Nonionic diethanolamide amphiphiles with isoprenoid-type hydrocarbon chains: thermotropic and lyotropic liquid crystalline phase behaviour

The thermotropic and lyotropic liquid crystalline phase behaviour of a series of diethanolamide amphiphiles with isoprenoid-type hydrocarbon chains (geranoyl, H-farnesoyl, and phytanoyl) has been investigated. When neat, both H-farnesoyl and phytanoyl diethanolamide form a smectic liquid crystalline structure at sub-zero temperatures. In addition, all three diethanolamides exhibit a glass transition temperature at around -73 °C. Geranoyl diethanolamide forms a lamellar crystalline phase with a lattice parameter of 17.4 ? following long term storage accompanied by the loss of the glass transition. In the presence of water, H-farnesoyl and phytanoyl diethanolamide form lyotropic liquid crystalline phases, whilst geranoyl diethanolamide forms an L(2) phase. H-farnesoyl diethanolamide forms a fluid lamellar phase (L(α)) at room temperature and up to ～ 40 °C. Phytanoyl diethanolamide displays a rich mesomorphism forming the inverse diamond (Q(II)(D)) and gyroid (Q(II)(G)) bicontinuous cubic phases in addition to an L(α) phase.     

Nonionic diethanolamide amphiphiles with unsaturated C18 hydrocarbon chains: thermotropic and lyotropic liquid crystalline phase behavior

The neat and lyotropic liquid crystalline phase behavior of three nonionic diethanolamide amphiphiles with C18 hydrocarbon chains containing one, two or three unsaturated bonds has been examined. This has allowed the effect of degree of unsaturation on the phase behavior of diethanolamide amphiphiles to be investigated. Neat linoleoyl and linolenoyl diethanolamide undergo a transition from a glassy liquid crystal to a liquid crystal at ～-85 °C, while neat oleoyl diethanolamide undergoes a transition at ～-60 °C to a liquid crystalline material before re-crystallizing at -34 °C. Oleoyl diethanolamide then undergoes a third transition from a crystalline phase to a smectic liquid crystalline phase at ～5 °C. In the absence of water, the transition temperature from a smectic liquid crystal to an isotropic liquid decreases with increasing unsaturation. The addition of water results in the formation of a lamellar phase (L(α)) for all three amphiphiles. The lamellar phase is stable under excess water conditions up to temperatures of at least 70 °C. Approximate partial binary amphiphile-water phase diagrams generated for the three unsaturated C18 amphiphiles indicate that the excess water point for each amphiphile occurs at ～60% (w/w) amphiphile.     

Enzyme mediated incorporation of zirconium-89 or copper-64 into a fragment antibody for same day imaging of epidermal growth factor receptor

Identification of tumors which over-express Epidermal Growth Factor Receptor (EGFR) is important in selecting patients for anti-EGFR therapies. Enzymatic bioconjugation was used to introduce positron-emitting radionuclides (⁸⁹Zr, ⁶⁴Cu) into an anti-EGFR antibody fragment for Positron Emission Tomography (PET) imaging the same day as injection. A monovalent antibody fragment with high affinity for EGFR was engineered to include a sequence that is recognized by the transpeptidase sortase A. Two different metal chelators, one for ⁸⁹Zr^IV and one for ⁶⁴Cu^II, were modified with a N-terminal glycine to enable them to act as substrates in sortase A mediated bioconjugation to the antibody fragment. Both fragments provided high-quality PET images of EGFR positive tumors in a mouse model at 3 hours post-injection, a significant advantage when compared to radiolabeled full antibodies that require several days between injection of the tracer and imaging. The use of enzymatic bioconjugation gives reproducible homogeneous products with the metal complexes selectively installed on the C-terminus of the antibody potentially simplifying regulatory approval.

Enzymatic bioconjugation to introduce positron-emitting radionuclides (⁸⁹Zr, ⁶⁴Cu) into an anti-EGFR antibody fragment allows same day imaging with positron emission tomography.     

Spectral flow as winding number and integral formulas

A general integral formula for the spectral flow of a path of unbounded selfadjoint Fredholm operators subject to certain summability conditions is derived from the interpretation of the spectral flow as a winding number.

     

Differential Galois theory of linear difference equations

We present a Galois theory of difference equations designed to measure the differential dependencies among solutions of linear difference equations. With this we are able to reprove Hölder’s theorem that the Gamma function satisfies no polynomial differential equation and are able to give general results that imply, for example, that no differential relationship holds among solutions of certain classes of q-hypergeometric equations.     

Another class of balanced graph designs: balanced circuit designs

A block considered as a set of elements together with its adjacency matrix A is called a C-block if A is the adjacency matrix of a circuit. A balanced circuit design with parameters v, b, r, k, λ (briefly, BCD(v, k, λ)) is an arrangement of v elements into bC-blocks such that each C-block contains k elements, each element occurs in exactly rC-blocks and any two distinct elements are linked in exactly λ C-blocks.We investigate conditions for the existence of BCD and show, in particular, that if the block-size k ? 6 and the trivial necessary conditions are satisfied, then the corresponding BCD exists.