The fundamental principles underlying the robustness and precision of tissue growth remain mysterious. In particular, most growth control cellular signals decay over short distances typically at micron length scale, whereas human tissues and organs are observed to reach well-controlled sizes on the scale of meters. The study of growth control elicits several fascinating questions that need to be addressed. Cells may adopt multiple control strategies simultaneously during tissue growth. What are the trade-offs between different strategies? Noise is present in cell division, gene expression, and signal transmission. How is robust control achieved despite intrinsic and extrinsic noise? Moreover, it is observed that patterning scales with tissue size and influences growth. What is the interplay between pattern formation and growth? We build mathematical models and perform stochastic simulations to explore different control strategies, characterize noise effects according to their sources, and investigate mechanisms that cells adopt to control proliferation in the presence of noise.

In addition to controlled growth, mechanisms of uncontrolled growth are important, for example in relation to cancer. We intend to analyze with use of models situations of uncontrolled growth in order to reveal control defects that may cause the formation of tumors and identify signatures for tumor growth. Another essential study yet to be undertaken relates to coordination between patterning and growth. We plan to include the dynamics of molecules that drive pattern formation in traditional cell lineage models, and investigate the dependence of cell proliferation on molecular feedback control and pattern regulation to illustrate the interplay between patterning and growth control.

A. Schematic diagram of simple negative feedback control. B. Simulations of tissue growth achieve a final size which is four times the size of the signaling molecule decay length under simple negative feedback control.