The
Japanese pearl oyster (Pinctada fucata) n16 framework matrix protein is an integral part of the growth
and formation of the mollusk shell biomineralization mechanism. It
is a required component of the extracellular matrix with a dual mineralization
role, as an anchor component to synchronize the assembly of the beta-chitin
and N-series, Pif-series protein extracellular matrix for aragonite
formation and as a regulator of aragonite formation itself. However,
the mechanism by which this protein controls aragonite formation is
not understood. Here, we investigate the mineralization potential
and kinetics of the 30 AA N-terminal portion of the n16 protein, n16N.
This sequence has been demonstrated to form either vaterite or aragonite
depending upon conditions. Using in situ potentiometric titration
methods, we find that n16N is indeed responsible for the self-assembly
characteristics found in vivo and in vitro but is not involved with
active Ca2+ binding or mineral nucleation processes. Upon
the basis of time- and peptide concentration-dependent sampling of
mineral deposits that form in solution, we find that n16N is responsible
for controlling where mineralization occurs in bulk solution. This
protein sequence acts as a molecular spacer that organizes the mineralization
space and promotes the formation of mineral constituents that contain
ACC, vaterite, and aragonite. Without the concerted action of the
n16N assemblage, unregulated calcite formation occurs exclusively.
Thus, the n16 protein provides the regulation needed to have the characteristic
polymorph, crystalline orientations, and related mechanical properties
associated to the microstructure of mollusk shells.
Starting from the 1-dimensional complex-valued Ornstein-Uhlenbeck process, we present two natural ways to imply the associated eigenfunctions of the 2-dimensional normal Ornstein-Uhlenbeck operators in the complex Hilbert space L 2 C (µ). We call the eigenfunctions Hermite-Laguerre-Ito polynomials. In addition, the Mehler summation formula for the complex process are shown. MSC: 60H10,60H07,60G15.
For a sequence of complex Wiener-Itô multiple integrals, the equivalence between the convergence of the symmetrized contraction norms and that of the non-symmetrized contraction norms is shown directly by means of a new version of complex Mallivian calculus using the Wirtinger derivatives of complex-valued functions.
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