Complex emergent systems of many interacting components, including complex biological systems, have the potential to perform quantifiable functions. Accordingly, we define ''functional information,'' I(E x), as a measure of system complexity. For a given system and function, x (e.g., a folded RNA sequence that binds to GTP), and degree of function, E x (e.g., the RNA-GTP binding energy), I(E x) ‫؍‬ ؊log2[F(Ex)], where F(Ex) is the fraction of all possible configurations of the system that possess a degree of function > E x. Functional information, which we illustrate with letter sequences, artificial life, and biopolymers, thus represents the probability that an arbitrary configuration of a system will achieve a specific function to a specified degree. In each case we observe evidence for several distinct solutions with different maximum degrees of function, features that lead to steps in plots of information versus degree of function.origin of life ͉ artificial life ͉ evolution ͉ aptamers ͉ emergent systems

Hydrogen isotope (δ 2 H) analysis is widely used in animal ecology to study continental-scale movement because δ 2 H can trace precipitation and climate. To understand the biochemical underpinnings of how hydrogen is incorporated into biomolecules, we measured the δ 2 H of individual amino acids (AAs) in Escherichia coli cultured in glucose-based or complex tryptone-based media in waters with δ 2 H values ranging from −55‰ to +1,070‰. The δ 2 H values of AAs in tryptone spanned a range of ∼250‰. In E. coli grown on glucose, the range of δ 2 H among AAs was nearly 200‰. The relative distributions of δ 2 H of AAs were upheld in cultures grown in enriched waters. In E. coli grown on tryptone, the δ 2 H of nonessential AAs varied linearly with the δ 2 H of media water, whereas δ 2 H of essential AAs was nearly identical to δ 2 H in diet. Model calculations determined that as much as 46% of hydrogen in some nonessential AAs originated from water, whereas no more than 12% of hydrogen in essential AAs originated from water. These findings demonstrate that δ 2 H can route directly at the molecular level. We conclude that the patterns and distributions in δ 2 H of AAs are determined through biosynthetic reactions, suggesting that δ 2 H could become a new biosignature for studying novel microbial pathways. Our results also show that δ 2 H of AAs in an organism's tissues provides a dual tracer for food and environmental (e.g., drinking) water.hydrogen isotopes | aminio acids | diet | Escherichia coli