Flat Lattices Research Articles

Fluidic shear stress alters clathrin dynamics and vesicle formation in endothelial cells

Endothelial cells (ECs) experience a variety of highly dynamic mechanical stresses. Among others, cyclic stretch and increased plasma membrane tension inhibit clathrin-mediated endocytosis (CME) in non-ECs. It remains elusive how ECs maintain CME in these biophysically unfavorable conditions. Previously, we have used simultaneous two-wavelength axial ratiometry (STAR) microscopy to show that endocytic dynamics are similar between statically cultured human umbilical vein endothelial cells (HUVECs) and fibroblast-like Cos-7 cells. Here, we asked whether biophysical stresses generated by blood flow influence CME. We used our data processing platform—DrSTAR—to examine if clathrin dynamics are altered in HUVECs after experiencing fluidic shear stress (FSS). We found that HUVECs cultivated under a physiological level of FSS had increased clathrin dynamics compared with static controls. FSS increased both clathrin-coated vesicle formation and nonproductive flat clathrin lattices by 2.3-fold and 1.9-fold, respectively. The curvature-positive events had significantly delayed curvature initiation relative to clathrin recruitment in flow-stimulated cells, highlighting a shift toward flat-to-curved clathrin transitions in vesicle formation. Overall, our findings indicate that clathrin dynamics and clathrin-coated vesicle formation can be modulated by the local physiological environment and represent an important regulatory mechanism.

SCATTERING OF ELECTROMAGNETIC WAVES ON FLAT GRID TWO-PERIODIC STRUCTURES

Context. One of the scientific hypotheses for the creation of nonreciprocal optical metasurfaces is based on the use of a wave channel in which rays of the direct and reverse diffraction scenarios are realized on two-periodic flat structures with nonlinear elements. Such processes in the nanometer wavelength range of electronic devices require precise calculations of the interaction of waves and microstructures of devices. It is also important to describe the behavior of antenna devices in mobile communications. Expanding the wavelength range of stable communication is achieved by using prefractal structures in antenna devices in combination with periodic structuring. Similar modeling problems arise when electromagnetic waves penetrate materials with a crystalline structure (radio transparency).
 Objective. To test this hypothesis, it is necessary to carry out mathematical modeling of the process of scattering of electromagnetic waves by metasurfaces under conditions of excitation of several diffraction orders. It is known that among two-periodic flat lattices of different structures there are five types that fill the plane. These are the Bravais grilles. The problem of scattering of an incident monochromatic TE polarized wave on a metal screen with recesses in two-periodic structures filled with silicon was considered.
 Method. The paper builds mathematical models for the study of spatial-amplitude spectra of metasurfaces on Brave lattices and gives some results of their numerical study. The condition for determining the diffraction orders propagating over the grating is proposed. Scattered field amplitudes are from the solution of the boundary value problem for the Helmholtz equation in the COMSOL Multiphysics 5.4 package. Similar problem formulations are possible when studying the penetration of an electromagnetic field into a crystalline substance.
 Results. Obtained relations for diffraction orders of electromagnetic waves scattered by a diffraction grating. The existence of wavelengths incident on a two-periodic lattice for which there is no reflected wave is shown for different shapes (rectangular, square, hexagonal) of periodic elements in the center of which a depression filled with silicon was made. Distributions of reflection coefficients for different geometric sizes of colored elements and recesses are given. The characteristics of the electric field at resonant modes in the form of modulus isolines show the nature of the interaction of the field over the periodic lattice and the scatterersdepressions. At the resonant wavelengths of the incident waves, standing waves appear in the scatterers.
 Conclusions. A mathematical model of the set of diffraction orders propagating from a square and hexagonal lattice into halfspace is proposed z >= 0. It has been shown that flat periodic lattice with square or hexagonal periodicity elements and resonant scatterers in the form of cylindrical recesses filled with silicon can produce a non-mirrored scattered field in metal. The response of the lattices to changes in the wavelength of the incident field by the structure of diffraction orders of the scattered field and high sensitivity to the rotation of the incident plane were revealed. The two-periodic lattices have prospects for creating anti-reflective surfaces of various devices. Two-periodic lattices have prospects for creating anti-reflective surfaces for various devices, laser or sensor electronic devices, antennas in mobile communication elements, and radio transparency elements. They have more advanced manufacturing technologies in relation to spatial crystal structures.

Canonical and non-canonical integrin-based adhesions dynamically interconvert

Adhesions are critical for anchoring cells in their environment, as signaling platforms and for cell migration. In line with these diverse functions different types of cell-matrix adhesions have been described. Best-studied are the canonical integrin-based focal adhesions. In addition, non-canonical integrin adhesions lacking focal adhesion proteins have been discovered. These include reticular adhesions also known as clathrin plaques or flat clathrin lattices, that are enriched in clathrin and other endocytic proteins, as well as extensive adhesion networks and retraction fibers. How these different adhesion types that share a common integrin backbone are related and whether they can interconvert is unknown. Here, we identify the protein stonin1 as a marker for non-canonical αVβ5 integrin-based adhesions and demonstrate by live cell imaging that canonical and non-canonical adhesions can reciprocally interconvert by the selective exchange of components on a stable αVβ5 integrin scaffold. Hence, non-canonical adhesions can serve as points of origin for the generation of canonical focal adhesions.

Flat clathrin lattices are linked to metastatic potential in colorectal cancer

Clathrin assembles at the cells' plasma membrane in a multitude of clathrin-coated structures (CCSs). Among these are flat clathrin lattices (FCLs), alternative clathrin structures that have been found in specific cell types, including cancer cells. Here we show that these structures are also present in different colorectal cancer (CRC) cell lines, and that they are extremely stable with lifetimes longer than 8 h. By combining cell models representative of CRC metastasis with advanced fluorescence imaging and analysis, we discovered that the metastatic potential of CRC is associated with an aberrant membranous clathrin distribution, resulting in a higher prevalence of FCLs in cells with a higher metastatic potential. These findings suggest that clathrin organization might play an important yet unexplored role in cancer metastasis.

Reticular adhesions are assembled at flat clathrin lattices and opposed by active integrin α5β1.

Reticular adhesions (RAs) consist of integrin αvβ5 and harbor flat clathrin lattices (FCLs), long-lasting structures with similar molecular composition as clathrin-mediated endocytosis (CME) carriers. Why FCLs and RAs colocalize is not known. Here, we show that RAs are assembled at FCLs in a process controlled by fibronectin (FN) and its receptor, integrin α5β1. We observed that cells on FN-rich matrices displayed fewer FCLs and RAs. CME machinery inhibition abolished RAs and live-cell imaging showed that RA establishment requires FCL coassembly. The inhibitory activity of FN was mediated by the activation of integrin α5β1 at Tensin1-positive fibrillar adhesions. Conventionally, endocytosis disassembles cellular adhesions by internalizing their components. Our results present a novel paradigm in the relationship between these two processes by showing that endocytic proteins can actively function in the assembly of cell adhesions. Furthermore, we show this novel adhesion assembly mechanism is coupled to cell migration via unique crosstalk between cell-matrix adhesions.

Lattice Green/Neumann function for the 2D Laplacian operator defined on square lattice on cylinders, tori and other geometries with some applications

The lattice Green functions for the discrete planar Laplacian defined on regular square lattice wrapped around cylinders and tori are rigorously defined and obtained in an exact analytic form. The method of images well-known in potential theory is implemented to derive for many other geometries with free boundaries (semi-infinite or finite cylinders and strips, rectangle) the related exact lattice Green-Neumann functions needed to readily solve discrete Neumann problems or, via a Neumann-to-Dirichlet mapping, discrete Dirichlet problems for these flat square lattices. Some applications are thus proposed as explicit expressions of two-point resistances for related resistor networks, and some probability-based characteristics regarding the associated Pòlya’s random walks.

MATHEMATICAL MODELING OF SCATTERING OF ELECTROMAGNETIC WAVES ON PLANE TWO-PERIODIC STRUCTURES

One of the scientific hypotheses for the creation of nonreciprocal optical metasurfaces is based on the use of a wave channel in which rays of the direct and reverse diffraction scenarios are realized on two-periodic flat structures with nonlinear elements.
 To test this hypothesis, it is necessary to carry out mathematical modeling of the process of scattering of electromagnetic waves by metasurfaces under conditions of excitation of several diffraction orders. It is known that among two-periodic flat lattices of different structures there are five types that fill the plane. These are the Bravais lattices. The problem of scattering of an incident monochromatic TE polarized wave on a metal screen with recesses in two-periodic structures filled with silicon was considered.
 In this paper, mathematical models are constructed for studying the spatial amplitude spectra of metasurfaces on Bravais lattices and some results of their numerical study are presented. Relationships are obtained for the diffraction orders of scattered electromagnetic waves by a diffraction grating. The existence of wavelengths of incident waves on a two-periodic grating for which there is no reflected wave is shown for different shapes (rectangular, square, hexagonal) of periodic elements in the center of which a recess filled with silicon was made. The distributions of the reflection coefficient are given for various geometric dimensions of periodic elements and recesses.

Actin polymerization promotes invagination of flat clathrin-coated lattices in mammalian cells by pushing at lattice edges

Clathrin-mediated endocytosis (CME) requires energy input from actin polymerization in mechanically challenging conditions. The roles of actin in CME are poorly understood due to inadequate knowledge of actin organization at clathrin-coated structures (CCSs). Using platinum replica electron microscopy of mammalian cells, we show that Arp2/3 complex-dependent branched actin networks, which often emerge from microtubule tips, assemble along the CCS perimeter, lack interaction with the apical clathrin lattice, and have barbed ends oriented toward the CCS. This structure is hardly compatible with the widely held “apical pulling” model describing actin functions in CME. Arp2/3 complex inhibition or epsin knockout produce large flat non-dynamic CCSs, which split into invaginating subdomains upon recovery from Arp2/3 inhibition. Moreover, epsin localization to CCSs depends on Arp2/3 activity. We propose an “edge pushing” model for CME, wherein branched actin polymerization promotes severing and invagination of flat CCSs in an epsin-dependent manner by pushing at the CCS boundary, thus releasing forces opposing the intrinsic curvature of clathrin lattices.

Molecular determinants of αVβ5 localization in flat clathrin lattices - role of αVβ5 in cell adhesion and proliferation.

ABSTRACTThe vitronectin receptor integrin αVβ5 can reside in two distinct adhesion structures – focal adhesions (FAs) and flat clathrin lattices (FCLs). Here, we investigate the mechanism that regulates the subcellular distribution of β5 in keratinocytes and show that β5 has approximately 7- and 5-fold higher affinity for the clathrin adaptors ARH (also known as LDLRAP1) and Numb, respectively, than for the talin 1 (TLN1); all proteins that bind to the membrane-proximal NPxY motif of the β5 cytoplasmic domain. Using mass spectrometry, we identified β5 interactors, including the Rho GEFs p115Rho-GEF and GEF-H1 (also known as ARHGEF1 and ARHGEF2, respectively), and the serine protein kinase MARK2, depletion of which diminishes the clustering of β5 in FCLs. Replacement of two serine residues (S759 and S762) in the β5 cytoplasmic domain with phospho-mimetic glutamate residues causes a shift in the localization of β5 from FAs into FCLs without affecting the interactions with MARK2, p115Rho-GEF or GEF-H1. Instead, we demonstrate that changes in the actomyosin-based cellular contractility by ectopic expression of activated Rho or disruption of microtubules regulates β5 localization. Finally, we present evidence that β5 in either FAs or FCLs functions to promote adhesion to vitronectin, cell spreading, and proliferation.

Curved domain-wall fermions

Abstract We consider fermion systems on a square lattice with a mass term having a curved domain-wall. Like conventional flat domain-wall fermions, massless and chiral edge states appear on the wall. In the cases of S1 and S2 domain-walls embedded into flat hypercubic lattices, we find that these edge modes feel gravity through the induced spin or spinc connections. The gravitational effect is encoded in the Dirac eigenvalue spectrum as a gap from zero. In the standard continuum extrapolation of the square lattice, we find good agreement with the analytic prediction in the continuum theory. We also find that the rotational symmetry of the edge modes is automatically recovered in the continuum limit. Subject Index B38

Dual clathrin and integrin signaling systems regulate growth factor receptor activation

The crosstalk between growth factor and adhesion receptors is key for cell growth and migration. In pathological settings, these receptors are drivers of cancer. Yet, how growth and adhesion signals are spatially organized and integrated is poorly understood. Here we use quantitative fluorescence and electron microscopy to reveal a mechanism where flat clathrin lattices partition and activate growth factor signals via a coordinated response that involves crosstalk between epidermal growth factor receptor (EGFR) and the adhesion receptor β5-integrin. We show that ligand-activated EGFR, Grb2, Src, and β5-integrin are captured by clathrin coated-structures at the plasma membrane. Clathrin structures dramatically grow in response to EGF into large flat plaques and provide a signaling platform that link EGFR and β5-integrin through Src-mediated phosphorylation. Disrupting this EGFR/Src/β5-integrin axis prevents both clathrin plaque growth and dampens receptor signaling. Our study reveals a reciprocal regulation between clathrin lattices and two different receptor systems to coordinate and enhance signaling. These findings have broad implications for the regulation of growth factor signaling, adhesion, and endocytosis.

Metal-insulator transition in infinitesimally weakly disordered flat bands

We study the effect of infinitesimal onsite disorder on d-dimensional all bands flat lattices. The lattices are generated from diagonal Hamiltonians by a sequence of (d + 1) local unitary transformations parametrized by angles ${\theta}_i$. Without loss of generality, we consider the case of two flat bands separated by a finite gap $\Delta$. The perturbed states originating from the flat bands are described by an effective tight binding network with finite on- and off-diagonal disorder strength which depends on the manifold angles ${\theta}_i$. The original infinitesimal onsite disorder strength W is only affecting the overall scale of the effective Hamiltonian. Upon variation of the manifold angles for d = 1 and d = 2 we find that localization persists for any choice of local unitaries, and the localization length can be maximized for specific values of ${\theta}_i$. Instead, in d = 3 we identify a non-perturbative metal-insulator transition upon varying the all bands flat manifold angles.

Abstract P419: Revealing The Dynamics Of Vesicle Formation During Clathrin-mediated Endocytosis In Living Endothelial Cells

Clathrin-mediated endocytosis (CME) is an essential cellular process for internalizing nutrients and therapeutics at endothelial cell barriers. Studying the formation of cargo containing endocytic vesicles in living cells is challenging due to the limited resolution of fluorescence microscopy and the highly dynamic nature of CME. Moreover, it is currently unknown how the physiological conditions present in vasculature affect CME in endothelial cells. To address this challenge we used a novel microscopy approach, Simultaneous Two-wavelength Axial Ratiometry (STAR), to image vesicle formation dynamics with nanometer axial resolution in living cells. High-throughput analysis revealed that 80% of de novo clathrin accumulations contributed to endocytosis while 20% remained flat, consistent in both human umbilical vein endothelial cells (HUVECs) and our test-bed model green monkey kidney fibroblast-like (Cos-7) cells. We next investigated the interplay between coat curvature and clathrin accumulation in vesicle initiation to identify the mechanism of vesicle formation. Our results support the flexible model of vesicle formation with curvature and clathrin accumulation initiating together at shorter-lived vesicles (<20s) and through a flat-to-curved transition of clathrin lattices at longer-lived vesicles (>20s). Finally, we addressed if physiological conditions present in vasculature alter the dynamics of vesicle formation. We show that increasing osmotic pressure decreased the total number of internalizations but had no impact on the number of flat clathrin accumulations or the mechanism of vesicle formation in Cos-7 cells. In future research, we will test the hypothesis that HUVECs have distinct mechanisms to retain vesicle formation under osmotic pressure or shear stress conditions similar to their native environment. Additionally targeted drug delivery to vascular endothelial cells, for example nanocarriers binding to flat lattices or CCVs leading to different therapeutic outcomes or bioavailability, can potentially be informed by identifying clathrin morphology and dynamics and the mechanisms of endocytosis using STAR microscopy.

Clathrin: the molecular shape shifter.

Clathrin is best known for its contribution to clathrin-mediated endocytosis yet it also participates to a diverse range of cellular functions. Key to this is clathrin's ability to assemble into polyhedral lattices that include curved football or basket shapes, flat lattices or even tubular structures. In this review, we discuss clathrin structure and coated vesicle formation, how clathrin is utilised within different cellular processes including synaptic vesicle recycling, hormone desensitisation, spermiogenesis, cell migration and mitosis, and how clathrin's remarkable 'shapeshifting' ability to form diverse lattice structures might contribute to its multiple cellular functions.

The structure and spontaneous curvature of clathrin lattices at the plasma membrane.

Clathrin-mediated endocytosis is the primary pathway for receptor and cargo internalization in eukaryotic cells. It is characterized by a polyhedral clathrin lattice that coats budding membranes. The mechanism and control of lattice assembly, curvature, and vesicle formation at the plasma membrane has been a matter of long-standing debate. Here, we use platinum replica and cryoelectron microscopy and tomography to present a structural framework of the pathway. We determine the shape and size parameters common to clathrin-mediated endocytosis. We show that clathrin sites maintain a constant surface area during curvature across multiple cell lines. Flat clathrin is present in all cells and spontaneously curves into coated pits without additional energy sources or recruited factors. Finally, we attribute curvature generation to loosely connected and pentagon-containing flat lattices that can rapidly curve when a flattening force is released. Together, these data present a universal mechanistic model of clathrin-mediated endocytosis.

Numerical simulation of magnetic skyrmions on flat lattices

We studied several types of flat lattices with direct exchange and Dzyaloshinskii-Moriya interaction between spins: a honeycomb lattice with 3 nearest neighbours (NN), a square lattice with 4 NN and a hexagonal or triangular lattice with 6 NN. For the analysis of data obtained during the Monte Carlo simulation, a convolutional neural network was used for the recognition of different phases of the spin system which was dependent on simulation parameters such as DMI and external magnetic field (Hz). Based on these data, the phase diagrams (Hz, D) for the different lattices were plotted. The various states of the systems under observation were visualised and the boundaries between the different phases were defined as a spiral, a skyrmion and others. The data from the numerical experiments will be used in further studies to determine the model parameters of the systems for the formation of a stable skyrmion state and the development of methods for controlling skyrmions in a magnetic film.

Lattice chain theories for dynamics of acoustic flexural phonons in nonpolar nanomaterials

Knowledge of lattice dynamics of acoustic flexural phonons is critically important in understanding the mechanical, electrical, and thermal properties of nanomaterials. However, the general nature of acoustic flexural phonons for the span of possible nanomaterials and the dependence of these on microscopic material properties remain unclear. Therefore, we develop general lattice chain theories to understand acoustic flexural vibrations in covalent and van der Waals lattices. The analytic theories suggest that the flexure branch has quadratic dispersion for low dimensional lattices in the long-wavelength limit, quite different from linear branches in bulk van der Waals bonded lattices like graphite. Surprisingly, interlayer van der Waals interactions in multilayer lattices do not determine the behavior of the flexural dispersion. The bonds of covalent interactions in multilayer and buckled monolayer lattices play different roles in determining the flexural dispersion with those in flat monolayer lattices, e.g., graphene. Further, based on the correspondence between microscopic and continuum dynamics, we provide a universal and effective approach to characterize the intrinsic bending rigidity of low dimensional nanomaterials using dispersion data.

Eden growth models for flat clathrin lattices with vacancies

Clathrin-mediated endocytosis is one of the major pathways by which cells internalise cargo molecules. Recently it has been shown that clathrin triskelia can first assemble as flat lattices before the membrane starts to bend. However, for fully assembled clathrin lattices high energetic and topological barriers exist for the flat-to-curved transition. Here we explore the possibility that flat clathrin lattices grow with vacancies that are not visible in traditional imaging techniques but would lower these barriers. We identify the Eden model for cluster growth as the most appropriate modeling framework and systematically derive the four possible variants that result from the specific architecture of the clathrin triskelion. Our computer simulations show that the different models lead to clear differences in the statistical distributions of cluster shapes and densities. Experimental results from electron microscopy and correlative light microscopy provide first indications for the model variants with a moderate level of lattice vacancies.

An integrated approach of form finding and construction simulation for glass fiber‐reinforced polymer elastic gridshells

SummaryGlass fiber‐reinforced polymer (GFRP) elastic gridshell is composed of long continuous GFRP tubes and achieves its shape through the elastic deformations during the lifting construction process. However, the complicated mechanical behaviors during the practical forming process are rarely examined in the previous researches. In this research, an innovative approach consolidating the form‐finding analysis and the construction simulation is proposed for the GFRP elastic gridshells. The integrated approach, which is developed with the ABAQUS and Python, is based on finite element analysis and iterative optimization; therefore, the mechanical deformations of gridshell can be accurately taken into account. The procedure of the integrated analysis is comprehensively presented by taking a typical double‐hump gridshell as an example. The form‐finding results (i.e., the flat lattices) derived from the iteration are found to be insensitive to the initial input. The structural behavior indexes (e.g., deflections, support reactions, and sectional stresses) during the lifting construction process are also available in the analysis. Based on the indexes, some general structural features of such gridshells are concluded. The achievements provide novel perspectives for the form‐finding analysis of GFRP elastic gridshells where lifting construction is involved, which is beneficial for the design and analysis of such structures.

Linking the Dynamics of Clathrin-Mediated Endocytosis with Membrane Shape Changes in Living Cells with Nanometer Axial Resolution

Clathrin-mediated endocytosis (CME) is essential for cellular homeostasis. Thus, a precise understanding of the biophysical properties of vesicle formation and internalization is necessary. Due to fast dynamics, heterogeneity, and the number of proteins involved in CME, our current knowledge is limited and biased. While fluorescence microscopy provides information about the spatio-temporal dynamics of proteins, it lacks evidence for membrane bending. In contrast, electron microscopy shows membrane curvature, but it lacks dynamic insight. Here, by using Simultaneous Two-wavelength Axial Ratiometry (STAR), we link clathrin dynamics with membrane shape changes. STAR is a TIRF based microscopy technique we developed that takes advantage of the variance in penetration depth generated by different laser wavelengths. By imaging proteins tagged with the EGFP-iRFP fusion (STAR probe), we can generate the ratio of fluorescent intensity and convert it into axial information. The initial transition of plasma membrane from flat to curved and its correlation with clathrin arrival, during endocytosis, remains unclear. We report three different bending dynamics in Cos-7 cells transfected with clathrin light chain STAR probe. Most often clathrin accumulates along with curvature generation, or curvature starts forming shortly before clathrin arrival. Rarely, clathrin first assembles as a flat lattice prior to vesicle formation. Surprisingly, a quarter of de novo clathrin assemblies does not induce curvature. We hypothesize that the flat lattices might be caused by the absence of activated receptors, curvature sensing/inducing proteins, or vesicle maturation markers. To test this and to further describe the difference in initial curvature generation, we are developing a three-color STAR approach to integrate endocytic components with membrane shape changes. In doing so, we hope to unify the physical process of vesicle formation in clathrin-mediated endocytosis with its dynamics.