We published 2 research papers and 1 review paper. Additionally, my group has published another review paper on the topic of cell-cell communication via diffusing molecules with ERC's support. In the two research papers, we have developed a new theoretical framework for understanding how spatial patterns arise in a field of cells that communicate through diffusing molecules. Spatial patterns arise from cells coordinating their gene expressions by sending signalling molecules to each other. Existing models - namely those using the Turing-patterning / reaction-diffusion equation - explain how spatial patterns form in a continuous field of cells (i.e. field of infinite number of cells) but they cannot account for fields with finite numbers of cells (e.g. 100s to 1000s of cells) in which the "grainy-ness" of cells must be taken into account. In two research papers (Maire and Youk; Olimpio, Dang, and Youk), we developed a theoretical framework to study fields with finite numbers of cells that form spatial patterns. In particular, Maire and Youk (Cell Systems, 2015) introduced a quantity called "entropy of population", which is the total number of static spatial patterns - which are patterns that remain still after being formed - that an arbitrary number of cells can create by communicating amongst them to coordinate their gene expressions. The entropy of population applies to any type of cells, whether they be bacteria or mammalian cells, since the work treats generic, arbitrary cells that possess a common circuit motif that is found across different species. In the second theoretical research-paper (Olimpio, Dang, and Youk, iScience (2018)), we further developed the framework that Maire and Youk introduced. The developed framework can now account for fields of cells that use more than one specie of signalling molecule and consisting of multiple types of cells. We have also developed the theoretical framework so that it can account for noisy sensing of the signalling molecule(s). We found that moderate amount of noise in gene-expression - which causes each cell to sense slightly different concentration of the signalling molecule from each other - to lead to more spatially organized patterns. We developed an analytical method - a method involving only pen and paper - that can replace exhaustive, complex computer simulations that involve many parameters for understanding spatial-pattern formation by a field of finite number of cells. We developed an analytical framework that uses a "pseudo-energy landscape" which is like the potential-energy landscapes in physics. Our theoretical framework provides insights into spatial pattern formations that complex computer simulations cannot provide. On the experimental side, we have been working with yeast cells with natural and engineered gene circuits to understand how cell-cell communication can control cell-proliferation, and in turn, how this affects the population dynamics.