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 (that are collectively called Intrinsic Physiological State or IPS functions) can be obtained through the Collins-Richmond (1962) 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.

In earlier communications, we have described the development of a novel assay based on fluorescence microscopy and image processing that can accurately quantify the three aforementioned distributions and account for unequal partitioning at cell division. We have also developed a numerical procedure that can accurately recover the three IPS functions from simulated data and under the assumption that the three phenotypic distributions are known with arbitrarily high accuracy. In practice, however, our measurements will have uncertainty due to random errors. Moreover, the three distributions will be determined from a finite sample of the cell population. For example, our earlier studies with E. coli cells carrying the genetic toggle network with a GFP marker have shown that the fluorescence microscopy assay only needs about 3,000 cells to compute the overall phenotypic distribution of a cell population with accuracy comparable to that achievable with flow cytometry. A sample of this size yields about 300 dividing cells.

The objective of the present study is to develop a robust numerical procedure that can accurately recover the IPS functions of cell populations from finite samples and in the presence of the aforementioned sources of error. We have simulated finite sampling from a cell population by generating a finite number of random deviates following a range of pre-selected distributions. These random deviates represent the total cell property of interest for each individual cell measured. To simulate the effects of uncertainty in the experimental data, we added random errors to the data and evaluated different methods for noise filtering. We have also employed nonparametric methods to estimate the three densities. Additionally, we have compared the NDF to the CDF formulation for solving the integral equation that yields the partition probability density function.

The developed algorithm was tested by applying it to study a population of E. coli cells with an IPTG-inducible genetic toggle network equipped with a gfpmut3 gene that functions as a reporter of intracellular expression levels. Results from the inverse modeling will be analyzed to understand how IPTG affects the reaction and division rates as well as the partitioning mechanism at cell division, and to elucidate the interplay between cell population heterogeneity and single-cell behavior.

References

Collins JF, Richmond MH. 1962. Rate of growth of Bacillus cereus between divisions. Journal of General Microbiology, 28,15-33