Research Article: Using a continuum model to decipher the mechanics of embryonic tissue spreading from time-lapse image sequences: An approximate Bayesian computation approach

Date Published: June 27, 2019

Publisher: Public Library of Science

Author(s): Tracy L. Stepien, Holley E. Lynch, Shirley X. Yancey, Laura Dempsey, Lance A. Davidson, Yi Jiang.


Advanced imaging techniques generate large datasets capable of describing the structure and kinematics of tissue spreading in embryonic development, wound healing, and the progression of many diseases. These datasets can be integrated with mathematical models to infer biomechanical properties of the system, typically identifying an optimal set of parameters for an individual experiment. However, these methods offer little information on the robustness of the fit and are generally ill-suited for statistical tests of multiple experiments. To overcome this limitation and enable efficient use of large datasets in a rigorous experimental design, we use the approximate Bayesian computation rejection algorithm to construct probability density distributions that estimate model parameters for a defined theoretical model and set of experimental data. Here, we demonstrate this method with a 2D Eulerian continuum mechanical model of spreading embryonic tissue. The model is tightly integrated with quantitative image analysis of different sized embryonic tissue explants spreading on extracellular matrix (ECM) and is regulated by a small set of parameters including forces on the free edge, tissue stiffness, strength of cell-ECM adhesions, and active cell shape changes. We find statistically significant trends in key parameters that vary with initial size of the explant, e.g., for larger explants cell-ECM adhesion forces are weaker and free edge forces are stronger. Furthermore, we demonstrate that estimated parameters for one explant can be used to predict the behavior of other similarly sized explants. These predictive methods can be used to guide further experiments to better understand how collective cell migration is regulated during development.

Partial Text

Advances in microscopy enable the generation of very large time-lapse datasets over the course of a few hours. Such time-lapse data contains a wealth of information describing both the structures involved in morphogenesis and their kinematics; this information can serve as the input for computational models that allow us to explore the biological and biophysical principles of morphogenesis and to predict the behavior of cells and tissues under a variety of perturbations. This presents many technical challenges, from collecting quality images suitable for machine vision tools to developing computational models that implement appropriate biophysics and physiological rules at useful spatial and temporal scales. To maximize the benefits of these approaches, experimental designs must be able to integrate image data with model simulations in a way that allows robust statistical assessment of model fitness or failure.

To explore the mechanical processes involved in collective migration during development, we microsurgically isolated ectodermal tissue from the animal cap region of gastrulating Xenopus embryos (Fig 1A). During gastrulation, this tissue spreads to cover the exterior of the embryo. Once isolated and placed on a fibronectin-coated substrate, tissue explants spread radially outward [46,47] (Fig 1B). The initial area of the explant affects the spreading rate with larger explants spreading faster than smaller ones (Fig 1C and 1D), suggesting that the initial area of an explant affects the mechanics of the tissue. To understand the source of these mechanical interactions, we sought to integrate a mathematical model of epiboly with kinematic data on tissue boundaries and internal strains from time-lapse data (Fig 1E; Materials and Methods). Through parameter estimation and statistical techniques, we correlated the effect of an explant’s initial area on estimated parameter values in the model.

Time-lapse imaging of tissue explant spreading generates complicated data sets that are information-rich. Here, we present a formal methodology for extracting mechanical mechanisms of tissue spreading in differently sized embryonic tissue explants by integrating complex image information with a mathematical model of cell migration. In order to directly relate the experimental kinematics of spreading of multiple tissue explants to mechanical properties of the tissue, we focused on one mathematical model, the previously-developed Eulerian mechanical model of Arciero et al. [11], that represents forces involved in migration within a 2D elastic continuum. In this modeling framework, extended here to represent Xenopus animal cap epiboly, we can directly couple experimentally derived kinematic data to model parameters that correspond to physical properties in the tissue.




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