### Abstract

Early in development, one X-chromosome in each cell of the female embryo is inactivated. Knowing the number of certain human tissue cells at the time of X-inactivation can improve our understanding of certain diseases such as cancer or genetic disorders as well as cellular development. However, the moment of X-inactivation in humans is difficult to observe directly. In this study, we developed a mathematical model using branching processes and asymptotic normal approximation that will more accurately determine a relationship between the number of cells at X-inactivation with the proportion of one allele found in normal heterozygous adult females. We then conducted computer simulations to show the adequacy of this model. Finally, this model was used to more accurately estimate the number of hemopoietic stem cells at X-inactivation using a real life data set.

Original language | English |
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Pages (from-to) | 758-771 |

Number of pages | 14 |

Journal | Biometrical Journal |

Volume | 45 |

Issue number | 6 |

DOIs | |

State | Published - 13 Oct 2003 |

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### Keywords

- Asymptotic normal distribution
- Branching process
- Martingale convergence
- Variance component model

### Cite this

*Biometrical Journal*,

*45*(6), 758-771. https://doi.org/10.1002/bimj.200390047

}

*Biometrical Journal*, vol. 45, no. 6, pp. 758-771. https://doi.org/10.1002/bimj.200390047

**A Stochastic Model Relating the Number of Cells at X-Inactivation to the Allelic Ratio in Normal Heterozygous Adult Females.** / Chen, George S.; Chen, Shande.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A Stochastic Model Relating the Number of Cells at X-Inactivation to the Allelic Ratio in Normal Heterozygous Adult Females

AU - Chen, George S.

AU - Chen, Shande

PY - 2003/10/13

Y1 - 2003/10/13

N2 - Early in development, one X-chromosome in each cell of the female embryo is inactivated. Knowing the number of certain human tissue cells at the time of X-inactivation can improve our understanding of certain diseases such as cancer or genetic disorders as well as cellular development. However, the moment of X-inactivation in humans is difficult to observe directly. In this study, we developed a mathematical model using branching processes and asymptotic normal approximation that will more accurately determine a relationship between the number of cells at X-inactivation with the proportion of one allele found in normal heterozygous adult females. We then conducted computer simulations to show the adequacy of this model. Finally, this model was used to more accurately estimate the number of hemopoietic stem cells at X-inactivation using a real life data set.

AB - Early in development, one X-chromosome in each cell of the female embryo is inactivated. Knowing the number of certain human tissue cells at the time of X-inactivation can improve our understanding of certain diseases such as cancer or genetic disorders as well as cellular development. However, the moment of X-inactivation in humans is difficult to observe directly. In this study, we developed a mathematical model using branching processes and asymptotic normal approximation that will more accurately determine a relationship between the number of cells at X-inactivation with the proportion of one allele found in normal heterozygous adult females. We then conducted computer simulations to show the adequacy of this model. Finally, this model was used to more accurately estimate the number of hemopoietic stem cells at X-inactivation using a real life data set.

KW - Asymptotic normal distribution

KW - Branching process

KW - Martingale convergence

KW - Variance component model

UR - http://www.scopus.com/inward/record.url?scp=0141429905&partnerID=8YFLogxK

U2 - 10.1002/bimj.200390047

DO - 10.1002/bimj.200390047

M3 - Article

AN - SCOPUS:0141429905

VL - 45

SP - 758

EP - 771

JO - Biometrical Journal

JF - Biometrical Journal

SN - 0323-3847

IS - 6

ER -