Interpreting Human Genetic Variation through Genomics and In Vivo Models

Improvements in genomic technology, both in the increased speed and reduced cost of sequencing, have expanded the appreciation of the abundance of human genetic variation. However the sheer amount of variation, as well as the varying type and genomic content of variation, poses a challenge in understanding the clinical consequence of a single mutation. This work uses several methodologies to interpret the observed variation in the human genome, and presents novel strategies for the prediction of allele pathogenicity.

Using the zebrafish model system as an in vivo assay of allele function, we identified a novel driver of Bardet-Biedl Syndrome (BBS) in CEP76. A combination of targeted sequencing of 785 cilia-associated genes in a cohort of BBS patients and subsequent in vivo functional assays recapitulating the human phenotype gave strong evidence for the role of CEP76 mutations in the pathology of an affected family. This portion of the work demonstrated the necessity of functional testing in validating disease-associated mutations, and added to the catalogue of known BBS disease genes.

Further study into the role of copy-number variations (CNVs) in a cohort of BBS patients showed the significant contribution of CNVs to disease pathology. Using high-density array comparative genomic hybridization (aCGH) we were able to identify pathogenic CNVs as small as several hundred bp. Dissection of constituent gene and in vivo experiments investigating epistatic interactions between affected genes allowed for an appreciation of several paradigms by which CNVs can contribute to disease. This study revealed that the contribution of CNVs to disease in BBS patients is much higher than previously expected, and demonstrated the necessity of consideration of CNV contribution in future (and retrospective) investigations of human genetic disease.

Finally, we used a combination of comparative genomics and in vivo complementation assays to identify second-site compensatory modification of pathogenic alleles. These pathogenic alleles, which are found compensated in other species (termed compensated pathogenic deviations [CPDs]), represent a significant fraction (from 3 – 10%) of human disease-associated alleles. In silico pathogenicity prediction algorithms, a valuable method of allele prioritization, often misrepresent these alleles as benign, leading to omission of possibly informative variants in studies of human genetic disease. We created a mathematical model that was able to predict CPDs and putative compensatory sites, and functionally showed in vivo that second-site mutation can mitigate the pathogenicity of disease alleles. Additionally, we made publically available an in silico module for the prediction of CPDs and modifier sites.

These studies have advanced the ability to interpret the pathogenicity of multiple types of human variation, as well as made available tools for others to do so as well.

Aspects of Motives: Finite-dimensionality, Chow-Kunneth Decompositions and Intersections of Cycles

This thesis analyzes the Chow motives of 3 types of smooth projective varieties: the desingularized elliptic self fiber product, the Fano surface of lines on a cubic threefold and an ample hypersurface of an Abelian variety. For the desingularized elliptic self fiber product, we use an isotypic decomposition of the motive to deduce the Murre conjectures. We also prove a result about the intersection product. For the Fano surface of lines, we prove the finite-dimensionality of the Chow motive. Finally, we prove that an ample hypersurface on an Abelian variety possesses a Chow-Kunneth decomposition for which a motivic version of the Lefschetz hyperplane theorem holds.

Latent Space and Social Psychological Models of Diffusion

The problem of social diffusion has animated sociological thinking on topics ranging from the spread of an idea, an innovation or a disease, to the foundations of collective behavior and political polarization. While network diffusion has been a productive metaphor, the reality of diffusion processes is often muddier. Ideas and innovations diffuse differently from diseases, but, with a few exceptions, the diffusion of ideas and innovations has been modeled under the same assumptions as the diffusion of disease. In this dissertation, I develop two new diffusion models for "socially meaningful" contagions that address two of the most significant problems with current diffusion models: (1) that contagions can only spread along observed ties, and (2) that contagions do not change as they spread between people. I augment insights from these statistical and simulation models with an analysis of an empirical case of diffusion - the use of enterprise collaboration software in a large technology company. I focus the empirical study on when people abandon innovations, a crucial, and understudied aspect of the diffusion of innovations. Using timestamped posts, I analyze when people abandon software to a high degree of detail.

To address the first problem, I suggest a latent space diffusion model. Rather than treating ties as stable conduits for information, the latent space diffusion model treats ties as random draws from an underlying social space, and simulates diffusion over the social space. Theoretically, the social space model integrates both actor ties and attributes simultaneously in a single social plane, while incorporating schemas into diffusion processes gives an explicit form to the reciprocal influences that cognition and social environment have on each other. Practically, the latent space diffusion model produces statistically consistent diffusion estimates where using the network alone does not, and the diffusion with schemas model shows that introducing some cognitive processing into diffusion processes changes the rate and ultimate distribution of the spreading information. To address the second problem, I suggest a diffusion model with schemas. Rather than treating information as though it is spread without changes, the schema diffusion model allows people to modify information they receive to fit an underlying mental model of the information before they pass the information to others. Combining the latent space models with a schema notion for actors improves our models for social diffusion both theoretically and practically.

The empirical case study focuses on how the changing value of an innovation, introduced by the innovations' network externalities, influences when people abandon the innovation. In it, I find that people are least likely to abandon an innovation when other people in their neighborhood currently use the software as well. The effect is particularly pronounced for supervisors' current use and number of supervisory team members who currently use the software. This case study not only points to an important process in the diffusion of innovation, but also suggests a new approach -- computerized collaboration systems -- to collecting and analyzing data on organizational processes.

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.

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.

Drivers of Dengue Within-Host Dynamics and Virulence Evolution

Dengue is an important vector-borne virus that infects on the order of 400 million individuals per year. Infection with one of the virus's four serotypes (denoted DENV-1 to 4) may be silent, result in symptomatic dengue 'breakbone' fever, or develop into the more severe dengue hemorrhagic fever/dengue shock syndrome (DHF/DSS). Extensive research has therefore focused on identifying factors that influence dengue infection outcomes. It has been well-documented through epidemiological studies that DHF is most likely to result from a secondary heterologous infection, and that individuals experiencing a DENV-2 or DENV-3 infection typically are more likely to present with more severe dengue disease than those individuals experiencing a DENV-1 or DENV-4 infection. However, a mechanistic understanding of how these risk factors affect disease outcomes, and further, how the virus's ability to evolve these mechanisms will affect disease severity patterns over time, is lacking. In the second chapter of my dissertation, I formulate mechanistic mathematical models of primary and secondary dengue infections that describe how the dengue virus interacts with the immune response and the results of this interaction on the risk of developing severe dengue disease. I show that only the innate immune response is needed to reproduce characteristic features of a primary infection whereas the adaptive immune response is needed to reproduce characteristic features of a secondary dengue infection. I then add to these models a quantitative measure of disease severity that assumes immunopathology, and analyze the effectiveness of virological indicators of disease severity. In the third chapter of my dissertation, I then statistically fit these mathematical models to viral load data of dengue patients to understand the mechanisms that drive variation in viral load. I specifically consider the roles that immune status, clinical disease manifestation, and serotype may play in explaining viral load variation observed across the patients. With this analysis, I show that there is statistical support for the theory of antibody dependent enhancement in the development of severe disease in secondary dengue infections and that there is statistical support for serotype-specific differences in viral infectivity rates, with infectivity rates of DENV-2 and DENV-3 exceeding those of DENV-1. In the fourth chapter of my dissertation, I integrate these within-host models with a vector-borne epidemiological model to understand the potential for virulence evolution in dengue. Critically, I show that dengue is expected to evolve towards intermediate virulence, and that the optimal virulence of the virus depends strongly on the number of serotypes that co-circulate. Together, these dissertation chapters show that dengue viral load dynamics provide insight into the within-host mechanisms driving differences in dengue disease patterns and that these mechanisms have important implications for dengue virulence evolution.