changes in the diffusion, growth, and death parameters was performed, in order to find a set of parameter values that accurately model observed tumor growth for a given patient. Additional changes were made to the diffusion parameters to account for the arrangement of nerve tracts in the brain, resulting in varying rates of diffusion. In general, small changes in the growth rates had a large impact on the outcome of the simulations, and for each patient there exists a set of parameters that allow the model to simulate a tumor that matches observed tumor growth in the patient over a period of two or three months. Furthermore, these results are more accurate with anisotropic diffusion, rather than isotropic diffusion. However, these parameters lead to inaccurate results for patients with tumors that undergo no observable growth over the given time interval. While it is possible to simulate long-term tumor growth, the simulation requires multiple comparisons to available MRI scans in order to find a set of parameters that provide an accurate prognosis.
prostate cancer is most commonly treated with hormonal therapy. The idea behind
hormonal therapy is to reduce androgen production, which prostate cancer cells
require for growth. Recently, the exploration of the synergistic effects of the drugs
used in hormonal therapy has begun. The aim was to build off of these recent
advancements and further refine the synergistic drug model. The advancements I
implement come by addressing biological shortcomings and improving the model’s
internal mechanistic structure. The drug families being modeled, anti-androgens,
and gonadotropin-releasing hormone analogs, interact with androgen production in a
way that is not completely understood in the scientific community. Thus the models
representing the drugs show progress through their ability to capture their effect
on serum androgen. Prostate-specific antigen is the primary biomarker for prostate
cancer and is generally how population models on the subject are validated. Fitting
the model to clinical data and comparing it to other clinical models through the
ability to fit and forecast prostate-specific antigen and serum androgen is how this
improved model achieves validation. The improved model results further suggest that
the drugs’ dynamics should be considered in adaptive therapy for prostate cancer.
The first model considers a monotherapy employing the immune checkpoint inhibitor anti-PD-1. The dynamics both with and without anti-PD-1 are studied, and mathematical analysis is performed in the case when no anti-PD-1 is administrated. Simulations are carried out to explore the effects of continuous treatment versus intermittent treatment. The outcome of the simulations does not demonstrate elimination of the tumor, suggesting the need for a combination type of treatment.
An extension of the aforementioned model is deployed to investigate the pairing of an immune checkpoint inhibitor anti-PD-L1 with an immunostimulant NHS-muIL12. Additionally, a generic drug-free model is developed to explore the dynamics of both exponential and logistic tumor growth functions. Experimental data are used for model fitting and parameter estimation in the monotherapy cases. The model is utilized to predict the outcome of combination therapy, and reveals a synergistic effect: Compared to the monotherapy case, only one-third of the dosage can successfully control the tumor in the combination case.
Finally, the treatment impact of oncolytic virus therapy in a previously developed and fit model is explored. To determine if one can trust the predictive abilities of the model, a practical identifiability analysis is performed. Particularly, the profile likelihood curves demonstrate practical unidentifiability, when all parameters are simultaneously fit. This observation poses concerns about the predictive abilities of the model. Further investigation showed that if half of the model parameters can be measured through biological experimentation, practical identifiability is achieved.
In Chapter 2, motivated by the work of de Pillis et al. (2013), a mathematical model employing six ordinary differential (ODEs) and delay differential equations (DDEs) is formulated to understand the effectiveness of DC vaccines, accounting for cell trafficking with a blood and tumor compartment. A preliminary analysis is performed, with numerical simulations used to show the existence of oscillatory behavior. The model is then reduced to a system of four ODEs. Both models are validated using experimental data from melanoma-induced mice. Conditions under which the model admits rich dynamics observed in a clinical setting, such as periodic solutions and bistability, are established. Mathematical analysis proves the existence of a backward bifurcation and establishes thresholds for R0 that ensure tumor elimination or existence. A sensitivity analysis determines which parameters most significantly impact the reproduction number R0. Identifiability analysis reveals parameters of interest for estimation. Results are framed in terms of treatment implications, including effective combination and monotherapy strategies.
In Chapter 3, a study of whether the observed complexity can be represented with a simplified model is conducted. The DC model of Chapter 2 is reduced to a non-dimensional system of two DDEs. Mathematical and numerical analysis explore the impact of immune response time on the stability and eradication of the tumor, including an analytical proof of conditions necessary for the existence of a Hopf bifurcation. In a limiting case, conditions for global stability of the tumor-free equilibrium are outlined.
Lastly, Chapter 4 discusses future directions to explore. There still remain open questions to investigate and much work to be done, particularly involving uncertainty analysis. An outline of these steps is provided for future undertakings.
Gompertz’s empirical equation remains the most popular one in describing cancer cell population growth in a wide spectrum of bio-medical situations due to its good fit to data and simplicity. Many efforts were documented in the literature aimed at understanding the mechanisms that may support Gompertz’s elegant model equation. One of the most convincing efforts was carried out by Gyllenberg and Webb. They divide the cancer cell population into the proliferative cells and the quiescent cells. In their two dimensional model, the dead cells are assumed to be removed from the tumor instantly. In this paper, we modify their model by keeping track of the dead cells remaining in the tumor. We perform mathematical and computational studies on this three dimensional model and compare the model dynamics to that of the model of Gyllenberg and Webb. Our mathematical findings suggest that if an avascular tumor grows according to our three-compartment model, then as the death rate of quiescent cells decreases to zero, the percentage of proliferative cells also approaches to zero. Moreover, a slow dying quiescent population will increase the size of the tumor. On the other hand, while the tumor size does not depend on the dead cell removal rate, its early and intermediate growth stages are very sensitive to it.
Background: To be effective, orally administered live Salmonella vaccines must first survive their encounter with the low pH environment of the stomach. To enhance survival, an antacid is often given to neutralize the acidic environment of the stomach just prior to or concomitant with administration of the vaccine. One drawback of this approach, from the perspective of the clinical trial volunteer, is that the taste of a bicarbonate-based acid neutralization system can be unpleasant. Thus, we explored an alternative method that would be at least as effective as bicarbonate and with a potentially more acceptable taste. Because ingestion of protein can rapidly buffer stomach pH, we examined the possibility that the protein-rich Ensure® Nutrition shakes would be effective alternatives to bicarbonate.
Results: We tested one Salmonella enterica serovar Typhimurium and three Salmonella Typhi vaccine strains and found that all strains survived equally well when incubated in either Ensure® or bicarbonate. In a low gastric pH mouse model, Ensure® worked as well or better than bicarbonate to enhance survival through the intestinal tract, although neither agent enhanced the survival of the S. Typhi test strain possessing a rpoS mutation.
Conclusions: Our data show that a protein-rich drink such as Ensure® Nutrition shakes can serve as an alternative to bicarbonate for reducing gastric pH prior to administration of a live Salmonella vaccine.
Leucine-responsive regulatory protein (Lrp) is known to be an indirect activator of type 1 fimbriae synthesis in Salmonella enterica serovar Typhimurium via direct regulation of FimZ, a direct positive regulator for type 1 fimbriae production. Using RT-PCR, we have shown previously that fimA transcription is dramatically impaired in both lrp-deletion (Δlrp) and constitutive-lrp expression (lrpC) mutant strains. In this work, we used chromosomal PfimA-lacZ fusions and yeast agglutination assays to confirm and extend our previous results. Direct binding of Lrp to PfimA was shown by an electrophoretic mobility shift assay (EMSA) and DNA footprinting assay. Site-directed mutagenesis revealed that the Lrp-binding motifs in PfimA play a role in both activation and repression of type 1 fimbriae production. Overproduction of Lrp also abrogates fimZ expression. EMSA data showed that Lrp and FimZ proteins independently bind to PfimA without competitive exclusion. In addition, both Lrp and FimZ binding to PfimA caused a hyper retardation (supershift) of the DNA-protein complex compared to the shift when each protein was present alone. Nutrition-dependent cellular Lrp levels closely correlated with the amount of type 1 fimbriae production. These observations suggest that Lrp plays important roles in type 1 fimbriation by acting as both a positive and negative regulator and its effect depends, at least in part, on the cellular concentration of Lrp in response to the nutritional environment.
The low pH of the stomach serves as a barrier to ingested microbes and must be overcome or bypassed when delivering live bacteria for vaccine or probiotic applications. Typically, the impact of stomach acidity on bacterial survival is evaluated in vitro, as there are no small animal models to evaluate these effects in vivo. To better understand the effect of this low pH barrier to live attenuated Salmonella vaccines, which are often very sensitive to low pH, we investigated the value of the histamine mouse model for this application. A low pH gastric compartment was transiently induced in mice by the injection of histamine. This resulted in a gastric compartment of approximately pH 1.5 that was capable of distinguishing between acid-sensitive and acid-resistant microbes. Survival of enteric microbes during gastric transit in this model directly correlated with their in vitro acid resistance. Because many Salmonella enterica serotype Typhi vaccine strains are sensitive to acid, we have been investigating systems to enhance the acid resistance of these bacteria. Using the histamine mouse model, we demonstrate that the in vivo survival of S. Typhi vaccine strains increased approximately 10-fold when they carried a sugar-inducible arginine decarboxylase system. We conclude that this model will be a useful for evaluating live bacterial preparations prior to clinical trials.
Salmonella enterica serovar Typhimurium, a gram-negative facultative rod-shaped bacterium causing salmonellosis and foodborne disease, is one of the most common isolated Salmonella serovars in both developed and developing nations. Several S. Typhimurium genomes have been completed and many more genome-sequencing projects are underway. Comparative genome analysis of the multiple strains leads to a better understanding of the evolution of S. Typhimurium and its pathogenesis. S. Typhimurium strain UK-1 (belongs to phage type 1) is highly virulent when orally administered to mice and chickens and efficiently colonizes lymphoid tissues of these species. These characteristics make this strain a good choice for use in vaccine development. In fact, UK-1 has been used as the parent strain for a number of nonrecombinant and recombinant vaccine strains, including several commercial vaccines for poultry. In this study, we conducted a thorough comparative genome analysis of the UK-1 strain with other S. Typhimurium strains and examined the phenotypic impact of several genomic differences. Whole genomic comparison highlights an extremely close relationship between the UK-1 strain and other S. Typhimurium strains; however, many interesting genetic and genomic variations specific to UK-1 were explored. In particular, the deletion of a UK-1-specific gene that is highly similar to the gene encoding the T3SS effector protein NleC exhibited a significant decrease in oral virulence in BALB/c mice. The complete genetic complements in UK-1, especially those elements that contribute to virulence or aid in determining the diversity within bacterial species, provide key information in evaluating the functional characterization of important genetic determinants and for development of vaccines.