A computational model for functional mapping of genes that regulate intra-cellular circadian rhythms

Systems mapping for hematopoietic progenitor cell heterogeneity

Cells with the same genotype growing under the same conditions can show different phenotypes, which is known as “population heterogeneity”. The heterogeneity of hematopoietic progenitor cells has an effect on their differentiation potential and lineage choices. However, the genetic mechanisms governing population heterogeneity remain unclear. Here, we present a statistical model for mapping the quantitative trait locus (QTL) that affects hematopoietic cell heterogeneity. This strategy, termed systems mapping, integrates a system of differential equations into the framework for systems mapping, allowing hypotheses regarding the interplay between genetic actions and cell heterogeneity to be tested. A simulation approach based on cell heterogeneity dynamics has been designed to test the statistical properties of the model. This model not only considers the traditional QTLs, but also indicates the methylated QTLs that can illustrate non-genetic individual differences. It has significant implications for probing the molecular, genetic and epigenetic mechanisms of hematopoietic progenitor cell heterogeneity.

Statistical challenges in the analysis of dynamic traits: implications for pharmacogenomic clinics

Analysis of dynamic traits is statistically challenging for several reasons. Since most of the dynamic traits result in irregular sparse longitudinal measurements, a unified approach for jointly modeling the mean trajectories and the underlying covariance structure is essential. When the traits are bivariate or multivariate in nature, modeling the covariance structure is really challenging. For the pharmacogenomic clinics, it is extremely important to have a comprehensive study of the whole biological system. In other words, if the traits under consideration result in some events (e.g., death, disease), then a joint analysis is required for the observed dynamic traits and the event-time. In statistics, there is a vast literature on such joint modeling using parametric, nonparametric and semiparametric approaches. In this article, we will discuss different aspects of modeling the longitudinal traits, their limitations and importance to pharmacogenomic clinics.

Dynamic modeling of genes controlling cancer stem cell proliferation

The growing evidence that cancer originates from stem cells (SC) holds a great promise to eliminate this disease by designing specific drug therapies for removing cancer SC. Translation of this knowledge into predictive tests for the clinic is hampered due to the lack of methods to discriminate cancer SC from non-cancer SC. Here, we address this issue by describing a conceptual strategy for identifying the genetic origins of cancer SC. The strategy incorporates a high-dimensional group of differential equations that characterizes the proliferation, differentiation, and reprogramming of cancer SC in a dynamic cellular and molecular system. The deployment of robust mathematical models will help uncover and explain many still unknown aspects of cell behavior, tissue function, and network organization related to the formation and division of cancer SC. The statistical method developed allows biologically meaningful hypotheses about the genetic control mechanisms of carcinogenesis and metastasis to be tested in a quantitative manner.

A dynamic model for functional mapping of biological rhythms

Functional mapping is a statistical method for mapping quantitative trait loci (QTLs) that regulate the dynamic pattern of a biological trait. This method integrates mathematical aspects of biological complexity into a mixture model for genetic mapping and tests the genetic effects of QTLs by comparing genotype-specific curve parameters. As a way of quantitatively specifying the dynamic behavior of a system, differential equations have proven to be powerful for modeling and unraveling the biochemical, molecular, and cellular mechanisms of a biological process, such as biological rhythms. The equipment of functional mapping with biologically meaningful differential equations provides new insights into the genetic control of any dynamic processes. We formulate a new functional mapping framework for a dynamic biological rhythm by incorporating a group of ordinary differential equations (ODE). The Runge-Kutta fourth order algorithm was implemented to estimate the parameters that define the system of ODE. The new model will find its implications for understanding the interplay between gene interactions and developmental pathways in complex biological rhythms.

Chronopharmaceutical drug delivery systems: Hurdles, hype or hope?

The current advances in chronobiology and the knowledge gained from chronotherapy of selected diseases strongly suggest that "the one size fits all at all times" approach to drug delivery is no longer substantiated, at least for selected bioactive agents and disease therapy or prevention. Thus, there is a critical and urgent need for chronopharmaceutical research (e.g., design and evaluation of robust, spatially and temporally controlled drug delivery systems that would be clinically intended for chronotherapy by different routes of administration). This review provides a brief overview of current drug delivery system intended for chronotherapy. In theory, such an ideal "magic pill" preferably with affordable cost, would improve the safety, efficacy and patient compliance of old and new drugs. However, currently, there are three major hurdles for the successful transition of such system from laboratory to patient bedside. These include the challenges to identify adequate (i) rhythmic biomaterials and systems, (ii) rhythm engineering and modeling, perhaps using system biology and (iii) regulatory guidance.

Nonparametric modeling of longitudinal covariance structure in functional mapping of quantitative trait loci

Estimation of the covariance structure of longitudinal processes is a fundamental prerequisite for the practical deployment of functional mapping designed to study the genetic regulation and network of quantitative variation in dynamic complex traits. We present a nonparametric approach for estimating the covariance structure of a quantitative trait measured repeatedly at a series of time points. Specifically, we adopt Huang et al.'s (2006, Biometrika 93, 85-98) approach of invoking the modified Cholesky decomposition and converting the problem into modeling a sequence of regressions of responses. A regularized covariance estimator is obtained using a normal penalized likelihood with an L(2) penalty. This approach, embedded within a mixture likelihood framework, leads to enhanced accuracy, precision, and flexibility of functional mapping while preserving its biological relevance. Simulation studies are performed to reveal the statistical properties and advantages of the proposed method. A real example from a mouse genome project is analyzed to illustrate the utilization of the methodology. The new method will provide a useful tool for genome-wide scanning for the existence and distribution of quantitative trait loci underlying a dynamic trait important to agriculture, biology, and health sciences.

A statistical model for the identification of genes governing the incidence of cancer with age

The cancer incidence increases with age. This epidemiological pattern of cancer incidence can be attributed to molecular and cellular processes of individual subjects. Also, the incidence of cancer with ages can be controlled by genes. Here we present a dynamic statistical model for explaining the epidemiological pattern of cancer incidence based on individual genes that regulate cancer formation and progression. We incorporate the mathematical equations of age-specific cancer incidence into a framework for functional mapping aimed at identifying quantitative trait loci (QTLs) for dynamic changes of a complex trait. The mathematical parameters that specify differences in the curve of cancer incidence among QTL genotypes are estimated within the context of maximum likelihood. The model provides testable quantitative hypotheses about the initiation and duration of genetic expression for QTLs involved in cancer progression. Computer simulation was used to examine the statistical behavior of the model. The model can be used as a tool for explaining the epidemiological pattern of cancer incidence.