Size Regulation and Nonequilibrium Growth of Biological Tissues

Abstract

Growth is one of the most profound concepts in biology, shared among all living organisms from bacteria to human beings, and has had a long history in physics as well. One of the major open questions in biology regarding growth is how organs in a growing animal regulate and coordinate their sizes to ensure proper body proportions. In this thesis, we study size coordination and growth regulation in biological tissues from multiple angles using phenomenological models borrowed from nonequilibrium statistical physics, control theory and the theory of elasticity as well as image processing algorithms to analyze biological data. Motivated by a recent observation in the fruit fly Drosophila that a single hormone secreted by the developing organs is instrumental in keeping the bilateral symmetry of the fly wings, we first investigate coordination between left and right organs via chemical signaling. We show that there are limits to the ability of the signal to ensure successful left/right symmetry, suggesting that organ sizes are primarily set autonomously. We then discuss an experimental collaboration with the biology lab of Pierre Leopold in France. We explain our efforts in mounting and imaging adult Drosophila wings, and developing image processing algorithms to automate the wing segmentation to measure wing size asymmetry. We also outline a code based on the Procrustes analysis to quantify shape asymmetry and see whether or not wing shape is also affected in response to mutations that cause an increase in size asymmetry between left/right wings. Finally, inspired by our analytical conclusion that final organ sizes are primarily set autonomously despite growth being an intrinsically noisy process, we look at noisy growth of individual tissues subject to mechanical feedbacks to understand what the implications of noise are in a growing tissue. We show that even the simplest model of noisy tissue growth exhibits a surprisingly rich behavior. For instance, we find that the growth displays power law correlations, and soft modes that lead to large variations in the size of marked clones of cells. Our models set the stage for future experimental and theoretical studies of nonequilibrium tissue growth in biology and physics alike.