The Lippmann–Schwinger Formula and One Dimensional Models with Dirac Delta Interactions

We show how a proper use of the Lippmann–Schwinger equation simplifies the calculations to obtain scattering states for one dimensional systems perturbed by N Dirac delta equations. Here, we consider two situations. In the former, attractive Dirac deltas perturbed the free one dimensional Schrödinger Hamiltonian. We obtain explicit expressions for scattering and Gamow states. For completeness, we show that the method to obtain bound states use comparable formulas, although not based on the Lippmann–Schwinger equation. Then, the attractive N deltas perturbed the one dimensional Salpeter equation. We also obtain explicit expressions for the scattering wave functions. Here, we need regularisation techniques that we implement via heat kernel regularisation

Visualizing spatially correlated dynamics that directs RNA conformational transitions

RNAs fold into three- dimensional ( 3D) structures that subsequently undergo large, functionally important, conformational transitions in response to a variety of cellular signals(1-3). RNA structures are believed to encode spatially tuned flexibility that can direct transitions along specific conformational pathways(4,5). However, this hypothesis has proved difficult to examine directly because atomic movements in complex biomolecules cannot be visualized in 3D by using current experimental methods. Here we report the successful implementation of a strategy using NMR that has allowed us to visualize, with complete 3D rotational sensitivity, the dynamics between two RNA helices that are linked by a functionally important trinucleotide bulge over timescales extending up to milliseconds. The key to our approach is to anchor NMR frames of reference onto each helix and thereby directly measure their dynamics, one relative to the other, using 'relativistic' sets of residual dipolar couplings ( RDCs)(6,7). Using this approach, we uncovered super- large amplitude helix motions that trace out a surprisingly structured and spatially correlated 3D dynamic trajectory. The two helices twist around their individual axes by approximately 536 and 1106 in a highly correlated manner ( R = 0.97) while simultaneously ( R = 0.81 - 0.92) bending by about 94 degrees. Remarkably, the 3D dynamic trajectory is dotted at various positions by seven distinct ligand- bound conformations of the RNA. Thus even partly unstructured RNAs can undergo structured dynamics that directs ligand- induced transitions along specific predefined conformational pathways.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/62506/1/nature06389.pd

Oral Manifestations of Dermatologic Disease: A Focus on Lichenoid Lesions

Lichenoid changes in the oral mucosa can be encountered in a wide range of lesions with varied etiologies including immune-mediated disorders, reactions to systemic medications and to dental materials. Dysplasia of the oral cavity can exhibit a lichenoid histology, which may mask the potentially cancerous component. Another unusual clinical disease, proliferative verrucous leukoplakia, can often mimic oral lichen planus clinically requiring careful correlation of the clinical and pathologic features