Exploring a mathematical framework for quantifying cell size- dependent glucose uptake in adipocytes

Insulin-stimulated glucose uptake (ISGU) in adipocytes is central to maintain systemic glucose homeostasis. Understanding how ISGU relates to adipocyte traits, such as cell-size, is critical for elucidating pressing questions related to metabolic dysfunction connected to adipose hypertrophy and hyperplasia. Cell size is considered a central trait reflecting multiple aspects of adipocyte metabolism. However, a robust quantitative approach to estimate ISGU for a specific cell size is currently missing. Here, in an attempt to move towards such a method, we have formulated an approach using a mathematical framework. The framework consists of a linear equation: the product of the known number of cells (calculated using coulter counter-based cell-size distributions) and the unknown ISGU/cell, compared to the absolute ISGU (measured using 14C-glucose tracer assays). To solve this equation, we formulate a minimization problem which is optimized to find the unknown ISGU/cell for the best solution. Using different formulations of the equation we can investigate the need for either cell size-dependent or independent ISGU/cell, to describe varying glucose uptake in a cell sample of various cell sizes. While the framework needs further refinement, we demonstrate that cell size-dependent uptake slightly improved the agreement between model and experimental data for some groups. Together, with further validation this could serve as a useful tool to resolve long-standing questions regarding size-dependent characteristics like adipocyte size and cellular function. Key findingsHerein we explore a method to quantify cell size-dependent glucose uptake in adipocytes