the spectral radius of a perturbation of a semigroup of positive linear operators. Biological applications are discussed.     

SYNCHRONOUS GROWTH OF CHLAMYDOMONAS REINHARDTII (CHLOROPHYCEAE): A REVIEW OF OPTIMAL CONDITIONS1

Chlamydomonas reinhardtii Dangeard was synchronized at optimal growth conditions under a 12:4 LD regime at 35 C and 20,000 lx with serial dilution to a standard starting cell density of (1.4 ± 0.2) × 10⁶ cells/ml. Synchronous growth and division were characterized by measuring cell number, cell volume and size distribution, dry weight, protein, carbon, nitrogen, chlorophyll, carotenoids, nucleic acids, nuclear and cytoplasmic division during the vegetative life cycle. The main properties of the present system are: Exponential growth with high productivity, high degrees of synchrony and reproducibility during repeated life cycles. The degree of synchrony of this light-dark synchronization system was evaluated and compared with those described in the literature using probit analysis of the time course of DNA synthesis, nuclear and cytoplasmic division and sporulation (increase in cell number). The results showed that the degree of synchrony is highest for cells grown under optimal conditions.     

基于独立元分析和非线性指数分析的脑电信号中伪迹分量的自动去除

脑电(electroencephalography,EEG)信号中不可避免地存在着眼动、心跳、肌电信号以及线性噪声等伪迹干扰,这些伪迹的存在极大地影响了脑电信号分析的准确性,因此在进行脑电信号分析前需要去除伪迹干扰。为了有效地去除伪迹,结合独立元分析和非线性指数分析,提出一种自动识别并去除脑电信号中伪迹分量的方法。该方法还可同时用于提取脑电信号中的基本节律如!波等。相应的模拟与实际脑电数据的实验结果表明所提议的方法具有很好的识别和去除脑电信号伪迹分量的性能。     

一类具有非线性控制和基层具有饱和吸收率的恒化器藻类模型

本文通过对藻类的增长率和基层的吸收率提出有生物意义的表达式,研究了一类具有非线性控制藻类恒花器模型．用定性理论证明了非线性控制可以使变产量的恒化器模型有一个全局渐进稳定的正平衡点．     

Gene-culture waves of advance

Major genetic and cultural changes may have been coupled during hominid evolution. Since hominids have had a wide geographical distribution for about one million years, any mutant gene or cultural innovation that became established had to spread from its origin. A pair of nonlinear diffusion equations is derived which models the propagation of a mutant gene and a cultural innovation. Both are assumed to originate in the same locality along a linear habitat. The mutant gene and its allele are semidominant, and the two cultural choices are transmitted according to what I call the logistic attraction-repulsion model. The genes influence cultural choice, and the two interact to determine fitness. Of particular interest is the case in which mutant gene and cultural innovation are mutually dependent, neither being able to spread without the other. Each equation of the pair is similar in form to Fisher's equation, with a linear function of the other dependent variable replacing the constant coefficient in the reaction term. The partial differential equations are solved numerically to obtain the asymptotic speeds. Their form also suggests an heuristic argument which has proved useful, but I have been unable to obtain any analytic results. The waves of the system are shown to be of two types, synchronous and asynchronous. When genes and culture are mutually dependent, synchronous travelling waves can exist. However, their existence is dependent on initial conditions, and the speed of propagation is slow.     

The burrowing crab Neohelice granulata affects the root strategies of the cordgrass Spartina densiflora in SW Atlantic salt marshes

Salt marshes are among the most productive systems of the world, with plant primary production limited by soil oxygen deficiency and nutrient availability. Nevertheless, root adaptations to anoxia and nutrient acquisition are different and often incompatible. The SW Atlantic salt marshes are characterized by high densities of the deep (up to 1 m) burrowing crab Neohelice granulata (Dana, 1851) that may change soil physical and chemical characteristics by burrow construction. In this work, we experimentally evaluated the hypothesis that crab burrowing can enhance soil oxygenation, causing changes in Spartina densiflora Brongniart below ground tissues from structures adapted to anoxia to systems adapted for nutrient acquisition. This response, in turn, would enhance plant productivity. Results from field observations show that oxygen availability is higher in zones with high burrow densities. As burrow densities increased, the plant root distribution changed from shallow (associated to low oxygen availability) to deeper and vertically homogeneous, with a positive correlation between burrow density and plant aboveground biomass. Experimental exclusion of crabs shows that they induce changes of root strategies from anoxia toleration to nutrient efficient acquisition, with increasing plant productivity. The invasive success that this plant shows in other parts of the world is likely to be due to their ability to tolerate harsh environmental conditions. Our results suggest that the morphological plasticity of S. densiflora is also important in their native zone given the characteristics of their specific habitat.     

A simple mathematical modeling of the growth of microorganism colonies

The growth rates of aspergillus, fusarium, and penicillium microorganism colonies in Czapex Dox Agar as a feed material, under room conditions, are observed to be linear. This phenomenon is mathematically modeled and exactly predicted on the basis of the exponential growth assumption of a single microorganism. The approach allows an easy determination of the multiplication constant of a had microorganisms been allowed to grow freely microorganism, in given conditions.     

一类单种群增长模型正解的振动性

利用一种新的方法研究了一类单种群增长模型—时滞微分方程N(t)=的解关于其正平衡点N=1的振动性,所获结果改进了已有文献中的相关结论。