Abstract
To study the mechanisms underlying developmental pattern formation in a tissue, one needs to analyze the dynamics of the regulators in time and space across the tissue of a specific architecture. This problem is essential for the developmental regulators (morphogens) that distribute over the tissues anisotropically, forming there maxima and gradients and guiding cellular processes in a dose-dependent manner. Here we present the PlantLayout pipeline for MATLAB software, which facilitates the computational studies of tissue patterning. With its help, one can build a structural model of a two-dimensional tissue, embed it into a mathematical model in ODEs, perform numerical simulations, and visualize the obtained results – everything on the same platform. As a result, one can study the concentration dynamics of developmental regulators over the cell layout reconstructed from the real tissue. PlantLayout allows studying the dynamics and the output of gene networks guided by the developmental regulator in specific cells. The gene networks could be different for different cell types. One of the obstacles that PlantLayout removes semi-automatically is the determination of the cell wall orientation which is relevant when cells in the tissue have a polarity. Additionally, PlantLayout allows automatically extracting other quantitative and qualitative features of the cells and the cell walls, which might help in the modeling of a developmental pattern, such as the length and the width of the cell walls, the set of the neighboring cells, cell volume and cell perimeter. We demonstrate PlantLayout performance on the model of phytohormone auxin distribution over the plant root tip.
Highlights
Pattern formation requires the activity of developmental regu lators to be controlled in time and space
PlantLayout pipeline to model tissue patterning We developed the PlantLayout pipeline in MATLAB software to facilitate the studies on the mechanisms of tissue patterning when the user needs to consider both the tissue architecture and the dynamics of the developmental regulators
The pipe line application is especially effective when the developmen tal regulator is able to move from cell to cell, gener ating gra- dients, maxima, and minima that are instructive for tissue patterning
Summary
Pattern formation requires the activity of developmental regu lators to be controlled in time and space. One of the first mathematical models for tissue patterning formation was Turing’s reaction-diffusion model describing the interaction of two regulators: an activator and an inhibitor (Turing, 1952). This model helped understand the mechanisms of the pattern formation of the gap genes’ distribution during Drosophila melanogaster embryogenesis (Lacalli, 1990) and of the patterning of palatal ridges (Economou et al, 2012) or digits (Raspopovic et al, 2014) during mouse embryogenesis. If the first mathematical models did not consider the cellular structure of the tissue at all, e. g. in Turing model (Turing, 1952), nowadays scientists are reducing the use of models with oversimplified rectangular tissues and start developing models on the realistic cell layouts
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