Structure of a rare non-standard sequence k-turn bound by L7Ae protein

Kt-23 from Thelohania solenopsae is a rare RNA kink turn (k-turn) where an adenine replaces the normal guanine at the 2n position. L7Ae is a member of a strongly conserved family of proteins that bind a range of k-turn structures in the ribosome, box C/D and H/ACA small nucleolar RNAs and U4 small nuclear RNA. We have solved the crystal structure of T. solenopsae Kt-23 RNA bound to Archeoglobus fulgidus L7Ae protein at a resolution of 2.95 Å. The protein binds in the major groove displayed on the outer face of the k-turn, in a manner similar to complexes with standard k-turn structures. The k-turn adopts a standard N3 class conformation, with a single hydrogen bond from A2b N6 to A2n N3. This contrasts with the structure of the same sequence located in the SAM-I riboswitch, where it adopts an N1 structure, showing the inherent plasticity of k-turn structure. This potentially can affect any tertiary interactions in which the RNA participates

The k-junction motif in RNA structure

The k-junction is a structural motif in RNA comprising a three-way helical junction based upon kink turn (k-turn) architecture. A computer program written to examine relative helical orientation identified the three-way junction of the Arabidopsis TPP riboswitch as an elaborated k-turn. The Escherichia coli TPP riboswitch contains a related k-junction, and analysis of >11 000 sequences shows that the structure is common to these riboswitches. The k-junction exhibits all the key features of an N1-class k-turn, including the standard cross-strand hydrogen bonds. The third helix of the junction is coaxially aligned with the C (canonical) helix, while the k-turn loop forms the turn into the NC (non-canonical) helix. Analysis of ligand binding by ITC and global folding by gel electrophoresis demonstrates the importance of the k-turn nucleotides. Clearly the basic elements of k-turn structure are structurally well suited to generate a three-way helical junction, retaining all the key features and interactions of the k-turn

Existence and uniqueness for Mean Field Games with state constraints

In this paper, we study deterministic mean field games for agents who operate in a bounded domain. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as for unrestricted state space because, for a large set of initial conditions, the uniqueness of the solution to the associated minimization problem is no longer guaranteed. We attack the problem by interpreting equilibria as measures in a space of arcs. In such a relaxed environment the existence of solutions follows by set-valued fixed point arguments. Then, we give a uniqueness result for such equilibria under a classical monotonicity assumption

The pseudospectral method for third-order differential equations

This is the published version, also available here: http://dx.doi.org/10.1137/0729094.Generalized quadrature rules are derived which assist in the selection of collocation points for the pseudospectral solution of differential equations. In particular, it is shown that for an nth-order differential equation in one space dimension with two-point derivative boundary conditions, an ideal choice of interior collocation points is the set of zeros of a Jacobi polynomial. The pseudospectral solution of a third-order initial-boundary value problem is considered and accuracy is assessed by examining how well the discrete eigenproblem approximates the continuous one. Convergence is established for a special choice of collocation points and numerical results are included to demonstrate the viability of the approach

A simple adaptive grid method in two dimensions

This is the published version, also available here: http://dx.doi.org/10.1137/0915049.This paper gives an interpretation of the concept of equidistribution in the context of adaptive grid generation for multidimensional problems. It is shown that the equidistribution principle cannot be satisfied throughout the domain of the problem and, based on this recognition, a local equidistribution principle is developed. A discrete formulation is described for grid generation in two space dimensions and a smoothing mechanism is presented for improving mesh quality. The adaptive grid method that is constructed contains three grid-quality parameters. Numerical examples illustrate adaptive grid generation using a prescribed monitor function and grid generation for numerical solution of partial differential equations. Results show that the method produces high quality grids and that it is fairly insensitive to the choice of parameters