This dissertation presents novel sequential dose-finding designs that adjust for inter-individual pharmacokinetic variability in phase I cancer clinical trials. Unlike most traditional dose-finding designs whose primary goals are the determination of a maximum safe dose, the goal of our proposed designs is to estimate a patient-specific dosing function such that the responses of patients can achieve a target safety level. Extending from a single compartment model in the pharmacokinetic theory, we first postulate a linear model to describe the relationship between the area under concentration-time curve, dose and predicted clearance. We propose a repeated least squares procedure that aims to sequentially determine dose according to individual ability of metabolizing the drug. To guarantee consistent estimation of the individualized dosing function at the end of a trial, we apply repeated least squares subject to a consistency constraint based on an eigenvalue theory for stochastic linear regression. We empirically determine the convergence rate of the eigenvalue constraint using a real data set from an irinotecan study in colorectal carcinoma patients, and calibrate the procedure to minimize a loss function that accounts for the dosing costs of study subjects and future patients. When compared to the traditional body surface area and an equation based dosing methods, the simulation results demonstrate that the repeated least squares procedure control the dosing cost and allow for precise estimation of the dosing function. Furthermore, in order to enhance the generality and robustness of the dose-finding designs, we generalize the linear association to a nonlinear relationship between the response and a linear combination of dose and predicted clearance. We propose a two-stage sequential design, the semiparametric link-adapted recursion, which targets at individualizing dose assignments meanwhile adapting for an unknown nonlinear link function connecting the response and dose along with predicted clearance. The repeat least squares with eigenvalue constraint design is utilized as the first stage, and the second stage recursively applies an iterative semiparametric least squares approach to estimate the dosing function and determine dosage for next patient. The simulation results demonstrate that: at first, the performance of repeated least squares with eigenvalue constraint design is acceptably robust to model misspecifications; at second, as its performance is close to that of repeated least squares procedure under parametric models, the semiparametric link-adapted recursion does not sacrifice much estimation accuracy to gain robustness against model misspecifications; at last, compared to the repeated least squares procedure, the semiparametric link-adapted recursion can significantly improve the dosing costs and estimation precision under the semiparametric models.

Prodigiosins and tambjamines are natural compounds from bacterial and marine sources belonging to a family containing a common 4-methoxy-2,2'-bipyrrole core. These compounds have received a lot of interest due to their promising biological activities. Studies have suggested DNA as a potential therapeutic target for the natural prodigiosin and tambjamine due to their ability to facilitate oxidative DNA cleavage in the presence of Cu2+. Based on this we sought to study the metal binding activity of new prodigiosin and tambjamine analogues. A new prodigiosin analogue was synthesized and complexed with Cu2+. This revealed 1:1 complex formation between the tripyrrole and Cu2+ that was confirmed by mass spectra and NMR spectra analysis. In addition in situ studies also revealed that our new analogues of prodigiosin cannot bind Zn2+ when the methoxy group on ring B is replaced by an alkyl group or when one of the ring nitrogens is methylated. Our UV-Vis experiments with calf thymus DNA showed that prodigiosins and tambjamines bind DNA mainly through an external mode, suggesting that hydrogen bonding between the pyrrole ring nitrogens and the bases of DNA takes precedence over stacking interactions. For the new Cu2+ complex synthesized however, we observed spectral changes that suggest intercalation into DNA. DNA cleavage experiments revealed that the prodigiosin-Cu complex is able to convert supercoiled DNA into its linear form. The data from the gel shift assays fit well to a first-order consecutive reaction model. In addition to preformed metal complexes, we showed DNA cleavage by in situ complexation of the ligands in the presence of Cu2+. However, although we showed Zn2+ complex formation with prodigiosin analogues, in situ studies did not show induction of DNA cleavage by Zn2+ complexes under our experimental conditions.

Glioblastoma is the most common adult malignant primary brain tumor with one of the worst prognosis. With a survival of 10 to 12 months, glioblastoma remains one of the most challenging disease to treat. The standard treatment method involves maximal possible resection of the tumor followed by radiation and chemotherapy. However, the short half-life of most chemotherapeutic drugs, high systemic toxicity and inability to cross the blood brain barrier inhibits effective delivery of the chemotherapeutics to the tumor. An ideal drug delivery system can reach the tumor site with high efficiency and continuously release the drug at the tumor site for an extended period. Adult stem cells including neural stem cells (NSC) and mesenchymal stem cells (MSC) have inherent tumor trophic properties allowing for site-specific delivery of chemotherapeutics. They can also be genetically engineered to secrete the chemotherapeutic drug continuously making them ideal candidates for cell-based delivery system for treating glioblastoma. MSC have been isolated from a wide range of sources including bone marrow, umbilical cord, adipose tissue, liver, multiple dental tissues and induced pluripotent stem cells. MSC are also easily amenable to viral modification allowing for easy manipulation to produce chemotherapeutic drugs. Additionally, more than 350 clinical trials using MSC have successfully established the safety of using MSC for cell-based therapies. Collectively these factors have led to the widespread use of MSC in cancer therapy. MSC have been successfully transduced to produce chemotherapeutic drugs to treat glioma, melanoma, lung cancer, ovarian cancer and breast cancer. Despite the multitudes of advantages that cell therapy provides they are limited in three main domains (1) Low cell retention and survival at the site of the tumor (2) In ability to co-deliver multiple therapeutics and (3) In ability to deliver drugs other than peptide based drugs. This thesis details the work to engineer mesenchymal stem cells to tackle these three issues and develop a system that can increase the efficacy of glioblastoma treatment. To increase the cellular retention and survival we engineered MSC to form multicellular spheroids and cell sheets. To co-delivery multiple therapeutics we engineered MSC to form MSC/DNA-templated nanoparticle hybrid cluster to co-deliver drugs for cancer therapy. The system showed superior performance due to the increased retention of the cells and nanoparticle at the tumor site. Finally, to deliver drugs other peptide based we engineered graphene oxide cellular patches for mesenchymal stem cells. Graphene oxide can carry diverse therapeutics and can kill the cancer cells without affecting the cellular viability of MSC.