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Free keywords:
cancer; clonal extinction and diversity; mathematical modelling
Abstract:
Cancers are rarely caused by single mutations, but often develop as a result of
the combined effects of multiple mutations. For most cells, the number of
possible cell divisions is limited because of various biological constraints,
such as progressive telomere shortening, cell senescence cascades or a hierarchically
organized tissue structure. Thus, the risk of accumulating cells
carrying multiple mutations is low. Nonetheless, many diseases are based
on the accumulation of such multiple mutations. We model a general, hierarchically
organized tissue by a multi-compartment approach, allowing any
number of mutations within a cell. We derive closed solutions for the deterministic
clonal dynamics and the reproductive capacity of single clones. Our
results hold for the average dynamics in a hierarchical tissue characterized
by an arbitrary combination of proliferation parameters. We show that
hierarchically organized tissues strongly suppress cells carrying multiple
mutations and derive closed solutions for the expected size and diversity of
clonal populations founded by a single mutant within the hierarchy. We discuss
the example of childhood acute lymphoblastic leukaemia in detail and
find good agreement between our predicted results and recently observed
clonal diversities in patients. This result can contribute to the explanation
of very diverse mutation profiles observed by whole genome sequencing of
many different cancers.
