Sinusoidal Substrate Research Articles

A minimal physical model for curvotaxis driven by curved protein complexes at the cell’s leading edge

Cells often migrate on curved surfaces inside the body, such as curved tissues, blood vessels, or highly curved protrusions of other cells. Recent in vitro experiments provide clear evidence that motile cells are affected by the curvature of the substrate on which they migrate, preferring certain curvatures to others, termed "curvotaxis." The origin and underlying mechanism that gives rise to this curvature sensitivity are not well understood. Here, we employ a "minimal cell" model which is composed of a vesicle that contains curved membrane protein complexes, that exert protrusive forces on the membrane (representing the pressure due to actin polymerization). This minimal-cell model gives rise to spontaneous emergence of a motile phenotype, driven by a lamellipodia-like leading edge. By systematically screening the behavior of this model on different types of curved substrates (sinusoidal, cylinder, and tube), we show that minimal ingredients and energy terms capture the experimental data. The model recovers the observed migration on the sinusoidal substrate, where cells move along the grooves (minima), while avoiding motion along the ridges. In addition, the model predicts the tendency of cells to migrate circumferentially on convex substrates and axially on concave ones. Both of these predictions are verified experimentally, on several cell types. Altogether, our results identify the minimization of membrane-substrate adhesion energy and binding energy between the membrane protein complexes as key players of curvotaxis in cell migration.

Controlling kinetics of self-propelled rod-like swimmers near multi sinusoidal substrate

Motility is defined as the movement of cells by some form of self-propulsion. Some organisms motile by using long flagella that quickly rotate to propel them over various surfaces (in swarming and swimming mechanism), while few motile without the aid of flagella (in twitching, sliding and gliding mechanism). Among these modes, gliding motility is adopted by a rod-shaped organism famously known as gliding bacteria. It is hypothesized that in such type of motility, organism motile under their own power by secreting a layer of slime on the substrate. In this study, an active wall is considered as a substrate and a two-dimensional wavy sheet as an organism. Slip effects are also employed in the current work. The physical properties of the slime are governed by a suitable constitutive equation of couple stress model. A sixth order BVP is obtained by utilizing lubrication assumption. For an appropriate fixed pair of flow rate and organism speed the BVP is solved by MATLAB built-in function bvp-5c. This solution is utilized in the mechanical equilibrium conditions which are obviously not satisfied yet. To satisfy these conditions, the pair of flow rate and gliding speed is refined by a root finding algorithm (modified Newton–Raphson method). By employing this numerical scheme, various figures are shown to demonstrate the effect of several associated parameters on organism speed, flow rate, energy expended by the glider, streamlines and longitudinal velocity. It is observed from the graphical results that organism speed and energy consumption is directly proportional to the couple stress parameter and slip effects.

3D Shape of Epithelial Cells on Curved Substrates

It is widely recognized that the shape of epithelial cells is determined by the tension generated by the actomyosin cortex and the adhesion of cells to the substrate and to each other. To account for these biological and structural contributions to cell shape, different physical models have been proposed. However, an experimental procedure that would allow a validation of a minimal physical model for the shape of epithelial cells in 3D has not yet been proposed. In this study, we cultured MDCK epithelial cells on substrates with a sinusoidal profile, allowing us to measure the shape of the cells on various positive and negative curvatures. We found that MDCK cells are thicker in the valleys than on the crests of sinusoidal substrates. The influence of curvature on the shape of epithelial cells could not be understood with a model using only differential apical, basal and lateral surface energies. However, the addition of an apical line tension was sufficient to quantitatively account for the experimental measurements. The model also accounts for the shape of MDCK cells that overexpress E-cadherin. On the other hand, when reducing myosin II activity with blebbistatin, we measured a saturation of the difference in cell thickness between valleys and crests, suggesting the need for a term limiting large cell deformations. Our results show that a minimal model that accounts for epithelial cell shape needs to include an apical line tension in addition to differential surface energies, highlighting the importance of structures that produce anisotropic tension in epithelial cells, such as the actin belt linking adherens junctions. In the future, our experimental procedure could be used to test a wider range of physical models for the shape of epithelia in curved environments, including, for example, continuous models.

Kinetic friction force in a three-layer model with commensurate substrates

A chain of harmonically interacting particles confined between two sinusoidal substrate potentials has been analysed. When the top substrate is driven through an attached spring with a constant velocity, the influence of the system parameters on the kinetic friction force was examined in the system with commensurate substrates. It was shown that the friction reached its maximum value when the equilibrium distance of the intermediate particles was an integer multiple of the space period of the upper and lower substrate potentials, which led to the maximum energy loss. This loss can be reduced by the increase of interparticle interaction of the middle layer.

VALIDATION OF THE KUMMER FRICTION MODEL FOR RUBBER COMPOUNDS ON SINUSOIDAL TRACKS BY FEA SIMULATIONS AND EXPERIMENTAL TECHNIQUES

ABSTRACT A refinement of the Kummer friction model is considered to determine the friction coefficient through analysis of the mechanical properties of rubber compound materials. An experimental sets of trials was carried out with a linear friction tester evaluating the friction coefficient for CB filled SBR on an ideal sinusoidal substrate under lubricated conditions. Lubricated conditions were chosen to obtain the pure hysteresis contribution of the friction coefficient, eliminating the effect of adhesion. For finite element analysis (FEA) simulations a visco-hyperelastic material model is considered to estimate the actual strain level close to the contact area. Based on the proper analysis of the temperature and frequency dependence behavior of experimental model rubber compounds, master curves for the viscoelastic moduli are constructed. Dynamic data were selected based on the strain level evaluated by first FEA simulations, actual temperature, and excitation frequency of each experiment. The proposed refined friction model and the simulated friction coefficient from FEA based on the precise evaluation of the material property show good prediction within the ideal experimental conditions.

Dependence of static friction force on stiffness in a confined chain with the incommensurate and commensurate structrue

It is used that a series of interacting atoms. They are confined between two sinusoidal substrate potentials. When the top substrate is driven by the external driving force, its velocity changes from zero to non-zero. The dependence of the static friction force on the strength is presented for the incommensurate(the spiral mean and the golden mean ) and commensurate structrue. It is found that incommensurate structures is more likely to produce superlubricate phenomenon more than commensurate structures under different stiffness coefficients.

A Biophysical Model for Curvature-Guided Cell Migration

The latest experiments have shown that adherent cells can migrate according to cell-scale curvature variations via a process called curvotaxis. Despite identification of key cellular factors, a clear understanding of the mechanism is lacking. We employ a mechanical model featuring a detailed description of the cytoskeleton filament networks, the viscous cytosol, the cell adhesion dynamics, and the nucleus. We simulate cell adhesion and migration on sinusoidal substrates. We show that cell adhesion on three-dimensional curvatures induces a gradient of pressure inside the cell that triggers the internal motion of the nucleus. We propose that the resulting out-of-equilibrium position of the nucleus alters cell migration directionality, leading to cell motility toward concave regions of the substrate, resulting in lower potential energy states. Altogether, we propose a simple mechanism explaining how intracellular mechanics enable the cells to react to substratum curvature, induce a deterministic cell polarization, and break down cells basic persistent random walk, which correlates with latest experimental evidences.

A computational design framework for two-layered elastic stamps in nanoimprint lithography and microcontact printing

Mechanical micro- and nano-patterning processes rely on engineering the interactions between a stamp and a substrate to accommodate surface roughness and particle defects while retaining the geometric integrity of printed features. We introduce a set of algorithms for rapidly simulating the stamp–substrate contact, and we use them to show that advantageous behavior can occur when the stamp consists of a finite-thickness layer bonded to a layer with different elastic properties. The simulations use two-dimensional load-response functions describing in discrete space the response of a stamp surface's shape to a localized unit load. These load-response functions incorporate the contributions both of local, indentation-like displacements and of plate-like bending of finite-thickness stamp layers. The algorithms solve iteratively for contact pressure distributions that, when spatially convolved with the load response, yield deformations consistent with the properties of the stamp and the substrate. We investigate three determinants of stamp performance: conformation to sinusoidal substrate topographies, distortion of material around stamp protrusions, and conformation to isolated spherical dust particles trapped between the stamp and the substrate. All simulation results are encapsulated in dimensionless models that can be applied to the efficient selection of stamp geometries, materials, and loading conditions. A particularly striking finding is that a stamp with a finite-thickness compliant coating bonded to a more rigid support can conform more closely to a trapped particle under a given load than a homogeneous stamp with the properties of the coating. This finding could be used to minimize the impact of particle defects on patterning processes.

Solid-state dewetting on curved substrates

Based on the thermodynamic variation to the free energy functional, we propose a sharp-interface model for simulating solid-state dewetting of thin films on rigid curved substrates in two dimensions. This model describes the interface evolution which occurs through surface diffusion-controlled mass transport and contact point migration along the curved substrate. Furthermore, the surface energy anisotropy is easily included into the model, and the contact point migration is explicitly described by the relaxed contact angle boundary condition. We implement the mathematical model by a semi-implicit parametric finite element method to study several interesting phenomena, such as "small" particle migration on curved substrates and templated solid-state dewetting on a pre-patterned substrate. Based on ample numerical simulations, we demonstrate that, the migration velocity of a "small" solid particle is proportional to the substrate curvature gradient $\hat{\kappa}'$ and inversely proportional to the square root of the area of the particle $\sqrt{A}$, and it decreases when the isotropic Young angle $\theta_i$ increases. In addition, we also observe four periodic categories of dewetting on a pre-patterned sinusoidal substrate. Our approach can provide a convenient and powerful tool to exploring how to produce well-organized nanoparticles by making use of template-assisted solid-state dewetting.

Devil's staircase and the absence of chaos in the dc- and ac-driven overdamped Frenkel-Kontorova model.

The devil's staircase structure arising from the complete mode locking of an entirely nonchaotic system, the overdamped dc+ac driven Frenkel-Kontorova model with deformable substrate potential, was observed. Even though no chaos was found, a hierarchical ordering of the Shapiro steps was made possible through the use of a previously introduced continued fraction formula. The absence of chaos, deduced here from Lyapunov exponent analyses, can be attributed to the overdamped character and the Middleton no-passing rule. A comparative analysis of a one-dimensional stack of Josephson junctions confirmed the disappearance of chaos with increasing dissipation. Other common dynamic features were also identified through this comparison. A detailed analysis of the amplitude dependence of the Shapiro steps revealed that only for the case of a purely sinusoidal substrate potential did the relative sizes of the steps follow a Farey sequence. For nonsinusoidal (deformed) potentials, the symmetry of the Stern-Brocot tree, depicting all members of particular Farey sequence, was seen to be increasingly broken, with certain steps being more prominent and their relative sizes not following the Farey rule.

Self-Powered Pressure Sensor with fully encapsulated 3D printed wavy substrate and highly-aligned piezoelectric fibers array

Near-field electrospinning (NFES) is capable of precisely deposit one-dimensional (1D) or two-dimensional (2D) highly aligned micro/nano fibers (NMFs) by electrically discharged a polymer solution. In this paper, a new integration of three-dimensional (3D) architectures of NFES electrospun polyvinylidene fluoride (PVDF) NMFs with the 3D printed topologically tailored substrate are demonstrated in a direct-write and in-situ poled manner, called wavy- substrate self-powered sensors (WSS). The fabrication steps are composed of the additive manufacture of 3D printed flexible and sinusoidal wavy substrate, metallization and NFES electrospun fibers in the 3D topology. This 3D architecture is capable of greatly enhancing the piezoelectric output. Finally, the proposed piezoelectrically integrated 3D architecture is applied to the self-powered sensors such as foot pressure measurement, human motion monitoring and finger-induced power generation. The proposed technique demonstrates the advancement of existing electrospinning technologies in constructing 3D structures and several promising applications for biomedical and wearable electronics.

Pattern-induced anchoring transitions in nematic liquid crystals

In this paper we revisit the problem of a nematic liquid crystal in contact with patterned substrates. The substrate is modelled as a periodic array of parallel infinite grooves of well-defined cross-section sculpted on a chemically homogeneous substrate which favours local homeotropic anchoring of the nematic. We consider three cases: a sawtooth, a crenellated and a sinusoidal substrate. We analyse this problem within the modified Frank–Oseen formalism. We argue that, for substrate periodicities much larger than the extrapolation length, the existence of different nematic textures with distinct far-field orientations, as well as the anchoring transitions between them, are associated with the presence of topological defects either on or close to the substrate. For the sawtooth and sinusoidal cases, we observe a homeotropic to planar anchoring transition as the substrate roughness increases. On the other hand, a homeotropic to oblique anchoring transition is observed for crenellated substrates. In this case, the anchoring phase diagram shows a complex dependence on the substrate roughness and substrate anchoring strength.

Effect of thickness and boundary conditions on the behavior of viscoelastic layers in sliding contact with wavy profiles

In this work, the sliding contact of viscoelastic layers of finite thickness on rigid sinusoidal substrates is investigated within the framework of Green's functions approach. The periodic Green's functions are determined by means of a novel formalism, which can be applied, in general, to either 2D and 3D viscoelastic periodic contacts, regardless of the contact geometry and boundary conditions.Specifically, two different configurations are considered here: a free layer with a uniform pressure applied on the top, and a layer rigidly confined on the upper boundary. It is shown that the thickness affects the contact behavior differently, depending on the boundary conditions. In particular, the confined layer exhibits increasing contact stiffness when the thickness is reduced, leading to higher loads for complete contact to occur. The free layer, instead, becomes more and more compliant as thickness is reduced.We find that, in partial contact, the layer thickness and the boundary conditions significantly affect the frictional behavior. In fact, at low contact penetrations, the confined layer shows higher friction coefficients compared to the free layer case; whereas, the scenario is reversed at large contact penetrations. Furthermore, for confined layers, the sliding speed related to the friction coefficient peak is shifted as the contact penetration increases. However, once full contact is established, the friction coefficient shows a unique behavior regardless of the layer thickness and boundary conditions.

Shapiro steps for skyrmion motion on a washboard potential with longitudinal and transverse ac drives

We numerically study the behavior of two-dimensional skyrmions in the presence of a quasi-one-dimensional sinusoidal substrate under the influence of externally applied dc and ac drives. In the overdamped limit, when both dc and ac drives are aligned in the longitudinal direction parallel to the direction of the substrate modulation, the velocity-force curves exhibit classic Shapiro step features when the frequency of the ac drive matches the washboard frequency that is dynamically generated by the motion of the skyrmions over the substrate, similar to previous observations in superconducting vortex systems. In the case of skyrmions, the additional contribution to the skyrmion motion from a non-dissipative Magnus force shifts the location of the locking steps to higher dc drives, and we find that the skyrmions move at an angle with respect to the direction of the dc drive. For a longitudinal dc drive and a perpendicular or transverse ac drive, the overdamped system exhibits no Shapiro steps; however, when a finite Magnus force is present we find pronounced transverse Shapiro steps along with complex two-dimensional periodic orbits of the skyrmions in the phase-locked regimes. Both the longitudinal and transverse ac drives produce locking steps whose widths oscillate with increasing ac drive amplitude. We examine the role of collective skyrmion interactions and find that additional fractional locking steps occur for both longitudinal and transverse ac drives. At higher skyrmion densities, the system undergoes a series of dynamical order-disorder transitions, with the skyrmions forming a moving solid on the phase locking steps and a fluctuating dynamical liquid in regimes between the steps.

Shapiro steps in the commensurate structures with integer value of the winding number

Abstract Dynamical mode locking phenomena and the appearance of Shapiro steps are studied in commensurate structures with integer values of winding number in the dc- and ac-driven overdamped Frenkel-Kontorova model. While in the standard case with sinusoidal substrate potential, the system reduces to the single particles model in which only harmonic steps exist and analytical form for the step size can be revealed, in the case of deformable potential, the presence of many degrees of freedom strongly influences the Shapiro steps. Whole series of subharmonic steps appear, and the two types of response functions, the one for the commensurate structures with odd and the one for the commensurate structures with even winding number have been observed.

Dependence of static friction force on stiffness and lubricant structure in a confined chain

We use a chain of harmonically interacting atoms confined between two sinusoidal substrate potentials in which the top substrate is driven by the driving force. This system is closely related to physical situations with confined lubricant films. The dependence of the static friction force on the system parameters such as the equilibrium spacing and the strength is presented. It is found that the better lubricant films are materials with larger interatomic interaction strength, and the lubricant structure is in the certain region.

Transport and diffusion properties of interacting colloidal particles in two-dimensional microchannels with a periodic potential.

We report a Brownian dynamics simulation study of a two-dimensional system of repulsive colloidal particles in a channel geometry with a sinusoidal substrate potential under influence of a constant driving. The effect of this driving on the structure, mobility, and diffusion is discussed as well as the appearance of kink and antikink solitons. The competing order principles of the hexagonal crystal structure, the period of the substrate, and the layering due to the confining walls can be either commensurable or incommensurable. The combination of those three leads to new effects. The simultaneous occurrence of kinks and antikinks can be observed, due to the energy difference between boundary- and midlanes, and similarities to the electron-hole conductivity in a semiconductor can be found.

Filling and wetting transitions on sinusoidal substrates: a mean-field study of the Landau–Ginzburg model

We study the interfacial phenomenology of a fluid in contact with a one-dimensional array of infinitely long grooves of sinusoidal section, characterized by the periodicity length L and amplitude A. The system is modelled by the Landau–Ginzburg–Wilson functional, with fluid-substrate couplings which control the wettability of the substrate. We investigate the filling and wetting phenomena within the mean-field approximation, and compare with the predictions of the macroscopic and interfacial Hamiltonian theories. For large values of L and under bulk coexistence conditions, we observe first-order filling transitions between dry (D) and partially filled (F) interfacial states, and wetting transitions between partially filled F and completely wet (W) interfacial states of the same order as for the flat substrate. Depending on the order of the wetting transition, the transition temperature is either shifted towards lower temperatures for first-order wetting or it coincides with the wetting temperature on the flat substrate for continuous wetting. On the other hand, if the groove height is of order of the correlation length, only wetting transitions between D and W states are observed under bulk coexistence conditions. For this case, the transition temperature shift obeys approximately Wenzel's phenomenological law if the substrate favors first-order wetting, but it remains unshifted for continuous wetting. The borderline between the small and large L regimes correspond to a D − F − W triple point if wetting is first-order, and a D − F critical point for continuous wetting. Beyond bulk coexistence conditions, filling and first-order wetting transitions continue into off-coexistence filling and prewetting lines, which end up at critical points. Our findings show that the macroscopic theory only describes accurately the filling transition close to bulk coexistence and large L, while microscopic structure of the fluid is essential to understand wetting and filling away from bulk coexistence.

Miniaturized pattern formation in elastic films cast on sinusoidally patterned substrates.

The various morphologies that are formed when van der Waals forces or electric field is induced between film cast on a sinusoidal substrate and in contact proximity with a contactor or electrode are studied. Remarkably smaller length scales are achieved (λc < 2.96h) than those obtained with films cast on flat substrates. With van der Waals interactions, the patterns are uniformly formed throughout the film but are not regularly ordered. When electric field is used at critical voltage, more ordered, localized patterns are formed at the zones of large local interaction strengths. When these patterns are evolved by increasing the applied voltage, coexistence of all three phases-cavities, stripes, and columns-is observed throughout the film. The localized patterns that are initially formed vary with the voltage applied and strongly dictate the phases of evolution. A patterned substrate/patterned contactor assembly can be made to operate like its unpatterned counterpart by making the interaction strength same everywhere and yet yield uniform, regularly ordered, highly miniaturized patterns. Such patterns are very useful in various applications like microfluidics; they are formed with great ease and can be morphologically tuned by tuning the externally applied electric field.

Role of primary bile salts in the regulation of sinusoidal substrate uptake in rat liver

Background Bile salts undergo enterohepatic circulation which is essential for bile salt homeostasis. From the biliary tract, they are excreted into the small intestine, absorbed into the blood and transported back to the liver. The sinusoidal uptake systems of the liver efficiently extract bile salts and other substrates from portal blood. In rat liver, these systems include Ntcp (sodium taurocholate cotransporting polypeptide) and the organic anion transporting polypeptides Oatp1a1, Oatp1a4 and Oatp1b2. While Ntcp represents the major basolateral uptake transporter for conjugated bile salts, the Oatps have broad substrate spectra including estrogenor leukotriene-conjugates. Their transport function is regulated by long-term and short-term mechanisms. Long-term adaptation of bile salt transporters involve changes at the level of gene expression and transporter degradation, while short-term regulation includes covalent transporter modifications, substrate availability and rapid endoand exocytosis of transporter-containing vesicles (reviewed in [1]). Ntcp as well as Oatp1a1 and Oatp1a4 underlie short-term control which has been demonstrated in several in vitro models. Hypoosmolarity or cAMP for instance increase the Ntcp-dependent bile salt uptake (increase of Vmax) within minutes by translocation of intracellular Ntcp to the plasma membrane [2,3]. In contrast, rapid clathrin-dependent endocytosis of Ntcp was demonstrated only recently by activation of PKC with phorbolesters [4,5]. However, to date in vivo-studies on short-term regulation of basolateral transporters are rare. Bile salt inflow to the liver may increase considerably under pathophysiological conditions or postprandial under physiological conditions [6]. To date, the interrelation between substrate load and transport activity is largely unknown. Therefore, the aim of this study was to investigate the role of primary bile salts in short-term feedback regulation of sinusoidal substrate uptake in perfused rat liver.