Mathematics, University of Iowa, 2 West Washington Street, Iowa City, IA, 52242, USA.
Applied Mathematical and Computational Sciences, University of Iowa, 2 West Washington Street, Iowa City, IA, 52242, USA.
Bull Math Biol. 2024 Nov 27;87(1):7. doi: 10.1007/s11538-024-01386-x.
Metabolic fluxes are the rates of life-sustaining chemical reactions within a cell and metabolites are the components. Determining the changes in these fluxes is crucial to understanding diseases with metabolic causes and consequences. Kinetic flux profiling (KFP) is a method for estimating flux that utilizes data from isotope tracing experiments. In these experiments, the isotope-labeled nutrient is metabolized through a pathway and integrated into the downstream metabolite pools. Measurements of proportion labeled for each metabolite in the pathway are taken at multiple time points and used to fit an ordinary differential equations model with fluxes as parameters. We begin by generalizing the process of converting diagrams of metabolic pathways into mathematical models composed of differential equations and algebraic constraints. The scaled differential equations for proportions of unlabeled metabolite contain parameters related to the metabolic fluxes in the pathway. We investigate flux parameter identifiability given data collected only at the steady state of the differential equation. Next, we give criteria for valid parameter estimations in the case of a large separation of timescales with fast-slow analysis. Bayesian parameter estimation on simulated data from KFP experiments containing both irreversible and reversible reactions illustrates the accuracy and reliability of flux estimations. These analyses provide constraints that serve as guidelines for the design of KFP experiments to estimate metabolic fluxes.
代谢通量是细胞内维持生命的化学反应的速率，而代谢物则是这些反应的组成部分。确定这些通量的变化对于理解具有代谢原因和后果的疾病至关重要。动力学通量分析（KFP）是一种估计通量的方法，它利用同位素示踪实验的数据。在这些实验中，同位素标记的营养物质通过途径代谢，并整合到下游代谢物池中。在多个时间点测量途径中每个代谢物的标记比例，并用于拟合具有通量作为参数的常微分方程模型。我们首先将代谢途径的图形转化为由微分方程和代数约束组成的数学模型的过程进行推广。未标记代谢物比例的比例的比例微分方程包含与途径中的代谢通量相关的参数。我们研究了仅在微分方程的稳定状态下收集数据时通量参数可识别性。接下来，我们在快速-缓慢分析具有大时间尺度分离的情况下，给出了有效参数估计的标准。来自 KFP 实验的包含不可逆和可逆反应的模拟数据的贝叶斯参数估计说明了通量估计的准确性和可靠性。这些分析提供了约束条件，为设计 KFP 实验以估计代谢通量提供了指导。
