(182i) Construction of a Semi-Stochastic Intracellular Signaling Model Via Global Sensitivity Analysis and Probability Density Estimation

Biological models often describe the population-average dynamics of signaling pathways through a deterministic modeling approach. However, recent single-cell studies have revealed that cells from a clonal population exhibit a large degree of cell-to-cell variability [1]. The cell-to-cell variability is believed to originate from intrinsic (stochastic chemical kinetics) and extrinsic (different initial conditions between cells) sources. Previous studies have applied stochastic modeling methodologies such as Gillespie’s algorithm [2] to simulate the single-cell dynamics. However, this method is often computationally expensive; this is particularly problematic as many biological models have a large number of states and parameters, which inevitably leads to the formidable computational cost.

As an alternative to the stochastic simulation framework, a semi-stochastic modeling approach has been proposed [3], which uses a deterministic model with model parameters that have distributions. More specifically, a pre-specified probability density function (PDF) of the model parameters is used to generate different parameter values, which are subsequently used in the deterministic model to simulate corresponding distinct signaling dynamics. This approach allows simulation of cell-to-cell variability with a manageable computational cost. However, the PDF of the model parameters is usually unknown a priori as values of the model parameters are difficult to measure experimentally; therefore, the PDF needs to be inferred from measurements.

In this study, a sequential approach that consists of global sensitivity analysis and probability density estimation is proposed to systematically estimate the PDF of model parameters. First, a sampling-based global sensitivity analysis method [4] is implemented to identify a set of model parameters that impact model outputs most significantly. Next, the PDF of the identified parameters is estimated by minimizing the difference between the measured and predicted output probability densities, which are approximated through particle filtering [5] and kernel density estimation [6]. Through the proposed methodology, the parameter PDF of a dynamic model can be inferred accurately, which can be used to construct a semi-stochastic model to identify the source of heterogeneity and to quantify their magnitude in the single-cell dynamics. As a test case, the proposed methodology is applied to estimate the PDF of the NFκB signaling pathway model [7], which includes about 150 model parameters, to validate the capability of the proposed approach.

[1] Mitchell, S.; Hoffmann, A. Identifying noise sources governing cell-to-cell variability. Curr. Opin. Syst. Biol., 2018, 8, 39-45.

[2] Gillespie, D.T. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem., 1977, 82, 2340–2361.

[3]Hasenauer, J.; Waldherr, S.; Doszczak, M.; Scheurich, P.; Radde, N.; Allgöwer, F. Analysis of heterogeneous cell populations: A density-based modeling and identification framework. J. Process Control, 2011, 21, 1417–1425.

[4] Chu, Y.; Hahn, J. Parameter set selection for estimation of nonlinear dynamic systems. AIChE J., 2007, 53, 2858-2870

[5] Rawlings, J. B.; Bakshi, B. R. Particle filtering and moving horizon estimation. Comp. & Chem. Eng., 2006, 30, 1529-1541.

[6] Silverman, B.W. Density estimation for statistics and data analysis. Chapman & Hall/CPC: London, 1986.

[7] Lee, D.; Ding, Y.; Jayaraman, A.; Kwon, J.S. Mathematical Modeling and Parameter Estimation of Intracellular Signaling Pathway: Application to LPS-induced NFκB Activation and TNFα Production in Macrophages, Processes, 2018, 6, 21.