Variations and fluctuations are characteristic features of biological systems and are also manifested in cell cultures. Here, we describe a computational pipeline for identifying the range of three-dimensional (3D) cell-aggregate sizes in which nonisometric scaling emerges in the presence of joint mass and metabolic rate fluctuations. The 3D cell-laden spheroids with size and single-cell metabolic rates described by probability density functions were randomly generated in silico. The distributions of the resulting metabolic rates of the spheroids were computed by modeling oxygen diffusion and reaction. Then, a method for estimating scaling exponents of correlated variables through statistically significant data collapse of joint probability distributions was developed. The method was used to identify a physiologically relevant range of spheroid sizes, where both nonisometric scaling and a minimum oxygen concentration (0.04 mol⋅m⁻³) is maintained. The in silico pipeline described enables the prediction of the number of experiments needed for an acceptable collapse and, thus, a consistent estimate of scaling parameters. Using the pipeline, we also show that scaling exponents may be significantly different in the presence of joint mass and metabolic-rate variations typically found in cells. Our study highlights the importance of incorporating fluctuations and variability in size and metabolic rates when estimating scaling exponents. It also suggests the need for taking into account their covariations for better understanding and interpreting experimental observations both in vitro and in vivo and brings insights for the design of more predictive and physiologically relevant in vitro models.

变化和波动是生物系统的特征，也体现在细胞培养物中。在这里，我们描述了一个计算管道，用于识别三维 (3D) 细胞聚集体大小的范围，其中在存在关节质量和代谢率波动的情况下出现非等距缩放。具有由概率密度函数描述的大小和单细胞代谢率的 3D 细胞负载球体是在计算机中随机生成的。通过模拟氧扩散和反应来计算得到的球体代谢率的分布。然后，开发了一种通过联合概率分布的统计显着数据崩溃来估计相关变量的缩放指数的方法。^-3 ) 保持不变。所描述的计算机流水线能够预测可接受的塌陷所需的实验数量，因此可以对缩放参数进行一致的估计。使用该管道，我们还表明，在存在细胞中常见的关节质量和代谢率变化的情况下，缩放指数可能存在显着差异。我们的研究强调了在估计缩放指数时结合大小和代谢率的波动和可变性的重要性。它还表明需要考虑它们的协变，以便更好地理解和解释体外和体内的实验观察结果，并为设计更具预测性和生理相关性的体外模型提供见解。