Single-cell behavior and population heterogeneity: Fluorescence microscopy-based inverse population balance modeling

Cell population balance models can account for the phenotypic heterogeneity that characterizes isogenic cell populations. To utilize the predictive power of these models, however, we must determine the single-cell reaction and division rates as well as the partition probability density function of the cell population. These functions (collectively called Intrinsic Physiological State or IPS functions) can be obtained through the Collins-Richmond inverse cell population balance modeling methodology, if we know the phenotypic distributions of (a) the overall cell population, (b) the dividing cell subpopulation and (c) the newborn cell subpopulation.This first part of this thesis presents the development of a novel assay that combines fluorescence microscopy and image processing to determine these phenotypic distributions. Morphological criteria were developed for the automatic identification of dividing cells and validated through direct comparison with manually obtained measurements. The newborn cell subpopulation was obtained from the corresponding dividing cell subpopulation by collecting information from the two compartments separated by the constriction. Finally, we applied the assay to quantify the heterogeneity of E. coli cells carrying the genetic toggle network with a green fluorescent marker. Our measurements for the overall cell population were in excellent agreement with the distributions obtained via flow cytometry.In the second part of the thesis, we develop and test a robust computational procedure for solving the inverse problem that yields the IPS functions. We employed numerical simulations in conjunction with a thorough parametric analysis to investigate the effect of various factors on the accurate recovery of the IPS functions. We also formulated and solved a minimization problem to obtain the bivariate partition probability density function (PPDF), which presents the most computational challenges of all three IPS functions. We successfully tested our method against uncertainty stemming from both finite sampling and measurements errors in the experimental data. We also investigated the feasibility of a more general solution for the PPDF and proposed methods to extend and solve the inverse problem in 2-D. Finally, we demonstrated the abilities and potential of our method by applying it to a model biological system involving E. coli cells carrying the toggle artificial regulatory network.