Data from: 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.

从分子、细胞器、细胞到生物体的各类生物系统，其表面积与体积均会影响自身的生物学速率与动力学过程。因此，表面积体积比（surface-area-to-volume ratio, SA:V）以及表面积随体积的缩放关系，对生态学、生理学与进化生物学均具有深远影响。零阶几何预期认为，表面积与体重或体积的缩放遵循指数为2/3的幂律，这会对SA:V比值以及生物体尺寸限制产生相应影响；然而，生物体可通过适应性调整自身躯体与结构的表面积缩放关系及SA:V比值。这类策略可分为三类：(i) 类分形表面褶皱与皱缩；(ii) 经典几何异形化策略，即通过伸长、扁平化、增厚与中空化实现形态改变；(iii) 表面内化。本文构建了通用定量理论，用于建模上述三类策略对SA:V比值与表面积缩放关系的影响谱，覆盖了指数小于2/3、超线性缩放以及混合幂律等多种情形。将该理论应用于细胞研究，可定量评估膜分形性、形态变化、液泡、囊泡与线粒体对表面积缩放关系的影响，从而加深对细胞异速生长、形态学与进化过程的理解。对汇编数据的分析表明，真核浮游植物可通过中空化与表面内化策略提升有效表面积缩放能力，在较大尺寸的细胞中实现接近线性的表面积缩放。这一统一理论凸显了生物表面在代谢与形态进化中的核心作用。