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On the dynamics of activation of mammalian X chromosomes

Published online by Cambridge University Press:  14 April 2009

N. Mukunda
Affiliation:
Centre for Theoretical StudiesIndian Institute of ScienceBangalore 560 012, India
H. Sharat Chandra
Affiliation:
Centre for Theoretical StudiesIndian Institute of ScienceBangalore 560 012, India Microbiology Cell Biology LaboratoryIndian Institute of Science, Bangalore 560 012, India
Madhav Gadgil
Affiliation:
Centre for Theoretical StudiesIndian Institute of ScienceBangalore 560 012, India
A. K. Rajagopal
Affiliation:
Centre for Theoretical StudiesIndian Institute of ScienceBangalore 560 012, India
E. C. G. Sudarshan
Affiliation:
Centre for Theoretical StudiesIndian Institute of ScienceBangalore 560 012, India
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We have investigated a mathematical model of the process of activation of the X chromosomes in eutherian mammals. The model assumes that the activation is brought about over some definite time interval T by the complete saturation of N receptor sites on an X chromosome by M activating molecules (or multiples of M). The probability λ of a first hit on the receptor site is considered to be very much lower than that of subsequent hits; that is, we assume strong co-operative binding. Assuming further that an incomplete saturation of receptor sites is malfunctional, we can show that for proper activation of X chromosomes in normal diploid males and females, we must have λMT ≥ 3 and 0·96 ≤ N/M ≤ 1. An extension of this analysis for the triploid cases shows that under these conditions, we cannot explain the activation of two X's if the number of activating molecules is fixed at M. This suggests that there must be two classes of triploid embryos differing from each other in a step-wise manner in the number of activating molecules. In other words, triploids with two active X chromosomes would require 2M activating molecules as opposed to M molecules in triploids with a single active X. This interpretation of the two classes of triploids would be consistent with differing imprinting histories of the parental contributions to the triploid zygote.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1976

References

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