海定格刷形象物理机制的研究

通过对海定格刷形象时间特性的分析,提出了现象的动态理论模型,进行了数学推导并结合临床实验作了比较。给出的定量结果可作为开发新的眼科检测手段的基础。     

随机截尾时威布尔分布中参数的极大似然估计

一、引言在以生存期表示的生存数据分析中,最大特点是数据类型是不完全数据,即不是每个数据都是确切的主存时间,它包括死亡数据和截尾数据。根据调查观察的生存数据讨论其分布规律,即生存分布,不仅可研究疾病患者的生存规律,还可以进一步比较对疾病不同治疗方法(包括药物)的效果。在生存分布中,应用较广、效果较好之一的是威布尔分布。导出此分布的物理模式可作这样解释:凡是某一局部损伤或失效将引起整体功能的丧失,则整体失效时间(即寿命)的分布就服从威布尔分布,就像链条的寿命是链条中最弱环节的寿命一样,因而这种模式大体上符合生存—死亡模式。     

动态生命表寿命数收集与处理过程中常见问题的探讨

种群动态生命是研究野生动物存活过程的有用工具,而其可靠性则依赖于生命数据收集与处理过程中的正确性。章就野生动物动态生命表收集和处理过程中常见的右删失数据处理问题、个体死亡时间估计、同生群初始值N0估计以及早期死亡数据的估算问题提出了一点建议和讨论。     

谷氨酸发酵的动力学模型

本文利用实验所得数据对文献报道的有关谷氨酸发酵动力学模型逐一进行了模拟和比较分析,选出一组与实验数据拟合较好,而且是在一定理论下推导出来的模型。     

海岱地区大汶口文化时期人口死亡年龄的统计分布特征

人口死亡年龄是揭示一个族群健康状况和社会经济条件的重要指标。本文根据海岱地区大汶口文化时期九个墓地人骨遗存的发掘报告,运用定量统计的方法检验了人口死亡年龄分布特征。发现该区大汶口文化时期人口的死亡年龄分布近似服从正态分布。最后探讨了造成人口低死亡年龄的可能原因,并给出了这一概率分布的数学意义以及在史前人口学中的应用前景。     

从组织细胞DNA水平和红细胞钾离子含量推断死亡时间

准确的死亡时间推断可以为刑侦部门提供重要的线索,还可以为解决死亡纠纷事件以及社会保险等方面提供可靠的科学依据,因此,研究死亡时间的测定方法具有非常重要的法医学意义。本实验通过Feulgen染色图像的分析、细胞悬浮液FCM分析以及测定家兔死亡后心血红细胞钾含量的变化,发现死亡家兔组织的DNA含量随时间延长而减少、心血红细胞钾离子含量与死亡时间呈现一定的线性关系。提示对于死亡时间的推断,可以从组织细胞DNA水平和心血红细胞钾离子含量水平进行简单测定,从而较为简单准确得估计死亡时间。     

非线性常微分方程定性理论在生态学中的应用

三十年代时由于研究无线电的线路、器材的需要产生了数学中非线性常微分方程定性理论这样一个分支。经过几十年的发展,今天它能为很多的学科服务了,生物学就是其中的一门。下面通过几个例子看它在生态学中的应用。1.一个物种先给几个定义:出生率:单位时间里每一千个成员中出生的成员数与一千之比。死亡率:单位时间里每一千个成员中死亡的成员数与一千之比。增长率:单位时间里每一千个成员中增长的成员数与一千之比。显然以上三者有关系式:     

在年龄结构化动物种群的分析过程中常见的几种错误

分析动物各年龄组的种群数据有助于推断影响动物种群发展趋势的诸因素,而且便于设计出种群层次。然而,在研究近期文献资料时,我们发现存在三种错误。这些错误均可导致非正确的解释。即:1)在生命表分析中,将Sx与lx等同(Sx由各死亡年龄组推导而出,lx为存活率);2)在综合跨年龄组的成雌生育率时,不计算该年龄组的成雌死亡数;3)在用Leslie矩阵计算周限增长率时,以mx取代Fx。我们将探讨上述错误的含义及后果,并提出解决方法。     

亲本死亡时间对近太湖新银鱼人工授精受精率的影响

银鱼捕起后易死,较难用活的亲本进行人工繁殖,在实际生产中,多采用死的亲本进行人工受精,亲本死亡的时间对卵的受精率影响较大。本文对徐家河水库近太湖新银鱼亲本死亡时间与卵受精率的关系进行了系列研究,亲本死亡后240分钟内,每隔15分钟进行一次人工受精,结果表明,卵的受精率随着亲本死亡时间的延长,其受精率越来越低,240分钟后,受精率趋于0。水温在15℃以下,亲本死亡105分钟后进行人工受精,平均受精率为43%,因此建议水温在15℃以下近太湖新银鱼的人工受精应在亲本死亡后105分钟之内进行。       

超声波照射蝗虫卵的生物效应的研究

用固定频率、固定功率的超声波照射不同阶段的蝗虫卵,研究不同的作用时间对蝗虫卵孵化率和孵化时间的影响。探求超声波作用于生物所产生的效果及一些定量的数据,为今后研究超声波的育种和杀虫提供一些实验依据。结果表明:超声波对蝗虫卵的孵化率和孵化时间有明显的影响,既可以促进其孵化,也可以抑制其孵化,甚至导致其死亡。     

A mathematical model of the processes of mitochondrial death and reproduction during body irradiation

A method of construction of mathematical model of processes of death and reproduction of mitochondria based on morphometric measurements is proposed. Using the model the time of mitochondria death and reproduction during ionized irradiation of the organism is identified.     

A new mathematical model of the dynamics of an age cohort population

A new generalized conception of an organism is given. Based on this conception, a new mathematical model of ontogenesis of an individual and the survival of the age cohort of population was proposed. By using real data on the dynamics of the survival of the age cohort of population, the model enables one to determine the parameters characterizing the relationship man-environment in the context of survival and calculate the dynamics (from birth to death) of the model variables of the state of the organism.     

Log Transformation Improves Dating of Phylogenies

Phylogenetic trees inferred from sequence data often have branch lengths measured in the expected number of substitutions and therefore, do not have divergence times estimated. These trees give an incomplete view of evolutionary histories since many applications of phylogenies require time trees. Many methods have been developed to convert the inferred branch lengths from substitution unit to time unit using calibration points, but none is universally accepted as they are challenged in both scalability and accuracy under complex models. Here, we introduce a new method that formulates dating as a nonconvex optimization problem where the variance of log-transformed rate multipliers is minimized across the tree. On simulated and real data, we show that our method, wLogDate, is often more accurate than alternatives and is more robust to various model assumptions.     

Modeling Genome-Wide Dynamic Regulatory Network in Mouse Lungs with Influenza Infection Using High-Dimensional Ordinary Differential Equations

The immune response to viral infection is regulated by an intricate network of many genes and their products. The reverse engineering of gene regulatory networks (GRNs) using mathematical models from time course gene expression data collected after influenza infection is key to our understanding of the mechanisms involved in controlling influenza infection within a host. A five-step pipeline: detection of temporally differentially expressed genes, clustering genes into co-expressed modules, identification of network structure, parameter estimate refinement, and functional enrichment analysis, is developed for reconstructing high-dimensional dynamic GRNs from genome-wide time course gene expression data. Applying the pipeline to the time course gene expression data from influenza-infected mouse lungs, we have identified 20 distinct temporal expression patterns in the differentially expressed genes and constructed a module-based dynamic network using a linear ODE model. Both intra-module and inter-module annotations and regulatory relationships of our inferred network show some interesting findings and are highly consistent with existing knowledge about the immune response in mice after influenza infection. The proposed method is a computationally efficient, data-driven pipeline bridging experimental data, mathematical modeling, and statistical analysis. The application to the influenza infection data elucidates the potentials of our pipeline in providing valuable insights into systematic modeling of complicated biological processes.     

A Mathematical-Biological Joint Effort to Investigate the Tumor-Initiating Ability of Cancer Stem Cells

The involvement of Cancer Stem Cells (CSCs) in tumor progression and tumor recurrence is one of the most studied subjects in current cancer research. The CSC hypothesis states that cancer cell populations are characterized by a hierarchical structure that affects cancer progression. Due to the complex dynamics involving CSCs and the other cancer cell subpopulations, a robust theory explaining their action has not been established yet. Some indications can be obtained by combining mathematical modeling and experimental data to understand tumor dynamics and to generate new experimental hypotheses. Here, we present a model describing the initial phase of ErbB2⁺ mammary cancer progression, which arises from a joint effort combing mathematical modeling and cancer biology. The proposed model represents a new approach to investigate the CSC-driven tumorigenesis and to analyze the relations among crucial events involving cancer cell subpopulations. Using in vivo and in vitro data we tuned the model to reproduce the initial dynamics of cancer growth, and we used its solution to characterize observed cancer progression with respect to mutual CSC and progenitor cell variation. The model was also used to investigate which association occurs among cell phenotypes when specific cell markers are considered. Finally, we found various correlations among model parameters which cannot be directly inferred from the available biological data and these dependencies were used to characterize the dynamics of cancer subpopulations during the initial phase of ErbB2⁺ mammary cancer progression.     

A method for quantification of absolute amounts of nucleic acids by (RT)-PCR and a new mathematical model for data analysis

Accurate quantification of nucleic acids by competitive (RT)-PCR requires a valid internal standard, a reference for data normalization and an adequate mathematical model for data analysis. We report here an effective procedure for the generation of homologous RNA internal standards and a strategy for synthesizing and using a reference target RNA in quantification of absolute amounts of nucleic acids. Further, a new mathematical model describing the general kinetic features of competitive PCR was developed. The model extends the validity of quantitative competitive (RT)-PCR beyond the exponential phase. The new method eliminates the errors arising from different amplification efficiencies of the co-amplified sequences and from heteroduplex formation in the system. The high accuracy (relative error <2%) is comparable to the recently developed real time detection 5'-nuclease PCR. Also, corresponding computer software has been devised for practical data analysis.     

Estimating Lymphocyte Division and Death Rates from CFSE Data

The division tracking dye, carboxyfluorescin diacetate succinimidyl ester (CFSE) is currently the most informative labeling technique for characterizing the division history of cells in the immune system. Gett and Hodgkin [Nat. Immunol. 1:239–244, 2000] have pioneered the quantitative analysis of CFSE data. We confirm and extend their data analysis approach using simple mathematical models. We employ the extended Gett and Hodgkin [Nat. Immunol. 1:239–244, 2000] method to estimate the time to first division, the fraction of cells recruited into division, the cell cycle time, and the average death rate from CFSE data on T cells stimulated under different concentrations of IL-2. The same data is also fitted with a simple mathematical model that we derived by reformulating the numerical model of Deenick et al. [J. Immunol. 170:4963–4972, 2003]. By a non-linear fitting procedure we estimate parameter values and confidence intervals to identify the parameters that are influenced by the IL-2 concentration. We obtain a significantly better fit to the data when we assume that the T cell death rate depends on the number of divisions cells have completed. We provide an outlook on future work that involves extending the Deenick et al. [J. Immunol. 170:4963–4972, 2003] model into the classical smith-martin model, and into a model with arbitrary probability distributions for death and division through subsequent divisions.     

High-throughput analysis of growth differences among phage strains

Although methods such as spectrophotometry are useful for identifying growth differences among bacterial strains, it is currently difficult to similarly determine whether bacteriophage strains differ in growth using high throughput methods. Here we use automated spectrophotometry to develop an in vitro method for indirectly distinguishing fitness (growth) differences among virus strains, based on direct measures of their infected bacterial hosts. We used computer simulations of a mathematical model for phage growth to predict which features of bacterial growth curves were best associated with differences in growth among phage strains. We then tested these predictions using the in vitro method to confirm which of the inferred viral growth traits best reflected known fitness differences among genotypes of the RNA phage phi-6, when infecting a Pseudomonas syringae host. Results showed that the inferred phage trait of time-to-extinction (time required to drive bacterial density below detectable optical density) reliably correlated with genotype rankings based on absolute fitness (phage titer per ml). These data suggested that the high-throughput analysis was valuable for identifying growth differences among virus strains, and that the method may be especially useful for high throughput analyses of fitness differences among phage strains cultured and/or evolved in liquid (unstructured) environments.