Modeling the survival of T-cell lymphocytes using compound branching processes

Radiotherapy has been a method of choice in cancer treatment for a number of years. Mathematical modeling is an important tool in studying the survival behavior of any cell as well as its radiosensitivity. One particular cell under investigation is the normal T-cell, the radiosensitivity of which may be indicative to the patient's tolerance to radiation doses.^ The model derived is a compound branching process with a random initial population of T-cells that is assumed to have compound distribution. T-cells in any generation are assumed to double or die at random lengths of time. This population is assumed to undergo a random number of generations within a period of time. The model is then used to obtain an estimate for the survival probability of T-cells for the data under investigation. This estimate is derived iteratively by applying the likelihood principle. Further assessment of the validity of the model is performed by simulating a number of subjects under this model.^ This study shows that there is a great deal of variation in T-cells survival from one individual to another. These variations can be observed under normal conditions as well as under radiotherapy. The findings are in agreement with a recent study and show that genetic diversity plays a role in determining the survival of T-cells. ^

A Bayesian analysis for spatial processes with application to mapping

In geographical epidemiology, maps of disease rates and disease risk provide a spatial perspective for researching disease etiology. For rare diseases or when the population base is small, the rate and risk estimates may be unstable. Empirical Bayesian (EB) methods have been used to spatially smooth the estimates by permitting an area estimate to "borrow strength" from its neighbors. Such EB methods include the use of a Gamma model, of a James-Stein estimator, and of a conditional autoregressive (CAR) process. A fully Bayesian analysis of the CAR process is proposed. One advantage of this fully Bayesian analysis is that it can be implemented simply by using repeated sampling from the posterior densities. Use of a Markov chain Monte Carlo technique such as Gibbs sampler was not necessary. Direct resampling from the posterior densities provides exact small sample inferences instead of the approximate asymptotic analyses of maximum likelihood methods (Clayton & Kaldor, 1987). Further, the proposed CAR model provides for covariates to be included in the model. A simulation demonstrates the effect of sample size on the fully Bayesian analysis of the CAR process. The methods are applied to lip cancer data from Scotland, and the results are compared. ^

Genetic integration of a nuclear -encoded mitochondrial gene with cardiac function

Cardiovascular disease (CVD) is the leading cause of death in the United States. One manifestation of CVD known to increase mortality is an enlarged, or hypertrophic heart. Hypertrophic cardiomyocytes adapt to increased contractile demand at the genetic level with a re-emergence of the fetal gene program and a downregulation of fatty acid oxidation genes with concomitant increased reliance on glucose-based metabolism. To understand the transcriptional regulatory pathways that implement hypertrophic directives we analyzed the upstream promoter region of the muscle specific isoform of the nuclear-encoded mitochondrial gene, carnitine palmitoyltransferase-1β (CPT-1β) in cultured rat neonatal cardiac myocytes. This enzyme catalyzes the rate-limiting step of fatty acid entry into β-oxidation and is downregulated in cardiac hypertrophy and failure, making it an attractive model for the study of hypertrophic gene regulation and metabolic adaptations. We demonstrate that the muscle-enriched transcription factors GATA-4 and SRF synergistically activate CPT-1β; moreover, DNA binding to cognate sites and intact protein structure are required. This mechanism coordinates upregulation of energy generating processes with activation of the energy consuming contractile promoter for cardiac α-actin. We hypothesized that fatty acid or glucose responsive transcription factors may also regulate CPT-1β. Oleate weakly stimulates CPT-1β activity; in contrast, the glucose responsive Upstream Stimulatory Factors (USF) dramatically depresses the CPT-1β reporter. USF regulates CPT-1β through a novel physical interaction with the cofactor PGC-1 and abrogation of MEF2A/PGC-1 synergistic stimulation. In this way, USF can inversely regulate metabolic gene programs and may play a role in the shift of metabolic substrate preference seen in hypertrophy. Failing hearts have elevated expression of the nuclear hormone receptor COUP-TF. We report that COUP-TF significantly suppresses reporter transcription independent of DNA binding and specific interactions with GATA-4, Nkx2.5 or USF. In summary, CPT-1β transcriptional regulation integrates mitochondrial gene expression with two essential cardiac functions: contraction and metabolic substrate oxidation. ^

Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins.

cAMP-response element binding (CREB) proteins are involved in transcriptional regulation in a number of cellular processes (e.g., neural plasticity and circadian rhythms). The CREB family contains activators and repressors that may interact through positive and negative feedback loops. These loops can be generated by auto- and cross-regulation of expression of CREB proteins, via CRE elements in or near their genes. Experiments suggest that such feedback loops may operate in several systems (e.g., Aplysia and rat). To understand the functional implications of such feedback loops, which are interlocked via cross-regulation of transcription, a minimal model with a positive and negative loop was developed and investigated using bifurcation analysis. Bifurcation analysis revealed diverse nonlinear dynamics (e.g., bistability and oscillations). The stability of steady states or oscillations could be changed by time delays in the synthesis of the activator (CREB1) or the repressor (CREB2). Investigation of stochastic fluctuations due to small numbers of molecules of CREB1 and CREB2 revealed a bimodal distribution of CREB molecules in the bistability region. The robustness of the stable HIGH and LOW states of CREB expression to stochastic noise differs, and a critical number of molecules was required to sustain the HIGH state for days or longer. Increasing positive feedback or decreasing negative feedback also increased the lifetime of the HIGH state, and persistence of this state may correlate with long-term memory formation. A critical number of molecules was also required to sustain robust oscillations of CREB expression. If a steady state was near a deterministic Hopf bifurcation point, stochastic resonance could induce oscillations. This comparative analysis of deterministic and stochastic dynamics not only provides insights into the possible dynamics of CREB regulatory motifs, but also demonstrates a framework for understanding other regulatory processes with similar network architecture.

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.

Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins.

cAMP-response element binding (CREB) proteins are involved in transcriptional regulation in a number of cellular processes (e.g., neural plasticity and circadian rhythms). The CREB family contains activators and repressors that may interact through positive and negative feedback loops. These loops can be generated by auto- and cross-regulation of expression of CREB proteins, via CRE elements in or near their genes. Experiments suggest that such feedback loops may operate in several systems (e.g., Aplysia and rat). To understand the functional implications of such feedback loops, which are interlocked via cross-regulation of transcription, a minimal model with a positive and negative loop was developed and investigated using bifurcation analysis. Bifurcation analysis revealed diverse nonlinear dynamics (e.g., bistability and oscillations). The stability of steady states or oscillations could be changed by time delays in the synthesis of the activator (CREB1) or the repressor (CREB2). Investigation of stochastic fluctuations due to small numbers of molecules of CREB1 and CREB2 revealed a bimodal distribution of CREB molecules in the bistability region. The robustness of the stable HIGH and LOW states of CREB expression to stochastic noise differs, and a critical number of molecules was required to sustain the HIGH state for days or longer. Increasing positive feedback or decreasing negative feedback also increased the lifetime of the HIGH state, and persistence of this state may correlate with long-term memory formation. A critical number of molecules was also required to sustain robust oscillations of CREB expression. If a steady state was near a deterministic Hopf bifurcation point, stochastic resonance could induce oscillations. This comparative analysis of deterministic and stochastic dynamics not only provides insights into the possible dynamics of CREB regulatory motifs, but also demonstrates a framework for understanding other regulatory processes with similar network architecture.

Outcome-based adaptive randomization for binary data in clinical trials---Compare and contrast

Monte Carlo simulation has been conducted to investigate parameter estimation and hypothesis testing in some well known adaptive randomization procedures. The four urn models studied are Randomized Play-the-Winner (RPW), Randomized Pôlya Urn (RPU), Birth and Death Urn with Immigration (BDUI), and Drop-the-Loses Urn (DL). Two sequential estimation methods, the sequential maximum likelihood estimation (SMLE) and the doubly adaptive biased coin design (DABC), are simulated at three optimal allocation targets that minimize the expected number of failures under the assumption of constant variance of simple difference (RSIHR), relative risk (ORR), and odds ratio (OOR) respectively. Log likelihood ratio test and three Wald-type tests (simple difference, log of relative risk, log of odds ratio) are compared in different adaptive procedures. ^ Simulation results indicates that although RPW is slightly better in assigning more patients to the superior treatment, the DL method is considerably less variable and the test statistics have better normality. When compared with SMLE, DABC has slightly higher overall response rate with lower variance, but has larger bias and variance in parameter estimation. Additionally, the test statistics in SMLE have better normality and lower type I error rate, and the power of hypothesis testing is more comparable with the equal randomization. Usually, RSIHR has the highest power among the 3 optimal allocation ratios. However, the ORR allocation has better power and lower type I error rate when the log of relative risk is the test statistics. The number of expected failures in ORR is smaller than RSIHR. It is also shown that the simple difference of response rates has the worst normality among all 4 test statistics. The power of hypothesis test is always inflated when simple difference is used. On the other hand, the normality of the log likelihood ratio test statistics is robust against the change of adaptive randomization procedures. ^

Adherence to a lifestyle physical activity program: Trends over time and associations with processes of change and physical activity

Research on lifestyle physical activity interventions suggests that they help individuals meet the new recommendations for physical activity made by the Centers for Disease Control and Prevention (CDC) and the American College of Sports Medicine (ACSM). The purpose of this research was to describe the rates of adherence to two lifestyle physical activity intervention arms and to examine the association between adherence and outcome variables, using data from Project PRIME, a lifestyle physical activity intervention based on the transtheoretical model and conducted by the Cooper Institute of Aerobics Research, Dallas, Texas. Participants were 250 sedentary healthy adults, aged 35 to 70 years, primarily non-Hispanic White, and in the contemplation and preparation stages of readiness to change. They were randomized to a group (PRIME G) or a mail- and telephone-delivered condition (PRIME C). Adherence measures included attending class (PRIME G), completing a monthly telephone call with a health educator (PRIME C), and completing homework assignments and self-monitoring minutes of moderate- to vigorous physical activity (both groups). In the first results paper, adherence over time and between conditions was examined: Attendance in group, completing the monthly telephone call, and homework completion decreased over time, and participants in PRIME G were more likely to complete homework than those in PRIME C. Paper 2 aimed to determine whether the adherence measures predicted achievement of the CDC/ACSM physical activity guideline. In separate models for the two conditions, a latent variable measuring adherence was found to predict achievement of the guideline. Paper 3 examined the association between adherence measures and the transtheoretical model's processes of change within each condition. For both, participants who completed at least two thirds of the homework assignments improved their use of the processes of change more than those who completed less than that amount. These results suggest that encouraging adherence to a lifestyle physical activity intervention, at least among already motivated volunteers, may increase the likelihood of beneficial changes in the outcomes. ^