| dc.description.abstract | Systems biology research employs a quantitative model to interpret experimental measurements and make new predictions of the system to be tested in the new sets of experiments. Therefore, the construction of an accurate model is a key step in the overall systems biology study. Usually, a model developed in the past concerns mostly about the dynamics of cells at the population-level instead of those of individual cells in the population. However, with the recent advances in single-cell experimental techniques, it has been revealed that individual cells in a genetically homogeneous cell population behave heterogeneously in response to an external stimulus. This new discovery requires a different modeling approach to represent and analyze the heterogeneous cell population dynamics.
In this study, a systematic modeling framework is proposed to develop a mathematical model for an intracellular signaling pathway in a heterogeneous cell population. To this end, two sources of the cellular heterogeneity are required to be incorporated: cell-to cell differences and reaction stochasticity. Specifically, the former and latter sources are taken into account by an individual-based population model (IBPM) and kinetic Monte Carlo (kMC) model, respectively.
First, this study proposes a systematic approach to construct an IBPM to incorporate the cell-to-cell differences. In an IPBM, the dynamics of an intracellular signaling pathway in the population are represented by a set of ordinary differential equations (ODEs), but the model parameters will follow multivariate probability density functions (PDFs) to take into account the cell-to-cell differences among the individual cells. Therefore, the construction of an IBPM requires its ODE model to be developed first. To this end, an integrative approach, which consists of first-principles modeling, identifiability analysis, parameter estimation, and model refinement, is employed to develop and calibrate the ODE model systematically. At the same time, two new methods for developing a semi-mechanistic model have been proposed in order to speed up the overall ODE model development
process even when underlying mechanisms are partially known. Both methods improve the prediction accuracy by coupling the first-principle model with the data-driven model inferred from experimental measurements by rendering model parameters time-varying in the first method and by adding additional correction terms to model states’ trajectories in the second method. Once a deterministic ODE model is developed, model parameters’ PDFs need to be estimated. In this regard, a numerical scheme is proposed to efficiently estimate the parameters’ PDFs. Specifically, the proposed scheme consists of dimension reduction and surrogate modeling to efficiently identify the parameters’ PDFs from the available single-cell measurements.
Second, an on-lattice kMC model is developed for incorporating reaction stochasticity, which is the second source of the cellular heterogeneity, as well as the temporal evolution of the membrane configuration. By modeling the multivalent binding kinetics between bacterial toxin and ganglioside expressed on cell membranes as a case system, the accuracy of the kMC model is validated, and how it is different from its corresponding deterministic model is examined.
In summary, this study has proposed a systematic modeling approach to construct a mathematical model for an intracellular signaling pathway by addressing their parameter and structural uncertainty to simulate the cell-to-cell heterogeneity. To validate the proposed methodologies, the NFkB signaling pathway and binding kinetics between ganglioside and bacterial toxins such as cholera toxin are modeled and calibrated as case studies. | en |
