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Abstract Mathematical models of viral dynamics in vivo provide incredible insights into the mechanisms for the nonlinear interaction between virus and host cell populations, the dynamics of viral drug resistance, and the way to eliminate virus infection from individual patients by drug treatment. The integration of these mathematical models with high-throughput genetic and genomic data within a statistical framework will raise a hope for effective treatment of infections with HIV virus through developing potent antiviral drugs based on individual patients’ genetic makeup. In this opinion article, we will show a conceptual model for mapping and dictating a comprehensive picture of genetic control mechanisms for viral dynamics through incorporating a group of differential equations that quantify the emergent properties of a system.

Genetic imprinting, or called the parent-of-origin effect, has been recognized to play an important role in the formation and pathogenesis of human diseases. Although the epigenetic mechanisms that establish genetic imprinting have been a focus of many genetic studies, our knowledge about the number of imprinting genes and their chromosomal locations and interactions with other genes is still scarce, limiting precise inference of the genetic architecture of complex diseases. In this article, we present a statistical model for testing and estimating the effects of genetic imprinting on complex diseases using a commonly used case–control design with family structure. For each subject sampled from a case and control population, we not only genotype its own single nucleotide polymorphisms (SNPs) but also collect its parents’ genotypes. By tracing the transmission pattern of SNP alleles from parental to offspring generation, the model allows the characterization of genetic imprinting effects based on Pearson tests of a 2 × 2 contingency table. The model is expanded to test the interactions between imprinting effects and additive, dominant and epistatic effects in a complex web of genetic interactions. Statistical properties of the model are investigated, and its practical usefulness is validated by a real data analysis. The model will provide a useful tool for genome-wide association studies aimed to elucidate the picture of genetic control over complex human diseases. [ABSTRACT FROM PUBLISHER]

Traditional approaches for genetic mapping are to simply associate the genotypes of a quantitative trait locus (QTL) with the phenotypic variation of a complex trait. A more mechanistic strategy has emerged to dissect the trait phenotype into its structural components and map specific QTLs that control the mechanistic and structural formation of a complex trait. We describe and assess such a strategy, called structural mapping, by integrating the internal structural basis of trait formation into a QTL mapping framework. Electrical impedance spectroscopy (EIS) has been instrumental for describing the structural components of a phenotypic trait and their interactions. By building robust mathematical models on circuit EIS data and embedding these models within a mixture model-based likelihood for QTL mapping, structural mapping implements the EM algorithm to obtain maximum likelihood estimates of QTL genotype-specific EIS parameters. The uniqueness of structural mapping is to make it possible to test a number of hypotheses about the pattern of the genetic control of structural components. We validated structural mapping by analyzing an EIS data collected for QTL mapping of frost hardiness in a controlled cross of jujube trees. The statistical properties of parameter estimates were examined by simulation studies. Structural mapping can be a powerful alternative for genetic mapping of complex traits by taking account into the biological and physical mechanisms underlying their formation. [ABSTRACT FROM AUTHOR]