Growth equations for skeletal muscle derived from the cytonuclear ratio and growth constraining supplementary functions

Abstract

AbstractFor purely hypertrophic muscle it is postulated that the growth rate in number of nuclei is proportional to the cytoplasmic mass per nucleus multiplied by a growth constraining supplementary function. Growth constraint depends on the distance from any one of the limit number of nuclei, the limit muscle mass or the limit cytoplasmic mass per nucleus. Furthermore, theory and evidence are presented for a power (allometric) relationship between total number of nuclei (n) and muscle mass (m) given by the equation n = gmh. Evidence points to two clusters of values for h, one in the vicinity of h = 2/3 and the other h = 1/2. Both may depend on a linear relationship between number of nuclei inside muscle fibre and fibre cross-sectional area. The difference between the two situations can be derived from basic assumptions on either local or systemic diffusion mediated control of the number or division of satellite cell nuclei, leading directly to values of h either equal to 2/3 or V2. For likely values of h and suitable choices of growth constraints, almost all well known growth functions in the literature are derived as potentially applicable to total number of nuclei, or muscle mass or their ratio. Muscle mass growth will show a sigmoidal form for h = 1. This explains sigmoidal growth in body mass as it is mostly dominated by muscle mass. A possible linear growth phase before maturity is explicable from the cessation of either length (h = 1) or nuclear (h = 0) growth in muscle fibres, while cytoplasmic growth continues to maturity. Furthermore, two rat examples indicate that whole body protein growth can be described by the equations derived for muscle mass growth.