Mathematical Modeling of Perifusion Cell Culture Experiments

In perifusion cell cultures, the culture medium flows continuously through a chamber containing immobilized cells and the effluent is collected at the end. In our main applications, gonadotropin releasing hormone (GnRH) or oxytocin is introduced into the chamber as the input. They stimulate the cells to secrete luteinizing hormone (LH), which is collected in the effluent. To relate the effluent LH concentration to the cellular processes producing it, we develop and analyze a mathematical model consisting of coupled partial differential equations describing the intracellular signaling and the movement of substances in the cell chamber. We analyze three different data sets and give cellular mechanisms that explain the data. Our model indicates that two negative feedback loops, one fast and one slow, are needed to explain the data and we give their biological bases. We demonstrate that different LH outcomes in oxytocin and GnRH stimulations might originate from different receptor dynamics. We analyze the model to understand the influence of parameters, like the rate of the medium flow or the fraction collection time, on the experimental outcomes. We investigate how the rate of binding and dissociation of the input hormone to and from its receptor influence its movement down the chamber. Finally, we formulate and analyze simpler models that allow us to predict the distortion of a square pulse due to hormone-receptor interactions and to estimate parameters using perifusion data. We show that in the limit of high binding and dissociation the square pulse moves as a diffusing Gaussian and in this limit the biological parameters can be estimated.

Quantifying Eukaryotic Gene Regulation in Hormone Response and Disease.

Quantifying the function of mammalian enhancers at the genome or population scale has been longstanding challenge in the field of gene regulation. Studies of individual enhancers have provided anecdotal evidence on which many foundational assumptions in the field are based. Genome-scale studies have revealed that the number of sites bound by a given transcription factor far outnumber the genes that the factor regulates. In this dissertation we describe a new method, chromatin immune-enriched reporter assays (ChIP-reporters), and use that approach to comprehensively test the enhancer activity of genomic loci bound by the glucocorticoid receptor (GR). Integrative genomics analyses of our ChIP-reporter data revealed an unexpected mechanism of glucocorticoid (GC)-induced gene regulation. In that mechanism, only the minority of GR bound sites acts as GC-inducible enhancers. Many non-GC-inducible GR binding sites interact with GC-induced sites via chromatin looping. These interactions can increase the activity of GC-induced enhancers. Finally, we describe a method that enables the detection and characterization of the functional effects of non-coding genetic variation on enhancer activity at the population scale. Taken together, these studies yield both mechanistic and genetic evidence that provides context that informs the understanding of the effects of multiple enhancer variants on gene expression.