Structural characterization of interaction of K11 and K63 mixed-linkage polyubiquitin chains with the tUIMs of epsin1

Ubiquitylation or covalent attachment of ubiquitin (Ub) to a variety of substrate proteins in cells is a versatile post-translational modification involved in the regulation of numerous cellular processes. The distinct messages that polyubiquitylation encodes are attributed to the multitude of conformations possible through attachment of ubiquitin monomers within a polyubiquitin chain via a specific lysine residue. Thus the hypothesis is that linkage defines polyubiquitin conformation which in turn determines specific recognition by cellular receptors. Ubiquitylation of membrane surface receptor proteins plays a very important role in regulating receptor-mediated endocytosis as well as endosomal sorting for lysosomal degradation. Epsin1 is an endocytic adaptor protein with three tandem UIMs (Ubiquitin Interacting Motifs) which are responsible for the highly specific interaction between epsin and ubiquitylated receptors. Epsin1 is also an oncogenic protein and its expression is upregulated in some types of cancer. Recently it has been shown that novel K11 and K63 mixed-linkage polyubiquitin chains serve as internalization signal for MHC I (Major Histocompatibility Complex I) molecule through their association with the tUIMs of epsin1. However the molecular mode of action and structural details of the interaction between polyubiquitin chains on receptors and tUIMs of epsin1 is yet to be determined. This information is crucial for the development of anticancer therapeutics targeting epsin1. The molecular basis for the linkage-specific recognition of K11 and K63 mixed-linkage polyubiquitin chains by the tandem UIMs of the endocytic adaptor protein epsin1 is investigated using a combination of NMR methods.

POSITIVE FILTERED P_N METHOD FOR LINEAR TRANSPORT EQUATIONS AND THE ASSOCIATED OPTIMIZATION ALGORITHM

We propose a positive, accurate moment closure for linear kinetic transport equations based on a filtered spherical harmonic (FP_N) expansion in the angular variable. The FP_N moment equations are accurate approximations to linear kinetic equations, but they are known to suffer from the occurrence of unphysical, negative particle concentrations. The new positive filtered P_N (FP_N+) closure is developed to address this issue. The FP_N+ closure approximates the kinetic distribution by a spherical harmonic expansion that is non-negative on a finite, predetermined set of quadrature points. With an appropriate numerical PDE solver, the FP_N+ closure generates particle concentrations that are guaranteed to be non-negative. Under an additional, mild regularity assumption, we prove that as the moment order tends to infinity, the FP_N+ approximation converges, in the L2 sense, at the same rate as the FP_N approximation; numerical tests suggest that this assumption may not be necessary. By numerical experiments on the challenging line source benchmark problem, we confirm that the FP_N+ method indeed produces accurate and non-negative solutions. To apply the FP_N+ closure on problems at large temporal-spatial scales, we develop a positive asymptotic preserving (AP) numerical PDE solver. We prove that the propose AP scheme maintains stability and accuracy with standard mesh sizes at large temporal-spatial scales, while, for generic numerical schemes, excessive refinements on temporal-spatial meshes are required. We also show that the proposed scheme preserves positivity of the particle concentration, under some time step restriction. Numerical results confirm that the proposed AP scheme is capable for solving linear transport equations at large temporal-spatial scales, for which a generic scheme could fail. Constrained optimization problems are involved in the formulation of the FP_N+ closure to enforce non-negativity of the FP_N+ approximation on the set of quadrature points. These optimization problems can be written as strictly convex quadratic programs (CQPs) with a large number of inequality constraints. To efficiently solve the CQPs, we propose a constraint-reduced variant of a Mehrotra-predictor-corrector algorithm, with a novel constraint selection rule. We prove that, under appropriate assumptions, the proposed optimization algorithm converges globally to the solution at a locally q-quadratic rate. We test the algorithm on randomly generated problems, and the numerical results indicate that the combination of the proposed algorithm and the constraint selection rule outperforms other compared constraint-reduced algorithms, especially for problems with many more inequality constraints than variables.