An allometric interpretation of the spatio-temporal organization of molecular and cellular processes

Summary Different levels of organization distinguished by characteristics spatial dimensions, E_c, and relaxation times, T_r, of biological processes ranging from electron transport in energy transduction to growth of microbial and plant cells, are shown to be related through a relation that may be interpreted as allometric and characterized by two different slopes. Processes, at levels of organization occurring in spatial dimensions of micrometers and relaxing in the order of minutes, delimit a transition point between the two curves, that we interpret as a limit for the emergence of macroscopic coherence. The characteristic spatial dimension, E_c, and the relaxation time, T_r, contain dynamical information about the processes occurring at a given level of organization. When a steady state of a biological process at a certain level of organization becomes unstable, the system undergoes a transition to another level of organization. To exemplify the appearance of macroscopic order at levels of organization further from the transition point we present in this report various experimental systems involving many levels of organization allometrically related that exhibit different kinds of self-organized behavior, i.e. bistability, oscillations, changes in (a)symmetry.