Mathematical modelling of tissue development

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A fundamental question in biology is how a single eukaryotic cell (e.g., zygote, stem cell) produces the complexity required to develop into a complete multicellular organism. This single cell divides and initiates the orchestrated events guiding progeny to differentiate and diversify in a timely manner to generate functional tissue composed of billions of cells. Tissue development involves many regulatory mechanisms, but it remains to be discovered how they coordinate and carry out this complex process in a controlled fashion. One key temporal mechanism involved in tissue development is the cell cycle. Cell cycle duration influences the amount of time a cell has to grow and divide. In early tissue development, cell cycle duration changes dramatically, starting out fast to generate cells quickly and slowing down as cells differentiate. These changing cell cycle durations can play an important role in tissue development by controlling the expression of long gene transcripts, which are partially transcribed in short cell cycles. Genes must be fully transcribed to be expressed. Using mathematical simulations of cell proliferation, we recently identified an emergent property that this "transcriptional filter" can act as a tuning knob to control the generation of cell diversity, and the number and proportion of different cell types in a tissue. Our predictions are supported by comparison to single-cell RNA-seq data captured over embryonic development, as well as evolutionary genome analysis. Our results support the idea that cell cycle dynamics are important for controlling gene transcript expression and the diversity within a tissue. Here, we will extend this work and explore how diverse regulatory mechanisms can affect cell fate and normal tissue development in multicellular animals. We will address this by building a mathematical model of tissue development that captures how cellular mechanisms affect cell fate decisions and timing as well as spatial patterning. We will undertake this work following two long-term objectives. First, we will study the timing of transitions as cells differentiate and generate the various cell types needed for tissue development. We will explore a range of mechanisms, such as cell cycle dynamics, cell-cell communication and gene regulatory networks, that may affect tissue development timing. Second, we will explore how the mechanisms we model impact spatial tissue self-organization and development. We will extend our existing mathematical model to include 2D and 3D geometry and explore how cells differentiate and self-organize within these spaces. Our mathematical exploration of cell fate control and tissue development promises to have broad impact, as cell cycle and other regulatory mechanism dynamics we study are important in development, as cells age, during regeneration and repair, and during tumour growth. Our work has the potential to fundamentally alter the way we think about these processes.