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The laws governing life should be as simple as possible; however, theoretical investigations into allometric laws have become increasingly complex, with the long-standing debate over the scaling exponent in allometric laws persisting. This paper re-examines the same biological phenomenon using two different scales. On a macroscopic scale, a cell surface appears smooth, but on a smaller scale, it exhibits a fractal-like porous structure. To elaborate, a few examples are given. Employing the two-scale fractal theory, we theoretically predict and experimentally verify the scaling exponent values for basal, active, and maximal metabolic rates. This paper concludes that Rubner’s 2/3 law and Kleiber’s 3/4 law are two facets of the same truth, manifested across different scale approximations.

Through the development of TGFβ-inducible early gene-1 (TIEG1) knockout (KO) mice, we have demonstrated that TIEG1 plays an important role in osteoblast-mediated bone mineralization, and in bone resistance to mechanical strain. To further investigate the influence of TIEG1 in skeletal maintenance, osteocytes were analyzed by transmission electron microscopy using TIEG1 KO and wild-type mouse femurs at one, three and eight months of age. The results revealed an age-dependent change in osteocyte surface and density, suggesting a role for TIEG1 in osteocyte development. Moreover, there was a decrease in the amount of hypomineralized bone matrix surrounding the osteocytes in TIEG1 KO mice relative to wild-type controls. While little is known about the function or importance of this hypomineralized bone matrix immediately adjacent to osteocytes, this study reveals significant differences in this bone microenvironment and suggests that osteocyte function may be compromised in the absence of TIEG1 expression.

As a model of neurodegenerative disease, the study on SH-SY5Y cells is of great significance due to the complexity of cause and difficulty in cure. Based on this reality, we studied the influence of culture duration on the morphology and mechanical properties of living SH-SY5Y cells by atomic force microscopy (AFM). A comparative analysis was made to characterize the cell size and tip-cell adhesion, and their increased trends with the increase of cell culture duration were obtained, providing a guideline for the physiological characteristics of the cells. As the culture time increased from 24h to 48h, the measured average height and width of cells were increased by 0.59$\mu$m and 1.38$\mu$m, respectively. As for cell elasticity, statistical analysis showed that the difference between different parts of the cell was obvious. Additionally, the electrophysiological characteristic as an important indicator for measuring the functional activities of SH-SY5Y cells was investigated. Here, a homemade conductive atomic force microscope (C-AFM) provided an effective way for membrane potential recordings. It was successfully used to study the real-time responses of living SH-SY5Y cells to mechanical insertions, and a membrane potential with an amplitude of $-0.101$V was obtained without losing cell viability.