Persistent Homology Analysis of Brain Artery Trees.

New representations of tree-structured data objects, using ideas from topological data analysis, enable improved statistical analyses of a population of brain artery trees. A number of representations of each data tree arise from persistence diagrams that quantify branching and looping of vessels at multiple scales. Novel approaches to the statistical analysis, through various summaries of the persistence diagrams, lead to heightened correlations with covariates such as age and sex, relative to earlier analyses of this data set. The correlation with age continues to be significant even after controlling for correlations from earlier significant summaries.

Math 412 - Topology with Applications

Highlights of Data Expedition: • Students explored daily observations of local climate data spanning the past 35 years. • Topological Data Analysis, or TDA for short, provides cutting-edge tools for studying the geometry of data in arbitrarily high dimensions. • Using TDA tools, students discovered intrinsic dynamical features of the data and learned how to quantify periodic phenomenon in a time-series. • Since nature invariably produces noisy data which rarely has exact periodicity, students also considered the theoretical basis of almost-periodicity and even invented and tested new mathematical definitions of almost-periodic functions. Summary The dataset we used for this data expedition comes from the Global Historical Climatology Network. “GHCN (Global Historical Climatology Network)-Daily is an integrated database of daily climate summaries from land surface stations across the globe.” Source: https://www.ncdc.noaa.gov/oa/climate/ghcn-daily/ We focused on the daily maximum and minimum temperatures from January 1, 1980 to April 1, 2015 collected from RDU International Airport. Through a guided series of exercises designed to be performed in Matlab, students explore these time-series, initially by direct visualization and basic statistical techniques. Then students are guided through a special sliding-window construction which transforms a time-series into a high-dimensional geometric curve. These high-dimensional curves can be visualized by projecting down to lower dimensions as in the figure below (Figure 1), however, our focus here was to use persistent homology to directly study the high-dimensional embedding. The shape of these curves has meaningful information but how one describes the “shape” of data depends on which scale the data is being considered. However, choosing the appropriate scale is rarely an obvious choice. Persistent homology overcomes this obstacle by allowing us to quantitatively study geometric features of the data across multiple-scales. Through this data expedition, students are introduced to numerically computing persistent homology using the rips collapse algorithm and interpreting the results. In the specific context of sliding-window constructions, 1-dimensional persistent homology can reveal the nature of periodic structure in the original data. I created a special technique to study how these high-dimensional sliding-window curves form loops in order to quantify the periodicity. Students are guided through this construction and learn how to visualize and interpret this information. Climate data is extremely complex (as anyone who has suffered from a bad weather prediction can attest) and numerous variables play a role in determining our daily weather and temperatures. This complexity coupled with imperfections of measuring devices results in very noisy data. This causes the annual seasonal periodicity to be far from exact. To this end, I have students explore existing theoretical notions of almost-periodicity and test it on the data. They find that some existing definitions are also inadequate in this context. Hence I challenged them to invent new mathematics by proposing and testing their own definition. These students rose to the challenge and suggested a number of creative definitions. While autocorrelation and spectral methods based on Fourier analysis are often used to explore periodicity, the construction here provides an alternative paradigm to quantify periodic structure in almost-periodic signals using tools from topological data analysis.

Topoisomerase 1 (Top1)-associated Genome Instability in Yeast: Effects of Persistent Cleavage Complexes or Increased Top1 Levels

Topoisomerase 1 (Top1), a Type IB topoisomerase, functions to relieve transcription- and replication-associated torsional stress in DNA. Top1 cleaves one strand of DNA, covalently associates with the 3’ end of the nick to form a Top1-cleavage complex (Top1cc), passes the intact strand through the nick and finally re-ligates the broken strand. The chemotherapeutic drug, Camptothecin, intercalates at a Top1cc and prevents the crucial re-ligation reaction that is mediated by Top1, resulting in the conversion of a nick to a toxic double-strand break during DNA replication or the accumulation of Top1cc. This mechanism of action preferentially targets rapidly dividing tumor cells, but can also affect non-tumor cells when patients undergo treatment. Additionally, Top1 is found to be elevated in numerous tumor tissues making it an attractive target for anticancer therapies. We investigated the effects of Top1 on genome stability, effects of persistent Top1-cleavage complexes and elevated Top1 levels, in Saccharomyces cerevisiae. We found that increased levels of the Top1cc resulted in a five- to ten-fold increase in reciprocal crossovers, three- to fifteen fold increase in mutagenesis and greatly increased instability within the rDNA and CUP1 tandem arrays. Increased Top1 levels resulted in a fifteen- to twenty-two fold increase in mutagenesis and increased instability in rDNA locus. These results have important implications for understanding the effects of CPT and elevated Top1 levels as a chemotherapeutic agent.

Dynamic Compartmentalization of Persistent UPEC in the Superficial Bladder Epithelium

Urinary tract infections (UTIs) are typically caused by bacteria that colonize different regions of the urinary tract, mainly the bladder and the kidney. Approximately 25% of women that suffer from UTIs experience a recurrent infection within 6 months of the initial bout, making UTIs a serious economic burden resulting in more than 10 million hospital visits and $3.5 billion in healthcare costs in the United States alone. Type-1 fimbriated Uropathogenic E. coli (UPEC) is the major causative agent of UTIs, accounting for almost 90 % of bacterial UTIs. The unique ability of UPEC to bind and invade the superficial bladder epithelium allows the bacteria to persist inside epithelial niches and survive antibiotic treatment. Persistent, intracellular UPEC are retained in the bladder epithelium for long periods, making them a source of recurrent UTIs. Hence, the ability of UPEC to persist in the bladder is a matter of major health and economic concern, making studies exploring the underlying mechanism of UPEC persistence highly relevant.

In my thesis, I will describe how intracellular Uropathogenic E.coli (UPEC) evade host defense mechanisms in the superficial bladder epithelium. I will also describe some of the unique traits of persistent UPEC and explore strategies to induce their clearance from the bladder. I have discovered that the UPEC virulence factor Alpha-hemolysin (HlyA) plays a key role in the survival and persistence of UPEC in the superficial bladder epithelium. In-vitro and in-vivo studies comparing intracellular survival of wild type (WT) and hemolysin deficient UPEC suggested that HlyA is vital for UPEC persistence in the superficial bladder epithelium. Further in-vitro studies revealed that hemolysin helped UPEC persist intracellularly by evading the bacterial expulsion actions of the bladder cells and remarkably, this virulence factor also helped bacteria avoid t degradation in lysosomes.

To elucidate the mechanistic basis for how hemolysin promotes UPEC persistence in the urothelium, we initially focused on how hemolysin facilitates the evasion of UPEC expulsion from bladder cells. We found that upon entry, UPEC were encased in “exocytic vesicles” but as a result of HlyA expression these bacteria escaped these vesicles and entered the cytosol. Consequently, these bacteria were able to avoid expulsion by the cellular export machinery.

Since bacteria found in the cytosol of host cells are typically recognized by the cellular autophagy pathway and transported to the lysosomes where they are degraded, we explored why this was not the case here. We observed that although cytosolic HlyA expressing UPEC were recognized and encased by the autophagy system and transported to lysosomes, the bacteria appeared to avoid degradation in these normally degradative compartments. A closer examination of the bacteria containing lysosomes revealed that they lacked V-ATPase. V-ATPase is a well-known proton pump essential for the acidification of mammalian intracellular degradative compartments, allowing for the proper functioning of degradative proteases. The absence of V-ATPase appeared to be due to hemolysin mediated alteration of the bladder cell F-actin network. From these studies, it is clear that UPEC hemolysin facilitates UPEC persistence in the superficial bladder epithelium by helping bacteria avoid expulsion by the exocytic machinery of the cell and at the same time enabling the bacteria avoid degradation when the bacteria are shuttled into the lysosomes.

Interestingly even though UPEC appear to avoid elimination from the bladder cell their ability to multiple in bladder cells seem limited.. Indeed, our in-vitro and in-vivo experiments reveal that UPEC survive in superficial bladder epithelium for extended periods of time without a significantly change in CFU numbers. Indeed, we observed these bacteria appeared quiescent in nature. This observation was supported by the observation that UPEC genetically unable to enter a quiescence phase exhibited limited ability to persist in bladder cells in vitro and in vivo, in the mouse bladder.

The studies elucidated in this thesis reveal how UPEC toxin, Alpha-hemolysin plays a significant role in promoting UPEC persistence via the modulation of the vesicular compartmentalization of UPEC at two different stages of the infection in the superficial bladder epithelium. These results highlight the importance of UPEC Alpha-hemolysin as an essential determinant of UPEC persistence in the urinary bladder.

Developmental exposure to a complex PAH mixture causes persistent behavioral effects in naive Fundulus heteroclitus (killifish) but not in a population of PAH-adapted killifish.

Acute exposures to some individual polycyclic aromatic hydrocarbons (PAHs) and complex PAH mixtures are known to cause cardiac malformations and edema in the developing fish embryo. However, the heart is not the only organ impacted by developmental PAH exposure. The developing brain is also affected, resulting in lasting behavioral dysfunction. While acute exposures to some PAHs are teratogenically lethal in fish, little is known about the later life consequences of early life, lower dose subteratogenic PAH exposures. We sought to determine and characterize the long-term behavioral consequences of subteratogenic developmental PAH mixture exposure in both naive killifish and PAH-adapted killifish using sediment pore water derived from the Atlantic Wood Industries Superfund Site. Killifish offspring were embryonically treated with two low-level PAH mixture dilutions of Elizabeth River sediment extract (ERSE) (TPAH 5.04 μg/L and 50.4 μg/L) at 24h post fertilization. Following exposure, killifish were raised to larval, juvenile, and adult life stages and subjected to a series of behavioral tests including: a locomotor activity test (4 days post-hatch), a sensorimotor response tap/habituation test (3 months post hatch), and a novel tank diving and exploration test (3months post hatch). Killifish were also monitored for survival at 1, 2, and 5 months over 5-month rearing period. Developmental PAH exposure caused short-term as well as persistent behavioral impairments in naive killifish. In contrast, the PAH-adapted killifish did not show behavioral alterations following PAH exposure. PAH mixture exposure caused increased mortality in reference killifish over time; yet, the PAH-adapted killifish, while demonstrating long-term rearing mortality, had no significant changes in mortality associated with ERSE exposure. This study demonstrated that early embryonic exposure to PAH-contaminated sediment pore water caused long-term locomotor and behavioral alterations in killifish, and that locomotor alterations could be observed in early larval stages. Additionally, our study highlights the resistance to behavioral alterations caused by low-level PAH mixture exposure in the adapted killifish population. Furthermore, this is the first longitudinal behavioral study to use killifish, an environmentally important estuarine teleost fish, and this testing framework can be used for future contaminant assessment.