UC Irvine

Organ tissues are organized into cell lineages with a hierarchical structure. At the top of each lineage is a stem cell, whose main function is to maintain the tissue and serve as a blue-print for cell renewal. Downstream from the stem cells are daughter cells characterized by increasing degrees of "differentiation". The most differentiated cells are "worker cells" that do not engage in renewal but instead perform the function of the organ tissue. Cells engage in a constant turnover but maintain "homeostasis" (a nearly constant population, thought to be maintained by self-regulation). Homeostasis maintenance of healthy tissue is a topic that has been widely investigated, and yet the exact mechanisms governing stability remain unknown. In this work, we focus on the way cells regulate each other's decisions, e.g. to divide, differentiate, or die; this is achieved through a control network. Mathematically, cell regulation is expressed by means of dependencies of the rates on the current composition of the cell population (the feedback functions). At a steady state, a mutant population may arise that grows from low numbers and becomes harmful (malignant). Here we consider all possibilities of feedback on cell fate decisions that allow for homeostasis maintenance, and study the robustness of the corresponding system against mutations. To this end, we construct a series of mathematical models that incorporate different control networks and are based on a deterministic ODE description as well as a stochastic, spatial agent-based model description (chapter 3). We show that a mutant population, while characterized by different properties than the wild type cells, may not always have an evolutionary advantage. For example, mutants that do not participate in control can never be harmful to healthy tissue, while mutants that do not respond to control may rise from low numbers. Depending on the type of control network, different types of mutations can lead to a harmful expansion. In one class of cellular networks, only the loss of control of the probability of stem cells to self-renew confers this advantage, while in another class of networks this advantage can come from the alteration to control of any cell fate decision. We further compare properties of "minimal" networks (the ones that have the smallest number of control loops compatible with homeostasis) with "redundant" networks (containing an extra control loop). We find that all minimal networks are equally vulnerable to harmful mutations, and from an evolutionary viewpoint, it is advantageous to combine control loops. From an engineering prospective, not all such redundant systems are equally robust. For some of them, any mutation that weakens/eliminates one of the loops will lead to a population growth of stem cells. For others, the population of stem cells can actually shrink as a result of ``cutting'' one of the loops, thus slowing down further unwanted transformations. In general, a mutation that leads to an increase in the proportion of stem cells in the population is considered particularly harmful, because cancer stem cells are highly resistant to treatment and can repopulate the bulk of the tumor. We investigate what feedback may lead to this phenomenon we call "cancer stem cell enrichment". We find that in all scenarios, there must be negative feedback on the rate of divisions and/or positive feedback on the rate of death for this phenomenon to occur. These results may have implications for non-genetic drug resistance.