The energy cost of protein messages lead to a new protein information law

By considering the energy cost of messages carried by proteins as proportional to their information content we found experimental proof that proteins from all living organisms tend to have their estimated semantic content of information per unit mass, statistically, close to a constant. Thus, in the message carried by proteins −to achieve minimum energy waste− the rate of information content per unit mass tends to be optimized in living organisms. The experimental evidence of this new information law resembles a marathon where highly optimized proteins correspond to advanced runners followed by a main bunch and the stragglers −lowly optimized proteins. Our results suggest the existence of a continuous optimization process that living organisms had to face, in which a compromise between biological functionality, economic feasibility and the survival requirements is established.