  Some genes can promote or repress their own expressions, which is called
autoregulation. Although gene regulation is a central topic in biology,
autoregulation is much less studied. In general, it is extremely difficult to
determine the existence of autoregulation with direct biochemical approaches.
Nevertheless, some papers have observed that certain types of autoregulations
are linked to noise levels in gene expression. We generalize these results by
two propositions on discrete-state continuous-time Markov chains. These two
propositions form a simple but robust method to infer the existence of
autoregulation from gene expression data. This method only needs to compare the
mean and variance of the gene expression level. Compared to other methods for
inferring autoregulation, our method only requires non-interventional one-time
data, and does not need to estimate parameters. Besides, our method has few
restrictions on the model. We apply this method to four groups of experimental
data and find some genes that might have autoregulation. Some inferred
autoregulations have been verified by experiments or other theoretical works.
