 
Summary: 1 2 ... j n
1
2
i
m
M
gX
Time Observed expression values
Observed mixture percentages
Inferred expression values
Developmentalstageofembryo
Figure 1: The problem.
We are interested in characterizing the expression level of C. elegans genes as a function of the develop
mental stage of the embryo. For simplicity, we assume that we are interested in a single gene, and we define
gi as the expression level of the gene at stage i.
Unfortunately, it is not possible to measure this expression level directly in a highthroughput fashion.
Instead, we have a vector of observed expression values X = [x1, . . . , xn], where xj is the observed expression
level at time j. We also have a corresponding mixture measurement, summarized in a matrix M such that
Mi,j is the percentage of embryos at time j that are in developmental stage i. The problem is illustrated
schematically in Figure 1.
