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