General models for the spectra of surface area scaling strategies of cells and organisms: fractality, geometric dissimilitude, and internalization

Surface areas and volumes of biological systems—from molecules to organelles, cells, and organisms—affect their biological rates and kinetics. Therefore, surface-area-to-volume ratios and the scaling of surface area with volume profoundly influences ecology, physiology, and evolution. The zeroth-order geometric expectation is that surface area scales with body mass or volume as a power law with an exponent of two-thirds, with consequences for surface-area-to-volume (SA:V) ratios and constraints on size; however, organisms have adaptations for altering the surface area scaling and SA:V ratios of their bodies and structures. The strategies fall into three groups: (i) fractal-like surface convolutions and crinkles; (ii) classic geometric dissimilitude through elongating, flattening, fattening, and hollowing; and (iii) internalization of surfaces. Here I develop general quantitative theory to model the spectra of effects of these strategies on SA:V ratios and surface area scaling, from exponents of less than two-thirds to superlinear scaling and mixed-power laws. Applying the theory to cells helps quantitatively evaluate the effects of membrane fractality, shape-shifting, vacuoles, vesicles, and mitochondria on surface area scaling, informing understanding of cell allometry, morphology, and evolution. Analysis of compiled data indicates that through hollowness and surface internalization eukaryotic phytoplankton increase their effective surface area scaling, attaining near-linear scaling in larger cells. This unifying theory highlights the fundamental role of biological surfaces in metabolism and morphological evolution.