An epidemiological model of spatial coupling for trips longer than the infectious period.

One of the standard methods of accounting for inter-population disease spread in equation-based epidemiology models is through a transportation operator. Implicit in the use of the transportation operator, however, is an assumption that daily travel volumes are small compared to overall population sizes, an assumption that can break down for modern rates of international travel or local commuter traffic. Alternative types of coupling have been proposed in the limit that trip durations are much shorter than the infectious period. We present an extension of these phenomenological models that relaxes both assumptions. We show that the approach produces more accurate results when assessing the impact of mitigative actions using modern travel volumes.

Comparative cis-regulatory analyses identify new elements of the mouse Hoxc8 early enhancer.

The Hoxc8 early enhancer is a 200 bp region that controls the early phase of Hoxc8 expression during mouse embryonic development. This enhancer defines the domain of Hoxc8 expression in the neural tube and mesoderm of the posterior regions of the developing embryo. Five distinct cis-acting elements, A-E, were previously shown to govern early phase Hoxc8 expression. Significant divergence between mammalian and fish Hoxc8 early enhancer sequences and activities suggested additional cis-acting elements. Here we describe four additional cis-acting elements (F-I) within the 200 bp Hoxc8 early enhancer region identified by comparative regulatory analysis and transgene-mutation studies. These elements affect posterior neural tube and mesoderm expression of the reporter gene, either singly or in combination. Surprisingly, these new elements are missing from the zebrafish and Fugu Hoxc8 early enhancer sequences. Considering that fish enhancers direct robust reporter expression in transgenic mouse embryos, it is tempting to postulate that fish and mammalian Hoxc8 early enhancers utilize different sets of elements to direct Hoxc8 early expression. These observations reveal a remarkable plasticity in the Hoxc8 early enhancer, suggesting different modes of initiation and establishment of Hoxc8 expression in different species. We postulate that extensive restructuring and remodeling of Hox cis-regulatory regions occurring in different taxa lead to relatively different Hox expression patterns, which in turn may act as a driving force in generating diverse axial morphologies.

Divergence of Hoxc8 early enhancer parallels diverged axial morphologies between mammals and fishes.

There is considerable interest in understanding how cis-regulatory modifications drive morphological changes across species. Because developmental regulatory genes, including Hox genes, are remarkably conserved, their noncoding regulatory regions are likely sources for variations. Modifications of Hox cis-regulatory elements have potential to alter Hox gene expression and, hence, axial morphologies. In vertebrates, differences in the axial levels of Hox gene expression correlate with differences in the number and relative position of thoracic vertebrae. Variation in cis-regulatory elements of Hox genes can be identified by comparative sequence and reporter gene analyses in transgenic mouse embryos. Using these approaches, we show a remarkable divergence of the Hoxc8 early enhancers between mammals and fishes representing diverse axial morphologies. Extensive restructuring of the Hoxc8 early enhancer including nucleotide substitutions, inversion, and divergence result in distinct patterns of reporter gene expression along the embryonic axis. Our results provide an evolutionary perspective on how the enhancer elements are engineered and support the hypothesis that remodeling of Hox regulatory elements in different species has played a significant role in generating morphological diversity.