Mathematical Modeling and Parameter Estimation of Intracellular Signaling Pathway: Application to LPS-induced NF kappa B Activation and TNF alpha Production in Macrophages

Due to the intrinsic stochasticity, the signaling dynamics in a clonal population of cells exhibit cell-to-cell variability at the single-cell level, which is distinct from the population-average dynamics. Frequently, flow cytometry is widely used to acquire the single-cell level measurements by blocking cytokine secretion with reagents such as Golgiplug (TM). However, Golgiplug (TM) can alter the signaling dynamics, causing measurements to be misleading. Hence, we developed a mathematical model to infer the average single-cell dynamics based on the flow cytometry measurements in the presence of Golgiplug (TM) with lipopolysaccharide (LPS)-induced NFkB signaling as an example. First, a mathematical model was developed based on the prior knowledge. Then, average single-cell dynamics of two key molecules (TNF alpha and I kappa B alpha) in the NF kappa B signaling pathway were measured through flow cytometry in the presence of Golgiplug (TM) to validate the model and maximize its prediction accuracy. Specifically, a parameter selection and estimation scheme selected key model parameters and estimated their values. Unsatisfactory results from the parameter estimation guided subsequent experiments and appropriate model improvements, and the refined model was calibrated again through the parameter estimation. The inferred model was able to make predictions that were consistent with the experimental measurements, which will be used to construct a semi-stochastic model in the future.