Meshless Local Petrov-Galerkin Method for Rotating Euler-Bernoulli Beam

Free vibration problem of a rotating Euler-Bernoulli beam is solved with a truly meshless local Petrov-Galerkin method. Radial basis function and summation of two radial basis functions are used for interpolation. Radial basis function satisfies the Kronecker delta property and makes it simpler to apply the essential boundary conditions. Interpolation with summation of two radial basis functions increases the node carrying capacity within the sub-domain of the trial function and higher natural frequencies can be computed by selecting the complete domain as a sub-domain of the trial function. The mass and stiffness matrices are derived and numerical results for frequencies are obtained for a fixed-free beam and hinged-free beam simulating hingeless and articulated helicopter blades. Stiffness and mass distribution suitable for wind turbine blades are also considered. Results show an accurate match with existing literature.

Insights into the Structural Dynamics of Nucleocytoplasmic Transport of tRNA by Exportin-t

Exportin-t (Xpot) transports mature 5'- and 3'-end processed tRNA from the nucleus to the cytoplasm by associating with a small G-protein Ran (RAs-related nuclear protein), in the nucleus. The release of tRNA in cytoplasm involves RanGTP hydrolysis. Despite the availability of crystal structures of nuclear and cytosolic forms of Xpot, the molecular details regarding the sequential events leading to tRNA release and subsequent conformational changes occurring in Xpot remain unknown. We have performed a combination of classical all-atom and accelerated molecular dynamics simulations on a set of complexes involving Xpot to study a range of features including conformational flexibility of free and cargo-bound Xpot and functionally critical contacts between Xpot and its cargo. The systems investigated include free Xpot and its different complexes, bound either to Ran (GTP/GDP) or tRNA or both. This approach provided a statistically reliable estimate of structural dynamics of Xpot after cargo release. The mechanistic basis for Xpot opening after cargo release has been explained in terms of dynamic structural hinges, about which neighboring region could be displaced to facilitate the nuclear to cytosolic state transition. Post-RanGTP hydrolysis, a cascade of events including local conformational change in RanGTP and loss of critical contacts at Xpot/tRNA interface suggest factors responsible for eventual release of tRNA. The level of flexibility in different Xpot complexes varied depending on the arrangement of individual HEAT repeats. Current study provides one of the most comprehensive and robust analysis carried out on this protein using molecular dynamics schemes.