The binding of local anesthetics (LAs) to cell membranes is required for LAs to reach the target ion channels, but lipid interactions may also play a role in a purely membrane-mediated mode of activity. Here, we used solid-state NMR and further biophysical techniques to characterize the effect of six LAs covering a wide range of structures and properties (benzocaine, bupivacaine, mepivacaine, lidocaine, procaine, QX-314) on membranes. Membrane partitioning log D values (between 2.1 and 3.7) varied little with pH, in contrast to octanol partitioning. Membrane thinning was induced by most LAs, except for benzocaine. A conformational change in the lipid headgroup was observed, with a pronounced dependence on the protonation state, indicating the importance of the positive charge that is maintained by most membrane-bound LAs. We found stabilization of negative membrane curvature in the case of benzocaine, and of positive curvature in the case of bupivacaine, procaine, mepivacaine and, most pronouncedly, for QX-314. Comparing the LAs with respect of their influence on membranes as observed in the different experiments, benzocaine and QX-314 were always found at either extreme of the scale, with bupivacaine and lidocaine closer in their effect to benzocaine. This order of influence correlates with the depth of membrane insertion and with the protonation state, both of which were identified as key factors for LA behavior. Finally, we found indications that LAs are able to alter the activity of bacterial mechanosensitive channels without any expected LA binding sites, thus supporting a membrane-mediated activity of LAs.

Positive scalar curvature on foliations and the Euler class

The streaming operator, which generates a displacement of a particle on a straight line at a constant speed in transport theory, is derived algebraically from a spherical coordinate formulation of Newton’s second law. This derivation leads to an operator that has more partial derivatives than a Cartesian coordinate formulation of the operator. The additional partial derivatives, which are with respect to the normalized velocity variables of a particle, take into account the intrinsic curvature of a ball. Moreover, these partial derivatives mitigate ray effects, which arise when a finite number of normalized velocities (also called directions or discrete ordinates) are used to simulate a continuous S2 sphere of directions, by rotating the polar axis of the S2 sphere into the radial direction of the coordinate system. As a consequence of this rotation, the number of actual discrete ordinates is greatly amplified to an enormous number of effective discrete ordinates by a multiplier that is equal to the number of patches that partitions a spherical surface. In addition to the derivation of the streaming operator, we provide in closed form a solution to the system of characteristic equations that is equivalent to the streaming operator. Furthermore, the solution to the system of characteristic equations enables the construction of an integral operator that is the inverse to the streaming operator. Examples in which ray effects are immensely mitigated by spherical coordinates are presented.

ABSTRACT Large Eddy Simulations with flamelet-based thermochemistry are used to investigate the behavior of a premixed hydrogen-air flame stabilized by a bluff-body. Validation against experimental data is carried out first to demonstrate the model’s ability to predict both velocity field and flame structure. The capability of the model in predicting differential diffusion effects is then assessed, in particular regarding the coupling between differential diffusion, tangential strain and curvature, and their effect on mixture fraction redistribution and reaction rate variation. Results indicate that unstretched flamelet thermochemistry is capable of capturing the increase in mixture fraction caused by positive resolved strain, as well as negative variations of mixture fraction due to negative curvature. Furthermore, the model is observed to mimic the effects of negative Markstein length to a certain extent, so that positive tangential strain causes reaction rate increase. The interplay between resolved stretch and preferential diffusion is also shown to lead to a shorter flame length which is in better agreement with experimental observations as compared to simulations under unity Lewis number assumption. These findings highlight that the macroscopic effects of differential diffusion and stretch on the premixed hydrogen flame, characterized by significant strain levels, can be predicted using a flamelet-based approach and without recurring to strained flamelets database, which implies important simplifications in the combustion modeling of turbulent hydrogen-premixed flames and offers valuable insights for the design of novel combustors.

Abstract We develop a strictly geometric reformulation of General Relativity (GR) in which a scalar clock field ϕ defines the spacetime foliation through its timelike gradient nµ = -∇µϕ/ -(∇ϕ) 2 . The field ϕ is not a new dynamical degree of freedom and does not enter the action; its sole role is to generate a covariant, hypersurface-orthogonal slicing that renders the ADM lapse, shift, and extrinsic curvature algebraic functionals of (gµν , ϕ).Starting from the pure Einstein-Hilbert action, we carry out a complete 3 + 1 decomposition adapted to the clock-field foliation and derive the Hamiltonian constraint, momentum constraint, and full constraint algebra. All coincide exactly with their canonical GR counterparts, confirming that the theory propagates only the two tensorial graviton modes and contains no additional scalar or vector excitations. The Einstein equations are recovered identically, the ADM algebra remains first class, and both cosmological dynamics and linear perturbations match those of standard GR.The novelty of the construction is conceptual rather than dynamical: ϕ provides a covariant, relational time variable that fixes the foliation non-perturbatively, offering a clean geometric notion of time for canonical quantization and Wheeler-DeWitt evolution. Because the framework introduces no new fields, couplings, or potentials, it avoids the instabilities and extra degrees of freedom typical of scalar-tensor or modified-gravity theories.This yields a mathematically consistent and fully covariant formulation of GR with an internally defined geometric clock, opening new directions for relational observables, deparametrized quantum gravity, and emergent-time frameworks.

Abstract The cosmological implications of the geodetic brane gravity model, enhanced by geometrical terms of Gibbons-Hawking-York (GHY) type and Gibbons-Hawking-York-Myers type (GHYM), carefully constructed as combinations of intrinsic and extrinsic curvatures, are examined. All the geometrical terms under study belong to a set named Lovelock-type brane models. The combined model gives rise to a second-order differential equation of motion. Under a Friedmann-Robertson-Walker (FRW) geometry defined on a (3 + 1)-dimensional world volume, together with a perfect fluid matter content, the emerging universe of this model evolves in a 5-dimensional Minkowski background yielding peculiar facts. The resulting Friedmann-type equation is written in terms of energy density parameters, where fine-tuning is needed to probe interesting cosmological processes close to the current data. In this sense, Lovelock-type brane models might underlie the cosmic acceleration. Indeed, we find that these correction terms become significant at low energies/late times. The model exhibits self-accelerating (non-self-accelerating) behavior for the brane expansion, and in the case where the radiation-like contribution due to the existence of the extra dimension vanishes its behavior is the same as the Dvali-Gabadadze-Porrati (DGP) brane cosmology and its generalization to the Gauss-Bonnet (GB) brane gravity. Likewise, Einstein cosmology is recovered when the radiation-like contribution fades away along with the odd polynomials in brane extrinsic curvature.

The non-canonical inflammasome, comprising caspase-4 in humans, initiates pyroptosis upon sensing cytosolic lipopolysaccharide (LPS) from Gram-negative bacteria. Caspase-4 activation also depends on several guanylate-binding proteins (GBPs), which associate with the surface of cytosolic bacteria. Here, we investigated how caspase-4 accesses its cognate ligand, the hydrophobic lipid A moiety of LPS, and the role of GBPs in this process. GBP1 was essential for caspase-4 activation during infection. Mechanistically, GBP1 deformed the LPS-containing outer membrane of cytosolic bacteria, acting as a GTP-dependent mechanoenzyme. In vitro, GBP1 fragmented LPS micelles and promoted caspase-4/LPS complex formation, thereby enhancing LPS-induced caspase-4 activation. Fragmented LPS micelles presented additional micelle tips that served as binding and activation sites for caspase-4, indicating that caspase-4 engages LPS membranes with defined geometry rather than individual LPS molecules. Thus, GBP-mediated deformation of the LPS-rich outer bacterial membrane generates regions of positive curvature that expose lipid A, enabling caspase-4 binding, oligomerization, and activation.

Positive membrane curvature induced by a CFEM-domain protein is essential for fungal invasion of the host.

Abstract We study the positive Hermitian curvature flow for left-invariant metrics on 2-step nilpotent Lie groups G with a left-invariant complex structure J . We describe the long-time behavior of the flow under the assumption that $$J[\mathfrak {g}, \mathfrak {g}]$$ J [ g , g ] is contained in the center of $$\mathfrak {g}$$ g . We show that under our assumption the flow $$g_{t}$$ g t exists for all positive t and $$(G,(1+t)^{-1}g_{t})$$ ( G , ( 1 + t ) - 1 g t ) converges, in the Cheeger-Gromov topology, to a 2-step nilpotent Lie group with a non flat semi-algebraic soliton. Moreover, we prove that, in our class of Lie groups, there exists at most one semi-algebraic soliton solution, up to homothety. Similar results were proved by M. Pujia and J. Stanfield for nilpotent complex Lie groups [21, 24]. In the last part of the paper we study the Hermitian curvature flow for the same class of Lie groups.

Brain structures mediate the causal effects of socioeconomic status on mental disorders: A multi-stage Mendelian randomization study.

On the Structure of Compact Static Vacuum Spaces and Positive Isotropic Curvature

Membrane remodeling and higher-order structure formation by DivIVA.

ABSTRACT The control of supramolecular self-assembly on curved manifolds represents a challenge in soft matter. This work investigates chiral nematic phases confined to a toroidal geometry, where intrinsic helical twisting power competes with spatially varying curvature. We employ Physics-Informed Neural Networks (PINNs) to simulate self-assembly of chiral host-guest systems, mapping interactions between molecular chirality ( q 0 ), saddle-splay elasticity ( K 24 ), and bulk elastic anisotropy ( K 11 , K 22 , K 33 ). Our simulation results unveil a phase diagram governed by a ”geometric clamp” mechanism. Specifically, the saddle-splay potential – arising from coupling between the director field and negative Gaussian curvature – locally suppresses chiral induction. This yields spatially heterogeneous ground states where curvature-pinned achiral domains coexist with frustrated helical textures. We demonstrate that tuning the material’s elastic anisotropy offers a chemical route to select the orientation of these supramolecular domains, providing design principles for curvature-directed functional materials.

Using Real Seiberg–Witten theory, Miyazawa introduced an invariant of certain 4-manifolds with involution and used this invariant to construct infinitely many exotic involutions on ℂℙ 2 and infinitely many exotic smooth embeddings of ℝℙ 2 in S 4 . In this paper we extend Miyazawa’s construction to a large class of 4-manifolds, giving many infinite families of involutions on 4-manifolds which are conjugate by homeomorphisms but not by diffeomorphisms and many infinite families of exotic embeddings of nonorientable surfaces in 4-manifolds, where exotic means continuously isotopic but not smoothly isotopic. Exoticness of our construction is detected using Real Seiberg–Witten theory. We study Miyazawa’s invariant, relate it to the Real Seiberg–Witten invariants of Tian–Wang and prove various fundamental results concerning the Real Seiberg–Witten invariants such as: relation to positive scalar curvature, wall-crossing, a mod 2 formula for spin structures, a localisation formula relating ordinary and Real Seiberg–Witten invariants, a connected sum formula and a fibre sum formula.

Road geometry is the planning of the physical form of a road, taking into account technical, economic, and environmental aspects to ensure the safety and comfort of users. Kawitan Village Road, Kecamatan Salopa, faces various problems, such as damaged road conditions, steep slopes, curves, and the absence of shoulders and road markings, all of which have the potential to cause accidents. Redesign is a solution to these geometric problems, aiming to improve and enhance the road's condition. This study aims to redesign the geometric road and determine the horizontal and vertical alignment on the Salopa highway section of Kawitan Village, Tasikmalaya Regency, by using quantitative research to obtain primary data and Tata Cara Perencanaan Geometrik Jalan Antar Kota Tahun 1997 and the 2011 AASTHO reference for secondary data. The benefits of this study can provide technical solutions for improving road geometric conditions, as well as being a reference for practitioners in road geometric design. The results of the study show that the Salopa highway section of Kawitan Village, Tasikmalaya Regency has a design speed of 40 km/hour, a road length of 514.81 m, a road function Kolektor III B, a road type of 2/2 – TT. The horizontal alignment produces 3 SCS type curves with each angle and radius of 67.93˚ and 241 m, 110.191˚ and 99 m and 31.472˚ and 178 m. While the vertical alignment produces 3 convex curves with LV design values of 50 m, 25 m and 102 m and 3 concave curves with LV design values of 8 m, 32 m and 45 m.

The NBAR-domain containing protein endophilin, as a major player in many endocytic pathways, has offered considerable insight into BAR-domain driven membrane remodeling. However, understanding the interaction of the different subdomains of endophilin and their abilities to sense and generate negative Gaussian curvature are yet unanswered questions, with significant implications for the mechanisms and regulation of unconventional endocytic pathways. Using coarse-grained molecular dynamics simulation, we demonstrate the synergistic remodeling capabilities of the NBAR remodeling unit, as well as its ability to sort to and generate membrane regions with negative Gaussian curvature. We find that the assembly of NBAR scaffolds at regions of negative Gaussian curvature facilitate membrane hemifission in dynamic bud formation. These insights provide an additional role for endophilin scaffolds in endocytosis, as well as emphasizing the importance of developing new ways to study negative Gaussian curvature.

Transition metal dichalcogenides and their derivatives offer a versatile platform for exploring novel structural and functional properties in low-dimensional materials. In particular, Janus monolayers possess an intrinsic out-of-plane asymmetry that induces a built-in bending radius, which can strongly influence their physical behavior. In this work, we investigate the tubular structures formed by rolling Janus monolayers into the Janus nanotube with an extrinsic radius. Using a combination of atomistic simulations and continuum mechanics, we find that the total energy of the Janus nanotube is minimized when the tube radius equals the intrinsic bending radius of the Janus monolayer. An analytical expression for this characteristic radius is derived, providing a theoretical framework for understanding the stability of Janus nanotubes. Furthermore, we find that the optical phonon modes in these Janus nanotubes exhibit an anomalous dependence on the tube radius; i.e. their frequencies reach a maximum value near the characteristic radius, in contrast to the monotonic increase of optical phonon frequencies with radius in conventional nanotubes. The phonon anomaly is due to the soft phonon mode effect induced by the deviation from the most stable tubular configuration with the characteristic radius. These results uncover the coupling between intrinsic and extrinsic curvature in Janus systems and open new pathways for tuning vibrational and other properties in curved low-dimensional materials.

ABSTRACT Wrinkling is commonly observed as mechanical instability when a stiff thin film bound on a compliant thick substrate undergoes in‐plane compression exceeding a threshold. Despite significant efforts to create a broad range of surface patterns via wrinkling, little has been studied about a dynamic and transient wrinkling process, where a suspended polymer thin film undergoes liquid‐to‐solid phase transitions. Here, a spontaneous wrinkling process is reported when drying poly(vinyl alcohol) (PVA) soap films suspended on 3D printed wireframes with near‐zero or negative Gaussian curvatures. As water evaporates, a thickness gradient across the sample is developed, leading to non‐uniform drying rates, and a concentration gradient between the inner and outer sides (exposed to air) of the suspended PVA soap film induces a differential osmotic pressure. Together, these effects contribute to an in‐plane compressive stress, leading to the formation of surface wrinkles, whose growth is guided by the geometry of the frame. Importantly, the wrinkles evolve dynamically: the wavelength and number of the wrinkles can be tuned by altering the concentration of the PVA aqueous solutions, the initial mass, the relative humidity of the drying environment; the patterns of the resulting wrinkles can be programmed by the geometry of the wireframe.

Abstract We consider static spacetimes in spherical coordinates whose angular sector is described by a Finsler metric rather than the standard round metric on S 2 . Our first contribution is kinematical : maintaining arbitrary lapse and radial factors e ν ( r ) , e ϑ ( r ) , and relying solely on Killing symmetries and the null constraint, we derive model–independent relations for circular photon orbits and the effective dynamics. By specializing the angular sector to a Randers sphere of constant positive flag curvature, we obtain exact expressions for the conserved angular charge and the critical impact parameter, and we quantify a Finslerian Sagnac–type effect. Our second contribution is dynamical : we examine the field equations used in the literature to determine ( e ν , e ϑ ) . We revisit the family of hairy black holes in (Nekouee et al 2025 Class. Quantum Grav. 42 045002), demonstrating that the analysis therein neglects crucial non-reversible Finsler features. Furthermore, we show that the solutions presented as new reproduce previously known results in (Ovalle et al 2021 Phys. Dark Univ. 31 100744).

The protein caveolin-1 (cav1) is essential in the generation of caveolae, cup-like invaginations in the plasma membrane, but the mechanism of its action remains unclear. A recent cryo-EM structure revealed an 11-mer of cav1 (the 8S complex) forming a disk with a flat membrane-facing surface, raising the question of how a flat complex is able to generate membrane curvature. We previously conducted implicit-solvent and all-atom molecular dynamics simulations, which showed the 8S complex adopting a conical shape. The ability of the conical shape to remodel membranes was assumed but could not be confirmed. Here, we simulated the complex in discontinuous membrane patches of ∼30 nm diameter on the Anton 3 supercomputer. In a 2-μs simulation, a flat POPC membrane patch acquired pronounced positive curvature (curved away from the complex), converting into a hemisphere of 21-nm outer diameter. However, when the complex was constrained to prevent the conversion into a conical shape, the membrane patch acquired slightly negative curvature. These results show that the conical shape of the 8S complex is essential for positive curvature generation. A homology model of cav3 behaved very similarly to cav1, but the two recently discovered nonvertebrate caveolins remained flat and generated pronounced negative curvature. Simulations of cav1 in 70:30 POPC:cholesterol and other cholesterol-containing mixtures showed significantly lower curvature than in the pure POPC membrane or in an E. coli membrane mimic. This appears to be caused by cholesterol flipping from the distal to the proximal leaflet. No specific binding of cholesterol to the cav1 CRAC motif was observed, nor significant enrichment of cholesterol in contact with the complex. These observations lead to the hypothesis that cholesterol is enriched in caveolae not because of specific binding to caveolin, but because it can alleviate curvature stress due to its negative spontaneous curvature and its ability to rapidly flip-flop.