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.

Serotonin synthesis, release and reuptake in terminals: a mathematical model.

BACKGROUND: Serotonin is a neurotransmitter that has been linked to a wide variety of behaviors including feeding and body-weight regulation, social hierarchies, aggression and suicidality, obsessive compulsive disorder, alcoholism, anxiety, and affective disorders. Full understanding of serotonergic systems in the central nervous system involves genomics, neurochemistry, electrophysiology, and behavior. Though associations have been found between functions at these different levels, in most cases the causal mechanisms are unknown. The scientific issues are daunting but important for human health because of the use of selective serotonin reuptake inhibitors and other pharmacological agents to treat disorders in the serotonergic signaling system. METHODS: We construct a mathematical model of serotonin synthesis, release, and reuptake in a single serotonergic neuron terminal. The model includes the effects of autoreceptors, the transport of tryptophan into the terminal, and the metabolism of serotonin, as well as the dependence of release on the firing rate. The model is based on real physiology determined experimentally and is compared to experimental data. RESULTS: We compare the variations in serotonin and dopamine synthesis due to meals and find that dopamine synthesis is insensitive to the availability of tyrosine but serotonin synthesis is sensitive to the availability of tryptophan. We conduct in silico experiments on the clearance of extracellular serotonin, normally and in the presence of fluoxetine, and compare to experimental data. We study the effects of various polymorphisms in the genes for the serotonin transporter and for tryptophan hydroxylase on synthesis, release, and reuptake. We find that, because of the homeostatic feedback mechanisms of the autoreceptors, the polymorphisms have smaller effects than one expects. We compute the expected steady concentrations of serotonin transporter knockout mice and compare to experimental data. Finally, we study how the properties of the the serotonin transporter and the autoreceptors give rise to the time courses of extracellular serotonin in various projection regions after a dose of fluoxetine. CONCLUSIONS: Serotonergic systems must respond robustly to important biological signals, while at the same time maintaining homeostasis in the face of normal biological fluctuations in inputs, expression levels, and firing rates. This is accomplished through the cooperative effect of many different homeostatic mechanisms including special properties of the serotonin transporters and the serotonin autoreceptors. Many difficult questions remain in order to fully understand how serotonin biochemistry affects serotonin electrophysiology and vice versa, and how both are changed in the presence of selective serotonin reuptake inhibitors. Mathematical models are useful tools for investigating some of these questions.

Growth hormone mitigates against lethal irradiation and enhances hematologic and immune recovery in mice and nonhuman primates.

Medications that can mitigate against radiation injury are limited. In this study, we investigated the ability of recombinant human growth hormone (rhGH) to mitigate against radiation injury in mice and nonhuman primates. BALB/c mice were irradiated with 7.5 Gy and treated post-irradiation with rhGH intravenously at a once daily dose of 20 microg/dose for 35 days. rhGH protected 17 out of 28 mice (60.7%) from lethal irradiation while only 3 out of 28 mice (10.7%) survived in the saline control group. A shorter course of 5 days of rhGH post-irradiation produced similar results. Compared with the saline control group, treatment with rhGH on irradiated BALB/c mice significantly accelerated overall hematopoietic recovery. Specifically, the recovery of total white cells, CD4 and CD8 T cell subsets, B cells, NK cells and especially platelets post radiation exposure were significantly accelerated in the rhGH-treated mice. Moreover, treatment with rhGH increased the frequency of hematopoietic stem/progenitor cells as measured by flow cytometry and colony forming unit assays in bone marrow harvested at day 14 after irradiation, suggesting the effects of rhGH are at the hematopoietic stem/progenitor level. rhGH mediated the hematopoietic effects primarily through their niches. Similar data with rhGH were also observed following 2 Gy sublethal irradiation of nonhuman primates. Our data demonstrate that rhGH promotes hematopoietic engraftment and immune recovery post the exposure of ionizing radiation and mitigates against the mortality from lethal irradiation even when administered after exposure.

A genetically engineered thermally responsive sustained release curcumin depot to treat neuroinflammation.

Radiculopathy, a painful neuroinflammation that can accompany intervertebral disc herniation, is associated with locally increased levels of the pro-inflammatory cytokine tumor necrosis factor alpha (TNFα). Systemic administration of TNF antagonists for radiculopathy in the clinic has shown mixed results, and there is growing interest in the local delivery of anti-inflammatory drugs to treat this pathology as well as similar inflammatory events of peripheral nerve injury. Curcumin, a known antagonist of TNFα in multiple cell types and tissues, was chemically modified and conjugated to a thermally responsive elastin-like polypeptide (ELP) to create an injectable depot for sustained, local delivery of curcumin to treat neuroinflammation. ELPs are biopolymers capable of thermally-triggered in situ depot formation that have been successfully employed as drug carriers and biomaterials in several applications. ELP-curcumin conjugates were shown to display high drug loading, rapidly release curcumin in vitro via degradable carbamate bonds, and retain in vitro bioactivity against TNFα-induced cytotoxicity and monocyte activation with IC50 only two-fold higher than curcumin. When injected proximal to the sciatic nerve in mice via intramuscular (i.m.) injection, ELP-curcumin conjugates underwent a thermally triggered soluble-insoluble phase transition, leading to in situ formation of a depot that released curcumin over 4days post-injection and decreased plasma AUC 7-fold.

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.

Increased in vivo glucose recovery via nitric oxide release.

The in vivo glucose recovery of subcutaneously implanted nitric oxide (NO)-releasing microdialysis probes was evaluated in a rat model using saturated NO solutions to steadily release NO. Such methodology resulted in a constant NO flux of 162 pmol cm(-2) s(-1) from the probe membrane over 8 h of perfusion daily. The in vivo effects of enhanced localized NO were evaluated by monitoring glucose recovery over a 14 day period, with histological analysis thereafter. A difference in glucose recovery was observed starting at 7 days for probes releasing NO relative to controls. Histological analysis at 14 days revealed lessened inflammatory cell density at the probe surface and decreased capsule thickness. Collectively, the results suggest that intermittent sustained NO release from implant surfaces may improve glucose diffusion for subcutaneously implanted sensors by mitigating the foreign body reaction.

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.

Release of outer membrane vesicles by Gram-negative bacteria is a novel envelope stress response.

Conditions that impair protein folding in the Gram-negative bacterial envelope cause stress. The destabilizing effects of stress in this compartment are recognized and countered by a number of signal transduction mechanisms. Data presented here reveal another facet of the complex bacterial stress response, release of outer membrane vesicles. Native vesicles are composed of outer membrane and periplasmic material, and they are released from the bacterial surface without loss of membrane integrity. Here we demonstrate that the quantity of vesicle release correlates directly with the level of protein accumulation in the cell envelope. Accumulation of material occurs under stress, and is exacerbated upon impairment of the normal housekeeping and stress-responsive mechanisms of the cell. Mutations that cause increased vesiculation enhance bacterial survival upon challenge with stressing agents or accumulation of toxic misfolded proteins. Preferential packaging of a misfolded protein mimic into vesicles for removal indicates that the vesiculation process can act to selectively eliminate unwanted material. Our results demonstrate that production of bacterial outer membrane vesicles is a fully independent, general envelope stress response. In addition to identifying a novel mechanism for alleviating stress, this work provides physiological relevance for vesicle production as a protective mechanism.