Analytic Parameter Fitting in Stochastic Stem Cell Models

Abstract

Pluripotent stem cells produce all of the body's diverse cell types though lineages of cell division and differentiation. One goal of current stem cell research is to create predictive models of cell development hierarchies to validate our understanding of these hierarchies and to guide the design of artificial lineages to produce specific cell types for medical purposes. Stochastic models have been used to study stem cell lineages for nearly 50 years, but a continuing challenge is how to fit the parameters of complex models to noisy experimental cell population data. We have developed a technique that addresses this problem by creating algorithms to automatically generate exact analytical expressions for the probability distributions of different cell types at each successive generation as a function of the model parameters. These expressions can be used with conventional optimizers to find the best-fit model parameters. Although the analytic expressions grow exponentially for complex differentiation hierarchies, the resulting equations are manageable out to the number of generations typically used in experiments. We have tested our parameter fitting strategy using, as “experimental” data, Monte Carlo simulations of a three-parameter stochastic model we have developed for T-cell formation from lymphocyte progenitor cells. We organized the Monte Carlo results to mimic two possible experimental protocols. One mimicked replicate measurements of cell differentiation starting with single stems cells, and the other mimicked measurements starting with pooled groups of cells. Our approach yielded good convergence to the stochastic model parameters, even for relatively small numbers of starting cells, showing that this should be practical for fitting models to experimental data. Additionally, our results show that data from replicate single cell experiments allow more reliable model fitting than pooled experiments using the same number of initial stem cells.