3D Cell-Migration Studies using Two-Photon Engineered Polymer Scaffolds

We use two-photon polymerization to fabricate 3D scaffolds with precise control over pore size and shape for studying cell migration in 3D. These scaffolds allow movement of cells in all directions. The fabrication, imaging, and quantitative analysis method developed here can be used to do systematic cell studies in 3D.

Polymeric scaffolds for enhanced stability of melanin incorporated in liposomes

The use of melanin in bioinspired applications is mostly limited by its poor stability in solid films. This problem has been addressed here by incorporating melanin into dipalmitoyl phosphatidyl glycerol (DPPG) liposomes, which were then immobilized onto a solid substrate as an LbL film. Results from steady-state and time-resolved fluorescence indicated an increased stability for melanin incorporated into DPPG liposomes. If not protected by liposomes, melanin looses completely its fluorescence properties in LbL films. The thickness of the liposome-melanin layer obtained from neutron reflectivity data was 4.1 +/- 0.2 nm, consistent with the value estimated for the phospholipid bilayer of the liposomes, an evidence of the collapse of most liposomes. On the other hand, the final roughness indicated that some of the liposomes had their structure preserved. In summary, liposomes were proven excellent for encapsulation, thus providing a suitable environment, closer to the physiological conditions without using organic solvents or high pHs. (C) 2010 Elsevier Inc. All rights reserved.

Crossed products by twisted partial actions and graded algebras

For a twisted partial action e of a group G on an (associative non-necessarily unital) algebra A over a commutative unital ring k, the crossed product A x(Theta) G is proved to be associative. Given a G-graded k-algebra B = circle plus(g is an element of G) B-g with the mild restriction of homogeneous non-degeneracy, a criteria is established for B to be isomorphic to the crossed product B-1 x(Theta) G for some twisted partial action of G on B-1. The equality BgBg-1 B-g = B-g (for all g is an element of G) is one of the ingredients of the criteria, and if it holds and, moreover, B has enough local units, then it is shown that B is stably isomorphic to a crossed product by a twisted partial action of G. (c) 2008 Elsevier Inc. All rights reserved.

Nil graded self-similar algebras

In [19], [24] we introduced a family of self-similar nil Lie algebras L over fields of prime characteristic p > 0 whose properties resemble those of Grigorchuk and Gupta-Sidki groups. The Lie algebra L is generated by two derivations v(1) = partial derivative(1) + t(0)(p-1) (partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...))))), v(2) = partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...)))) of the truncated polynomial ring K[t(i), i is an element of N vertical bar t(j)(p) =0, i is an element of N] in countably many variables. The associative algebra A generated by v(1), v(2) is equipped with a natural Z circle plus Z-gradation. In this paper we show that for p, which is not representable as p = m(2) + m + 1, m is an element of Z, the algebra A is graded nil and can be represented as a sum of two locally nilpotent subalgebras. L. Bartholdi [3] andYa. S. Krylyuk [15] proved that for p = m(2) + m + 1 the algebra A is not graded nil. However, we show that the second family of self-similar Lie algebras introduced in [24] and their associative hulls are always Z(p)-graded, graded nil, and are sums of two locally nilpotent subalgebras.