Programming cell growth into different cluster shapes using diffusible signals

Abstract

Advances in genetic engineering technologies have allowed the construction of artificial genetic circuits, which have been used to generate spatial patterns of differential gene expression. However, the question of how cells can be programmed, and how complex the rules need to be, to achieve a desired tissue morphology has received less attention. Here, we address these questions by developing a mathematical model to study how cells can collectively grow into clusters with different structural morphologies by secreting diffusible signals that can influence cellular growth rates. We formulate how growth regulators can be used to control the formation of cellular protrusions and how the range of achievable structures scales with the number of distinct signals. We show that a single growth inhibitor is insufficient for the formation of multiple protrusions but may be achieved with multiple growth inhibitors, and that other types of signals can regulate the shape of protrusion tips. These examples illustrate how our approach could potentially be used to guide the design of regulatory circuits for achieving a desired target structure. Author summary Multicellular tissues exhibit a variety of shapes and spatial cellular arrangements. How can cells grow into clusters with certain structural features, and how complex do the corresponding growth regulatory mechanisms need to be? Here, we use a model where cells can secrete diffusible signals, and both the secretion rates of these signals as well as the growth rate of cells can be regulated based on their local chemical environment. The spatial profile of growth rate then drives any changes in the shape of the cluster as it expands. With this framework, we explore questions such as how easily (e.g., how many chemicals cells need to secrete) can we program the growth of a single protrusion, and when is it possible (or not possible) to grow multiple protrusions or a protrusion with a sharp tip. We find that the maximum number of protrusions, a measure of developmental complexity, can increase exponentially with the number of available signals. The mathematical framework we offer and the concrete predictions that follow could serve as useful guidelines for synthetic developmental biology experiments.