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Register a new userComparative study of non-invasive force and stress inference methods in tissue
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In the course of animal development, the shape of tissue emerges in part from mechanical and biochemical interactions between cells. Measuring stress in tissue is essential for studying morphogenesis and its physical constraints. Experimental measurements of stress reported thus far have been invasive, indirect, or local. One theoretical approach is force inference from cell shapes and connectivity, which is non-invasive, can provide a space-time map of stress and relies on prefactors. Here, to validate force- inference methods, we performed a comparative study of them. Three force-inference methods, which differ in their approach of treating indefiniteness in an inverse problem between cell shapes and forces, were tested by using two artificial and two experimental data sets. Our results using different datasets consistently indicate that our Bayesian force inference, by which cell-junction tensions and cell pressures are simultaneously estimated, performs best in terms of accuracy and robustness. Moreover, by measuring the stress anisotropy and relaxation, we cross-validated the force inference and the global annular ablation of tissue, each of which relies on different prefactors. A practical choice of force-inference methods in distinct systems of interest is discussed.
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During morphogenesis, the shape of a tissue emerges from collective cellular behaviors, which are in part regulated by mechanical and biochemical interactions between cells. Quantification of force and stress is therefore necessary to analyze the mechanisms controlling tissue morphogenesis. Recently, a mechanical measurement method based on force inference from cell shapes and connectivity has been developed. It is non-invasive, and can provide space-time maps of force and stress within an epithelial tissue, up to prefactors. We previously performed a comparative study of three force-inference methods, which differ in their approach of treating indefiniteness in an inverse problem between cell shapes and forces. In the present study, to further validate and compare the three force inference methods, we tested their robustness by measuring temporal fluctuation of estimated forces. Quantitative data of cell-level dynamics in a developing tissue suggests that variation of forces and stress will remain small within a short period of time ($sim$minutes). Here, we showed that cell-junction tensions and global stress inferred by the Bayesian force inference method varied less with time than those inferred by the method that estimates only tension. In contrast, the amplitude of temporal fluctuations of estimated cell pressures differs less between different methods. Altogether, the present study strengthens the validity and robustness of the Bayesian force-inference method.
Brain tissue is a heterogeneous material, constituted by a soft matrix filled with cerebrospinal fluid. The interactions between, and the complexity of each of these components are responsible for the non-linear rate-dependent behaviour that characterizes what is one of the most complex tissue in nature. Here, we investigate the influence of the cutting rate on the fracture properties of brain, through wire cutting experiments. We also present a model for the rate-dependent behaviour of fracture propagation in soft materials, which comprises the effects of fluid interaction through a poro-hyperelastic formulation. The method is developed in the framework of finite strain continuum mechanics, implemented in a commercial finite element code, and applied to the case of an edge-crack remotely loaded by a controlled displacement. Experimental and numerical results both show a toughening effect with increasing rates, which is linked to the energy dissipated by the fluid-solid interactions in the process zone ahead of the crack.
Phylogenetic comparative methods may fail to produce meaningful results when either the underlying model is inappropriate or the data contain insufficient information to inform the inference. The ability to measure the statistical power of these methods has become crucial to ensure that data quantity keeps pace with growing model complexity. Through simulations, we show that commonly applied model choice methods based on information criteria can have remarkably high error rates; this can be a problem because methods to estimate the uncertainty or power are not widely known or applied. Furthermore, the power of comparative methods can depend significantly on the structure of the data. We describe a Monte Carlo based method which addresses both of these challenges, and show how this approach both quantifies and substantially reduces errors relative to information criteria. The method also produces meaningful confidence intervals for model parameters. We illustrate how the power to distinguish different models, such as varying levels of selection, varies both with number of taxa and structure of the phylogeny. We provide an open-source implementation in the pmc (Phylogenetic Monte Carlo) package for the R programming language. We hope such power analysis becomes a routine part of model comparison in comparative methods.
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose dynamics are governed by the Chemical Master Equation. Despite its simple structure, no analytic solutions to the Chemical Master Equation are known for most systems. Moreover, stochastic simulations are computationally expensive, making systematic analysis and statistical inference a challenging task. Consequently, significant effort has been spent in recent decades on the development of efficient approximation and inference methods. This article gives an introduction to basic modelling concepts as well as an overview of state of the art methods. First, we motivate and introduce deterministic and stochastic methods for modelling chemical networks, and give an overview of simulation and exact solution methods. Next, we discuss several approximation methods, including the chemical Langevin equation, the system size expansion, moment closure approximations, time-scale separation approximations and hybrid methods. We discuss their various properties and review recent advances and remaining challenges for these methods. We present a comparison of several of these methods by means of a numerical case study and highlight some of their respective advantages and disadvantages. Finally, we discuss the problem of inference from experimental data in the Bayesian framework and review recent methods developed the literature. In summary, this review gives a self-contained introduction to modelling, approximations and inference methods for stochastic chemical kinetics.
In this paper, we study the trade-offs of different inference approaches for Bayesian matrix factorisation methods, which are commonly used for predicting missing values, and for finding patterns in the data. In particular, we consider Bayesian nonnegative variants of matrix factorisation and tri-factorisation, and compare non-probabilistic inference, Gibbs sampling, variational Bayesian inference, and a maximum-a-posteriori approach. The variational approach is new for the Bayesian nonnegative models. We compare their convergence, and robustness to noise and sparsity of the data, on both synthetic and real-world datasets. Furthermore, we extend the models with the Bayesian automatic relevance determination prior, allowing the models to perform automatic model selection, and demonstrate its efficiency.
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