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.

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.

Copper signaling axis as a target for prostate cancer therapeutics.

Previously published reports indicate that serum copper levels are elevated in patients with prostate cancer and that increased copper uptake can be used as a means to image prostate tumors. It is unclear, however, to what extent copper is required for prostate cancer cell function as we observed only modest effects of chelation strategies on the growth of these cells in vitro. With the goal of exploiting prostate cancer cell proclivity for copper uptake, we developed a "conditional lethal" screen to identify compounds whose cytotoxic actions were manifested in a copper-dependent manner. Emerging from this screen was a series of dithiocarbamates, which, when complexed with copper, induced reactive oxygen species-dependent apoptosis of malignant, but not normal, prostate cells. One of the dithiocarbamates identified, disulfiram (DSF), is an FDA-approved drug that has previously yielded disappointing results in clinical trials in patients with recurrent prostate cancer. Similarly, in our studies, DSF alone had a minimal effect on the growth of prostate cancer tumors when propagated as xenografts. However, when DSF was coadministered with copper, a very dramatic inhibition of tumor growth in models of hormone-sensitive and of castrate-resistant disease was observed. Furthermore, we determined that prostate cancer cells express high levels of CTR1, the primary copper transporter, and additional chaperones that are required to maintain intracellular copper homeostasis. The expression levels of most of these proteins are increased further upon treatment of androgen receptor (AR)-positive prostate cancer cell lines with androgens. Not surprisingly, robust CTR1-dependent uptake of copper into prostate cancer cells was observed, an activity that was accentuated by activation of AR. Given these data linking AR to intracellular copper uptake, we believe that dithiocarbamate/copper complexes are likely to be effective for the treatment of patients with prostate cancer whose disease is resistant to classical androgen ablation therapies.

HPV clearance and the neglected role of stochasticity.

Clearance of anogenital and oropharyngeal HPV infections is attributed primarily to a successful adaptive immune response. To date, little attention has been paid to the potential role of stochastic cell dynamics in the time it takes to clear an HPV infection. In this study, we combine mechanistic mathematical models at the cellular level with epidemiological data at the population level to disentangle the respective roles of immune capacity and cell dynamics in the clearing mechanism. Our results suggest that chance-in form of the stochastic dynamics of basal stem cells-plays a critical role in the elimination of HPV-infected cell clones. In particular, we find that in immunocompetent adolescents with cervical HPV infections, the immune response may contribute less than 20% to virus clearance-the rest is taken care of by the stochastic proliferation dynamics in the basal layer. In HIV-negative individuals, the contribution of the immune response may be negligible.

Bioluminescence imaging of glucose in tissue surrounding polyurethane and glucose sensor implants.

BACKGROUND: The bioluminescence technique was used to quantify the local glucose concentration in the tissue surrounding subcutaneously implanted polyurethane material and surrounding glucose sensors. In addition, some implants were coated with a single layer of adipose-derived stromal cells (ASCs) because these cells improve the wound-healing response around biomaterials. METHODS: Control and ASC-coated implants were implanted subcutaneously in rats for 1 or 8 weeks (polyurethane) or for 1 week only (glucose sensors). Tissue biopsies adjacent to the implant were immediately frozen at the time of explant. Cryosections were assayed for glucose concentration profile using the bioluminescence technique. RESULTS: For the polyurethane samples, no significant differences in glucose concentration within 100 μm of the implant surface were found between bare and ASC-coated implants at 1 or 8 weeks. A glucose concentration gradient was demonstrated around the glucose sensors. For all sensors, the minimum glucose concentration of approximately 4 mM was found at the implant surface and increased with distance from the sensor surface until the glucose concentration peaked at approximately 7 mM at 100 μm. Then the glucose concentration decreased to 5.5-6.5 mM more than 100 μmm from the surface. CONCLUSIONS: The ASC attachment to polyurethane and to glucose sensors did not change the glucose profiles in the tissue surrounding the implants. Although most glucose sensors incorporate a diffusion barrier to reduce the gradient of glucose and oxygen in the tissue, it is typically assumed that there is no steep glucose gradient around the sensors. However, a glucose gradient was observed around the sensors. A more complete understanding of glucose transport and concentration gradients around sensors is critical.

Amino acid permeases require COPII components and the ER resident membrane protein Shr3p for packaging into transport vesicles in vitro.

In S. cerevisiae lacking SHR3, amino acid permeases specifically accumulate in membranes of the endoplasmic reticulum (ER) and fail to be transported to the plasma membrane. We examined the requirements of transport of the permeases from the ER to the Golgi in vitro. Addition of soluble COPII components (Sec23/24p, Sec13/31p, and Sar1p) to yeast membrane preparations generated vesicles containing the general amino acid permease. Gap1p, and the histidine permease, Hip1p. Shr3p was required for the packaging of Gap1p and Hip1p but was not itself incorporated into transport vesicles. In contrast, the packaging of the plasma membrane ATPase, Pma1p, and the soluble yeast pheromone precursor, glycosylated pro alpha factor, was independent of Shr3p. In addition, we show that integral membrane and soluble cargo colocalize in transport vesicles, indicating that different types of cargo are not segregated at an early step in secretion. Our data suggest that specific ancillary proteins in the ER membrane recruit subsets of integral membrane protein cargo into COPII transport vesicles.

A population model of folate-mediated one-carbon metabolism.

BACKGROUND: Previous mathematical models for hepatic and tissue one-carbon metabolism have been combined and extended to include a blood plasma compartment. We use this model to study how the concentrations of metabolites that can be measured in the plasma are related to their respective intracellular concentrations. METHODS: The model consists of a set of ordinary differential equations, one for each metabolite in each compartment, and kinetic equations for metabolism and for transport between compartments. The model was validated by comparison to a variety of experimental data such as the methionine load test and variation in folate intake. We further extended this model by introducing random and systematic variation in enzyme activity. OUTCOMES AND CONCLUSIONS: A database of 10,000 virtual individuals was generated, each with a quantitatively different one-carbon metabolism. Our population has distributions of folate and homocysteine in the plasma and tissues that are similar to those found in the NHANES data. The model reproduces many other sets of clinical data. We show that tissue and plasma folate is highly correlated, but liver and plasma folate much less so. Oxidative stress increases the plasma S-adenosylmethionine/S-adenosylhomocysteine (SAM/SAH) ratio. We show that many relationships among variables are nonlinear and in many cases we provide explanations. Sampling of subpopulations produces dramatically different apparent associations among variables. The model can be used to simulate populations with polymorphisms in genes for folate metabolism and variations in dietary input.

Robust Uncertainty Quantification and Scalable Computation for Computer Models with Massive Output

Uncertainty quantification (UQ) is both an old and new concept. The current novelty lies in the interactions and synthesis of mathematical models, computer experiments, statistics, field/real experiments, and probability theory, with a particular emphasize on the large-scale simulations by computer models. The challenges not only come from the complication of scientific questions, but also from the size of the information. It is the focus in this thesis to provide statistical models that are scalable to massive data produced in computer experiments and real experiments, through fast and robust statistical inference.

Chapter 2 provides a practical approach for simultaneously emulating/approximating massive number of functions, with the application on hazard quantification of Soufri\`{e}re Hills volcano in Montserrate island. Chapter 3 discusses another problem with massive data, in which the number of observations of a function is large. An exact algorithm that is linear in time is developed for the problem of interpolation of Methylation levels. Chapter 4 and Chapter 5 are both about the robust inference of the models. Chapter 4 provides a new criteria robustness parameter estimation criteria and several ways of inference have been shown to satisfy such criteria. Chapter 5 develops a new prior that satisfies some more criteria and is thus proposed to use in practice.

Stereocomplexed poly(lactic acid)-poly(ethylene glycol) nanoparticles with dual-emissive boron dyes for tumor accumulation.

Responsive biomaterials play important roles in imaging, diagnostics, and therapeutics. Polymeric nanoparticles (NPs) containing hydrophobic and hydrophilic segments are one class of biomaterial utilized for these purposes. The incorporation of luminescent molecules into NPs adds optical imaging and sensing capability to these vectors. Here we report on the synthesis of dual-emissive, pegylated NPs with "stealth"-like properties, delivered intravenously (IV), for the study of tumor accumulation. The NPs were created by means of stereocomplexation using a methoxy-terminated polyethylene glycol and poly(D-lactide) (mPEG-PDLA) block copolymer combined with iodide-substituted difluoroboron dibenzoylmethane-poly(L-lactide) (BF2dbm(I)PLLA). Boron nanoparticles (BNPs) were fabricated in two different solvent compositions to study the effects on BNP size distribution. The physical and photoluminescent properties of the BNPs were studied in vitro over time to determine stability. Finally, preliminary in vivo results show that stereocomplexed BNPs injected IV are taken up by tumors, an important prerequisite to their use as hypoxia imaging agents in preclinical studies.

Pulsating tandem microbubble for localized and directional single-cell membrane poration.

The interaction of laser-generated tandem microbubble (maximum diameter of about 50  μm) with single (rat mammary carcinoma) cells is investigated in a 25-μm liquid layer. Antiphase and coupled oscillation of the tandem microbubble leads to the formation of alternating, directional microjets (with max microstreaming velocity of 10  m/s) and vortices (max vorticity of 350 000  s{-1}) in opposite directions. Localized and directional membrane poration (200 nm to 2  μm in pore size) can be produced by the tandem microbubble in an orientation and proximity-dependent manner, which is absent from a single oscillating microbubble of comparable size and at the same stand-off distance.

Nuclear import of Cdk/cyclin complexes: identification of distinct mechanisms for import of Cdk2/cyclin E and Cdc2/cyclin B1.

Reversible phosphorylation of nuclear proteins is required for both DNA replication and entry into mitosis. Consequently, most cyclin-dependent kinase (Cdk)/cyclin complexes are localized to the nucleus when active. Although our understanding of nuclear transport processes has been greatly enhanced by the recent identification of nuclear targeting sequences and soluble nuclear import factors with which they interact, the mechanisms used to target Cdk/cyclin complexes to the nucleus remain obscure; this is in part because these proteins lack obvious nuclear localization sequences. To elucidate the molecular mechanisms responsible for Cdk/cyclin transport, we examined nuclear import of fluorescent Cdk2/cyclin E and Cdc2/cyclin B1 complexes in digitonin-permeabilized mammalian cells and also examined potential physical interactions between these Cdks, cyclins, and soluble import factors. We found that the nuclear import machinery recognizes these Cdk/cyclin complexes through direct interactions with the cyclin component. Surprisingly, cyclins E and B1 are imported into nuclei via distinct mechanisms. Cyclin E behaves like a classical basic nuclear localization sequence-containing protein, binding to the alpha adaptor subunit of the importin-alpha/beta heterodimer. In contrast, cyclin B1 is imported via a direct interaction with a site in the NH2 terminus of importin-beta that is distinct from that used to bind importin-alpha.

Control of cyclin B1 localization through regulated binding of the nuclear export factor CRM1.

Activation of the Cyclin B/Cdc2 kinase complex triggers entry into mitosis in all eukaryotic cells. Cyclin B1 localization changes dramatically during the cell cycle, precipitously transiting from the cytoplasm to the nucleus at the beginning of mitosis. Presumably, this relocalization promotes the phosphorylation of nuclear targets critical for chromatin condensation and nuclear envelope breakdown. We show here that the previously characterized cytoplasmic retention sequence of Cyclin B1, responsible for its interphase cytoplasmic localization, is actually an autonomous nuclear export sequence, capable of directing nuclear export of a heterologous protein, and able to bind specifically to the recently identified export mediator, CRM1. We propose that the observed cytoplasmic localization of Cyclin B1 during interphase reflects the equilibrium between ongoing nuclear import and rapid CRM1-mediated export. In support of this hypothesis, we found that treatment of cells with leptomycin B, which disrupted Cyclin B1-CRM1 interactions, led to a marked nuclear accumulation of Cyclin B1. In mitosis, Cyclin B1 undergoes phosphorylation at several sites, a subset of which have been proposed to play a role in Cyclin B1 accumulation in the nucleus. Both CRM1 binding and the ability to direct nuclear export were affected by mutation of these phosphorylation sites; thus, we propose that Cyclin B1 phosphorylation at the G2/M transition prevents its interaction with CRM1, thereby reducing nuclear export and facilitating nuclear accumulation.

D-Amino acid peptide residualizing agents bearing N-hydroxysuccinimido- and maleimido-functional groups and their application for trastuzumab radioiodination.

INTRODUCTION: Proteins that undergo receptor-mediated endocytosis are subject to lysosomal degradation, requiring radioiodination methods that minimize loss of radioactivity from tumor cells after this process occurs. To accomplish this, we developed the residualizing radioiodination agent N(ϵ)-(3-[(*)I]iodobenzoyl)-Lys(5)-N(α)-maleimido-Gly(1)-D-GEEEK (Mal-D-GEEEK-[(*)I]IB), which enhanced tumor uptake but also increased kidney activity and necessitates generation of sulfhydryl moieties on the protein. The purpose of the current study was to synthesize and evaluate a new D-amino acid based agent that might avoid these potential problems. METHODS: N(α)-(3-iodobenzoyl)-(5-succinimidyloxycarbonyl)-D-EEEG (NHS-IB-D-EEEG), which contains 3 D-glutamates to provide negative charge and a N-hydroxysuccinimide function to permit conjugation to unmodified proteins, and the corresponding tin precursor were produced by solid phase peptide synthesis and subsequent conjugation with appropriate reagents. Radioiodination of the anti-HER2 antibody trastuzumab using NHS-IB-D-EEEG and Mal-D-GEEEK-IB was compared. Paired-label internalization assays on BT474 breast carcinoma cells and biodistribution studies in athymic mice bearing BT474M1 xenografts were performed to evaluate the two radioiodinated D-peptide trastuzumab conjugates. RESULTS: NHS-[(131)I]IB-D-EEEG was produced in 53.8%±13.4% and conjugated to trastuzumab in 39.5%±7.6% yield. Paired-label internalization assays with trastuzumab-NHS-[(131)I]IB-D-EEEG and trastuzumab-Mal-D-GEEEK-[(125)I]IB demonstrated similar intracellular trapping for both conjugates at 1h ((131)I, 84.4%±6.1%; (125)I, 88.6%±5.2%) through 24h ((131)I, 60.7%±6.8%; (125)I, 64.9%±6.9%). In the biodistribution experiment, tumor uptake peaked at 48 h (trastuzumab-NHS-[(131)I]IB-D-EEEG, 29.8%±3.6%ID/g; trastuzumab-Mal-D-GEEEK-[(125)I]IB, 45.3%±5.3%ID/g) and was significantly higher for (125)I at all time points. In general, normal tissue levels were lower for trastuzumab-NHS-[(131)I]IB-D-EEEG, with the differences being greatest in kidneys ((131)I, 2.2%±0.4%ID/g; (125)I, 16.9%±2.8%ID/g at 144 h). CONCLUSION: NHS-[(131)I]IB-D-EEEG warrants further evaluation as a residualizing radioiodination agent for labeling internalizing antibodies/fragments, particularly for applications where excessive renal accumulation could be problematic.