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Electron cryo-microscopy structures of the human peptide-loading complex shed light on its operation and on the onset of adaptive immune responses. Structure of a peptide loader The peptide-loading complex (PLC) is a dynamic membrane complex in the endoplasmic reticulum that regulates the transport and loading of antigenic peptides onto major histocompatibility complex class I (MHC-I) molecules. As such, this complex has a key role in important adaptive immune responses to infections and tumour progression. Here, Robert Tampé and colleagues report the structure of the human PLC by electron cryo-microscopy. The editing modules of the complex are centred around the TAP transporter, which delivers the peptides from the cytosol, and peptide loading appears to induce changes in the structure of MHC-I, releasing the stable peptide/MHC-I complexes from the PLC. This provides glimpses into the mechanism of the PLC, antigen processing and the onset of MHC-I-mediated immunity. The peptide-loading complex (PLC) is a transient, multisubunit membrane complex in the endoplasmic reticulum that is essential for establishing a hierarchical immune response. The PLC coordinates peptide translocation into the endoplasmic reticulum with loading and editing of major histocompatibility complex class I (MHC-I) molecules. After final proofreading in the PLC, stable peptide–MHC-I complexes are released to the cell surface to evoke a T-cell response against infected or malignant cells 1 , 2 . Sampling of different MHC-I allomorphs requires the precise coordination of seven different subunits in a single macromolecular assembly, including the transporter associated with antigen processing (TAP1 and TAP2, jointly referred to as TAP), the oxidoreductase ERp57, the MHC-I heterodimer, and the chaperones tapasin and calreticulin 3 , 4 . The molecular organization of and mechanistic events that take place in the PLC are unknown owing to the heterogeneous composition and intrinsically dynamic nature of the complex. Here, we isolate human PLC from Burkitt’s lymphoma cells using an engineered viral inhibitor as bait and determine the structure of native PLC by electron cryo-microscopy. Two endoplasmic reticulum-resident editing modules composed of tapasin, calreticulin, ERp57, and MHC-I are centred around TAP in a pseudo-symmetric orientation. A multivalent chaperone network within and across the editing modules establishes the proofreading function at two lateral binding platforms for MHC-I molecules. The lectin-like domain of calreticulin senses the MHC-I glycan, whereas the P domain reaches over the MHC-I peptide-binding pocket towards ERp57. This arrangement allows tapasin to facilitate peptide editing by clamping MHC-I. The translocation pathway of TAP opens out into a large endoplasmic reticulum lumenal cavity, confined by the membrane entry points of tapasin and MHC-I. Two lateral windows channel the antigenic peptides to MHC-I. Structures of PLC captured at distinct assembly states provide mechanistic insight into the recruitment and release of MHC-I. Our work defines the molecular symbiosis of an ABC transporter and an endoplasmic reticulum chaperone network in MHC-I assembly and provides insight into the onset of the adaptive immune response.

We give a complete classification of finite subgroups of automorphisms of K3 surfaces up to deformation. The classification is in terms of Hodge theoretic data associated to certain conjugacy classes of finite subgroups of the orthogonal group of the K3 lattice. The moduli theory of K3 surfaces, in particular the surjectivity of the period map and the strong Torelli theorem allow us to interpret this datum geometrically. Our approach is computer aided and involves Hermitian lattices over number fields.

PROPPINs (β-propellers that bind polyphosphoinositides) are PtdIns3P and PtdIns(3,5)P 2 binding autophagy related proteins. They contain two phosphatidylinositolphosphate (PIP) binding sites and a conserved FRRG motif is essential for PIP binding. Here we present the 2.0 Å resolution crystal structure of the PROPPIN Atg18 from Pichia angusta . We designed cysteine mutants for labelling with the fluorescence dyes to probe the distances of the mutants to the membrane. These measurements support a model for PROPPIN-membrane binding, where the PROPPIN sits in a perpendicular or slightly tilted orientation on the membrane. Stopped-flow measurements suggest that initial PROPPIN-membrane binding is driven by non-specific PIP interactions. The FRRG motif then retains the protein in the membrane by binding two PIP molecules as evident by a lower dissociation rate for Atg18 in comparison with its PIP binding deficient FTTG mutant. We demonstrate that the amine-specific cross-linker Bis(sulfosuccinimidyl)suberate (BS3), which is used for protein-protein cross-linking can also be applied for cross-linking proteins and phosphatidylethanolamine (PE). Cross-linking experiments with liposome bound Atg18 yielded several PE cross-linked peptides. We also observed intermolecular cross-linked peptides, which indicated Atg18 oligomerization. FRET-based stopped-flow measurements revealed that Atg18 rapidly oligomerizes upon membrane binding while it is mainly monomeric in solution.

We present an algorithm for computing zero-dimensional tropical varieties based on triangular decomposition and Newton polygon methods. From it, we derive algorithms for computing points on and links of higher-dimensional tropical varieties, using intersections with affine hyperplanes to reduce the dimension to zero. We use the algorithms to show that the tropical Grassmannians \\[{\\mathcal {G}}_{3,8}\\] and \\[{\\mathcal {G}}_{4,8}\\] are not simplicial.

Nanostructured silicon and silicon-aluminum compounds are synthesized by a novel synthesis strategy based on spark plasma sintering (SPS) of silicon nanopowder, mesoporous silicon (pSi), and aluminum nanopowder. The interplay of metal-assisted crystallization and inherent porosity is exploited to largely suppress thermal conductivity. Morphology and temperature-dependent thermal conductivity studies allow us to elucidate the impact of porosity and nanostructure on the macroscopic heat transport. Analytic electron microscopy along with quantitative image analysis is applied to characterize the sample morphology in terms of domain size and interpore distance distributions. We demonstrate that nanostructured domains and high porosity can be maintained in densified mesoporous silicon samples. In contrast, strong grain growth is observed for sintered nanopowders under similar sintering conditions. We observe that aluminum agglomerations induce local grain growth, while aluminum diffusion is observed in porous silicon and dispersed nanoparticles. A detailed analysis of the measured thermal conductivity between 300 and 773 K allows us to distinguish the effect of reduced thermal conductivity caused by porosity from the reduction induced by phonon scattering at nanosized domains. With a modified Landauer/Lundstrom approach the relative thermal conductivity and the scattering length are extracted. The relative thermal conductivity confirms the applicability of Kirkpatrick’s effective medium theory. The extracted scattering lengths are in excellent agreement with the harmonic mean of log-normal distributed domain sizes and the interpore distances combined by Matthiessen’s rule.

Let K be a number field, let A be a finite-dimensional K-algebra, let $\\operatorname {\\mathrm {J}}(A)$ denote the Jacobson radical of A and let $\\Lambda $ be an $\\mathcal {O}_{K}$ -order in A. Suppose that each simple component of the semisimple K-algebra $A/{\\operatorname {\\mathrm {J}}(A)}$ is isomorphic to a matrix ring over a field. Under this hypothesis on A, we give an algorithm that, given two $\\Lambda $ -lattices X and Y, determines whether X and Y are isomorphic and, if so, computes an explicit isomorphism $X \\rightarrow Y$ . This algorithm reduces the problem to standard problems in computational algebra and algorithmic algebraic number theory in polynomial time. As an application, we give an algorithm for the following long-standing problem: Given a number field K, a positive integer n and two matrices $A,B \\in \\mathrm {Mat}_{n}(\\mathcal {O}_{K})$ , determine whether A and B are similar over $\\mathcal {O}_{K}$ , and if so, return a matrix $C \\in \\mathrm {GL}_{n}(\\mathcal {O}_{K})$ such that $B= CAC^{-1}$ . We give explicit examples that show that the implementation of the latter algorithm for $\\mathcal {O}_{K}=\\mathbb {Z}$ vastly outperforms implementations of all previous algorithms, as predicted by our complexity analysis.

The identification of lipids in biological samples is gaining importance. The advent of mass spectrometry-based lipidomics accelerated the field allowing nowadays for identification and quantification of complete lipidomes. However, due to solubility difficulties and varying properties of different lipid classes, sample preparation for lipidomics is still an issue. Of the many lipid classes, phospholipids are the major components of biological membranes. In solution, they spontaneously form lipid vesicles of various structures such as liposomes. They are therefore often used as membrane mimics when studying biological membranes and membrane proteins. Here, we present a novel sample preparation strategy for shotgun lipidomics employing liposomes prepared from lipid standards or lipid mixtures allowing the analysis of phospholipids directly from lipid bilayers. We validated our strategy for lipid identification by tandem mass spectrometry in positive or negative ion mode using different phospholipid species from various classes. We further tested our strategy for relative quantification by mixing different ratios of phospholipid species as well as determining the distribution of lipid species in a natural lipid extract.

We consider the computational problem of determining the unit group of a finite ring, by which we mean the computation of a finite presentation together with an algorithm to express units as words in the generators. We show that the problem is equivalent to the number theoretic problems of factoring integers and solving discrete logarithms in finite fields. A similar equivalence is shown for the problem of determining the abelianization of the unit group or the first \\(K\\)-group of finite rings.

Let \\(K\\) be a number field, let \\(A\\) be a finite-dimensional semisimple \\(K\\)-algebra, and let \\(\\Lambda\\) be an \\(\\mathcal{O}_{K}\\)-order in \\(A\\). We give practical algorithms that determine whether \\(\\Lambda\\) has stably free cancellation (SFC). As an application, we determine all finite groups \\(G\\) of order at most \\(383\\) such that the integral group ring \\(\\mathbb{Z}[G]\\) has SFC.

We study Swan modules, which are a special class of projective modules over integral group rings, and their consequences for the homotopy classification of CW-complexes. We show that there exists a non-free stably free Swan module, thus resolving Problem A4 in the 1979 Problem List of C. T. C. Wall. As an application we show that, in all dimensions \\(n \\equiv 3\\) mod \\(4\\), there exist finite \\(n\\)-complexes which are homotopy equivalent after stabilising with multiple copies of \\(S^n\\), but not after a single stabilisation. This answers a question of M. N. Dyer. We also resolve a question of S. Plotnick concerning Swan modules associated to group automorphisms and, as an application, obtain a short and direct proof that there exists a group with \\(k\\)-periodic cohomology which does not have free period \\(k\\). In contrast to the original proof our R. J. Milgram, our proof circumvents the need to compute the Swan finiteness obstruction.