Hybrid stochastic simulations of intracellular reaction-diffusion systems.

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.

A simulation study of the standard design, the rolling six design, the CRM, and the modified CRM in Phase I clinical trials

The Phase I clinical trial is considered the "first in human" study in medical research to examine the toxicity of a new agent. It determines the maximum tolerable dose (MTD) of a new agent, i.e., the highest dose in which toxicity is still acceptable. Several phase I clinical trial designs have been proposed in the past 30 years. The well known standard method, so called the 3+3 design, is widely accepted by clinicians since it is the easiest to implement and it does not need a statistical calculation. Continual reassessment method (CRM), a design uses Bayesian method, has been rising in popularity in the last two decades. Several variants of the CRM design have also been suggested in numerous statistical literatures. Rolling six is a new method introduced in pediatric oncology in 2008, which claims to shorten the trial duration as compared to the 3+3 design. The goal of the present research was to simulate clinical trials and compare these phase I clinical trial designs. Patient population was created by discrete event simulation (DES) method. The characteristics of the patients were generated by several distributions with the parameters derived from a historical phase I clinical trial data review. Patients were then selected and enrolled in clinical trials, each of which uses the 3+3 design, the rolling six, or the CRM design. Five scenarios of dose-toxicity relationship were used to compare the performance of the phase I clinical trial designs. One thousand trials were simulated per phase I clinical trial design per dose-toxicity scenario. The results showed the rolling six design was not superior to the 3+3 design in terms of trial duration. The time to trial completion was comparable between the rolling six and the 3+3 design. However, they both shorten the duration as compared to the two CRM designs. Both CRMs were superior to the 3+3 design and the rolling six in accuracy of MTD estimation. The 3+3 design and rolling six tended to assign more patients to undesired lower dose levels. The toxicities were slightly greater in the CRMs.^

Cytochrome P450 in mammalian brain: Purification, anatomical distribution and regulation of the cytochrome P450 monooxygenase system in rat brain

The cytochrome P450 (P450) monooxygenase system plays a major role in metabolizing a wide variety of xenobiotic as well as endogenous compounds. In performing this function, it serves to protect the body from foreign substances. However, in a number of cases, P450 activates procarcinogens to cause harm. In most animals, the highest level of activity is found in the liver. Virtually all tissues demonstrate P450 activity, though, and the role of the P450 monooxygenase system in these other organs is not well understood. In this project I have studied the P450 system in rat brain; purifying NADPH-cytochrome P450 reductase (reductase) from that tissue. In addition, I have examined the distribution and regulation of expression of reductase and P450 in various anatomical regions of the rat brain.^ NADPH-cytochrome P450 reductase was purified to apparent homogeneity and cytochrome P450 partially purified from whole rat brain. Purified reductase from brain was identical to liver P450 reductase by SDS-PAGE and Western blot techniques. Kinetic studies utilizing cerebral P450 reductase reveal Km values in close agreement with those determined with enzyme purified from rat liver. Moreover, the brain P450 reductase was able to function successfully in a reconstituted microsomal system with partially purified brain cytochrome P450 and with purified hepatic P4501A1 as measured by 7-ethoxycoumarin and 7-ethoxyresorufin O-deethylation. These results indicate that the reductase and P450 components may interact to form a competent drug metabolism system in brain tissue.^ Since the brain is not a homogeneous organ, dependent upon the well orchestrated interaction of numerous parts, pathology in one nucleus may have a large impact upon its overall function. Hence, the anatomical distribution of the P450 monooxygenase system in brain is important in elucidating its function in that organ. Related to this is the regulation of P450 expression in brain. In order to study these issues female rats--both ovariectomized and not--were treated with a number of xenobiotic compounds and sex steroids. The brains from these animals were dissected into 8 discrete regions and the presence and relative level of message for P4502D and reductase determined using polymerase chain reaction. Results of this study indicate the presence of mRNA for reductase and P4502D isoforms throughout the rat brain. In addition, quantitative PCR has allowed the determination of factors affecting the expression of message for these enzymes. ^

Mixture modeling for joint analysis of survival, discrete, and continuous data

Mixture modeling is commonly used to model categorical latent variables that represent subpopulations in which population membership is unknown but can be inferred from the data. In relatively recent years, the potential of finite mixture models has been applied in time-to-event data. However, the commonly used survival mixture model assumes that the effects of the covariates involved in failure times differ across latent classes, but the covariate distribution is homogeneous. The aim of this dissertation is to develop a method to examine time-to-event data in the presence of unobserved heterogeneity under a framework of mixture modeling. A joint model is developed to incorporate the latent survival trajectory along with the observed information for the joint analysis of a time-to-event variable, its discrete and continuous covariates, and a latent class variable. It is assumed that the effects of covariates on survival times and the distribution of covariates vary across different latent classes. The unobservable survival trajectories are identified through estimating the probability that a subject belongs to a particular class based on observed information. We applied this method to a Hodgkin lymphoma study with long-term follow-up and observed four distinct latent classes in terms of long-term survival and distributions of prognostic factors. Our results from simulation studies and from the Hodgkin lymphoma study demonstrated the superiority of our joint model compared with the conventional survival model. This flexible inference method provides more accurate estimation and accommodates unobservable heterogeneity among individuals while taking involved interactions between covariates into consideration.^