A Mathematical Model of Liver Cell Aggregation <Emphasis Type="Italic">In Vitro</Emphasis>

The behavior of mammalian cells within three-dimensional structures is an area of intense biological research and underpins the efforts of tissue engineers to regenerate human tissues for clinical applications. In the particular case of hepatocytes (liver cells), the formation of spheroidal multicellular aggregates has been shown to improve cell viability and functionality compared to traditional monolayer culture techniques. We propose a simple mathematical model for the early stages of this aggregation process, when cell clusters form on the surface of the extracellular matrix (ECM) layer on which they are seeded. We focus on interactions between the cells and the viscoelastic ECM substrate. Governing equations for the cells, culture medium, and ECM are derived using the principles of mass and momentum balance. The model is then reduced to a system of four partial differential equations, which are investigated analytically and numerically. The model predicts that provided cells are seeded at a suitable density, aggregates with clearly defined boundaries and a spatially uniform cell density on the interior will form. While the mechanical properties of the ECM do not appear to have a significant effect, strong cell-ECM interactions can inhibit, or possibly prevent, the formation of aggregates. The paper concludes with a discussion of our key findings and suggestions for future work. Current address: Mathematical Biosciences Institute, The Ohio State University, Columbus, OH 43210, USA. Current address: Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, 24-29 St Giles’, Oxford, OX1 3LB, UK.     

Semi‐Markov Models with Phase‐Type Sojourn Distributions

Summary Continuous‐time multistate models are widely used for categorical response data, particularly in the modeling of chronic diseases. However, inference is difficult when the process is only observed at discrete time points, with no information about the times or types of events between observation times, unless a Markov assumption is made. This assumption can be limiting as rates of transition between disease states might instead depend on the time since entry into the current state. Such a formulation results in a semi‐Markov model. We show that the computational problems associated with fitting semi‐Markov models to panel‐observed data can be alleviated by considering a class of semi‐Markov models with phase‐type sojourn distributions. This allows methods for hidden Markov models to be applied. In addition, extensions to models where observed states are subject to classification error are given. The methodology is demonstrated on a dataset relating to development of bronchiolitis obliterans syndrome in post‐lung‐transplantation patients.     

A joint model for longitudinal continuous and time‐to‐event outcomes with direct marginal interpretation

Joint modeling of various longitudinal sequences has received quite a bit of attention in recent times. This paper proposes a so‐called marginalized joint model for longitudinal continuous and repeated time‐to‐event outcomes on the one hand and a marginalized joint model for bivariate repeated time‐to‐event outcomes on the other. The model has several appealing features. It flexibly allows for association among measurements of the same outcome at different occasions as well as among measurements on different outcomes recorded at the same time. The model also accommodates overdispersion. The time‐to‐event outcomes are allowed to be censored. While the model builds upon the generalized linear mixed model framework, it is such that model parameters enjoy a direct marginal interpretation. All of these features have been considered before, but here we bring them together in a unified, flexible framework. The model framework's properties are scrutinized using a simulation study. The models are applied to data from a chronic heart failure study and to a so‐called comet assay, encountered in preclinical research. Almost surprisingly, the models can be fitted relatively easily using standard statistical software.     

Nuclear Stress-Strain State over Micropillars: A Mechanical <i>In silico</i> Study

Cells adapt to their environment and stimuli of different origin. During confined migration through sub-cellular and sub-nuclear pores, they can undergo large strains and the nucleus, the most voluminous and the stiffest organelle, plays a critical role. Recently, patterned microfluidic devices have been employed to analyze the cell mechanical behavior and the nucleus self-deformations. In this paper, we present an in silico model to simulate the interactions between the cell and the underneath microstructured substrate under the effect of the sole gravity. The model lays on mechanical features only and it has the potential to assess the contribution of the nuclear mechanics on the cell global behavior. The cell is constituted by the membrane, the cytosol, the lamina, and the nucleoplasm. Each organelle is described through a constitutive law defined by specific mechanical parameters, and it is composed of a fluid and a solid phase leading to a viscoelastic behavior. Our main objective is to evaluate the influence of such mechanical components on the nucleus behavior. We have quantified the stress and strain distributions in the nucleus, which could be responsible of specific phenomena such as the lamina rupture or the expression of stretch-sensitive proteins.     

Variable selection in Bayesian generalized linear‐mixed models: An illustration using candidate gene case‐control association studies

The problem of variable selection in the generalized linear‐mixed models (GLMMs) is pervasive in statistical practice. For the purpose of variable selection, many methodologies for determining the best subset of explanatory variables currently exist according to the model complexity and differences between applications. In this paper, we develop a “higher posterior probability model with bootstrap” (HPMB) approach to select explanatory variables without fitting all possible GLMMs involving a small or moderate number of explanatory variables. Furthermore, to save computational load, we propose an efficient approximation approach with Laplace's method and Taylor's expansion to approximate intractable integrals in GLMMs. Simulation studies and an application of HapMap data provide evidence that this selection approach is computationally feasible and reliable for exploring true candidate genes and gene–gene associations, after adjusting for complex structures among clusters.     

Modelling climate‐change‐induced nonlinear thresholds in cephalopod population dynamics

A significant global challenge lies in our current inability to anticipate, and therefore prepare for, critical ecological thresholds (i.e. tipping points in ecosystems). This deficit stems largely from an inadequate understanding of the many complex interactions between species and the environment at the ecosystem level, and the paucity of mechanistic models relating environment to population dynamics at the species level. In marine ecosystems, abundant, short‐lived and fast‐growing species such as anchovies or squids, consistently function as ‘keystone’ groups whose population dynamics affect entire ecosystems. Increasing exploitation coupled with climate change impacts has the potential to affect these ecological groups and consequently, the entire marine ecosystem. There are currently very few models that predict the impact of climate change on these keystone groups. Here we use a combination of individual‐based bioenergetics and stage‐structured population models to characterize the fundamental capacity of cephalopods to respond to climate change. We demonstrate the potential for, and mechanisms behind, two unfavourable climate‐change‐induced thresholds in future population dynamics. Although one threshold was the direct consequence of a decrease in incubation time caused by ocean warming, the other threshold was linked to survivorship, implying the possibility of management through a modification of fishing mortality. Additional substantive changes in phenology were also predicted, with a possible loss in population resilience. Our results demonstrate the feasibility of predicting complex nonlinear dynamics with a reasonably simplistic mechanistic model, and highlight the necessity of developing such approaches for other species if attempts to moderate the impact of climate change on natural resources are to be effective.     

不同模型对拟合大兴安岭林火发生与气象因素关系的适用性

选用符合林火发生数据结构的Poisson和零膨胀Poisson(ZIP)模型对大兴安岭林区1980—2005年间林火发生与气象因素关系进行建模分析,并与普通最小二乘回归(ordinary least squares,OLS)方法的结果进行了对比分析.结果表明:OLS模型对研究区域林火发生与气象因素关系的拟合结果较差(R2=0.215);Poisson和ZIP模型的拟合效果较好,具有较好的火灾次数预测能力,且ZIP模型的预测能力高于Poisson模型.运用AIC和Vuong检验方法对Poisson和ZIP模型的拟合水平进行进一步检验,表明ZIP模型的数据拟合度优于Poisson模型.     

Hotspots of uncertainty in land‐use and land‐cover change projections: a global‐scale model comparison

Model‐based global projections of future land‐use and land‐cover (LULC) change are frequently used in environmental assessments to study the impact of LULC change on environmental services and to provide decision support for policy. These projections are characterized by a high uncertainty in terms of quantity and allocation of projected changes, which can severely impact the results of environmental assessments. In this study, we identify hotspots of uncertainty, based on 43 simulations from 11 global‐scale LULC change models representing a wide range of assumptions of future biophysical and socioeconomic conditions. We attribute components of uncertainty to input data, model structure, scenario storyline and a residual term, based on a regression analysis and analysis of variance. From this diverse set of models and scenarios, we find that the uncertainty varies, depending on the region and the LULC type under consideration. Hotspots of uncertainty appear mainly at the edges of globally important biomes (e.g., boreal and tropical forests). Our results indicate that an important source of uncertainty in forest and pasture areas originates from different input data applied in the models. Cropland, in contrast, is more consistent among the starting conditions, while variation in the projections gradually increases over time due to diverse scenario assumptions and different modeling approaches. Comparisons at the grid cell level indicate that disagreement is mainly related to LULC type definitions and the individual model allocation schemes. We conclude that improving the quality and consistency of observational data utilized in the modeling process and improving the allocation mechanisms of LULC change models remain important challenges. Current LULC representation in environmental assessments might miss the uncertainty arising from the diversity of LULC change modeling approaches, and many studies ignore the uncertainty in LULC projections in assessments of LULC change impacts on climate, water resources or biodiversity.     

A Bayesian Chi‐Squared Goodness‐of‐Fit Test for Censored Data Models

Summary We propose a Bayesian chi‐squared model diagnostic for analysis of data subject to censoring. The test statistic has the form of Pearson's chi‐squared test statistic and is easy to calculate from standard output of Markov chain Monte Carlo algorithms. The key innovation of this diagnostic is that it is based only on observed failure times. Because it does not rely on the imputation of failure times for observations that have been censored, we show that under heavy censoring it can have higher power for detecting model departures than a comparable test based on the complete data. In a simulation study, we show that tests based on this diagnostic exhibit comparable power and better nominal Type I error rates than a commonly used alternative test proposed by Akritas (1988, Journal of the American Statistical Association 83, 222–230). An important advantage of the proposed diagnostic is that it can be applied to a broad class of censored data models, including generalized linear models and other models with nonidentically distributed and nonadditive error structures. We illustrate the proposed model diagnostic for testing the adequacy of two parametric survival models for Space Shuttle main engine failures.     

Long-range transport of beech (<Emphasis Type="Italic">Fagus sylvatica</Emphasis> L.) pollen to Catalonia (north-eastern Spain)

Local and long-range transport of beech (Fagus sylvatica) pollen was analysed by using 23-year data (1983-2007) at six stations in Catalonia, Spain, and numerical simulations. Back trajectories and synoptic meteorology indicated a consistent north European provenance during beech pollen peak days. Specifically, the area from northern Italy to central Germany was the most probable source, as indicated by a source-receptor model based on back trajectories. For the event with the highest pollen levels (17 May 2004), back trajectories indicated a source in the Vosges (NE France) and the Schwarzwald (SW Germany) regions. By applying a mesoscale model (MM5) to this event, pollen transport could be further refined, allowing its entrance to Catalonia through the lower easternmost pass of the Pyrenees (the Alberes pass, 500 m a.s.l.) to be described. Hourly counts of Fagus pollen allowed the timing of pollen arrival during this episode to be matched with the model results regarding the above-mentioned passage. This study may help to interpret some results of modern beech genetic diversity and contribute to the understanding of paleopalynological records by taking long-range transport into consideration.     

SIRT2‐knockdown rescues GARS‐induced Charcot‐Marie‐Tooth neuropathy

Charcot‐Marie‐Tooth disease is the most common inherited peripheral neuropathy. Dominant mutations in the glycyl‐tRNA synthetase (GARS) gene cause peripheral nerve degeneration and lead to CMT disease type 2D. The underlying mechanisms of mutations in GARS (GARS^CMT2D) in disease pathogenesis are not fully understood. In this study, we report that wild‐type GARS binds the NAD⁺‐dependent deacetylase SIRT2 and inhibits its deacetylation activity, resulting in the acetylated α‐tubulin, the major substrate of SIRT2. The catalytic domain of GARS tightly interacts with SIRT2, which is the most CMT2D mutation localization. However, CMT2D mutations in GARS cannot inhibit SIRT2 deacetylation, which leads to a decrease of acetylated α‐tubulin. Genetic reduction of SIRT2 in the Drosophila model rescues the GARS‐induced axonal CMT neuropathy and extends the life span. Our findings demonstrate the pathogenic role of SIRT2‐dependent α‐tubulin deacetylation in mutant GARS‐induced neuropathies and provide new perspectives for targeting SIRT2 as a potential therapy against hereditary axonopathies.     

Allosteric changes in protein structure computed by a simple mechanical model: hemoglobin T<-->R2 transition

Information on protein dynamics has been usually inferred from spectroscopic studies of parts of the proteins, or indirectly from the comparison of the conformations assumed in the presence of different substrates or ligands. While molecular simulations also provide information on protein dynamics, they usually suffer from incomplete sampling of conformational space, and become prohibitively expensive when exploring the collective dynamics of large macromolecular structures. Here, we explore the dynamics of a well-studied allosteric protein, hemoglobin (Hb), to show that a simple mechanical model based on Gaussian fluctuations of residues can efficiently predict the transition between the tense (T, unliganded) and relaxed (R or R2, O(2) or CO-bound) forms of Hb. The passage from T into R2 is shown to be favored by the global mode of motion, which, in turn is driven by entropic effects. The major difference between the dynamics of the T and R2 forms is the loss of the hinge-bending role of alpha(1)-beta(2) (or alpha(2)-beta(1)) interfacial residues at alpha Phe36-His45 and beta Thr87-Asn102 in the R2 form, which implies a decreased cooperativity in the higher affinity (R2) form of Hb, consistent with many experimental studies. The involvement of the proximal histidine beta His92 in this hinge region suggests that the allosteric propagation of the local structural changes (induced upon O(2) binding) into global ones occur via hinge regions. This is the first demonstration that there is an intrinsic tendency of Hb to undergo T-->R2 transition, induced by purely elastic forces of entropic origin that are uniquely defined for the particular contact topology of the T form.     

Kinetic model of imidazologlycerol-phosphate synthetase from <Emphasis Type="Italic">Escherichia coli</Emphasis>

Based on the available experimental data, we developed a kinetic model of the catalytic cycle of imidazologlycerol-phosphate synthetase from Escherichia coli accounting for the synthetase and glutaminase activities of the enzyme. The rate equations describing synthetase and glutaminase activities of imidazologlycerol-phosphate synthetase were derived from this catalytic cycle. Using the literature data, we evaluated all kinetic parameters of the rate equations characterizing individually synthetase and glutaminase activities as well as the contribution of each activity depending on concentration of the substrates, products, and effectors. As shown, in the presence of 5 -phosphoribosylformimino-5-aminoimidazolo-4-carboxamideribonucleotide (ProFAR) and imidazologlycerol phosphate (IGP) glutaminase activity dominates over synthetase activity at sufficiently low concentrations of 5 -phosphoribulosylformimino-5-aminoimidazolo-4-carboxamideribonucleotide (PRFAR). Increased PRFAR concentrations resulted in decreased contribution of glutaminase activity and, consequently, increased the contribution of synthetase activity in the enzyme functioning.     

Light matters: testing the “Light Environment Hypothesis” under intra‐ and interspecific contexts

The “Light Environment Hypothesis” (LEH) proposes that evolution of interspecific variation in plumage color is driven by variation in light environments across habitats. If ambient light has the potential to drive interspecific variation, a similar influence should be expected for intraspecific recognition, as color signals are an adaptive response to the change in ambient light levels in different habitats. Using spectrometry, avian‐appropriate models of vision, and phylogenetic comparative methods, I quantified dichromatism and tested the LEH in both intra‐ and interspecific contexts in 33 Amazonian species from the infraorder Furnariides living in environments with different light levels. Although these birds are sexually monochromatic to humans, 81.8% of the species had at least one dichromatic patch in their plumage, mostly from dorsal areas, which provides evidence for a role for dichromatism in sex recognition. Furthermore, birds from habitats with high levels of ambient light had higher dichromatism levels, as well as brighter, more saturated, and more diverse plumages, suggesting that visual communication is less constrained in these habitats. Overall, my results provide support for the LEH and suggest that ambient light plays a major role in the evolution of color signals in this group of birds in both intra‐ and interspecific contexts. Additionally, plumage variation across light environments for these drab birds highlights the importance of considering ambient light and avian‐appropriate models of vision when studying the evolution of color signals in birds.     

Herbivory and population dynamics of invasive and native <Emphasis Type="Italic">Lespedeza</Emphasis>

Some exotic plants are able to invade habitats and attain higher fitness than native species, even when the native species are closely related. One explanation for successful plant invasion is that exotic invasive plant species receive less herbivory or other enemy damage than native species, and this allows them to achieve rapid population growth. Despite many studies comparing herbivory and fitness of native and invasive congeners, none have quantified population growth rates. Here, we examined the contribution of herbivory to the population dynamics of the invasive species, Lespedeza cuneata, and its native congener, L. virginica, using an herbivory reduction experiment. We found that invasive L. cuneata experienced less herbivory than L. virginica. Further, in ambient conditions, the population growth rate of L. cuneata (λ = 20.4) was dramatically larger than L. virginica (λ = 1.7). Reducing herbivory significantly increased fitness of only the largest L. virginica plants, and this resulted in a small but significant increase in its population growth rate. Elasticity analysis showed that the growth rate of these species is most sensitive to changes in the seed production of small plants, a vital rate that is relatively unaffected by herbivory. In all, these species show dramatic differences in their population growth rates, and only 2% of that difference can be explained by their differences in herbivory incidence. Our results demonstrate that to understand the importance of consumers in explaining the relative success of invasive and native species, studies must determine how consumer effects on fitness components translate into population-level consequences. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.