Abstract
Most tissues in multicellular organisms are maintained by continuous cell renewal processes. However, high turnover of many cells implies a large number of error-prone cell divisions. Hierarchical organized tissue structures with stem cell driven cell differentiation provide one way to prevent the accumulation of mutations, because only few stem cells are long lived. We investigate the deterministic dynamics of cells in such a hierarchical multi compartment model, where each compartment represents a certain stage of cell differentiation. The dynamics of the interacting system is described by ordinary differential equations coupled across compartments. We present analytical solutions for these equations, calculate the corresponding extinction times and compare our results to individual based stochastic simulations. Our general compartment structure can be applied to different tissues, as for example hematopoiesis, the epidermis, or colonic crypts. The solutions provide a description of the average time development of stem cell and non stem cell driven mutants and can be used to illustrate general and specific features of the dynamics of mutant cells in such hierarchically structured populations. We illustrate one possible application of this approach by discussing the origin and dynamics of PIG-A mutant clones that are found in the bloodstream of virtually every healthy adult human. From this it is apparent, that not only the occurrence of a mutant but also the compartment of origin is of importance.
Highlights
Many tissues have a hierarchical multi compartment structure in which each compartment represents a cell type at a certain stage of differentiation
We introduce in total kz1 compartments, where each compartment i represents a certain stage of cell differentiation with i~0 representing the stem cell pool
If a cell in a non stem cell compartment iw0 replicates, it can undergo three different processes: With probability ei, it divides into two more differentiated cells that migrate into the adjacent downstream compartment iz1
Summary
Many tissues have a hierarchical multi compartment structure in which each compartment represents a cell type at a certain stage of differentiation. If a cell in a non stem cell compartment iw0 replicates, it can undergo three different processes: With probability ei, it divides into two more differentiated cells that migrate into the adjacent downstream compartment iz. The average dynamics in this case can be captured by modifying the differentiation probabilities e This case is implicitly included in our model. One can assume a process at the stem cell level in which cell differentiation, cell death and self renewal are balanced such that the average number of cells remains constant, i.e. 2e0z2l0~1. For our purpose details of the dynamics in the stem cell compartment are not relevant, as long as the number of stem cells is constant
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
