Doctor of Philosophy

dissertationWe develop mathematical models relating measured biological markers to how animals process nutrients and toxins. Our models track molecules as they are ingested, transformed through metabolic processes, and excreted, and relate measurements of biological markers to these processes. We focus on specific problems of practical interest. We begin by developing a model of acetaminophen metabolism and use our model to estimate outcome of acetaminophen overdose patients. Acetaminophen overdose increasingly occurs as a result of chronic use. We analyze the dynamics of chronic use and find threshold dynamics that result from the structure of acetaminophen metabolism. We next study animal nitrogen metabolism. Nitrogen stable isotope ratios in consumer tissue are used by ecologists to estimate diet and trophic dynamics, but feedbacks between diet and physiology complicate the relationship between diet and the nitrogen isotope ratio of consumer tissue. We develop a model of animal nitrogen metabolism to study the influence of diet on stable nitrogen isotope ratios of consumer tissue. Finally, hair is often measured to understand how animals process nutrients and toxins because organic and inorganic substances are incorporated into hair, remaining inert for long periods of time. We develop a model based on the known physiology of hair growth to describe the signal averaging caused by bundling multiple hairs for segmental analysis

Deconvolution of isotope signals from bundles of multiple hairs

pre-printSegmental analysis of hair has been used in diverse fields ranging from forensics to ecology to measure the concentration of substances such as drugs and isotopes. Multiple hairs are typically combined into a bundle for segmental analysis to obtain a high-resolution series of measurements. Individual hair strands cycle through multiple phases of growth and grow at different rates when in the growth phase. Variation in growth of hair strands in a bundle can cause misalignment of substance concentration between hairs, attenuating the primary body signal. We developed a mathematical model based on the known physiology of hair growth to describe the signal averaging caused by bundling multiple hairs for segmental analysis. The model was used to form an inverse method to estimate the primary body signal from measurements of a hair bundle. The inverse method was applied to a previously described stable oxygen isotope chronology from the hair of a murder victim and provides a refined interpretation of the data. Aspects of the reconstruction were confirmed when the victim was later identified

Mathematical modeling of liver injury and dysfunction after acetaminophen overdose: early discrimination between survival and death

pre-printAcetaminophen is the leading cause of acute liver injury in the developed world. Timely administration of N-Acetylcysteine (N-Ac) prevents the progression of serious liver injury and disease, while failure to administer N-Ac within a critical time frame allows disease progression and in the most severe cases may result in liver failure or death. In this situation, liver transplantation may be the only life-saving measure. Thus, the outcome of an acetaminophen overdose depends upon the size of the overdose and the time to first administration of N-Ac. We developed a system of differential equations to describe acute liver injury due to acetaminophen overdose. The Model for Acetaminophen-induced Liver Damage (MALD) uses a patient's AST, ALT, and INR measurements on admission to estimate overdose amount, time elapsed since overdose, and outcome. The mathematical model was then tested on 53 patients from the University of Utah. With the addition of serum creatinine, eventual death was predicted with 100% sensitivity, 91% specificity, 67% PPV, and 100% NPV in this retrospective study. Using only initial AST, ALT, and INR measurements, the model accurately predicted subsequent laboratory values for the majority of individual patients. This is the first dynamical rather than statistical approach to determine poor prognosis in patients with life-threatening liver disease due to acetaminophen overdose. Conclusion: MALD provides a method to estimate overdose amount, time elapsed since overdose, and outcome from patient laboratory values commonly available on admission in cases of acute liver failure due to acetaminophen overdose and should be validated in multicentric prospective evaluation

Recombinant transmissible vaccines will be intrinsically contained despite the ability to superinfect

Introduction: Transmissible vaccines offer a novel approach to suppressing viruses in wildlife populations, with possible applications against viruses that infect humans as zoonoses – Lassa, Ebola, rabies. To ensure safety, current designs propose a recombinant vector platform in which the vector is isolated from the target wildlife population. Because using an endemic vector creates the potential for preexisting immunity to block vaccine transmission, these designs focus on vector viruses capable of superinfection, spreading throughout the host population following vaccination of few individuals. Areas covered: We present original theoretical arguments that, regardless of its R0 value, a recombinant vaccine using a superinfecting vector is not expected to expand its active infection coverage when released into a wildlife population that already carries the vector. However, if superinfection occurs at a high rate such that individuals are repeatedly infected throughout their lives, the immunity footprint in the population can be high despite a low incidence of active vaccine infections. Yet we provide reasons that the above expectation is optimistic. Expert Opinion: High vaccine coverage will typically require repeated releases or release into a population lacking the vector, but careful attention to vector choice and vaccine engineering should also help improve transmissible vaccine utility

Identifying the genetic basis of viral spillover using Lassa virus as a test case

The rate at which zoonotic viruses spill over into the human population varies significantly over space and time. Remarkably, we do not yet know how much of this variation is attributable to genetic variation within viral populations. This gap in understanding arises because we lack methods of genetic analysis that can be easily applied to zoonotic viruses, where the number of available viral sequences is often limited, and opportunistic sampling introduces significant population stratification. Here, we explore the feasibility of using patterns of shared ancestry to correct for population stratification, enabling genome-wide association methods to identify genetic substitutions associated with spillover into the human population. Using a combination of phylogenetically structured simulations and Lassa virus sequences collected from humans and rodents in Sierra Leone, we demonstrate that existing methods do not fully correct for stratification, leading to elevated error rates. We also demonstrate, however, that the Type I error rate can be substantially reduced by confining the analysis to a less-stratified region of the phylogeny, even in an already-small dataset. Using this method, we detect two candidate single-nucleotide polymorphisms associated with spillover in the Lassa virus polymerase gene and provide generalized recommendations for the collection and analysis of zoonotic viruses

Aberrant Water Homeostasis Detected by Stable Isotope Analysis

While isotopes are frequently used as tracers in investigations of disease physiology (i.e., 14C labeled glucose), few studies have examined the impact that disease, and disease-related alterations in metabolism, may have on stable isotope ratios at natural abundance levels. The isotopic composition of body water is heavily influenced by water metabolism and dietary patterns and may provide a platform for disease detection. By utilizing a model of streptozotocin (STZ)-induced diabetes as an index case of aberrant water homeostasis, we demonstrate that untreated diabetes mellitus results in distinct combinations, or signatures, of the hydrogen (δ2H) and oxygen (δ18O) isotope ratios in body water. Additionally, we show that the δ2H and δ18O values of body water are correlated with increased water flux, suggesting altered blood osmolality, due to hyperglycemia, as the mechanism behind this correlation. Further, we present a mathematical model describing the impact of water flux on the isotopic composition of body water and compare model predicted values with actual values. These data highlight the importance of factors such as water flux and energy expenditure on predictive models of body water and additionally provide a framework for using naturally occurring stable isotope ratios to monitor diseases that impact water homeostasis

Evolution and the duration of a doomed population

Many populations are doomed to extinction, but little is known about how evolution contributes to their longevity. We address this by modeling an asexual population consisting of genotypes whose abundances change independently according to a system of continuous branching diffusions. Each genotype is characterized by its initial abundance, growth rate, and reproductive variance. The latter two components determine the genotype's “risk function” which describes its per capita probability of extinction at any time. We derive the probability distribution of extinction times for a polymorphic population, which can be expressed in terms of genotypic risk functions. We use this to explore how spontaneous mutation, abrupt environmental change, or population supplementation and removal affect the time to extinction. Results suggest that evolution based on new mutations does little to alter the time to extinction. Abrupt environmental changes that affect all genotypes can have more substantial impact, but, curiously, a beneficial change does more to extend the lifetime of thriving than threatened populations of the same initial abundance. Our results can be used to design policies that meet specific conservation goals or management strategies that speed the elimination of agricultural pests or human pathogens

A little goes a long way: Weak vaccine transmission facilitates oral vaccination campaigns against zoonotic pathogens.

Zoonotic pathogens such as Ebola and rabies pose a major health risk to humans. One proven approach to minimizing the impact of a pathogen relies on reducing its prevalence within animal reservoir populations using mass vaccination. However, two major challenges remain for vaccination programs that target free-ranging animal populations. First, limited or challenging access to wild hosts, and second, expenses associated with purchasing and distributing the vaccine. Together, these challenges constrain a campaign's ability to maintain adequate levels of immunity in the host population for an extended period of time. Transmissible vaccines could lessen these constraints, improving our ability to both establish and maintain herd immunity in free-ranging animal populations. Because the extent to which vaccine transmission could augment current wildlife vaccination campaigns is unknown, we develop and parameterize a mathematical model that describes long-term mass vaccination campaigns in the US that target rabies in wildlife. The model is used to investigate the ability of a weakly transmissible vaccine to (1) increase vaccine coverage in campaigns that fail to immunize at levels required for herd immunity, and (2) decrease the expense of campaigns that achieve herd immunity. When parameterized to efforts that target rabies in raccoons using vaccine baits, our model indicates that, with current vaccination efforts, a vaccine that transmits to even one additional host per vaccinated individual could sufficiently augment US efforts to preempt the spread of the rabies virus. Higher levels of transmission are needed, however, when spatial heterogeneities associated with flight-line vaccination are incorporated into the model. In addition to augmenting deficient campaigns, our results show that weak vaccine transmission can reduce the costs of vaccination campaigns that are successful in attaining herd immunity

Spatial structure undermines parasite suppression by gene drive cargo

Gene drives may be used in two ways to curtail vectored diseases. Both involve engineering the drive to spread in the vector population. One approach uses the drive to directly depress vector numbers, possibly to extinction. The other approach leaves intact the vector population but suppresses the disease agent during its interaction with the vector. This second application may use a drive engineered to carry a genetic cargo that blocks the disease agent. An advantage of the second application is that it is far less likely to select vector resistance to block the drive, but the disease agent may instead evolve resistance to the inhibitory cargo. However, some gene drives are expected to spread so fast and attain such high coverage in the vector population that, if the disease agent can evolve resistance only gradually, disease eradication may be feasible. Here we use simple models to show that spatial structure in the vector population can greatly facilitate persistence and evolution of resistance by the disease agent. We suggest simple approaches to avoid some types of spatial structure, but others may be intrinsic to the populations being challenged and difficult to overcome