The definition of life under operator theory proposes that life is the organization of autonomous entities, or “operators”, that produce effects within their environment without losing their individuality. Living operators grow in complexity from prokaryotic cells to animals to whole societies. In order for these operators to create effects they must first be able to sense the changing state of their environment. Information theory has demonstrated promising results in quantifying how well operators can discern signals from a heterogeneous environment filled with noise. Here, we present a study on two different types of cellular response in populations of individual cells: one in which the majority of individual cells respond to the external stimuli and another in which smaller proportion of cells respond. We are particularly interested in the case where the mean level of response to external stimuli (e.g. protein production) is the same, but the distribution of responses among the individual cells is different. We find that information theory can help us enumerate the differentiable states of external stimuli and thus help to isolate the mechanisms by which living organisms respond to changes in their environment.
