Narrow Results

Many tissues undergo a steady turnover, where cell divisions are on average balanced with cell deaths. Cell fate decisions such as stem cell (SC) differentiations, proliferations, or differentiated cell (DC) deaths, may be controlled by cell populations through cell-to-cell signaling. Here, we examine a class of mathematical models of turnover in SC lineages to understand engineering design principles of control (feedback) loops, that may operate in such systems. By using ordinary differential equations that describe the co-dynamics of SCs and DCs, we study the effect of different types of mutations that interfere with feedback present within cellular networks. For instance, we find that mutants that do not participate in feedback are less dangerous in the sense that they will not rise from low numbers, whereas mutants that do not respond to feedback signals could rise and replace the wild-type population. Additionally, we asked if different feedback networks can have different degrees of resilience against such mutations. We found that all minimal networks, that is networks consisting of exactly one feedback loop that is sufficient for homeostatic stability of the wild-type population, are equally vulnerable. Mutants with a weakened/eliminated feedback parameter might expand from lower numbers and either enter unlimited growth or reach an equilibrium with an increased number of SCs and DCs. Therefore, from an evolutionary viewpoint, it appears advantageous to combine feedback loops, creating redundant feedback networks. Interestingly, from an engineering prospective, not all such redundant systems are equally resilient. For some of them, any mutation that weakens/eliminates one of the loops will lead to a population growth of SCs. For others, the population of SCs can actually shrink as a result of “cutting” one of the loops, thus slowing down further unwanted transformations.

Clonal dominance in hematopoietic stem cell populations is an important question of interest but not one we can directly answer. Any estimates are based on indirect measurement. For marked populations, we can equate empirical and theoretical moments for binomial sampling, in particular we can use the well-known formula for the sampling variation of a binomial proportion. The empirical variance itself cannot always be reliably estimated and some caution is needed. We describe the difficulties here and identify ready solutions which only require appropriate use of variance-stabilizing transformations. From these we obtain estimators for the steady state, or dynamic equilibrium, of the number of hematopoietic stem cells involved in repopulating the marrow. The calculations themselves are not too involved. We give the distribution theory for the estimator as well as simple approximations for practical application. As an illustration, we rework on data recently gathered to address the question as to whether or not reconstitution of marrow grafts in the clinical setting might be considered to be oligoclonal.