Outline of a theory of cellular heterogeneity.

In the effort to advance toward a theory of cellular function that is not completely mechanistic, I have encountered a variable whose significance is often overlooked. This is the degree of heterogeneity of organic tissue, which may vary from highly homogeneous conditions to quite large degrees of heterogeneity, primarily with respect ot chemical bonding. For several decades, I have dealt with the theoretical analysis of this type of problem, and here I give a condensed outline of the conceptual changes to which such an analysis is likely to lead. I believe the time is ripe to compare these theoretical arguments with observations. The data that occasion this note are those of Rubin [Rubin, H. (1984) Proc. Natl. Acad. Sci. USA 81, 5121-5125]; they and numerous similar observations suggest the possibility of an advance toward a nonreductionist model of cellular function along lines that are here indicated; the theoretical model is thought of as operating entirely within the framework of quantum mechanics.

Biological application of the statistical concepts used in the Second Law.

The idea that living things violate the Second Law has been suggested many times. We point out that any mathematical formalism can be applied to a variety of physical processes; here to all molecules on the one hand (Boltzmann) and to messages of the genetic code on the other. The latter is an application of what is known as Shannon's law of communications theory. One application can be valid without the other, in particular if we suspect Shannon's law, this does not imply a breakdown of the molecular law leading to thermodynamics. To avoid a defect of Shannon's law, a widening of the representative "space" of the genome is proposed; the new space, called here the "polymeric space" is found to have properties that make it particularly suitable as a vehicle of biological description. We find that in this manner an apparent violation of Shannon's law can be accounted for.