Actin-Myosin Spatial Patterns from a Simplified Isotropic Viscoelastic Model

F-actin networks are involved in cell mechanical processes ranging from motility to endocytosis. The mesoscale architecture of assemblies of individual F-actin polymers that gives rise to micrometer-scale rheological properties is poorly understood, despite numerous in vivo and vitro studies. In vitro networks have been shown to organize into spatial patterns when spatially confined, including dense spherical shells inside spherical emulsion droplets. Here we develop a simplified model of an isotropic, compressible, viscoelastic material continually assembling and disassembling. We demonstrate that spherical shells emerge naturally when the strain relaxation rate (corresponding to internal network reorganization) is slower than the disassembly rate (corresponding to F-actin depolymerization). These patterns are consistent with recent experiments, including a collapse of shells to a central high-density focus of F-actin when either assembly or disassembly is reduced with drugs. Our results demonstrate how complex spatio-temporal patterns can emerge without spatially distributed force generation, polar alignment of F-actin polymers, or spatially nonuniform regulation of F-actin by upstream biochemical networks.     

Actin-Myosin Spatial Patterns from a Simplified Isotropic Viscoelastic Model

F-actin networks are involved in cell mechanical processes ranging from motility to endocytosis. The mesoscale architecture of assemblies of individual F-actin polymers that gives rise to micrometer-scale rheological properties is poorly understood, despite numerous in vivo and vitro studies. In vitro networks have been shown to organize into spatial patterns when spatially confined, including dense spherical shells inside spherical emulsion droplets. Here we develop a simplified model of an isotropic, compressible, viscoelastic material continually assembling and disassembling. We demonstrate that spherical shells emerge naturally when the strain relaxation rate (corresponding to internal network reorganization) is slower than the disassembly rate (corresponding to F-actin depolymerization). These patterns are consistent with recent experiments, including a collapse of shells to a central high-density focus of F-actin when either assembly or disassembly is reduced with drugs. Our results demonstrate how complex spatio-temporal patterns can emerge without spatially distributed force generation, polar alignment of F-actin polymers, or spatially nonuniform regulation of F-actin by upstream biochemical networks.     

Ten Years of the Relative Risk Model and Regional Scale Ecological Risk Assessment

It has been 10 years since the publication of the relative risk model (RRM) for regional scale ecological risk assessment. The approach has since been used successfully for a variety of freshwater, marine, and terrestrial environments in North America, South America, and Australia. During this period the types of stressors have been expanded to include more than contaminants. Invasive species, habitat loss, stream alteration and blockage, temperature, change in land use, and climate have been incorporated into the assessments. Major developments in the RRM have included the extensive use of geographical information systems, uncertainty analysis using Monte Carlo techniques, and its application to retrospective assessments to determine causation. The future uses of the RRM include assessments for forestry and conservation management, an increasing use in invasive species evaluation, and in sustainability. Developments in risk communication, the use of Bayesian approaches, and in uncertainty analyses are on the horizon.     

A Regional Ecological Risk Assessment of the Kaipara Harbour,New Zealand,Using a Relative Risk Model

A regional ecological risk assessment was conducted for the Kaipara Harbour catchment in New Zealand. The Relative Risk Model was used to prioritize management of the sources of stress and habitats of concern in the basin. Semi-structured interviews with 25 representative stakeholders were conducted to obtain the resource-users’ perspectives and to identify the regional stressor sources and receptor habitat data for the model. For this risk analysis we divided the catchment into nine ecological districts. Mixed-methodological approaches including content analysis, geospatial analysis, and source documentation were used to categorize source and habitat rankings, based on the relative abundance of each in the nine ecological districts. Risk characterization revealed that fishing pressure and tidal energy pose the largest sources of perceived risk to the catchment; shellfish and Maui dolphin habitats are the receptors estimated to be at greatest risk; and the Kaipara and Rodney ecological districts are the sub-regions estimated with the greatest combined risk. A Monte Carlo analysis confirmed the source inputs and revealed greater uncertainty than the estimated habitat input results. The results of this assessment can be used by policy-makers, conservation groups, and municipalities to inform the future management efforts in the harbor and catchment.     

Asymptotic Relative Efficiency of Some Jackknife Estimators of a Common Odds Ratio

In the situation of several 2 × 2 tables the asymptotic relative efficiencies of certain jackknife estimators of a common odds ratio are investigated in the case that the number of tables is fixed while the sample sizes within each table tend to infinity. The estimators show very good results over a wide range of parameters. Some situations in which the estimators have low asymptotic relative efficiency are pointed out:.     

A Regional Multiple Stressor Risk Assessment of the Codorus Creek Watershed Applying the Relative Risk Model

The relative risk model (RRM) used in Port Valdez, AK, and in Oregon's Willamette/McKenzie Watershed was applied to the Codorus Creek Watershed in south central Pennsylvania. The assessment evaluated the relative risk model for its applicability for ranking ecological risks within the Codorus Creek Watershed. The Codorus Creek Watershed approach included ranking stressors and habitats for regions within the watershed. Geographical Information Systems were vital in compiling and comparing stressor and habitat spatial data from regions in the watershed. The risk of ecological impacts to degrade assessment endpoints were calculated and ranked by quantitatively determining the interactions of the stressors and habitats as defined in the conceptual site model. Uncertainty assessment was conducted and the impact upon the relative ranks and risk conclusions evaluated. To determine regional risks, risk management information was gathered identifying areas to be protected, areas of high stress, and areas where additional information is needed. The results supported the applicability of the RRM and suggested areas and stressors for restoration efforts in the Codorus Creek Watershed. Two critical sets of conclusions were drawn from the assessment. First, in the Codorus Creek Watershed, the most significant stressor is agriculture land use, the most significantly impacted endpoint is water quality, and the most vulnerable habitats are those for macroinvertebrates and warm-water fish. Second, this risk assessment demonstrates the feasibility of using the RRM for assessing risk from multiple stressors on habitats with multiple assessment endpoints in an eastern watershed.     

On the Asymptotic Relative Efficiency of the Mantel-Haenszel Test

The Mantel-Haenszel test is optimal when the odds ratio is constant. This paper investigates the effects of departures from the assumption of a constant odds ratio on the behavior of the Mantel-Haenzel test. A simple approximation is proposed for the non-null distribution of the test statistic. Based on this approximation, the asymptotic relative efficiency of the Mantel-Haenszel test, compared to the overall χ² test for no partial association, is calculated. For the case of 2 strata, it is shown that the Mantel-Haenszel test is efficient as long as the logarithms of the odds ratios are of the same sign and their absolute values exceed 1.     

一个具有随机传染率艾滋病模型的渐近行为(英文)

研究了艾滋病传播的随机模型.我们给出了一个条件,在这个条件下,无论环境干扰有多强,随机Logistic方程的平凡解是渐近稳定的.我们的结论与Roberts和Saha的结论构成对艾滋病传播模型的一个完整的分析.     

一类具阶段结构的捕食者-食饵模型的渐进性质

研究了一类具阶段结构的捕食者-食饵模型的渐近性质．文中假设由幼年阶段转化为成年阶段的转化率依赖于幼年个体数量．建立了捕食种群一致持续生存与绝灭的条件．证明了稳定的周期解的存在性．     

The Relative Power of Two Asymptotic Multivariate Tests for Homogeneity in a Contingency Table

In a three way contingency table two multivariate tests for homogeneity have been proposed by the author (1983) a the “catanova” test, which is a trace “metric” test and b the “multinova” test which is determinant based. Both tests are asymptotically distributed as chi-square. In this paper, the power values of the tests are compared and conditions are given for preference of each test.     

Confidence Intervals for the Relative Risk Ratio Parameter from Survival Data Under a Random Censorship Model in Biomedical and Epidemiologic Studies (By Simulation)

The present paper reports the results of a Monte Carlo simulation study to examine the performance of several approximate confidence intervals for the Relative Risk Ratio (RRR) parameter in an epidemiologic study, involving two groups of individuals. The first group consists of n₁ individuals, called the experimental group, who are exposed to some carcinogen, say radiation, whose effect on the incidence of some form of cancer, say skin cancer, is being investigated. The second group consists of n₂ individuals (called the control group) who are not exposed to the carcinogen. Two cases are considered in which the life times (or time to cancer) in the two groups follow (i) the exponential and (ii) the Weibull distributions. The case when the life times follow a Rayleigh distribution follows as a particular case. A general random censorship model is considered in which the life times of the individuals are censored on the right by random censoring times following (i) the exponential and (ii) the Weibull distributions. The Relative Risk Ratio parameter in the study is defined as the ratio of the hazard rates in the two distributions of the times to cancer. Approximate confidence intervals are constructed for the RRR parameter using its maximum likelihood estimator (m.l.e) and several other methods, including a method due to FIELLER. SPROTT'S (1973) and Cox's (1953) suggestions, as well as the Box-Cox (1964) transformation, are also utilized to construct approximate confidence intervals. The performance of these confidence intervals in small samples is investigated by means of some Monte Carlo simulations based on 500 random samples. Our simulation study indicates that many of these confidence intervals perform quite well in samples of size 10 and 15, in terms of the coverage probability and expected length of the interval.     

Model-Based Tumor Growth Dynamics and Therapy Response in a Mouse Model of De Novo Carcinogenesis

Tumorigenesis is a complex, multistep process that depends on numerous alterations within the cell and contribution from the surrounding stroma. The ability to model macroscopic tumor evolution with high fidelity may contribute to better predictive tools for designing tumor therapy in the clinic. However, attempts to model tumor growth have mainly been developed and validated using data from xenograft mouse models, which fail to capture important aspects of tumorigenesis including tumor-initiating events and interactions with the immune system. In the present study, we investigate tumor growth and therapy dynamics in a mouse model of de novo carcinogenesis that closely recapitulates tumor initiation, progression and maintenance in vivo. We show that the rate of tumor growth and the effects of therapy are highly variable and mouse specific using a Gompertz model to describe tumor growth and a two-compartment pharmacokinetic/ pharmacodynamic model to describe the effects of therapy in mice treated with 5-FU. We show that inter-mouse growth variability is considerably larger than intra-mouse variability and that there is a correlation between tumor growth and drug kill rates. Our results show that in vivo tumor growth and regression in a double transgenic mouse model are highly variable both within and between subjects and that mathematical models can be used to capture the overall characteristics of this variability. In order for these models to become useful tools in the design of optimal therapy strategies and ultimately in clinical practice, a subject-specific modelling strategy is necessary, rather than approaches that are based on the average behavior of a given subject population which could provide erroneous results.     

Gene Systems Network Inferred from Expression Profiles in Hepatocellular Carcinogenesis by Graphical Gaussian Model

Hepatocellular carcinoma (HCC) in a liver with advanced-stage chronic hepatitis C (CHC) is induced by hepatitis C virus, which chronically infects about 170 million people worldwide. To elucidate the associations between gene groups in hepatocellular carcinogenesis, we analyzed the profiles of the genes characteristically expressed in the CHC and HCC cell stages by a statistical method for inferring the network between gene systems based on the graphical Gaussian model. A systematic evaluation of the inferred network in terms of the biological knowledge revealed that the inferred network was strongly involved in the known gene-gene interactions with high significance Open image in new window , and that the clusters characterized by different cancer-related responses were associated with those of the gene groups related to metabolic pathways and morphological events. Although some relationships in the network remain to be interpreted, the analyses revealed a snapshot of the orchestrated expression of cancer-related groups and some pathways related with metabolisms and morphological events in hepatocellular carcinogenesis, and thus provide possible clues on the disease mechanism and insights that address the gap between molecular and clinical assessments.     

Ecological Risk Assessment of China's Freshwater Ecosystems Applying the Relative Risk Model: Toward an Ecosystem-Based Water Management in China

The relative risk model (RRM) was applied to evaluate the ecological risk characterization of the freshwater ecosystems in China, from both overall and region-specific levels. Ten large-scale river basins (further broken into 15 risk regions) in China were chosen as the study objects; 10 sources, two habitats, and seven endpoints were identified as risk components. The results reveal the status of ecosystem conditions, key ecological risk issues, and the spatial heterogeneity of the freshwater ecosystems in China. The policy implications for the ecosystem-based water management contained in the results are discussed. The results obtained in this article provide a deeper understanding of the ecological risk characterization of the freshwater ecosystems in China, and aid in promoting the applications of the RRM as the tool for ecosystem-based water management.     

Effects of Exogenous Electromagnetic Fields on a Simplified Ion Channel Model

In this paper, we calculate the effect of an exogenous perturbation (an electromagnetic field [EMF] oscillating in the range of microwave frequencies in the range of 1 GHz) on the flux of two ion species through a cylindrical ion channel, implementing a continuous model, the Poisson–Smoluchowski system of equations, to study the dynamics of charged particle density inside the channel. The method was validated through comparison with Brownian dynamics simulations, supposed to be more accurate but computationally more demanding, obtaining a very good agreement. No EMF effects were observed for low field intensities below the level for thermal effects, as the highly viscous regime and the simplicity of the channel do not exhibit resonance phenomena. For high intensities of the external field (>10⁵ V/m), we observed slightly different behavior of ion concentration oscillations and ion currents as a function of EMF orientation with respect to the channel axis.