The origins of the Redfield nitrogen-to-phosphorus ratio are in a homoeostatic protein-to-rRNA ratio

One of the most intriguing patterns in the biosphere is the similarity of the atomic nitrogen-to-phosphorus ratio (N:P)=16 found in waters throughout the deep ocean and in the plankton in the upper ocean. Although A.C. Redfield proposed in 1934 that the intracellular properties of plankton were central to this pattern, no theoretical significance for N:P=16 in cells had been found. Here, we use theoretical modelling and a compilation of literature data for prokaryotic and eukaryotic microbes to show that the balance between two fundamental processes, protein and rRNA synthesis, results in a stable biochemical attractor that homoeostatically produces a given protein:rRNA ratio. Furthermore, when biochemical constants and reasonable kinetic parameters for protein synthesis and ribosome production under nutrient-replete conditions are applied in the model, it predicts a stable protein:rRNA ratio of 3±0.7, which corresponds to N:P=16±3. The model also predicts that N-limitation, by constraining protein synthesis rates, will result in N:P ratios below the Redfield value while P-limitation, by constraining RNA production rates, will produce ratios above the Redfield value. Hence, one of most biogeochemically significant patterns on Earth is inherently rooted in the fundamental structure of life.