A statistical model for genetic mapping of viral infection by integrating epidemiological behavior

The Genomic Physics of COVID-19 Pathogenesis and Spread

Coronavirus disease (COVID-19) spreads mainly through close contact of infected persons, but the molecular mechanisms underlying its pathogenesis and transmission remain unknown. Here, we propose a statistical physics model to coalesce all molecular entities into a cohesive network in which the roadmap of how each entity mediates the disease can be characterized. We argue that the process of how a transmitter transforms the virus into a recipient constitutes a triad unit that propagates COVID-19 along reticulate paths. Intrinsically, person-to-person transmissibility may be mediated by how genes interact transversely across transmitter, recipient, and viral genomes. We integrate quantitative genetic theory into hypergraph theory to code the main effects of the three genomes as nodes, pairwise cross-genome epistasis as edges, and high-order cross-genome epistasis as hyperedges in a series of mobile hypergraphs. Charting a genome-wide atlas of horizontally epistatic hypergraphs can facilitate the systematic characterization of the community genetic mechanisms underlying COVID-19 spread. This atlas can typically help design effective containment and mitigation strategies and screen and triage those more susceptible persons and those asymptomatic carriers who are incubation virus transmitters.

Systems mapping of HIV-1 infection

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.

Modeling haplotype-haplotype interactions in case-control genetic association studies

Haplotype analysis has been increasingly used to study the genetic basis of human diseases, but models for characterizing genetic interactions between haplotypes from different chromosomal regions have not been well developed in the current literature. In this article, we describe a statistical model for testing haplotype-haplotype interactions for human diseases with a case-control genetic association design. The model is formulated on a contingency table in which cases and controls are typed for the same set of molecular markers. By integrating well-established quantitative genetic principles, the model is equipped with a capacity to characterize physiologically meaningful epistasis arising from interactions between haplotypes from different chromosomal regions. The model allows the partition of epistasis into different components due to additive × additive, additive × dominance, dominance × additive, and dominance × dominance interactions. We derive the EM algorithm to estimate and test the effects of each of these components on differences in the pattern of genetic variation between cases and controls and, therefore, examine their role in the pathogenesis of human diseases. The method was further extended to investigate gene-environment interactions expressed at the haplotype level. The statistical properties of the models were investigated through simulation studies and its usefulness and utilization validated by analyzing the genetic association of sarcoidosis from a human genetics project.