(60cu) Identification of Cell-to-Cell Heterogeneity through Systems Engineering Approaches

With recent advances in the ability to measure gene and protein expression at the single-cell level, it has been found that cells from a clonal population exhibit a large degree of cell-to-cell variability. Previous studies have applied stochastic modeling methodologies such as Gillespie’s algorithm to simulate the single-cell dynamics. However, this method is often computationally expensive. Alternatively, a semi-stochastic modeling approach has been proposed. 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 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, surrogate modeling, and probability density estimation is proposed to estimate the PDF of model parameters. First, a global sensitivity analysis method is used to identify a set of important model parameters. Second, a number of PDF of the identified parameters are sampled for generating the corresponding PDF of the outputs. These generated data then are used to develop a surrogate model to correlate the PDFs of the parameters and outputs. Next, the PDF of the identified parameters is estimated by minimizing the difference between the measured and predicted output PDF with the developed surrogate model. Through the proposed methodology, the parameter PDF 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.