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.

A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

R5 clade C SHIV strains with tier 1 or 2 neutralization sensitivity: tools to dissect env evolution and to develop AIDS vaccines in primate models.

BACKGROUND: HIV-1 clade C (HIV-C) predominates worldwide, and anti-HIV-C vaccines are urgently needed. Neutralizing antibody (nAb) responses are considered important but have proved difficult to elicit. Although some current immunogens elicit antibodies that neutralize highly neutralization-sensitive (tier 1) HIV strains, most circulating HIVs exhibiting a less sensitive (tier 2) phenotype are not neutralized. Thus, both tier 1 and 2 viruses are needed for vaccine discovery in nonhuman primate models. METHODOLOGY/PRINCIPAL FINDINGS: We constructed a tier 1 simian-human immunodeficiency virus, SHIV-1157ipEL, by inserting an "early," recently transmitted HIV-C env into the SHIV-1157ipd3N4 backbone [1] encoding a "late" form of the same env, which had evolved in a SHIV-infected rhesus monkey (RM) with AIDS. SHIV-1157ipEL was rapidly passaged to yield SHIV-1157ipEL-p, which remained exclusively R5-tropic and had a tier 1 phenotype, in contrast to "late" SHIV-1157ipd3N4 (tier 2). After 5 weekly low-dose intrarectal exposures, SHIV-1157ipEL-p systemically infected 16 out of 17 RM with high peak viral RNA loads and depleted gut CD4+ T cells. SHIV-1157ipEL-p and SHIV-1157ipd3N4 env genes diverge mostly in V1/V2. Molecular modeling revealed a possible mechanism for the increased neutralization resistance of SHIV-1157ipd3N4 Env: V2 loops hindering access to the CD4 binding site, shown experimentally with nAb b12. Similar mutations have been linked to decreased neutralization sensitivity in HIV-C strains isolated from humans over time, indicating parallel HIV-C Env evolution in humans and RM. CONCLUSIONS/SIGNIFICANCE: SHIV-1157ipEL-p, the first tier 1 R5 clade C SHIV, and SHIV-1157ipd3N4, its tier 2 counterpart, represent biologically relevant tools for anti-HIV-C vaccine development in primates.

Oscillations by minimal bacterial suicide circuits reveal hidden facets of host-circuit physiology.

Synthetic biology seeks to enable programmed control of cellular behavior though engineered biological systems. These systems typically consist of synthetic circuits that function inside, and interact with, complex host cells possessing pre-existing metabolic and regulatory networks. Nevertheless, while designing systems, a simple well-defined interface between the synthetic gene circuit and the host is frequently assumed. We describe the generation of robust but unexpected oscillations in the densities of bacterium Escherichia coli populations by simple synthetic suicide circuits containing quorum components and a lysis gene. Contrary to design expectations, oscillations required neither the quorum sensing genes (luxR and luxI) nor known regulatory elements in the P(luxI) promoter. Instead, oscillations were likely due to density-dependent plasmid amplification that established a population-level negative feedback. A mathematical model based on this mechanism captures the key characteristics of oscillations, and model predictions regarding perturbations to plasmid amplification were experimentally validated. Our results underscore the importance of plasmid copy number and potential impact of "hidden interactions" on the behavior of engineered gene circuits - a major challenge for standardizing biological parts. As synthetic biology grows as a discipline, increasing value may be derived from tools that enable the assessment of parts in their final context.

Impact of simian immunodeficiency virus infection on chimpanzee population dynamics.

Like human immunodeficiency virus type 1 (HIV-1), simian immunodeficiency virus of chimpanzees (SIVcpz) can cause CD4+ T cell loss and premature death. Here, we used molecular surveillance tools and mathematical modeling to estimate the impact of SIVcpz infection on chimpanzee population dynamics. Habituated (Mitumba and Kasekela) and non-habituated (Kalande) chimpanzees were studied in Gombe National Park, Tanzania. Ape population sizes were determined from demographic records (Mitumba and Kasekela) or individual sightings and genotyping (Kalande), while SIVcpz prevalence rates were monitored using non-invasive methods. Between 2002-2009, the Mitumba and Kasekela communities experienced mean annual growth rates of 1.9% and 2.4%, respectively, while Kalande chimpanzees suffered a significant decline, with a mean growth rate of -6.5% to -7.4%, depending on population estimates. A rapid decline in Kalande was first noted in the 1990s and originally attributed to poaching and reduced food sources. However, between 2002-2009, we found a mean SIVcpz prevalence in Kalande of 46.1%, which was almost four times higher than the prevalence in Mitumba (12.7%) and Kasekela (12.1%). To explore whether SIVcpz contributed to the Kalande decline, we used empirically determined SIVcpz transmission probabilities as well as chimpanzee mortality, mating and migration data to model the effect of viral pathogenicity on chimpanzee population growth. Deterministic calculations indicated that a prevalence of greater than 3.4% would result in negative growth and eventual population extinction, even using conservative mortality estimates. However, stochastic models revealed that in representative populations, SIVcpz, and not its host species, frequently went extinct. High SIVcpz transmission probability and excess mortality reduced population persistence, while intercommunity migration often rescued infected communities, even when immigrating females had a chance of being SIVcpz infected. Together, these results suggest that the decline of the Kalande community was caused, at least in part, by high levels of SIVcpz infection. However, population extinction is not an inevitable consequence of SIVcpz infection, but depends on additional variables, such as migration, that promote survival. These findings are consistent with the uneven distribution of SIVcpz throughout central Africa and explain how chimpanzees in Gombe and elsewhere can be at equipoise with this pathogen.

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.

Crafting analytical tools to study institutional change

Most powerful analytical tools used in the social sciences are well suited for studying static situations. Static and mechanistic analysis, however, is not adequate to understand the changing world in which we live. In order to adequately address the most pressing social and environmental challenges looming ahead, we need to develop analytical tools for analyzing dynamic situations -particularly institutional change. In this paper, we develop an analytical tool to study institutional change, more specifically, the evolution of rules and norms. We believe that in order for such an analytical tool to be useful to develop a general theory of institutional change, it needs to enable the analyst to concisely record the processes of change in multiple specific settings so that lessons from such settings can eventually be integrated into a more general predictive theory of change. Copyright © The JOIE Foundation 2010.

Can We Learn in the Sandbox Together?: Interprofessional Case Conferences as Facilitation Tools

Duke Medicine utilized interprofessional case conferences (ICCs) from 2008-2012 with the objective of modeling and facilitating development of teamwork skills among diverse health profession students, including physical therapy, physician assistant, medical doctor and nursing. The purpose of this publication was to describe the operational process used to develop and implement the ICCs and measure the success of the ICCs in order to shape future work. The ICCs were offered to develop skills and attitudes essential for participation in healthcare teams. Students were facilitated by faculty of different professions to conduct a comprehensive historical assessment of a standardized patient (SP), determine pertinent physical and lab assessments to undertake, and develop and share a comprehensive management plan. Cases included patient problems that were authentic and relevant to each professional student in attendance. The main barriers to implementation are outlined and the focus on the process of working together is highlighted. Evaluation showed high satisfaction rates among participants and the outcomes from these experiences are presented. The limitations of these results are discussed and recommendations for future assessment are emphasized. The ICCs demonstrated that students will come together voluntarily to learn in teams, even at a research-focused institution, and express benefit from the collaborative exercise.

Computer vision tools for low-cost and noninvasive measurement of autism-related behaviors in infants.

The early detection of developmental disorders is key to child outcome, allowing interventions to be initiated which promote development and improve prognosis. Research on autism spectrum disorder (ASD) suggests that behavioral signs can be observed late in the first year of life. Many of these studies involve extensive frame-by-frame video observation and analysis of a child's natural behavior. Although nonintrusive, these methods are extremely time-intensive and require a high level of observer training; thus, they are burdensome for clinical and large population research purposes. This work is a first milestone in a long-term project on non-invasive early observation of children in order to aid in risk detection and research of neurodevelopmental disorders. We focus on providing low-cost computer vision tools to measure and identify ASD behavioral signs based on components of the Autism Observation Scale for Infants (AOSI). In particular, we develop algorithms to measure responses to general ASD risk assessment tasks and activities outlined by the AOSI which assess visual attention by tracking facial features. We show results, including comparisons with expert and nonexpert clinicians, which demonstrate that the proposed computer vision tools can capture critical behavioral observations and potentially augment the clinician's behavioral observations obtained from real in-clinic assessments.

Computer vision tools for the non-invasive assessment of autism-related behavioral markers

The early detection of developmental disorders is key to child outcome, allowing interventions to be initiated that promote development and improve prognosis. Research on autism spectrum disorder (ASD) suggests behavioral markers can be observed late in the first year of life. Many of these studies involved extensive frame-by-frame video observation and analysis of a child's natural behavior. Although non-intrusive, these methods are extremely time-intensive and require a high level of observer training; thus, they are impractical for clinical and large population research purposes. Diagnostic measures for ASD are available for infants but are only accurate when used by specialists experienced in early diagnosis. This work is a first milestone in a long-term multidisciplinary project that aims at helping clinicians and general practitioners accomplish this early detection/measurement task automatically. We focus on providing computer vision tools to measure and identify ASD behavioral markers based on components of the Autism Observation Scale for Infants (AOSI). In particular, we develop algorithms to measure three critical AOSI activities that assess visual attention. We augment these AOSI activities with an additional test that analyzes asymmetrical patterns in unsupported gait. The first set of algorithms involves assessing head motion by tracking facial features, while the gait analysis relies on joint foreground segmentation and 2D body pose estimation in video. We show results that provide insightful knowledge to augment the clinician's behavioral observations obtained from real in-clinic assessments.

A COMPARISON OF MARKET CLEARING TOOLS IN ELECTRICITY SYSTEMS

To maintain a strict balance between demand and supply in the US power systems, the Independent System Operators (ISOs) schedule power plants and determine electricity prices using a market clearing model. This model determines for each time period and power plant, the times of startup, shutdown, the amount of power production, and the provisioning of spinning and non-spinning power generation reserves, etc. Such a deterministic optimization model takes as input the characteristics of all the generating units such as their power generation installed capacity, ramp rates, minimum up and down time requirements, and marginal costs for production, as well as the forecast of intermittent energy such as wind and solar, along with the minimum reserve requirement of the whole system. This reserve requirement is determined based on the likelihood of outages on the supply side and on the levels of error forecasts in demand and intermittent generation. With increased installed capacity of intermittent renewable energy, determining the appropriate level of reserve requirements has become harder. Stochastic market clearing models have been proposed as an alternative to deterministic market clearing models. Rather than using a fixed reserve targets as an input, stochastic market clearing models take different scenarios of wind power into consideration and determine reserves schedule as output. Using a scaled version of the power generation system of PJM, a regional transmission organization (RTO) that coordinates the movement of wholesale electricity in all or parts of 13 states and the District of Columbia, and wind scenarios generated from BPA (Bonneville Power Administration) data, this paper explores a comparison of the performance between a stochastic and deterministic model in market clearing. The two models are compared in their ability to contribute to the affordability, reliability and sustainability of the electricity system, measured in terms of total operational costs, load shedding and air emissions. The process of building the models and running for tests indicate that a fair comparison is difficult to obtain due to the multi-dimensional performance metrics considered here, and the difficulty in setting up the parameters of the models in a way that does not advantage or disadvantage one modeling framework. Along these lines, this study explores the effect that model assumptions such as reserve requirements, value of lost load (VOLL) and wind spillage costs have on the comparison of the performance of stochastic vs deterministic market clearing models.

New tools provide a second look at HDV ribozyme structure, dynamics and cleavage.

The hepatitis delta virus (HDV) ribozyme is a self-cleaving RNA enzyme essential for processing viral transcripts during rolling circle viral replication. The first crystal structure of the cleaved ribozyme was solved in 1998, followed by structures of uncleaved, mutant-inhibited and ion-complexed forms. Recently, methods have been developed that make the task of modeling RNA structure and dynamics significantly easier and more reliable. We have used ERRASER and PHENIX to rebuild and re-refine the cleaved and cis-acting C75U-inhibited structures of the HDV ribozyme. The results correct local conformations and identify alternates for RNA residues, many in functionally important regions, leading to improved R values and model validation statistics for both structures. We compare the rebuilt structures to a higher resolution, trans-acting deoxy-inhibited structure of the ribozyme, and conclude that although both inhibited structures are consistent with the currently accepted hammerhead-like mechanism of cleavage, they do not add direct structural evidence to the biochemical and modeling data. However, the rebuilt structures (PDBs: 4PR6, 4PRF) provide a more robust starting point for research on the dynamics and catalytic mechanism of the HDV ribozyme and demonstrate the power of new techniques to make significant improvements in RNA structures that impact biologically relevant conclusions.