Control of stress propagation in the cytoplasm by prestress and loading frequency

One fundamental question in cell biology is how mechanical stresses are distributed inside the cytoplasm. Recently we have developed a synchronous detection approach to map cytoplasmic displacements and stresses using yellow fluorescent protein tagged mitochondria as fiducial markers of the cytoskeleton (CSK) in response to a localized load applied via an RGD-coated magnetic bead (7). We have shown that stresses are propagated to remote sites in the cytoplasm, a finding that contradicts continuum model predictions. Here we show that long distance force propagation in the cytoplasm was abolished when the contractile prestress in the CSK was lowered by relaxing agents and enhanced when the prestress was increased by contractile agonists. Surprisingly, when the loading frequency was varied from 0.03 Hz to 30 Hz, the total area of induced displacements (an index of the extent of stress propagation) first increased with loading frequency and then decreased with loading frequency. These results demonstrate that the long distance force propagation in living adherent cells might be controlled by the level of contractile prestress in the CSK and by the loading frequency.     

Effect of plant interaction on wind-induced crop motion

Plant motion due to wind affects plant growth, a phenomenon called thigmomorphogenesis. Despite intensive studies of the turbulence over plant canopies, the study of plant motion induced by wind has often been limited to individual trees or cereal plants. Few models of global canopy motions are available. Moreover the numerical analysis of models that are based on individual stems becomes time consuming when dealing with crops. A model of motion within the canopies is proposed here using a wave propagation equation within a homogenized continuous medium, and a forcing function representing turbulent gusts advected over the canopy. This model is derived from a discrete model of a set of plant shoots represented as individual oscillators, including elastic contacts between shoots. Such contacts induce nonlinearities into the wave equation. A new experimental method to measure stem dynamical properties and elastic collision properties is presented with an illustration on alfalfa stems. Results obtained modeling plant motions in an alfalfa crop are presented.     

Modeling of the detachment of a molecule from a surface: illustration of the "Bell-Evans effect"

This article deals with the modeling of the detachment of a molecule initially adsorbed on a surface and submitted to an external force whose strength increases with time. By means of an atomic force microscope (AFM), it is possible to measure the force when the molecule separates from the substrate. However, it is known that this force depends to a large extend on the rate at which the pulling force is applied ("Bell-Evans effect"). Two models are described to illustrate this behavior. First, a random walk approach is suggested to reveal the fundamental principle of the escape over a time-dependent energy barrier. Second, a multi bead-and-spring model is proposed to mimic the AFM experiment and numerical simulations, based on Brownian dynamics, are performed.     

干旱半干旱区斑块状植被格局形成模拟研究进展

斑块状植被格局是世界上干旱半干旱区常见的景观类型,它们的形成、组成结构和演替过程研究,对于揭示区域生态系统变化的关键过程具有重要意义。鉴于基于地面调查和遥感技术的方法难以全面刻画斑块状植被格局的形成过程及机制,借助于模型模拟成为解决这一问题的有效方法。自20世纪90年代初至今,斑块状植被格局形成的连续和离散模拟研究不断涌现,然而,连续模拟侧重于植被格局形成的一般机理,缺乏与现实格局的对比和验证,离散模拟单元选择与规则制定等仍需不断研究。在简要回顾斑块状格局形成的反馈机制基础上,重点综述了斑块状植被格局形成的连续和离散模拟的最新研究进展,并指出了现有研究的不足。干旱半干旱区小尺度上植物和水的反馈作用决定了大尺度的斑块状植被格局,充分揭示植被-土壤水分相互作用机理是模型模拟研究的关键,放牧强度和降水格局等外部环境对干旱半干旱区斑块状植被格局特征具有重要影响。在未来研究中,应加强模型模拟结果与实际观测的植被格局比较和验证,重视局域环境条件、生态系统功能在模型中的表达,构建综合连续和离散模型各自优点的混合模型,注重斑块状植被格局形成过程中的标准子模型及模型开发和集成平台的研发,同时强调面向格局模拟和构建空间显式的斑块状植被格局形成模型。     

Theoretical modeling of mechanical homeostasis of a mammalian cell under gravity-directed vector

Translocation of dense nucleus along gravity vector initiates mechanical remodeling of a eukaryotic cell. In our previous experiments, we quantified the impact of gravity vector on cell remodeling by placing an MC3T3-E1 cell onto upward (U)-, downward (D)-, or edge-on (E)- orientated substrate. Our experimental data demonstrate that orientation dependence of nucleus longitudinal translocation is positively correlated with cytoskeletal (CSK) remodeling of their expressions and structures and also is associated with rearrangement of focal adhesion complex (FAC). However, the underlying mechanism how CSK network and FACs are reorganized in a mammalian cell remains unclear. In this paper, we developed a theoretical biomechanical model to integrate the mechanosensing of nucleus translocation with CSK remodeling and FAC reorganization induced by a gravity vector. The cell was simplified as a nucleated tensegrity structure in the model. The cell and CSK filaments were considered to be symmetrical. All elements of CSK filaments and cytomembrane that support the nucleus were simplified as springs. FACs were simplified as an adhesion cluster of parallel bonds with shared force. Our model proposed that gravity vector-directed translocation of the cell nucleus is mechanically balanced by CSK remodeling and FAC reorganization induced by a gravitational force. Under gravity, dense nucleus tends to translocate and exert additional compressive or stretching force on the cytoskeleton. Finally, changes of the tension force acting on talin by microfilament alter the size of FACs. Results from our model are in qualitative agreement with those from experiments.     

Joint regression analysis of correlated data using Gaussian copulas

Summary .  This article concerns a new joint modeling approach for correlated data analysis. Utilizing Gaussian copulas, we present a unified and flexible machinery to integrate separate one-dimensional generalized linear models (GLMs) into a joint regression analysis of continuous, discrete, and mixed correlated outcomes. This essentially leads to a multivariate analogue of the univariate GLM theory and hence an efficiency gain in the estimation of regression coefficients. The availability of joint probability models enables us to develop a full maximum likelihood inference. Numerical illustrations are focused on regression models for discrete correlated data, including multidimensional logistic regression models and a joint model for mixed normal and binary outcomes. In the simulation studies, the proposed copula-based joint model is compared to the popular generalized estimating equations, which is a moment-based estimating equation method to join univariate GLMs. Two real-world data examples are used in the illustration.     

An extension of the Cormack-Jolly-Seber model for continuous covariates with application to Microtus pennsylvanicus

Recent developments in the Cormack-Jolly-Seber (CJS) model for analyzing capture-recapture data have focused on allowing the capture and survival rates to vary between individuals. Several methods have been developed in which capture and survival are functions of auxiliary variables that may be discrete, constant over time, or apply to the population as a whole, but the problem has not been solved for continuous covariates that vary with both time and individual. This article proposes a new method to handle such covariates by modeling changes over time via a diffusion process and using logistic functions to link the variable to the CJS capture and survival rates. Bayesian methods are used to estimate the model parameters. The method is applied to study the effect of body mass on the survival of the North American meadow vole, Microtus pennsylvanicus.     

Divided medium-based model for analyzing the dynamic reorganization of the cytoskeleton during cell deformation

Cell deformability and mechanical responses of living cells depend closely on the dynamic changes in the structural architecture of the cytoskeleton (CSK). To describe the dynamic reorganization and the heterogeneity of the prestressed multi-modular CSK, we developed a two-dimensional model for the CSK which was taken to be a system of tension and compression interactions between the nodes in a divided medium. The model gives the dynamic reorganization of the CSK consisting of fast changes in connectivity between nodes during medium deformation and the resulting mechanical behavior is consistent with the strain-hardening and prestress-induced stiffening observed in cells in vitro. In addition, the interaction force networks which occur and balance to each other in the model can serve to identify the main CSK substructures: cortex, stress fibers, intermediate filaments, microfilaments, microtubules and focal adhesions. Removing any of these substructures results in a loss of integrity in the model and a decrease in the prestress and stiffness, and suggests that the CSK substructures are highly interdependent. The present model may therefore provide a useful tool for understanding the cellular processes involving CSK reorganization, such as mechanotransduction, migration and adhesion processes.     

Multi-Formalism Modelling and Simulation: Application to Cardiac Modelling

Cardiovascular modelling has been a major research subject for the last decade. Different cardiac models have been developed at a cellular level as well as at the whole organ level. Most of these models are defined by a comprehensive cellular modelling using continuous formalisms or by a tissue-level modelling often based on discrete formalisms. Nevertheless, both views still suffer from difficulties that reduce their clinical applications: the first approach requires heavy computational resources while the second one is not able to reproduce certain pathologies. This paper presents an original methodology trying to gather advantages from both approaches, by means of a hybrid model mixing discrete and continuous formalisms. This method has been applied to define a hybrid model of cardiac action potential propagation on a 2D grid of endocardial cells, combining cellular automata and a set of cells defined by the Beeler-Reuter model. For simulations under physiological and ischemic conditions, results show that the action potential propagation as well as electrogram reconstructions are consistent with clinical diagnosis. Finally, the advantage of the proposed approach is discussed within the frame of cardiac modelling and simulation.     

A Computer Model of Engineered Cardiac Monolayers

Engineered monolayers created using microabrasion and micropatterning methods have provided a simplified in vitro system to study the effects of anisotropy and fiber direction on electrical propagation. Interpreting the behavior in these culture systems has often been performed using classical computer models with continuous properties. However, such models do not account for the effects of random cell shapes, cell orientations, and cleft spaces inherent in these monolayers on the resulting wavefront conduction. This work presents a novel methodology for modeling a monolayer of cardiac tissue in which the factors governing cell shape, cell-to-cell coupling, and degree of cleft space are not constant but rather are treated as spatially random with assigned distributions. This modeling approach makes it possible to simulate wavefront propagation in a manner analogous to performing experiments on engineered monolayer tissues. Simulated results are compared to previously published measured data from monolayers used to investigate the role of cellular architecture on conduction velocities and anisotropy ratios. We also present an estimate for obtaining the electrical properties from these networks and demonstrate how variations in the discrete cellular architecture affect the macroscopic conductivities. The simulations support the common assumption that under normal ranges of coupling strength, tissues with relatively uniform distributions of cell shapes and connectivity can be represented using continuous models with conductivities derived from random discrete cellular architecture using either global or local estimates. The results also reveal that in the presence of abrupt changes in cell orientation, local estimates of tissue properties predict smoother changes in conductivity that may not adequately predict the discrete nature of propagation at the transition sites.     

Sampling Animal Movement Paths Causes Turn Autocorrelation

Animal movement models allow ecologists to study processes that operate over a wide range of scales. In order to study them, continuous movements of animals are translated into discrete data points, and then modelled as discrete models. This discretization can bias the representation of the movement path. This paper shows that discretizing correlated random movement paths creates a biased path by creating correlations between successive turning angles. The discretization also biases statistical tests for correlated random walks (CRW) and causes an overestimate in distances travelled; a correction is given for these biases. This effect suggests that there is a natural scale to CRWs, but that distance-discretized CRWs are in a sense, scale invariant. Perhaps a new null model for continuous movement paths is needed. Authors need to be aware of the biases caused by discretizing correlated random walks, and deal with them appropriately.     

Investigation of Combining Plant Genotypic Values and Molecular Marker Information for Constructing Core Subsets

In the present study, a strategy was proposed for constructing plant core subsets by clusters based on the combination of continuous data for genotypic values and discrete data for molecular marker InformaUon. A mixed linear model approach was used to predict genotyplc values for eliminating the environment effect. The ＂mixed genetic distance＂ was designed to solve the difficult problem of combining continuous and discrete data to construct a core subset by cluster. Four commonly used genetic distances for continuous data （Euclidean distance, standardized Euclidean distance, city block distance, and Mahalanobls distance） were used to assess the validity of the conUnuous data part of the mixed genetic distance; three commonly used genetic distances for discrete data （cosine distance, correlaUon distance, and Jaccard distance） were used to assess the validity of the discrete data part of the mixed genetic distance, A rice germplasm group with eight quantitative traits and information for 60 molecular markers was used to evaluate the validity of the new strategy. The results suggest that the validity of both parts of the mixed geneUc distance are equal to or higher than the common geneUc distance. The core subset constructed on the basis of a combination of data for genotyplc values and molecular marker information was more representative than that constructed on the basis of data from genotypic values or molecular marker informaUon alone. Moreover, the strategy of using combined data was able to treat dominant marker informaUon and could combine any other continuous data and discrete data together to perform cluster to construct a plant core subset.     

Invited review: engineering approaches to cytoskeletal mechanics.

An outstanding problem in cell biology is how cells sense mechanical forces and how those forces affect cellular functions. Various biophysical and biochemical mechanisms have been invoked to answer this question. A growing body of evidence indicates that the deformable cytoskeleton (CSK), an intracellular network of interconnected filamentous biopolymers, provides a physical basis for transducing mechanical signals into biochemical signals. Therefore, to understand how mechanical forces regulate cellular functions, it is important to know how cells respond to changes in the CSK force balance and to identify the underlying mechanisms that control transmission of mechanical forces throughout the CSK and bring it to equilibrium. Recent developments of new experimental techniques for measuring cell mechanical properties and novel theoretical models of cellular mechanics make it now possible to identify and quantitate the contributions of various CSK structures to the overall balance of mechanical forces in the cell. This review focuses on engineering approaches that have been used in the past two decades in studies of the mechanics of the CSK.     

Longitudinal profiling of health care units based on continuous and discrete patient outcomes

Monitoring health care quality involves combining continuous and discrete outcomes measured on subjects across health care units over time. This article describes a Bayesian approach to jointly modeling multilevel multidimensional continuous and discrete outcomes with serial dependence. The overall goal is to characterize trajectories of traits of each unit. Underlying normal regression models for each outcome are used and dependence among different outcomes is induced through latent variables. Serial dependence is accommodated through modeling the pairwise correlations of the latent variables. Methods are illustrated to assess trends in quality of health care units using continuous and discrete outcomes from a sample of adult veterans discharged from 1 of 22 Veterans Integrated Service Networks with a psychiatric diagnosis between 1993 and 1998.     

Durotaxis as an elastic stability phenomenon

It is well documented that directed motion of cells is influenced by substrate stiffness. When cells are cultured on a substrate of graded stiffness, they tend to move from softer to stiffer regions--a process known as durotaxis. In this study, we propose a mathematical model of durotaxis described as an elastic stability phenomenon. We model the cytoskeleton (CSK) as a planar system of prestressed elastic line elements representing actin stress fibers (SFs), which are anchored via focal adhesions (FAs) at their end points to an elastic substrate of variable stiffness. The prestress in the SFs exerts a pulling force on FAs reducing thereby their chemical potential. Using Maxwell's global stability criterion, we obtain that the model stability increases as it is moved from a softer towards a stiffer region of the substrate. Numerical simulations reveal that elastic stability of SFs has a predominantly stabilizing effect, greater than the stabilizing effect of decreasing chemical potential of FAs. This is a novel finding which indicates that elasticity of the CSK plays an important role in cell migration and mechanosensing in general.     

Long-distance propagation of forces in a cell

A fundamental question in the field of mechanotransduction is how forces propagate inside a cell. Recent experiments have shown that a force of a physiological magnitude, applied via a focal adhesion, can propagate a long distance into the cell. This observation disagrees with existing models that regard the cell as a homogeneous body. We show that this "action at a distance" results from the inhomogeneity in the cell: a prestressed and stiff actin bundle guides the propagation of forces over long distances. Our models highlight the enormous ratios of the prestress and the modulus of the actin bundle to the modulus of the cytoskeleton network. For a normal cell, the models predict that forces propagate over characteristic lengths comparable to the size of the cell. The characteristic lengths can be altered, however, by treatments of the cell. We provide experimental evidence and discuss biological implications.     

A moving–resting process with an embedded Brownian motion for animal movements

Animal movements are of great importance in studying home ranges, migration routes, resource selection, and social interactions. The Global Positioning System provides relatively continuous animal tracking over time and long distances. Nevertheless, the continuous trajectory of an animal’s movement is usually only observed at discrete time points. Brownian bridge models have been used to model movement of an animal between two observed locations within a reasonably short time interval. Assuming that animals are in perpetual motion, these models ignore inactivity such as resting or sleeping. Using the latest developments in applied probability, we propose a moving–resting process model where an animal is assumed to alternate between a moving state, during which it moves in a Brownian motion, and a resting state, during which it does not move. Theoretical properties of the process are studied as a first step towards more realistic models for animal movements. Analytic expressions are derived for the distribution of one increment and two consecutive increments, and are validated with simulations. The induced bridge model conditioning on the starting and end points is used to compute an animal’s probability of occurrence in an observation area during the time of observation, which has wide applications in wildlife behavior research.     

A behavioral study of healthy and cancer genes by modeling electrical network

In recent years, gene network modeling is gaining popularity in genomics to monitor the activity profile of genes. More specifically, the objective of the network modeling concept is to study the genetic behavior associated with disease. Previous researchers have designed network model at nucleotide level which produces more complexity for designing circuits mostly in case of gene expression studies. Whereas the authors have designed the present network model, based on amino acid level which is simpler as well as more appropriate for prediction of the genetic abnormality. In the present concept, SISO continuous and discrete system models of genes are realized using Foster network. The model is designed based on hydropathy index value of amino acids to study the biological system behavior. The time and phase response in continuous (s) domain and pole-zero distribution in discrete (z) domain are used as measurement metric in the present study. The simulated responses of the system show genetic instability for cancer genes which truly reflects the medical reports. The proposed modeling concept can be used, to accurately identify or separate out the diseased genes from healthy genes.