New experimental approaches to the population balance equation:Eulerian and Lagrangian viewpoints

Abstract

Cell-to-cell variability in an asynchronous population of cells can be generally related to genetic differences, to different positions in the cell cycle, to the exposure of a heterogeneous environment, or to stochastic variations due to the low number of molecules in individual cells. To experimentally measure this cell to cell variability in response to different extra-cellular environments, one must measure the cells' phenotype using either an Eulerian or Lagrangian reference frame. In the Eulerian reference frame one measures the state of an entire cell population at discrete time points. In order to extract the single-cell dynamics from a time series of such measurements it is necessary to solve an inverse problem that extracts single cell behavior from the population data. This requires assumptions about cell behavior that may not be accurate in all cases. In contrast, in the Lagrangian reference frame one tracks individual cells over time and the dynamic properties of cells directly result from the observations. The properties of the entire cell population are then obtained as the sum of contributions of the individual components. Experimental data generated with the Eulerian viewpoint is primarily generated using flow cytometry. This instrument yields the cellular property distribution as a snapshot in time and cells are discarded after the measurement. Automated flow cytometry was developed to obtain high frequency snapshots of the cellular property distribution over time. This technique was used in this thesis to both quantitatively and qualitatively describe the cell cycle dynamics of CHO cells, transient gene expression in CHO cells, and to develop a fed-batch control strategy for CHO cells. To evaluate the single cell variability using the Lagrangian reference frame we have developed a novel flow cytometry instrument that is able to track individual, suspended cells in time. Individual cells can be repeatedly measured as they grow and express different proteins or as they respond to specific external stimuli of the growth environment. The measurement approach takes advantage of the Segre Silberberg effect that applies when dilute particles are subjected to Poiseuille flow in a capillary. Under such conditions particles of a given size and shape self-organize on the same streamline and keep their relative position in an oscillatory flow regime. We demonstrate that tens and perhaps hundreds of suspended cells can be tracked over hours with this device. With the developed instrument we have followed the Gfp expression modulated by variation in growth temperature as well as the induction kinetics of Gfp in individual yeast and CHO cells over extended periods of time. The data indicate a large variability of the kinetic response of individual cells that is not apparent if the Eulerian reference frame is used with conventional flow cytometry. Thus, the instrument permits evaluation of suspended cell populations at a level of detail that can not be achieved by existing instrumentation. The developed approach will be useful in the study of individual cell behavior and helpful in the rapid development of new drugs.