# A Mathematical Model of Cancer Stem Cell Lineage Population Dynamics with Mutation Accumulation and Telomere Length Hierarchies

Mathematical Modelling of Natural Phenomena (2012)

- Volume: 7, Issue: 1, page 136-165
- ISSN: 0973-5348

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topKapitanov, G.. "A Mathematical Model of Cancer Stem Cell Lineage Population Dynamics with Mutation Accumulation and Telomere Length Hierarchies." Mathematical Modelling of Natural Phenomena 7.1 (2012): 136-165. <http://eudml.org/doc/222327>.

@article{Kapitanov2012,

abstract = {There is evidence that cancer develops when cells acquire a sequence of mutations that
alter normal cell characteristics. This sequence determines a hierarchy among the cells,
based on how many more mutations they need to accumulate in order to become cancerous.
When cells divide, they exhibit telomere loss and differentiate, which defines another
cell hierarchy, on top of which is the stem cell. We propose a mutation-generation model,
which combines the mutation-accumulation hierarchy with the differentiation hierarchy of
the cells, allowing us to take a step further in examining cancer development and growth.
The results of the model support the hypothesis of the cancer stem cell’s role in cancer
pathogenesis: a very small fraction of the cancer cell population is responsible for the
cancer growth and development. Also, according to the model, the nature of mutation
accumulation is sufficient to explain the faster growth of the cancer cell population.
However, numerical results show that in order for a cancer to develop within a reasonable
time frame, cancer cells need to exhibit a higher proliferation rate than normal
cells.},

author = {Kapitanov, G.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {cancer; stem cells; cancer stem cell; mathematical model; mutation; telomere shortening},

language = {eng},

month = {1},

number = {1},

pages = {136-165},

publisher = {EDP Sciences},

title = {A Mathematical Model of Cancer Stem Cell Lineage Population Dynamics with Mutation Accumulation and Telomere Length Hierarchies},

url = {http://eudml.org/doc/222327},

volume = {7},

year = {2012},

}

TY - JOUR

AU - Kapitanov, G.

TI - A Mathematical Model of Cancer Stem Cell Lineage Population Dynamics with Mutation Accumulation and Telomere Length Hierarchies

JO - Mathematical Modelling of Natural Phenomena

DA - 2012/1//

PB - EDP Sciences

VL - 7

IS - 1

SP - 136

EP - 165

AB - There is evidence that cancer develops when cells acquire a sequence of mutations that
alter normal cell characteristics. This sequence determines a hierarchy among the cells,
based on how many more mutations they need to accumulate in order to become cancerous.
When cells divide, they exhibit telomere loss and differentiate, which defines another
cell hierarchy, on top of which is the stem cell. We propose a mutation-generation model,
which combines the mutation-accumulation hierarchy with the differentiation hierarchy of
the cells, allowing us to take a step further in examining cancer development and growth.
The results of the model support the hypothesis of the cancer stem cell’s role in cancer
pathogenesis: a very small fraction of the cancer cell population is responsible for the
cancer growth and development. Also, according to the model, the nature of mutation
accumulation is sufficient to explain the faster growth of the cancer cell population.
However, numerical results show that in order for a cancer to develop within a reasonable
time frame, cancer cells need to exhibit a higher proliferation rate than normal
cells.

LA - eng

KW - cancer; stem cells; cancer stem cell; mathematical model; mutation; telomere shortening

UR - http://eudml.org/doc/222327

ER -

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