Diversity in Atomic Structures of Zeolite-Templated Carbons and the Consequences for Macroscopic Properties

Zeolite-templated carbons (ZTCs) are a family of ordered microporous carbons with extralarge surface areas and micropore volumes, which are synthesized by carbon deposition within the confined spaces of zeolite micropores. There has been great controversy regarding the atomic structures of ZTCs, which encompass two extremes: (1) three-dimensionally connected curved open-blade-type carbon moieties and (2) ideal tubular structures (commonly referred to as "Schwarzites"). In this study, through a combination of experimental analyses and theoretical calculations, we demonstrate that the atomic structure of ZTCs is difficult to define as a single entity, and it widely varies depending on their synthesis conditions. Carbon deposition using a large organic precursor and low-temperature framework densification generates ZTCs predominantly composed of open-blade-type moieties, characterized by low surface curvature and abundant H-terminated edge sites. Meanwhile, synthesis using a small precursor with high-temperature densification produces ZTCs with an increased portion of closed-strut carbon moieties (or closed-fullerene-like nodes), exhibiting large surface curvature and diminished edge sites. The variations in the atomic structure of ZTCs result in significant differences in their macroscopic properties, such as N2/CO2 adsorption, oxidative stability, work function, and electrocatalytic properties, despite the presence of comparable pore structures. Therefore, ZTCs demonstrate the potential to synthesize ordered nanoporous carbons with tunable physicochemical properties.

Role of Surface Curvature in Gold Nanostar Properties and Applications

Gold nanostars (AuNSs) are nanoparticles with intricate three-dimensional structures and shape-dependent optoelectronic properties. For example, AuNSs uniquely display three distinct surface curvatures, i.e. neutral, positive, and negative, which provide different environments to adsorbed ligands. Hence, these curvatures are used to introduce different surface chemistries in nanoparticles. This review summarizes and discusses the role of surface curvature in AuNS properties and its impact on biomedical and chemical applications, including surface-enhanced Raman spectroscopy, contrast agent performance, and catalysis. We examine the main synthetic approaches to generate AuNSs, control their morphology, and discuss their benefits and drawbacks. We also describe the optical characteristics of AuNSs and discuss how these depend on nanoparticle morphology. Finally, we analyze how AuNS surface curvature endows them with properties distinctly different from those of other nanoparticles, such as strong electromagnetic fields at the tips and increased hydrophilic environments at the indentations, together making AuNSs uniquely useful for biosensing, imaging, and local chemical manipulation.

Curvature in Biological Systems: Its Quantification, Emergence, and Implications across the Scales

Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology is supported by numerous experimental and theoretical investigations in recent years. In this review, first, a brief introduction to the key ideas of surface curvature in the context of biological systems is given and the challenges that arise when measuring surface curvature are discussed. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales is addressed with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological, and mechanical processes but that curvature acts also as a signal that co-determines these processes.

Free-Form Surface Partitioning and Simulation Verification Based on Surface Curvature

To address the problem of low overall machining efficiency of free-form surfaces and difficulty in ensuring machining quality, this paper proposes a MATLAB-based free-form surface division method. The surface division is divided into two stages: Partition area identification and area boundary determination. In the first stage, the free-form surface is roughly divided into convex, concave, and saddle regions according to the curvature of the surface, and then the regions are subdivided based on the fuzzy c-means clustering algorithm. In the second stage, according to the clustering results, the Voronoi diagram algorithm is used to finally determine the boundary of the surface patch. We used NURBS to describe free-form surfaces and edit a set of MATLAB programs to realize the division of surfaces. The proposed method can easily and quickly divide the surface area, and the simulation results show that the proposed method can shorten machining time by 36% compared with the traditional machining method. It is proved that the method is practical and can effectively improve the machining efficiency and quality of complex surfaces.

Curvature-Selective Nanocrystal Surface Ligation Using Sterically-Encumbered Metal-Coordinating Ligands

Organic ligands are critical in determining the physiochemical properties of inorganic nanocrystals. However, precise nanocrystal surface modification is extremely difficult to achieve. Most research focuses on finding ligands that fully passivate the nanocrystal surface, with an emphasis on the supramolecular structure generated by the ligand shell. Inspired by molecular metal-coordination complexes, we devised an approach based on ligand anchoring groups that are flanked by encumbering organic substituents and are chemoselective for binding to nanocrystal corner, edge, and facet sites. Through experiment and theory, we affirmed that the surface-ligand steric pressures generated by these organic substituents are significant enough to impede binding to regions of low nanocurvature, such as nanocrystal facets, and to promote binding to regions of high curvature such as nanocrystal edges.

Effect of Surface Curvature on the Mechanical and Mass-Transport Properties of Additively Manufactured Tissue Scaffolds with Minimal Surfaces

The design of scaffolds for tissue engineering has to consider two trade-off properties: mechanical and mass-transport properties. This is particularly true for additively manufactured scaffolds with the structures of minimal surfaces, and notably, the influence of the surface curvature of the structure on the mechanical and mass-transport properties remains unclear. This work presents our study on the scaffolds designed with the structure of triply periodic minimal surfaces (TPMS), with a focus on discovering the influence of surface curvature on the mechanical response and the mass-transport property or permeability of the scaffolds. Based on the entropy weight fuzzy comprehensive evaluation method, a model representative of both mechanical and permeable properties of scaffolds was developed; scanning electron microscopy (SEM) and finite element analysis (FEA) were also used to reveal the influence mechanism of curvature on structural fracture and deformation behavior. AlSi10Mg samples of scaffolds designed with different surface curvatures were manufactured using selective laser melting (SLM), and their mechanical and permeable properties were examined and characterized by both experiments and simulations. Our results illustrate that at the same porosity, the more concentrated the curvature distribution of the same type of unit, the better trade-off mechanical and mass-transport properties the scaffolds have. Particularly, at the porosity of 55%, the compressive elastic modulus and permeability of the Dte structure are increased by 2.03 times and 1.95 times compared with the Diamond unit, respectively. The fusion structure can greatly improve permeability performance at the cost of mechanical properties. Our results also show that porosity has the greatest influence on mechanical and permeable properties, followed by the surface curvature. The study illustrates that the surface curvature has a significant influence on the mechanical and permeable properties of scaffolds, and that the developed scaffold performance evaluation scheme is an effective means for the optimization and evaluation of scaffold performance.

In silico and in vivo studies of the effect of surface curvature on the osteoconduction of porous scaffolds

Recent evidence shows that the curvature of porous scaffold plays a significant role in guiding tissue regeneration. However, the underlying mechanism remains controversial to date. In this study, we developed an in silico model to simulate the effect of surface curvature on the osteoconduction of scaffold implants, which comprises the primary aspects of bone regeneration. Selective laser melting was used to manufacture a titanium scaffold with channels representative of different strut curvatures for in vivo assessment. The titanium scaffold was implanted in the femur condyles of rabbits to validate the mathematical model. Simulation results suggest that the curvature affected the distribution of growth factors and subsequently induced the migration of osteoblast lineage cells and bone deposition to the locations with higher curvature. The predictions of the mathematical model are in good agreement with the in vivo assessment results, in which newly formed bone first appeared adjacent to the vertices of the major axes in elliptical channels. The mechanism of curvature-guided osteoconduction may provide a guide for the design optimization of scaffold implants to achieve enhanced bone ingrowth.

Milliscale Substrate Curvature Promotes Myoblast Self-Organization and Differentiation

Biological tissues comprise complex structural environments known to influence cell behavior via multiple interdependent sensing and transduction mechanisms. Yet, and despite the predominantly nonplanar geometry of these environments, the impact of tissue-size (milliscale) curvature on cell behavior is largely overlooked or underestimated. This study explores how concave, hemicylinder-shaped surfaces 3-50 mm in diameter affect the migration, proliferation, orientation, and differentiation of C2C12 myoblasts. Notably, these milliscale cues significantly affect cell responses compared with planar substrates, with myoblasts grown on surfaces 7.5-15 mm in diameter showing prevalent migration and alignment parallel to the curvature axis. Moreover, surfaces within this curvature range promote myoblast differentiation and the formation of denser, more compact tissues comprising highly oriented multinucleated myotubes. Based on the similarity of effects, it is further proposed that myoblast susceptibility to substrate curvature depends on mechanotransduction signaling. This model thus supports the notion that cellular responses to substrate curvature and compliance share the same molecular pathways and that control of cell behavior can be achieved via modulation of either individual parameter or in combination. This correlation is relevant for elucidating how muscle tissue forms and heals, as well as for designing better biomaterials and more appropriate cell-surface interfaces.

Interaction of Alpha-Synuclein and Its Mutants with Rigid Lipid Vesicle Mimics of Varying Surface Curvature

Abnormal aggregation of alpha-synuclein (α-syn), an intrinsically disordered neuronal protein, is strongly implicated in the development of Parkinson's disease. Efforts to better understand α-syn's native function and its pathogenic role in neurodegeneration have revealed that the protein interacts with anionic lipid vesicles via adoption of an amphipathic α-helical structure; however, the ability of α-syn to remodel lipid membranes has made it difficult to decipher the role of vesicle surface curvature in protein binding behavior. In this study, sodium dodecyl sulfate (SDS)-coated gold nanoparticles (AuNPs), which mimic bilayer vesicle architecture, were synthesized in order to conduct a systematic investigation into the binding interaction of α-syn and two of its mutants (A30P and E46K) with rigid lipid vesicle mimics of defined surface curvature. By incorporating a rigid AuNP core (∼10-100 nm), the ability of α-syn to remodel the vesicle mimics was removed and their surface curvature could be fixed. Proteomics studies showed that, upon binding of free α-syn to the surface of SDS-AuNPs, the N-terminus of α-syn became less solvent accessible, whereas its C-terminus became more accessible. Interestingly, α-syn's non-amyloid-β component (NAC) region also exhibited increased solvent accessibility, suggesting that α-syn bound to rigid vesicle-like structures could possess heightened aggregation propensity and therefore pathogenicity. Additionally, both the A30P and E46K mutations were found to adopt distinct binding modes on the mimics' surface. In contrast with previous reports, similar binding affinities were observed for WT, A30P, and E46K α-syn toward SDS-AuNPs of all sizes, indicating the potential importance of vesicle deformability in determining α-syn binding behavior.

Endosomal Organization of CpG Constructs Correlates with Enhanced Immune Activation

This Letter describes how the endosomal organization of immunostimulatory nanoconstructs can tune the in vitro activation of macrophages. Nanoconstructs composed of gold nanoparticles conjugated with unmethylated cytosine-phosphate-guanine (CpG) oligonucleotides have distinct endosomal distributions depending on the surface curvature. Mixed-curvature constructs produce a relatively high percentage of hollow endosomes, where constructs accumulated primarily along the interior edges. These constructs achieved a higher level of toll-like receptor (TLR) 9 activation along with the enhanced secretion of proinflammatory cytokines and chemokines compared to constant-curvature constructs that aggregated mostly in the center of the endosomes. Our results underscore the importance of intraendosomal interactions in regulating immune responses and targeted delivery.

Three-Dimensional Surface Reconstruction of the Human Cochlear Nucleus: Implications for Auditory Brain Stem Implant Design

Objective  The auditory brain stem implant (ABI) is a neuroprosthesis placed on the surface of the cochlear nucleus (CN) to provide hearing sensations in children and adults who are not candidates for cochlear implantation. Contemporary ABI arrays are stiff and do not conform to the curved brain stem surface. Recent advancements in microfabrication techniques have enabled the development of flexible surface arrays, but these have only been applied in animal models. Herein, we measure the surface curvature of the human CN and adjoining regions to assist in the design and placement of next-generation conformable clinical ABI arrays. Three-dimensional (3D) reconstructions from ultrahigh T1-weighted brain magnetic resonance imaging (MRI) sequences and histologic reconstructions based on postmortem adult human brain stem specimens were used. Design  This is a retrospective review of radiologic data and postmortem histologic axial sections. Setting  This is set at the tertiary referral center. Participants  Data were acquired from healthy adults. Main Outcome Measures  The main outcome measures are principal curvature values (Kmin and Kmax) and global radius of curvature. Results  The CN was successfully extracted and rendered as a 3D surface in all cases. Significant curvatures of the CN in both histologic and radiographic reconstructions were found with global radius of curvature ranging from 2.08 to 8.5 mm. In addition, local curvature analysis revealed that the surface is highly complex. Conclusion  Detailed rendering of the human CN is feasible using histology and 3D MRI reconstruction and highlights complex surface topography that is not recapitulated by contemporary stiff ABI arrays.

Shape-Specific Patterning of Polymer-Functionalized Nanoparticles

Chemically and topographically patterned nanoparticles (NPs) with dimensions on the order of tens of nanometers have a diverse range of applications and are a valuable system for fundamental research. Recently, thermodynamically controlled segregation of a smooth layer of polymer ligands into pinned micelles (patches) offered an approach to nanopatterning of polymer-functionalized NPs. Control of the patch number, size, and spatial distribution on the surface of spherical NPs has been achieved, however, the role of NP shape remained elusive. In the present work, we report the role of NP shape, namely, the effect of the local surface curvature, on polymer segregation into surface patches. For polymer-functionalized metal nanocubes, we show experimentally and theoretically that the patches form preferentially on the high-curvature regions such as vertices and edges. An in situ transformation of the nanocubes into nanospheres leads to the change in the number and distribution of patches; a process that is dominated by the balance between the surface energy and the stretching energy of the polymer ligands. The experimental and theoretical results presented in this work are applicable to surface patterning of polymer-capped NPs with different shapes, thus enabling the exploration of patch-directed self-assembly, as colloidal surfactants, and as templates for the synthesis of hybrid nanomaterials.

Local Solid Shape

Local solid shape applies to the surface curvature of small surface patches—essentially regions of approximately constant curvatures—of volumetric objects that are smooth volumetric regions in Euclidean 3-space. This should be distinguished from local shape in pictorial space. The difference is categorical. Although local solid shape has naturally been explored in haptics, results in vision are not forthcoming. We describe a simple experiment in which observers judge shape quality and magnitude of cinematographic presentations. Without prior training, observers readily use continuous shape index and Casorati curvature scales with reasonable resolution.

Diffusion accessibility as a method for visualizing macromolecular surface geometry

Important three-dimensional spatial features such as depth and surface concavity can be difficult to convey clearly in the context of two-dimensional images. In the area of macromolecular visualization, the computer graphics technique of ray-tracing can be helpful, but further techniques for emphasizing surface concavity can give clearer perceptions of depth. The notion of diffusion accessibility is well-suited for emphasizing such features of macromolecular surfaces, but a method for calculating diffusion accessibility has not been made widely available. Here we make available a web-based platform that performs the necessary calculation by solving the Laplace equation for steady state diffusion, and produces scripts for visualization that emphasize surface depth by coloring according to diffusion accessibility. The URL is http://services.mbi.ucla.edu/DiffAcc/.

The tarani mutation alters surface curvature in Arabidopsis leaves by perturbing the patterns of surface expansion and cell division

The leaf surface usually stays flat, maintained by coordinated growth. Growth perturbation can introduce overall surface curvature, which can be negative, giving a saddle-shaped leaf, or positive, giving a cup-like leaf. Little is known about the molecular mechanisms that underlie leaf flatness, primarily because only a few mutants with altered surface curvature have been isolated and studied. Characterization of mutants of the CINCINNATA-like TCP genes in Antirrhinum and Arabidopsis have revealed that their products help maintain flatness by balancing the pattern of cell proliferation and surface expansion between the margin and the central zone during leaf morphogenesis. On the other hand, deletion of two homologous PEAPOD genes causes cup-shaped leaves in Arabidopsis due to excess division of dispersed meristemoid cells. Here, we report the isolation and characterization of an Arabidopsis mutant, tarani (tni), with enlarged, cup-shaped leaves. Morphometric analyses showed that the positive curvature of the tni leaf is linked to excess growth at the centre compared to the margin. By monitoring the dynamic pattern of CYCLIN D3;2 expression, we show that the shape of the primary arrest front is strongly convex in growing tni leaves, leading to excess mitotic expansion synchronized with excess cell proliferation at the centre. Reduction of cell proliferation and of endogenous gibberellic acid levels rescued the tni phenotype. Genetic interactions demonstrated that TNI maintains leaf flatness independent of TCPs and PEAPODs.

The effect of nanoscale surface curvature on the oligomerization of surface-bound proteins

The influence of surface topography on protein conformation and association is used routinely in biological cells to orchestrate and coordinate biomolecular events. In the laboratory, controlling the surface curvature at the nanoscale offers new possibilities for manipulating protein-protein interactions and protein function at surfaces. We have studied the effect of surface curvature on the association of two proteins, α-lactalbumin (α-LA) and β-lactoglobulin (β-LG), which perform their function at the oil-water interface in milk emulsions. To control the surface curvature at the nanoscale, we have used a combination of polystyrene (PS) nanoparticles (NPs) and ultrathin PS films to fabricate chemically pure, hydrophobic surfaces that are highly curved and are stable in aqueous buffer. We have used single-molecule force spectroscopy to measure the contour lengths Lc for α-LA and β-LG adsorbed on highly curved PS surfaces (NP diameters of 27 and 50 nm, capped with a 10 nm thick PS film), and we have compared these values in situ with those measured for the same proteins adsorbed onto flat PS surfaces in the same samples. The Lc distributions for β-LG adsorbed onto a flat PS surface contain monomer and dimer peaks at 60 and 120 nm, respectively, while α-LA contains a large monomer peak near 50 nm and a dimer peak at 100 nm, with a tail extending out to 200 nm, corresponding to higher order oligomers, e.g. trimers and tetramers. When β-LG or α-LA is adsorbed onto the most highly curved surfaces, both monomer peaks are shifted to much smaller values of Lc. Furthermore, for β-LG, the dimer peak is strongly suppressed on the highly curved surface, whereas for α-LA the trimer and tetramer tail is suppressed with no significant change in the dimer peak. For both proteins, the number of higher order oligomers is significantly reduced as the curvature of the underlying surface is increased. These results suggest that the surface curvature provides a new method of manipulating protein-protein interactions and controlling the association of adsorbed proteins, with applications to the development of novel biosensors.

Friction coefficients in a longitudinal direction between the finger pad and selected materials for different normal forces and curvatures

This study investigated the effect of object curvature, normal force and material on skin friction coefficient. Twelve subjects slid their middle fingertip pad against a test object with small (11 mm), medium (18, 21 mm) or large (flat object) radii of curvature, while maintaining a normal force of 1, 10 or 20 N. Tested materials were aluminium and four rubber hoses. The average friction coefficient was 0.6 for aluminium and 0.9 for the rubber hoses. As normal force increased from 1 to 20 N, the average friction coefficient decreased 46%. Friction coefficient did not vary significantly with object curvature. The citation of friction coefficient data requires careful attention to normal force levels with which they are measured, but not so much to object curvature between 11 mm and infinity. This study provides skin friction coefficient data that are needed for design of objects that are manipulated with the hands. The investigation of the effect of object curvature on skin friction coefficient has important implications to ergonomics practices as many objects handled in everyday activities have curved surfaces.