This approach identifies model parameters that are able to robustly predict results of new experiments. Direct measurement of biomechanical properties during spreading is not possible in many cases, but can be inferred through mathematical and statistical means. Tissue spreading is critical during wound healing and the progression of many diseases including cancer. In this paper, we describe a robust methodology for inferring mechanical processes that drive tissue spreading in embryonic development. 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. New 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. These predictive methods can be used to guide further experiments to better understand how collective cell migration is regulated during development. Furthermore, we demonstrate that estimated parameters for one explant can be used to predict the behavior of other similarly sized explants.
BLASTOPORE LATERLA FREE
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. 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. Here, we demonstrate this method with a 2D Eulerian continuum mechanical model of spreading embryonic tissue.
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. However, these methods offer little information on the robustness of the fit and are generally ill-suited for statistical tests of multiple experiments.
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. In the step and ramp models (Models 2A & B) the main forces driving blastopore closure begin near the start of ventral involution (so ε≈0), and blastopore closure occurs at a fixed strain (ε = εC) however, the strain at tP varies with temperature.Īdvanced 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. The generalized model (Model 1) assumes temperature only affects the speed of morphogenesis, therefore each morphogenetic event occurs at fixed, but unspecified strains (εP,εC,…). We approximate this deformation as uniform stretching of a strip of material (B). A strip of tissue (A, to right of each whole embryo schematic) experiences spatially and temporally varying stresses (open arrows stresses from deep tissues not shown), which elongate it and change its shape. In the step and ramp models (Models 2A & B) tP is used, as an estimate of the timing of cell behaviors that exert morphogenetic forces, to predict tC. In the generalized model (Model 1) we assumed all morphogenetic durations (tP, tC, etc) changed by the same proportion with temperature. Involution begins on the dorsal side at t = 0, and begins on the ventral side at tP the blastopore closes at tC.
The ectoderm and neurectoderm (gray) spreads over the embryo during gastrulation. (A) Diagrams of blastopore closure from the lateral side.
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