UC Santa Barbara

Mathematical modeling of biological processes has contributed significantly to improving our understanding of how different biological systems function, how and why different diseases start and develop, and how the diseases can be prevented or treated. In the first part of this dissertation, we use mechanistic modeling together with local and global sensitivity analyses to explore why different patients and/or different cancer types respond differently to retinoic acid (RA), an anticancer drug. Our findings indicate that the efficacy of RA treatment highly depends on intracellular levels of four main RA binding proteins namely, retinoic acid receptor (RAR), cellular retinoic acid binding proteins (CRABP1 and CRABP2) and cytochrome P450 (CYP). These proteins are expressed at different levels in different patients and/or cell types. Our results indicate that CRABP2 and RAR are the most and the least important receptors, respectively, in regulating the response to RA treatment at physiological concentrations (1–10 nM). However, at pharmacological concentrations of RA (0.1–1 μM), CYP and RAR are the most sensitive parameters of the model. These results can help in the development of pharmacological methods to increase the efficacy of the drug. In the second part of this dissertation, we study the positive side effects of RA therapy on blood clotting abnormalities in cancer patients. Although there are several lines of evidence regarding the improvement of hemostatic complications such as thrombosis and disseminated intravascular coagulation (DIC) in cancer patients undergoing RA therapy, the mechanisms underlying this improvement have yet to be understood. We build mechanistic and pharmacokinetics models and use in vitro and pharmacokinetics data from the literature to test the hypothesis that this improvement is due to RA-induced upregulation of thrombomodulin (TM) on the endothelial cells. Our results indicate that treatment with a single daily oral dose of 110 mg/m^2 RA, increases the TM concentration by almost two folds. We then show that this RA-induced TM upregulation reduces the peak thrombin levels and endogenous thrombin potential (ETP) up to 50 and 49%, respectively. Our results demonstrate that progressive reductions in plasma levels of RA, observed in continuous RA therapy with a once-daily oral dose of 110 mg/m^2 RA do not influence TM-mediated decrease in thrombin generation. This observation raises the hypothesis that continuous RA treatment will have more consistent therapeutic effects on coagulation disorders than on cancer. Our results reveal that the upregulation of TM expression on the endothelial cells over the course of RA therapy could significantly contribute to the treatment of coagulation abnormalities in cancer patients. In the last part of this dissertation, we use mechanistic modeling to study sodium homeostasis disturbance in the brain during migraines. Previous animal and human studies have revealed that migraine sufferers have higher levels of cerebrospinal fluid (CSF) and brain tissue sodium than control groups, while the underlying mechanisms of this increase are not known. Under the hypothesis that disturbances in sodium transport mechanisms at the blood-CSF barrier (BCSFB) and/or the blood-brain barrier (BBB) are the underlying cause of the elevated CSF and brain, we develop a mechanistic model of a rat’s brain to compare the significance of the BCSFB and the BBB in controlling CSF and brain tissue sodium levels. Our model consists of the ventricular system, subarachnoid space, brain tissue and blood. We model sodium transport from blood to CSF across the BCSFB, and from blood to brain tissue across the BBB by influx permeability coefficients P_BCSFB and P_BBB, respectively, while sodium movement from CSF into blood across the BCSFB, and from brain tissue to blood across the BBB were modeled by efflux permeability coefficients P_BCSFB^' and P_BBB^', respectively. We then perform a global sensitivity analysis to investigate the sensitivity of the ventricular CSF, subarachnoid CSF and brain tissue sodium levels to pathophysiological variations in P_BCSFB, P_BBB, P_BCSFB^' and P_BBB^'. Our findings indicate that the ventricular CSF sodium concentration is highly influenced by perturbations of P_BCSFB, and to a much lesser extent by perturbations of P_BCSFB^'. Brain tissue and subarachnoid CSF sodium concentrations are more sensitive to pathophysiological variations of P_BBB and P_BBB^' than variations of P_BCSFB and P_BCSFB^' within 30 minutes of the onset of the perturbations. However, P_BCSFB is the most sensitive model parameter, followed by P_BBB and P_BBB^', in controlling brain tissue and subarachnoid CSF sodium levels within 3 hours of the perturbation onset. Our findings suggest that increased influx permeability of the BCSFB to sodium caused by altered homeostasis of the enzymes which transport sodium from blood to CSF is the potential cause of elevated brain sodium levels in migraines.