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A deterministic model for the occurrence and dynamics of multiple mutations in hierarchically organized tissues.

Werner B, Dingli D, Traulsen A - J R Soc Interface (2013)

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Evolutionary Theory Group, Max Planck Institute for Evolutionary Biology, Plön, Germany.

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.

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Clonal expansion within a hierarchically organized tissue. Cell proliferation is driven by a few slow-dividing stem cells, giving rise to faster dividing progenitor cells. After some differentiation steps, the mature tissue cells are obtained. Initially cells have no mutations, but mutants can arise and expand within the hierarchy. These cells either vanish or gain an additional mutation, which again potentially spreads within the hierarchy. Different colours code for a different number of mutations, whereas different shapes indicate different mutations. (Online version in colour.)
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RSIF20130349F2: Clonal expansion within a hierarchically organized tissue. Cell proliferation is driven by a few slow-dividing stem cells, giving rise to faster dividing progenitor cells. After some differentiation steps, the mature tissue cells are obtained. Initially cells have no mutations, but mutants can arise and expand within the hierarchy. These cells either vanish or gain an additional mutation, which again potentially spreads within the hierarchy. Different colours code for a different number of mutations, whereas different shapes indicate different mutations. (Online version in colour.)

Mentions: We describe the deterministic dynamics of a cell population within a hierarchically organized tissue structure, which initially carries no mutation. A cell may commit further into the hierarchy (differentiate), mutate or self-renew. This occurs with probability ɛ, u and 1 − ɛ − u, respectively. In figure 1, a schematic of the resulting hierarchical structure is shown. Compartments to the right represent downstream compartments of more specialized (differentiated) cells, while compartments to the bottom represent states of cells which accumulated an additional mutation. During one cell division, a cell either mutates and moves one compartment to the bottom, differentiates and produces two cells in the next downstream compartment to the right or self-renews and produces an additional cell within its original compartment. This leads to an expansion of clonal populations within the hierarchy that potentially accumulates several (distinct) mutations during the differentiation process. This is schematically shown in figure 2.Figure 2.


A deterministic model for the occurrence and dynamics of multiple mutations in hierarchically organized tissues.

Werner B, Dingli D, Traulsen A - J R Soc Interface (2013)

Clonal expansion within a hierarchically organized tissue. Cell proliferation is driven by a few slow-dividing stem cells, giving rise to faster dividing progenitor cells. After some differentiation steps, the mature tissue cells are obtained. Initially cells have no mutations, but mutants can arise and expand within the hierarchy. These cells either vanish or gain an additional mutation, which again potentially spreads within the hierarchy. Different colours code for a different number of mutations, whereas different shapes indicate different mutations. (Online version in colour.)
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4043170&req=5

RSIF20130349F2: Clonal expansion within a hierarchically organized tissue. Cell proliferation is driven by a few slow-dividing stem cells, giving rise to faster dividing progenitor cells. After some differentiation steps, the mature tissue cells are obtained. Initially cells have no mutations, but mutants can arise and expand within the hierarchy. These cells either vanish or gain an additional mutation, which again potentially spreads within the hierarchy. Different colours code for a different number of mutations, whereas different shapes indicate different mutations. (Online version in colour.)
Mentions: We describe the deterministic dynamics of a cell population within a hierarchically organized tissue structure, which initially carries no mutation. A cell may commit further into the hierarchy (differentiate), mutate or self-renew. This occurs with probability ɛ, u and 1 − ɛ − u, respectively. In figure 1, a schematic of the resulting hierarchical structure is shown. Compartments to the right represent downstream compartments of more specialized (differentiated) cells, while compartments to the bottom represent states of cells which accumulated an additional mutation. During one cell division, a cell either mutates and moves one compartment to the bottom, differentiates and produces two cells in the next downstream compartment to the right or self-renews and produces an additional cell within its original compartment. This leads to an expansion of clonal populations within the hierarchy that potentially accumulates several (distinct) mutations during the differentiation process. This is schematically shown in figure 2.Figure 2.

Bottom Line: 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.

View Article: PubMed Central - PubMed

Affiliation: Evolutionary Theory Group, Max Planck Institute for Evolutionary Biology, Plön, Germany.

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.

Show MeSH
Related in: MedlinePlus