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

George S. Chen, Shande Chen

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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 languageEnglish
Pages (from-to)758-771
Number of pages14
JournalBiometrical Journal
Volume45
Issue number6
DOIs
Publication statusPublished - 13 Oct 2003

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Keywords

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

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