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.

Refractive changes after descemet stripping endothelial keratoplasty: a simplified mathematical model.

PURPOSE: To develop a mathematical model that can predict refractive changes after Descemet stripping endothelial keratoplasty (DSEK). METHODS: A mathematical formula based on the Gullstrand eye model was generated to estimate the change in refractive power of the eye after DSEK. This model was applied to four DSEK cases retrospectively, to compare measured and predicted refractive changes after DSEK. RESULTS: The refractive change after DSEK is determined by calculating the difference in the power of the eye before and after DSEK surgery. The power of the eye post-DSEK surgery can be calculated with modified Gullstrand eye model equations that incorporate the change in the posterior radius of curvature and change in the distance between the principal planes of the cornea and lens after DSEK. Analysis of this model suggests that the ratio of central to peripheral graft thickness (CP ratio) and central thickness can have significant effect on refractive change where smaller CP ratios and larger graft thicknesses result in larger hyperopic shifts. This model was applied to four patients, and the average predicted hyperopic shift in the overall power of the eye was calculated to be 0.83 D. This change reflected in a mean of 93% (range, 75%-110%) of patients' measured refractive shifts. CONCLUSIONS: This simplified DSEK mathematical model can be used as a first step for estimating the hyperopic shift after DSEK. Further studies are necessary to refine the validity of this model.

Interleukin-15 receptor blockade in non-human primate kidney transplantation.

BACKGROUND: Interleukin (IL)-15 is a chemotactic factor to T cells. It induces proliferation and promotes survival of activated T cells. IL-15 receptor blockade in mouse cardiac and islet allotransplant models has led to long-term engraftment and a regulatory T-cell environment. This study investigated the efficacy of IL-15 receptor blockade using Mut-IL-15/Fc in an outbred non-human primate model of renal allotransplantation. METHODS: Male cynomolgus macaque donor-recipient pairs were selected based on ABO typing, major histocompatibility complex class I typing, and carboxy-fluorescein diacetate succinimidyl ester-based mixed lymphocyte responses. Once animals were assigned to one of six treatment groups, they underwent renal transplantation and bilateral native nephrectomy. Serum creatinine level was monitored twice weekly and as indicated, and protocol biopsies were performed. Rejection was defined as a increase in serum creatinine to 1.5 mg/dL or higher and was confirmed histologically. Complete blood counts and flow cytometric analyses were performed periodically posttransplant; pharmacokinetic parameters of Mut-IL-15/Fc were assessed. RESULTS: Compared with control animals, Mut-IL-15/Fc-treated animals did not demonstrate increased graft survival despite adequate serum levels of Mut-IL-15/Fc. Flow cytometric analysis of white blood cell subgroups demonstrated a decrease in CD8 T-cell and natural killer cell numbers, although this did not reach statistical significance. Interestingly, two animals receiving Mut-IL-15/Fc developed infectious complications, but no infection was seen in control animals. Renal pathology varied widely. CONCLUSIONS: Peritransplant IL-15 receptor blockade does not prolong allograft survival in non-human primate renal transplantation; however, it reduces the number of CD8 T cells and natural killer cells in the peripheral blood.

Intravital microscopy evaluation of angiogenesis and its effects on glucose sensor performance.

An optical window model for the rodent dorsum was used to perform chronic and quantitative intravital microscopy and laser Doppler flowmetry of microvascular networks adjacent to functional and non-functional glucose sensors. The one-sided configuration afforded direct, real-time observation of the tissue response to bare (unmodified, smooth surface) sensors and sensors coated with porous poly-L-lactic acid (PLLA). Microvessel length density and red blood cell flux (blood perfusion) within 1 mm of the sensors were measured bi-weekly over 2 weeks. When non-functional sensors were fully implanted beneath the windows, the porous coated sensors had two-fold more vasculature and significantly higher blood perfusion than bare sensors on Day 14. When functional sensors were implanted percutaneously, as in clinical use, no differences in baseline current, neovascularization, or tissue perfusion were observed between bare and porous coated sensors. However, percutaneously implanted bare sensors had two-fold more vascularity than fully implanted bare sensors by Day 14, indicating the other factors, such as micromotion, might be stimulating angiogenesis. Despite increased angiogenesis adjacent to percutaneous sensors, modest sensor current attenuation occurred over 14 days, suggesting that factors other than angiogenesis may play a dominant role in determining sensor function.

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.