Fluorescence microscopy is a powerful technique for in vivo visualization of localization processes, levels of expression, protein kinetics, and protein-protein interactions, at the level of individual cells. When studying cell cultures, the population aspect adds another dimension to the available information for parameter estimation, compared to single cells. A single experiment generates an abundance of data and it is necessary to be able to handle uncertainties for individual cells as well as the variations between cells. As a result, one is faced with a hierarchical system identification problem where single cell models have to be extended with an additional level describing the variation of parameters between individuals of the population.
We present a system identification framework including single cell modeling, image processing, and parameter estimation. The framework is intended for dynamic models with both intrinsic and extrinsic stochastic elements. Given the purpose of the model, an appropriate structure and mathematical expressions should be chosen, which most certainly will evolve during the model building process. The objective of image processing is to lump the spatiotemporal data content in the microscopy images into time-series, where the resulting aggregated entities reflect something that is described by the model or vice versa. Estimation of model parameters is performed both on individual and population level using a maximum likelihood approach. Certain aspects of this framework are exemplified by results from an investigation on the RAS/cAMP/PKA-pathway in yeast.
The framework provides an integrated approach for the process of system identification using microscopy images of cell populations, and puts emphasis on an iterative workflow. It also highlights, and aims at quantifying, an important fact of biological systems: the inter-individual variability that suggests that many parameters in single cell models should not be thought of as fixed but are better understood from their statistical properties in a population perspective.
Authors and affiliations
Joachim Almquist, Fraunhofer-Chalmers Centre
Mikael Sunnåker, Fraunhofer-Chalmers Centre
Jonas Hagmar, Fraunhofer-Chalmers Centre
Mats Kvarnström, Fraunhofer-Chalmers Centre
Mats Jirstrand, Fraunhofer-Chalmers Centre