Flexibility Properties in Complex Analysis and Affine Algebraic Geometry

In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka–Forstnerič manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930s, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview chapter we present three classes of properties: (1) density property, (2) flexibility, and (3) Oka–Forstnerič. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones.

Geometry and kinematics of the Roisan-Cignana Shear Zone, and the orogenic evolution of the Dent Blanche Tectonic System (Western Alps)

The Dent Blanche Tectonic System (DBTS) is a composite thrust sheet derived from the previously thinned passive Adriatic continental margin. A kilometric high-strain zone, the Roisan-Cignana Shear Zone (RCSZ) defines the major tectonic boundary within the DBTS and separates it into two subunits, the Dent Blanche s.s. nappe to the northwest and the Mont Mary nappe to the southeast. Within this shear zone, tectonic slices of Mesozoic and pre-Alpine meta-sediments became amalgamated with continental basement rocks of the Adriatic margin. The occurrence of high pressure assemblages along the contact between these tectonic slices indicates that the amalgamation occurred prior to or during the subduction process, at an early stage of the Alpine orogenic cycle. Detailed mapping, petrographic and structural analysis show that the Roisan-Cignana Shear Zone results from several superimposed Alpine structural and metamorphic stages. Subduction of the continental fragments is recorded by blueschist-facies deformation, whereas the Alpine collision is reflected by a greenschist facies overprint associated with the development of large-scale open folds. The postnappe evolution comprises the development of low-angle brittle faults, followed by large-scale folding (Vanzone phase) and finally brittle extensional faults. The RCSZ shows that fragments of continental crust had been torn off the passive continental margin prior to continental collision, thus recording the entire history of the orogenic cycle. The role of preceding Permo-Triassic lithospheric thinning, Jurassic rifting, and ablative subduction processes in controlling the removal of crustal fragments from the reactivated passive continental margin is discussed. Results of this study constrain the temporal sequence of the tectono-metamorphic processes involved in the assembly of the DBTS, but they also show limits on the interpretation. In particular it remains difficult to judge to what extent precollisional rifting at the Adriatic continental margin preconditioned the efficiency of convergent processes, i.e. accretion, subduction, and orogenic exhumation.

Modeling the Histidine–Phenylalanine Interaction: The NH···π Hydrogen Bond of Imidazole·Benzene

NH···π hydrogen bonds occur frequently between the amino acid side groups in proteins and peptides. Data-mining studies of protein crystals find that ~80% of the T-shaped histidine···aromatic contacts are CH···π, and only ~20% are NH···π interactions. We investigated the infrared (IR) and ultraviolet (UV) spectra of the supersonic-jet-cooled imidazole·benzene (Im·Bz) complex as a model for the NH···π interaction between histidine and phenylalanine. Ground- and excited-state dispersion-corrected density functional calculations and correlated methods (SCS-MP2 and SCS-CC2) predict that Im·Bz has a Cs-symmetric T-shaped minimum-energy structure with an NH···π hydrogen bond to the Bz ring; the NH bond is tilted 12° away from the Bz C₆ axis. IR depletion spectra support the T-shaped geometry: The NH stretch vibrational fundamental is red shifted by −73 cm⁻¹ relative to that of bare imidazole at 3518 cm⁻¹, indicating a moderately strong NH···π interaction. While the Sₒ(A1g) → S₁(B₂u) origin of benzene at 38 086 cm⁻¹ is forbidden in the gas phase, Im·Bz exhibits a moderately intense Sₒ → S₁ origin, which appears via the D₆h → Cs symmetry lowering of Bz by its interaction with imidazole. The NH···π ground-state hydrogen bond is strong, De=22.7 kJ/mol (1899 cm⁻¹). The combination of gas-phase UV and IR spectra confirms the theoretical predictions that the optimum Im·Bz geometry is T shaped and NH···π hydrogen bonded. We find no experimental evidence for a CH···π hydrogen-bonded ground-state isomer of Im·Bz. The optimum NH···π geometry of the Im·Bz complex is very different from the majority of the histidine·aromatic contact geometries found in protein database analyses, implying that the CH···π contacts observed in these searches do not arise from favorable binding interactions but merely from protein side-chain folding and crystal-packing constraints. The UV and IR spectra of the imidazole·(benzene)₂ cluster are observed via fragmentation into the Im·Bz+ mass channel. The spectra of Im·Bz and Im·Bz₂ are cleanly separable by IR hole burning. The UV spectrum of Im·Bz₂ exhibits two 000 bands corresponding to the Sₒ → S₁ excitations of the two inequivalent benzenes, which are symmetrically shifted by −86/+88 cm⁻¹ relative to the 000 band of benzene.

SrGAP2-Dependent Integration of Membrane Geometry and Slit-Robo-Repulsive Cues Regulates Fibroblast Contact Inhibition of Locomotion

Migrating fibroblasts undergo contact inhibition of locomotion (CIL), a process that was discovered five decades ago and still is not fully understood at the molecular level. We identify the Slit2-Robo4-srGAP2 signaling network as a key regulator of CIL in fibroblasts. CIL involves highly dynamic contact protrusions with a specialized actin cytoskeleton that stochastically explore cell-cell overlaps between colliding fibroblasts. A membrane curvature-sensing F-BAR domain pre-localizes srGAP2 to protruding edges and terminates their extension phase in response to cell collision. A FRET-based biosensor reveals that Rac1 activity is focused in a band at the tip of contact protrusions, in contrast to the broad activation gradient in contact-free protrusions. SrGAP2 specifically controls the duration of Rac1 activity in contact protrusions, but not in contact-free protrusions. We propose that srGAP2 integrates cell edge curvature and Slit-Robo-mediated repulsive cues to fine-tune Rac1 activation dynamics in contact protrusions to spatiotemporally coordinate CIL.

Inherited structural controls on fault geometry, architecture and hydrothermal activity: an example from Grimsel Pass, Switzerland

Exhumed faults hosting hydrothermal systems provide direct insight into relationships between faulting and fluid flow, which in turn are valuable for making hydrogeological predictions in blind settings. The Grimsel Breccia Fault (Aar massif, Central Swiss Alps) is a late Neogene, exhumed dextral strike-slip fault with a maximum displacement of 25–45 m, and is associated with both fossil and active hydrothermal circulation. We mapped the fault system and modelled it in three dimensions, using the distinctive hydrothermal mineralisation as well as active thermal fluid discharge (the highest elevation documented in the Alps) to reveal the structural controls on fluid pathway extent and morphology. With progressive uplift and cooling, brittle deformation inherited the mylonitic shear zone network at Grimsel Pass; preconditioning fault geometry into segmented brittle reactivations of ductile shear zones and brittle inter-shear zone linkages. We describe ‘pipe’-like, vertically oriented fluid pathways: (1) within brittle fault linkage zones and (2) through alongstrike- restricted segments of formerly ductile shear zones reactivated by brittle deformation. In both cases, low-permeability mylonitic shear zones that escaped brittle reactivation provide important hydraulic seals. These observations show that fluid flow along brittle fault planes is not planar, but rather highly channelised into sub-vertical flow domains, with important implications for the exploration and exploitation of geothermal energy.