New insight into cataract formation: enhanced stability through mutual attraction

Small-angle neutron scattering experiments and molecular dynamics simulations combined with an application of concepts from soft matter physics to complex protein mixtures provide new insight into the stability of eye lens protein mixtures. Exploring this colloid-protein analogy we demonstrate that weak attractions between unlike proteins help to maintain lens transparency in an extremely sensitive and nonmonotonic manner. These results not only represent an important step towards a better understanding of protein condensation diseases such as cataract formation, but provide general guidelines for tuning the stability of colloid mixtures, a topic relevant for soft matter physics and industrial applications.     

Lower bounds on volumes of hyperbolic Haken 3-manifolds

We prove a volume inequality for 3-manifolds having metrics ``bent' along a surface and satisfying certain curvature conditions. The result makes use of Perelman's work on the Ricci flow and geometrization of closed 3-manifolds. Corollaries include a new proof of a conjecture of Bonahon about volumes of convex cores of Kleinian groups, improved volume estimates for certain Haken hyperbolic 3-manifolds, and a lower bound on the minimal volume of orientable hyperbolic 3-manifolds. An appendix compares estimates of volumes of hyperbolic 3-manifolds drilled along a closed embedded geodesic with experimental data.

     

Observation of the reversibility of a covalent pyrrolobenzodiazepine (PBD) DNA adduct by HPLC/MS and CD spectroscopy

Pyrrolobenzodiazepines (PBDs) are sequence-selective DNA minor-groove binding agents that covalently bond to guanine with a reported preference for Pu-G-Pu sequences (Pu = Purine). Using HPLC/MS and Circular Dichroism (CD) methodologies, we have established for the first time that the aminal bond formed between PBD molecules and DNA is reversible. Furthermore, we have shown that while the rate of aminal bond cleavage does not depend on the sequence preference of a PBD molecule for a particular binding site, the rate of re-formation of the PBD-DNA adduct does. We have also shown that the PBD anthramycin (2) appears to be an exception to this rule in that, during cleavage from the DNA, its C-ring aromatizes and it cannot then re-attach due to a loss of electrophilicity at the C11-position. Although the C-ring aromatization of anthramycin has been previously reported to occur in the absence of DNA and after treatment with trifluoroacetic acid (TFA), in this case no pH lowering was required, with the DNA itself appearing to catalyse the process.     

On the design of experiments for determining ternary mixture free energies from static light scattering data using a nonlinear partial differential equation

We mathematically design sets of static light scattering experiments to provide for model-independent measurements of ternary liquid mixing free energies to a desired level of accuracy. A parabolic partial differential equation (PDE), linearized from the full nonlinear PDE [D. Ross, G. Thurston, and C. Lutzer, J. Chem. Phys. 129, 064106 (2008)], describes how data noise affects the free energies to be inferred. The linearized PDE creates a net of spacelike characteristic curves and orthogonal, timelike curves in the composition triangle, and this net governs diffusion of information coming from light scattering measurements to the free energy. Free energy perturbations induced by a light scattering perturbation diffuse along the characteristic curves and towards their concave sides, with a diffusivity that is proportional to the local characteristic curvature radius. Consequently, static light scattering can determine mixing free energies in regions with convex characteristic curve boundaries, given suitable boundary data. The dielectric coefficient is a Lyapunov function for the dynamical system whose trajectories are PDE characteristics. Information diffusion is heterogeneous and system-dependent in the composition triangle, since the characteristics depend on molecular interactions and are tangent to liquid-liquid phase separation coexistence loci at critical points. We find scaling relations that link free energy accuracy, total measurement time, the number of samples, and the interpolation method, and identify the key quantitative tradeoffs between devoting time to measuring more samples, or fewer samples more accurately. For each total measurement time there are optimal sample numbers beyond which more will not improve free energy accuracy. We estimate the degree to which many-point interpolation and optimized measurement concentrations can improve accuracy and save time. For a modest light scattering setup, a sample calculation shows that less than two minutes of measurement time is, in principle, sufficient to determine the dimensionless mixing free energy of a non-associating ternary mixture to within an integrated error norm of 0.003. These findings establish a quantitative framework for designing light scattering experiments to determine the Gibbs free energy of ternary liquid mixtures.     

The computational complexity of knot genus and spanning area

We show that the problem of deciding whether a polygonal knot in a closed three-dimensional manifold bounds a surface of genus at most is NP-complete. We also show that the problem of deciding whether a curve in a PL manifold bounds a surface of area less than a given constant is NP-hard.

     

Synthetic magnetic opals

We present studies of novel nanocomposites of BiNi impregnated into the structure of opals as well as inverse opals. Atomic force microscopy and high resolution elemental analyses show a highly ordered structure and uniform distribution of the BiNi filler in the matrix. These BiNi-based nanocomposites are found to exhibit distinct ferromagnetic-like ordering with transition temperature of about 675 K. As far as we know there exists no report in literature on any BiNi compound which is magnetic.