Metabolic allometric scaling model: combining cellular transportation and heat dissipation constraints

Living organisms need energy to be 'alive'. Energy is produced by the biochemical processing of nutrients, and the rate of energy production is called the metabolic rate. Metabolism is very important from evolutionary and ecological perspectives, and for organismal development and functioning. It depends on different parameters, of which organism mass is considered to be one of the most important. Simple relationships between the mass of organisms and their metabolic rates were empirically discovered by M. Kleiber in 1932. Such dependence is described by a power function, whose exponent is referred to as the allometric scaling coefficient. With the increase of mass, the metabolic rate usually increases more slowly; if mass increases by two times, the metabolic rate increases less than two times. This fact has far-reaching implications for the organization of life. The fundamental biological and biophysical mechanisms underlying this phenomenon are still not well understood. The present study shows that one such primary mechanism relates to transportation of substances, such as nutrients and waste, at a cellular level. Variations in cell size and associated cellular transportation costs explain the known variance of the allometric exponent. The introduced model also includes heat dissipation constraints. The model agrees with experimental observations and reconciles experimental results across different taxa. It ties metabolic scaling to organismal and environmental characteristics, helps to define perspective directions of future research and allows the prediction of allometric exponents based on characteristics of organisms and the environments they live in.