Theoretical and computational studies of growing tissues

Life around us, from the micron to macroscopic scale, is multi-cellular. One of the major drivers of multicellularity is growth and subsequent division of cells. Typically, the cells require energy to undergo growth and division and hence are out of equilibrium in the language of Physics. Cells undergo division and form a collective entity called tissue. Hence, tissue is a form of matter which is out of equilibrium, knowledge about which in the context of physics is little. The present thesis fills this gap and is concerned with theoretical and computational studies addressing the physics of growing tissues at different scales. Four major problems have been addressed in the thesis- (a) Physical mechanism behind the emergence of super-diffusive single cell dynamics in a growing in vitro tumor spheroid (b) Rationale for the usage of passive tracer probes to sense the local stress in tumor spheroids (c) Aging dynamics in growing two dimensional tissue monolayers and (d) Statistical mechanical theory for the spatio-temporal evolution of Intra-tumor heterogeneity in tumors. (a) Mechanism behind super-diffusive single cell dynamics in growing tumor spheroids: Chapter 2 to Chapter 4 deals with the development of a computational multicellular tumor model and its comparison to experiments. Using the model, it is established that the dynamics of single cells in a growing tissue is superdiffusive and spatially heterogeneous. In chapter 5, the model is used to make predictions regarding the surface roughness of the growing tumor as a function of intercellular attraction. In chapter 6, a phase diagram pertaining to single cell dynamics is predicted in evolving tissues. (b) Rationale for the usage of passive tracer probes to sense the local stress in tumor spheroids: Recent experiments have used tracer beads to sense the local stress in growing tumor spheroids. However, a priori it is not clear if we can use passive beads to measure cell properties which are active entities. In chapter 7, using the tumor spheroid model and numerical solution of the modified Deans equation, we establish the rationale behind the usage of tracer beads to sense tumor spheroid properties. (c) Aging dynamics in growing two dimensional tissue monolayers: In a recent experiment on MDCK growing cell monolayer, it was established that the properties of the tissue is time dependent similar to abiotic many body systems undergoing aging dynamics. In chapter 8, a computational model is developed which captures the experimental findings quantitatively and makes predictions testable in imaging experiments. (d) Spatio-temporal evolution of Intra-tumor heterogeneity in tumors: Through multi-region sequencing experiments, it has been established there exists widespread intra-tumor heterogeneity. In Chapter 9, a statistical mechanical theory is presented which can quantitatively capture the heterogeneity measured in multi-region sequencing experiments. Using the theoretical framework, we show there exists massive sample to sample variations in tumors. Taken together, the present thesis utilizes ideas from statistical and many-body physics to build quantitative models of growing tissues and makes predictions which can be readily tested in experiments.Physic