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.

Phosphorus export from a restored wetland ecosystem in response to natural and experimental hydrologic fluctuations

Wetland restoration is a commonly used approach to reduce nutrient loading to freshwater and coastal ecosystems, with many wetland restoration efforts occurring in former agricultural fields. Restored wetlands are expected to be effective at retaining or removing both nitrogen and phosphorus (P), yet restoring wetland hydrology to former agricultural fields can lead to the release of legacy fertilizer P. Here, we examined P cycling and export following rewetting of the Timberlake Restoration Project, a 440 ha restored riverine wetland complex in the coastal plain of North Carolina. We also compared P cycling within the restored wetland to two minimally disturbed nearby wetlands and an adjacent active agricultural field. In the restored wetland we observed increased soluble reactive phosphorus (SRP) concentrations following initial flooding, consistent with our expectations that P bound to iron would be released under reducing conditions. SRP concentrations in spring were 2.5 times higher leaving the restored wetland than a forested wetland and an agricultural field. During two large-scale drawdown and rewetting experiments we decreased the water depth by 1 m in ∼10 ha of inundated wetland for 2 weeks, followed by reflooding. Rewetting following experimental drainage had no effect on SRP concentrations in winter, but SRP concentrations did increase when the experiment was repeated during summer. Our best estimates suggest that this restored wetland could release legacy fertilizer P for up to a decade following hydrologic restoration. The time lag between restoration and biogeochemical recovery should be incorporated into management strategies of restored wetlands. Copyright 2010 by the American Geophysical Union.

Microbial inactivation of Pseudomonas putida and Pichia pastoris using gene silencing.

Antisense deoxyoligonucleotide (ASO) gene silencing was investigated as a potential disinfection tool for industrial and drinking water treatment application. ASOs bind with their reverse complementary mRNA transcripts thereby blocking protein translation. While ASO silencing has mainly been studied in medicine, it may be useful for modulating gene expression and inactivating microorganisms in environmental applications. In this proof of concept work, gene targets were sh ble (zeocin resistance) and todE (catechol-2,3-dioxygenase) in Pichia pastoris and npt (kanamycin resistance) in Pseudomonas putida. A maximum 0.5-fold decrease in P. pastoris cell numbers was obtained following a 120 min incubation with single-stranded DNA (ssDNA) concentrations ranging from 0.2 to 200 nM as compared to the no ssDNA control. In P. putida, a maximum 5.2-fold decrease was obtained after 90 min with 400 nM ssDNA. While the silencing efficiencies varied for the 25 targets tested, these results suggest that protein activity as well as microbial growth can be altered using ASO gene silencing-based tools. If successful, this technology has the potential to eliminate some of the environmental and health issues associated with the use of strong chemical biocides. However, prior to its dissemination, more research is needed to increase silencing efficiency and develop effective delivery methods.

An alphavirus vector overcomes the presence of neutralizing antibodies and elevated numbers of Tregs to induce immune responses in humans with advanced cancer.

Therapeutic anticancer vaccines are designed to boost patients' immune responses to tumors. One approach is to use a viral vector to deliver antigen to in situ DCs, which then activate tumor-specific T cell and antibody responses. However, vector-specific neutralizing antibodies and suppressive cell populations such as Tregs remain great challenges to the efficacy of this approach. We report here that an alphavirus vector, packaged in virus-like replicon particles (VRP) and capable of efficiently infecting DCs, could be repeatedly administered to patients with metastatic cancer expressing the tumor antigen carcinoembryonic antigen (CEA) and that it overcame high titers of neutralizing antibodies and elevated Treg levels to induce clinically relevant CEA-specific T cell and antibody responses. The CEA-specific antibodies mediated antibody-dependent cellular cytotoxicity against tumor cells from human colorectal cancer metastases. In addition, patients with CEA-specific T cell responses exhibited longer overall survival. These data suggest that VRP-based vectors can overcome the presence of neutralizing antibodies to break tolerance to self antigen and may be clinically useful for immunotherapy in the setting of tumor-induced immunosuppression.

Ecological homogenization of urban USA

A visually apparent but scientifically untested outcome of land-use change is homogenization across urban areas, where neighborhoods in different parts of the country have similar patterns of roads, residential lots, commercial areas, and aquatic features. We hypothesize that this homogenization extends to ecological structure and also to ecosystem functions such as carbon dynamics and microclimate, with continental-scale implications. Further, we suggest that understanding urban homogenization will provide the basis for understanding the impacts of urban land-use change from local to continental scales. Here, we show how multi-scale, multidisciplinary datasets from six metropolitan areas that cover the major climatic regions of the US (Phoenix, AZ; Miami, FL; Baltimore, MD; Boston, MA; Minneapolis-St Paul, MN; and Los Angeles, CA) can be used to determine how household and neighborhood characteristics correlate with land-management practices, land-cover composition, and landscape structure and ecosystem functions at local, regional, and continental scales. © The Ecological Society of America.

Convergent Surface Water Distributions in U.S. Cities

Earth's surface is rapidly urbanizing, resulting in dramatic changes in the abundance, distribution and character of surface water features in urban landscapes. However, the scope and consequences of surface water redistribution at broad spatial scales are not well understood. We hypothesized that urbanization would lead to convergent surface water abundance and distribution: in other words, cities will gain or lose water such that they become more similar to each other than are their surrounding natural landscapes. Using a database of more than 1 million water bodies and 1 million km of streams, we compared the surface water of 100 US cities with their surrounding undeveloped land. We evaluated differences in areal (A WB) and numeric densities (N WB) of water bodies (lakes, wetlands, and so on), the morphological characteristics of water bodies (size), and the density (D C) of surface flow channels (that is, streams and rivers). The variance of urban A WB, N WB, and D C across the 100 MSAs decreased, by 89, 25, and 71%, respectively, compared to undeveloped land. These data show that many cities are surface water poor relative to undeveloped land; however, in drier landscapes urbanization increases the occurrence of surface water. This convergence pattern strengthened with development intensity, such that high intensity urban development had an areal water body density 98% less than undeveloped lands. Urbanization appears to drive the convergence of hydrological features across the US, such that surface water distributions of cities are more similar to each other than to their surrounding landscapes. © 2014 The Author(s).

Assessing the homogenization of urban land management with an application to US residential lawn care.

Changes in land use, land cover, and land management present some of the greatest potential global environmental challenges of the 21st century. Urbanization, one of the principal drivers of these transformations, is commonly thought to be generating land changes that are increasingly similar. An implication of this multiscale homogenization hypothesis is that the ecosystem structure and function and human behaviors associated with urbanization should be more similar in certain kinds of urbanized locations across biogeophysical gradients than across urbanization gradients in places with similar biogeophysical characteristics. This paper introduces an analytical framework for testing this hypothesis, and applies the framework to the case of residential lawn care. This set of land management behaviors are often assumed--not demonstrated--to exhibit homogeneity. Multivariate analyses are conducted on telephone survey responses from a geographically stratified random sample of homeowners (n = 9,480), equally distributed across six US metropolitan areas. Two behaviors are examined: lawn fertilizing and irrigating. Limited support for strong homogenization is found at two scales (i.e., multi- and single-city; 2 of 36 cases), but significant support is found for homogenization at only one scale (22 cases) or at neither scale (12 cases). These results suggest that US lawn care behaviors are more differentiated in practice than in theory. Thus, even if the biophysical outcomes of urbanization are homogenizing, managing the associated sustainability implications may require a multiscale, differentiated approach because the underlying social practices appear relatively varied. The analytical approach introduced here should also be productive for other facets of urban-ecological homogenization.

Antisense Gene Silencing and Bacteriophages as Novel Disinfection Processes for Engineered Systems

The growth and proliferation of invasive bacteria in engineered systems is an ongoing problem. While there are a variety of physical and chemical processes to remove and inactivate bacterial pathogens, there are many situations in which these tools are no longer effective or appropriate for the treatment of a microbial target. For example, certain strains of bacteria are becoming resistant to commonly used disinfectants, such as chlorine and UV. Additionally, the overuse of antibiotics has contributed to the spread of antibiotic resistance, and there is concern that wastewater treatment processes are contributing to the spread of antibiotic resistant bacteria.

Due to the continually evolving nature of bacteria, it is difficult to develop methods for universal bacterial control in a wide range of engineered systems, as many of our treatment processes are static in nature. Still, invasive bacteria are present in many natural and engineered systems, where the application of broad acting disinfectants is impractical, because their use may inhibit the original desired bioprocesses. Therefore, to better control the growth of treatment resistant bacteria and to address limitations with the current disinfection processes, novel tools that are both specific and adaptable need to be developed and characterized.

In this dissertation, two possible biological disinfection processes were investigated for use in controlling invasive bacteria in engineered systems. First, antisense gene silencing, which is the specific use of oligonucleotides to silence gene expression, was investigated. This work was followed by the investigation of bacteriophages (phages), which are viruses that are specific to bacteria, in engineered systems.


For the antisense gene silencing work, a computational approach was used to quantify the number of off-targets and to determine the effects of off-targets in prokaryotic organisms. For the organisms of Escherichia coli K-12 MG1655 and Mycobacterium tuberculosis H37Rv the mean number of off-targets was found to be 15.0 + 13.2 and 38.2 + 61.4, respectively, which results in a reduction of greater than 90% of the effective oligonucleotide concentration. It was also demonstrated that there was a high variability in the number of off-targets over the length of a gene, but that on average, there was no general gene location that could be targeted to reduce off-targets. Therefore, this analysis needs to be performed for each gene in question. It was also demonstrated that the thermodynamic binding energy between the oligonucleotide and the mRNA accounted for 83% of the variation in the silencing efficiency, compared to the number of off-targets, which explained 43% of the variance of the silencing efficiency. This suggests that optimizing thermodynamic parameters must be prioritized over minimizing the number of off-targets. In conclusion for the antisense work, these results suggest that off-target hybrids can account for a greater than 90% reduction in the concentration of the silencing oligonucleotides, and that the effective concentration can be increased through the rational design of silencing targets by minimizing off-target hybrids.

Regarding the work with phages, the disinfection rates of bacteria in the presence of phages was determined. The disinfection rates of E. coli K12 MG1655 in the presence of coliphage Ec2 ranged up to 2 h-1, and were dependent on both the initial phage and bacterial concentrations. Increasing initial phage concentrations resulted in increasing disinfection rates, and generally, increasing initial bacterial concentrations resulted in increasing disinfection rates. However, disinfection rates were found to plateau at higher bacterial and phage concentrations. A multiple linear regression model was used to predict the disinfection rates as a function of the initial phage and bacterial concentrations, and this model was able to explain 93% of the variance in the disinfection rates. The disinfection rates were also modeled with a particle aggregation model. The results from these model simulations suggested that at lower phage and bacterial concentrations there are not enough collisions to support active disinfection rates, which therefore, limits the conditions and systems where phage based bacterial disinfection is possible. Additionally, the particle aggregation model over predicted the disinfection rates at higher phage and bacterial concentrations of 108 PFU/mL and 108 CFU/mL, suggesting other interactions were occurring at these higher concentrations. Overall, this work highlights the need for the development of alternative models to more accurately describe the dynamics of this system at a variety of phage and bacterial concentrations. Finally, the minimum required hydraulic residence time was calculated for a continuous stirred-tank reactor and a plug flow reactor (PFR) as a function of both the initial phage and bacterial concentrations, which suggested that phage treatment in a PFR is theoretically possible.

In addition to determining disinfection rates, the long-term bacterial growth inhibition potential was determined for a variety of phages with both Gram-negative and Gram-positive bacteria. It was determined, that on average, phages can be used to inhibit bacterial growth for up to 24 h, and that this effect was concentration dependent for various phages at specific time points. Additionally, it was found that a phage cocktail was no more effective at inhibiting bacterial growth over the long-term than the best performing phage in isolation.

Finally, for an industrial application, the use of phages to inhibit invasive Lactobacilli in ethanol fermentations was investigated. It was demonstrated that phage 8014-B2 can achieve a greater than 3-log inactivation of Lactobacillus plantarum during a 48 h fermentation. Additionally, it was shown that phages can be used to protect final product yields and maintain yeast viability. Through modeling the fermentation system with differential equations it was determined that there was a 10 h window in the beginning of the fermentation run, where the addition of phages can be used to protect final product yields, and after 20 h no additional benefit of the phage addition was observed.

In conclusion, this dissertation improved the current methods for designing antisense gene silencing targets for prokaryotic organisms, and characterized phages from an engineering perspective. First, the current design strategy for antisense targets in prokaryotic organisms was improved through the development of an algorithm that minimized the number of off-targets. For the phage work, a framework was developed to predict the disinfection rates in terms of the initial phage and bacterial concentrations. In addition, the long-term bacterial growth inhibition potential of multiple phages was determined for several bacteria. In regard to the phage application, phages were shown to protect both final product yields and yeast concentrations during fermentation. Taken together, this work suggests that the rational design of phage treatment is possible and further work is needed to expand on this foundation.

A computational analysis of antisense off-targets in prokaryotic organisms

© 2014 .The adoption of antisense gene silencing as a novel disinfectant for prokaryotic organisms is hindered by poor silencing efficiencies. Few studies have considered the effects of off-targets on silencing efficiencies, especially in prokaryotic organisms. In this computational study, a novel algorithm was developed that determined and sorted the number of off-targets as a function of alignment length in Escherichia coli K-12 MG1655 and Mycobacterium tuberculosis H37Rv. The mean number of off-targets per a single location was calculated to be 14.1. ±. 13.3 and 36.1. ±. 58.5 for the genomes of E. coli K-12 MG1655 and M. tuberculosis H37Rv, respectively. Furthermore, when the entire transcriptome was analyzed, it was found that there was no general gene location that could be targeted to minimize or maximize the number of off-targets. In an effort to determine the effects of off-targets on silencing efficiencies, previously published studies were used. Analyses with acpP, ino1, and marORAB revealed a statistically significant relationship between the number of short alignment length off-targets hybrids and the efficacy of the antisense gene silencing, suggesting that the minimization of off-targets may be beneficial for antisense gene silencing in prokaryotic organisms.

X-linked inhibitor of apoptosis protein mediates tumor cell resistance to antibody-dependent cellular cytotoxicity.

Inflammatory breast cancer (IBC) is the deadliest, distinct subtype of breast cancer. High expression of epidermal growth factor receptors [EGFR or human epidermal growth factor receptor 2 (HER2)] in IBC tumors has prompted trials of anti-EGFR/HER2 monoclonal antibodies to inhibit oncogenic signaling; however, de novo and acquired therapeutic resistance is common. Another critical function of these antibodies is to mediate antibody-dependent cellular cytotoxicity (ADCC), which enables immune effector cells to engage tumors and deliver granzymes, activating executioner caspases. We hypothesized that high expression of anti-apoptotic molecules in tumors would render them resistant to ADCC. Herein, we demonstrate that the most potent caspase inhibitor, X-linked inhibitor of apoptosis protein (XIAP), overexpressed in IBC, drives resistance to ADCC mediated by cetuximab (anti-EGFR) and trastuzumab (anti-HER2). Overexpression of XIAP in parental IBC cell lines enhances resistance to ADCC; conversely, targeted downregulation of XIAP in ADCC-resistant IBC cells renders them sensitive. As hypothesized, this ADCC resistance is in part a result of the ability of XIAP to inhibit caspase activity; however, we also unexpectedly found that resistance was dependent on XIAP-mediated, caspase-independent suppression of reactive oxygen species (ROS) accumulation, which otherwise occurs during ADCC. Transcriptome analysis supported these observations by revealing modulation of genes involved in immunosuppression and oxidative stress response in XIAP-overexpressing, ADCC-resistant cells. We conclude that XIAP is a critical modulator of ADCC responsiveness, operating through both caspase-dependent and -independent mechanisms. These results suggest that strategies targeting the effects of XIAP on caspase activation and ROS suppression have the potential to enhance the activity of monoclonal antibody-based immunotherapy.

Wear and its effects on dental topography measures in howling monkeys (Alouatta palliata).

OBJECTIVES: Three dental topography measurements: Dirichlet Normal Energy (DNE), Relief Index (RFI), and Orientation Patch Count Rotated (OPCR) are examined for their interaction with measures of wear, within and between upper and lower molars in Alouatta palliata. Potential inferences of the "dental sculpting" phenomenon are explored. MATERIALS AND METHODS: Fifteen occluding pairs of howling monkey first molars (15 upper, 15 lower) opportunistically collected from La Pacifica, Costa Rica, were selected to sample wear stages ranging from unworn to heavily worn as measured by the Dentine Exposure Ratio (DER). DNE, RFI, and OPCR were measured from three-dimensional surface reconstructions (PLY files) derived from high-resolution CT scans. Relationships among the variables were tested with regression analyses. RESULTS: Upper molars have more cutting edges, exhibiting significantly higher DNE, but have significantly lower RFI values. However, the relationships among the measures are concordant across both sets of molars. DER and EDJL are curvilinearly related. DER is positively correlated with DNE, negatively correlated with RFI, and uncorrelated with OPCR. EDJL is not correlated with DNE, or RFI, but is positively correlated with OPCR among lower molars only. DISCUSSION: The relationships among these metrics suggest that howling monkey teeth adaptively engage macrowear. DNE increases with wear in this sample presumably improving food breakdown. RFI is initially high but declines with wear, suggesting that the initially high RFI safeguards against dental senescence. OPCR values in howling monkey teeth do not show a clear relationship with wear changes.

Introducing molaR: a New R Package for Quantitative Topographic Analysis of Teeth (and Other Topographic Surfaces)

© 2016 Springer Science+Business Media New YorkResearchers studying mammalian dentitions from functional and adaptive perspectives increasingly have moved towards using dental topography measures that can be estimated from 3D surface scans, which do not require identification of specific homologous landmarks. Here we present molaR, a new R package designed to assist researchers in calculating four commonly used topographic measures: Dirichlet Normal Energy (DNE), Relief Index (RFI), Orientation Patch Count (OPC), and Orientation Patch Count Rotated (OPCR) from surface scans of teeth, enabling a unified application of these informative new metrics. In addition to providing topographic measuring tools, molaR has complimentary plotting functions enabling highly customizable visualization of results. This article gives a detailed description of the DNE measure, walks researchers through installing, operating, and troubleshooting molaR and its functions, and gives an example of a simple comparison that measured teeth of the primates Alouatta and Pithecia in molaR and other available software packages. molaR is a free and open source software extension, which can be found at the doi:10.13140/RG.2.1.3563.4961(molaR v. 2.0) as well as on the Internet repository CRAN, which stores R packages.