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A multi-part theorem is presented concerning the morphogenesis of high-symmetry structures made of three-dimensional morphological units (MU's) free to move on the surface of a sphere. All parts of each MU interact non-specifically with the remainder of the structure, via an isotropic function of distance. Summing all interactions gives a net figure of merit, X, that depends upon MU positions and orientations. The structure evolves via gradient dynamics, each MU moving down the local gradient of I. The analysis is reresented with generality in Fourier space, which eases the expression of symmetry. Structures near symmetry, but far from a local minimum of I, are analyzed. For each, a symmetrical configuration can be found, for which X is an extremum with respect to symmetry-breaking perturbations. Under gradient dynamics, a quadratic measure of such deviations from symmetry decreases monotonically, anywhere in the large basin of attraction of a local minimum. Thus: high symmetry is an attractor. Application is made to icosahedral virus capsids. The Symmetrization Theorem shows that a stable capsid, maintained by non-specific interactions among its capsomeres, could arise generically in a "bottom-up" process. For animated evolutions that selfassemble into high symmetry, visit http://www.albany.edu/~cmarzec/
The larvae of Orthocladiinae (Diptera: Chironomidae) of the Holarctic region : keys and diagnoses
(1983)
Material of the domestic fowl of appropriate ages, ranging from twelve hours' incubation to the adult bird, was prepared for the purpose of studying the production and development of the germ cells. The primordial germ cells arise in the extra-embryonic region anterior to the head fold in the region of the zone of junction during the primitive-streak stage. These germ cells migrate, through the blood stream, to the region of the future gonad, where they develop into the definitive germ plasm. There is no widespread degeneration of the primordial germ cells after their arrival in the gonadal region, nor is there any widespread transformation of somatic cells into definitive germ cells.