Comparison of parametric and nonparametric methods to map oligogenes by linkage

A sample of 95 sib pairs affected with insulin-dependent diabetes and typed with their normal parents for 28 markers on chromosome 6 has been analyzed by several methods. When appropriate parameters are efficiently estimated, a parametric model is equivalent to the β model, which is superior to nonparametric alternatives both in single point tests (as found previously) and in multipoint tests. Theory is given for meta-analysis combined with allelic association, and problems that may be associated with errors of map location and/or marker typing are identified. Reducing by multipoint analysis the number of association tests in a dense map can give a 3-fold reduction in the critical lod, and therefore in the cost of positional cloning.

Expression of the Hox gene complex in the indirect development of a sea urchin

Hox complex genes control spatial patterning mechanisms in the development of arthropod and vertebrate body plans. Hox genes are all expressed during embryogenesis in these groups, which are all directly developing organisms in that embryogenesis leads at once to formation of major elements of the respective adult body plans. In the maximally indirect development of a large variety of invertebrates, the process of embryogenesis leads only to a free-living, bilaterally organized feeding larva. Maximal indirect development is exemplified in sea urchins. The 5-fold radially symmetric adult body plan of the sea urchin is generated long after embryogenesis is complete, by a separate process occurring within imaginal tissues set aside in the larva. The single Hox gene complex of Strongylocentrotus purpuratus contains 10 genes, and expression of eight of these genes was measured by quantitative methods during both embryonic and larval developmental stages and also in adult tissues. Only two of these genes are used significantly during the entire process of embryogenesis per se, although all are copiously expressed during the stages when the adult body plan is forming in the imaginal rudiment. They are also all expressed in various combinations in adult tissues. Thus, development of a microscopic, free-living organism of bilaterian grade, the larva, does not appear to require expression of the Hox gene cluster as such, whereas development of the adult body plan does. These observations reflect on mechanisms by which bilaterian metazoans might have arisen in Precambrian evolution.

Mathematical analysis of activation thresholds in enzyme-catalyzed positive feedbacks: application to the feedbacks of blood coagulation.

A hierarchy of enzyme-catalyzed positive feedback loops is examined by mathematical and numerical analysis. Four systems are described, from the simplest, in which an enzyme catalyzes its own formation from an inactive precursor, to the most complex, in which two sequential feedback loops act in a cascade. In the latter we also examine the function of a long-range feedback, in which the final enzyme produced in the second loop activates the initial step in the first loop. When the enzymes generated are subject to inhibition or inactivation, all four systems exhibit threshold properties akin to excitable systems like neuron firing. For those that are amenable to mathematical analysis, expressions are derived that relate the excitation threshold to the kinetics of enzyme generation and inhibition and the initial conditions. For the most complex system, it was expedient to employ numerical simulation to demonstrate threshold behavior, and in this case long-range feedback was seen to have two distinct effects. At sufficiently high catalytic rates, this feedback is capable of exciting an otherwise subthreshold system. At lower catalytic rates, where the long-range feedback does not significantly affect the threshold, it nonetheless has a major effect in potentiating the response above the threshold. In particular, oscillatory behavior observed in simulations of sequential feedback loops is abolished when a long-range feedback is present.