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

Abstract

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.\n\nAuthor SummaryNew imaging tools and automated microscopes are able to produce terabytes of detailed images of protein activity and cell movements as tissues change shape and grow. Yet, efforts to infer useful quantitative information from these large datasets have been limited by the inability to integrate image analysis and computational models with rigorous statistical methods. In this paper, we describe a robust methodology for inferring mechanical processes that drive tissue spreading in embryonic development. Tissue spreading is critical during wound healing and the progression of many diseases including cancer. Direct measurement of biomechanical properties during spreading is not possible in many cases, but can be inferred through mathematical and statistical means. This approach identifies model parameters that are able to robustly predict results of new experiments. These methods can be integrated with more general studies of morphogenesis and to guide further experiments to better understand how tissue spreading is regulated during development and potentially control spreading during wound healing and cancer.