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.

Irisin and FNDC5 in retrospect: An exercise hormone or a transmembrane receptor?

FNDC5 (fibronectin domain-containing [protein] 5) was initially discovered and characterized by two groups in 2002. In 2011 FNDC5 burst into prominence as the parent of irisin, a small protein containing the fibronectin type III domain. Irisin was proposed to be secreted by skeletal muscle cells in response to exercise, and to circulate to fat tissue where it induced a transition to brown fat. Since brown fat results in dissipation of energy, this pathway is of considerable interest for metabolism and obesity. Here I review the original discoveries of FNDC5 and the more recent discovery of irisin. I note in particular three problems in the characterization of irisin: the antibodies used to detect irisin in plasma lack validity; the recombinant protein used to demonstrate activity in cell culture was severely truncated; and the degree of shedding of soluble irisin from the cell surface has not been quantitated. The original discovery proposing that FNDC5 may be a transmembrane receptor may deserve a new look.

Chromosomal organization of adrenergic receptor genes.

The adrenergic receptors (ARs) (subtypes alpha 1, alpha 2, beta 1, and beta 2) are a prototypic family of guanine nucleotide binding regulatory protein-coupled receptors that mediate the physiological effects of the hormone epinephrine and the neurotransmitter norepinephrine. We have previously assigned the genes for beta 2- and alpha 2-AR to human chromosomes 5 and 10, respectively. By Southern analysis of somatic cell hybrids and in situ chromosomal hybridization, we have now mapped the alpha 1-AR gene to chromosome 5q32----q34, the same position as beta 2-AR, and the beta 1-AR gene to chromosome 10q24----q26, the region where alpha 2-AR is located. In mouse, both alpha 2- and beta 1-AR genes were assigned to chromosome 19, and the alpha 1-AR locus was localized to chromosome 11. Pulsed field gel electrophoresis has shown that the alpha 1- and beta 2-AR genes in humans are within 300 kilobases (kb) and the distance between the alpha 2- and beta 1-AR genes is less than 225 kb. The proximity of these two pairs of AR genes and the sequence similarity that exists among all the ARs strongly suggest that they are evolutionarily related. Moreover, they likely arose from a common ancestral receptor gene and subsequently diverged through gene duplication and chromosomal duplication to perform their distinctive roles in mediating the physiological effects of catecholamines. The AR genes thus provide a paradigm for understanding the evolution of such structurally conserved yet functionally divergent families of receptor molecules.

Impaired formation of beta-adrenergic receptor-nucleotide regulatory protein complexes in pseudohypoparathyroidism.

Decreased activity of the guanine nucleotide regulatory protein (N) of the adenylate cyclase system is present in cell membranes of some patients with pseudohypoparathyrodism (PHP-Ia) whereas others have normal activity of N (PHP-Ib). Low N activity in PHP-Ia results in a decrease in hormone (H)-stimulatable adenylate cyclase in various tissues, which might be due to decreased ability to form an agonist-specific high affinity complex composed of H, receptor (R), and N. To test this hypothesis, we compared beta-adrenergic agonist-specific binding properties in erythrocyte membranes from five patients with PHP-Ia (N = 45% of control), five patients with PHP-Ib (N = 97%), and five control subjects. Competition curves that were generated by increasing concentrations of the beta-agonist isoproterenol competing with [125I]pindolol were shallow (slope factors less than 1) and were computer fit to a two-state model with corresponding high and low affinity for the agonist. The agonist competition curves from the PHP-Ia patients were shifted significantly (P less than 0.02) to the right as a result of a significant (P less than 0.01) decrease in the percent of beta-adrenergic receptors in the high affinity state from 64 +/- 22% in PHP-Ib and 56 +/- 5% in controls to 10 +/- 8% in PHP-Ia. The agonist competition curves were computer fit to a "ternary complex" model for the two-step reaction: H + R + N in equilibrium HR + N in equilibrium HRN. The modeling was consistent with a 60% decrease in the functional concentration of N, and was in good agreement with the biochemically determined decrease in erythrocyte N protein activity. These in vitro findings in erythrocytes taken together with the recent observations that in vivo isoproterenol-stimulated adenylate cyclase activity is decreased in patients with PHP (Carlson, H. E., and A. S. Brickman, 1983, J. Clin. Endocrinol. Metab. 56:1323-1326) are consistent with the notion that N is a bifunctional protein interacting with both R and the adenylate cyclase. It may be that in patients with PHP-Ia a single molecular and genetic defect accounts for both decreased HRN formation and decreased adenylate cyclase activity, whereas in PHP-Ib the biochemical lesion(s) appear not to affect HRN complex formation.

Identification of late larval stage developmental checkpoints in Caenorhabditis elegans regulated by insulin/IGF and steroid hormone signaling pathways.

Organisms in the wild develop with varying food availability. During periods of nutritional scarcity, development may slow or arrest until conditions improve. The ability to modulate developmental programs in response to poor nutritional conditions requires a means of sensing the changing nutritional environment and limiting tissue growth. The mechanisms by which organisms accomplish this adaptation are not well understood. We sought to study this question by examining the effects of nutrient deprivation on Caenorhabditis elegans development during the late larval stages, L3 and L4, a period of extensive tissue growth and morphogenesis. By removing animals from food at different times, we show here that specific checkpoints exist in the early L3 and early L4 stages that systemically arrest the development of diverse tissues and cellular processes. These checkpoints occur once in each larval stage after molting and prior to initiation of the subsequent molting cycle. DAF-2, the insulin/insulin-like growth factor receptor, regulates passage through the L3 and L4 checkpoints in response to nutrition. The FOXO transcription factor DAF-16, a major target of insulin-like signaling, functions cell-nonautonomously in the hypodermis (skin) to arrest developmental upon nutrient removal. The effects of DAF-16 on progression through the L3 and L4 stages are mediated by DAF-9, a cytochrome P450 ortholog involved in the production of C. elegans steroid hormones. Our results identify a novel mode of C. elegans growth in which development progresses from one checkpoint to the next. At each checkpoint, nutritional conditions determine whether animals remain arrested or continue development to the next checkpoint.

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.