Erratum: Pairing-induced motion of source and inert particles driven by surface tension [Phys. Rev. E 106, 024604 (2022)]

This corrects the article DOI: 10.1103/PhysRevE.106.024604.

Mathematical modeling for the synchronization of two interacting active rotors

We investigate the synchronization of active rotors. A rotor is composed of a free-rotating arm with a particle that releases a surface-active chemical compound. It exhibits self-rotation due to the surface tension gradient originating from the concentration field of the surface-active compound released from the rotor. In a system with two active rotors, they should interact through the concentration field. Thus, the interaction between them does not depend only on the instantaneous positions, but also on the dynamics of the concentration field. By numerical simulations, we show that in-phase and antiphase synchronizations occur depending on the distance between the two rotors. The stability of the synchronization mode is analyzed based on phase reduction theorem through the calculation of the concentration field in the co-rotating frame with the active rotor. We also confirm that the numerical results meet the prediction by theoretical analyses.

New types of complex motion of a simple camphor boat

We discuss the motion of a rectangular camphor boat, considering the position of a camphor pill in relation to the boat's stern as the control parameter. The boat moves because the pill releases surface active molecules that decrease the surface tension and support the motion. We introduce a new experimental system in which the boat rotates on a long arm around the axis located at the centre of a Petri dish; thus, the motion is restricted to a circle and can be studied under stationary conditions for a long time. The experiments confirmed two previously reported modes of motion: continuous motion when the pill was located at the boat edge and pulsating (intermittent) motion if it was close to the boat centre (Suematsu et al., J. Phys. Chem. C, 2010, 114(21), 9876-9882). For intermediate pill locations, we observed a new, unreported type of motion characterised by oscillating speed (i.e. oscillating motion). Different modes of motion can be observed for the same pill location. The experimental results are qualitatively confirmed using a simple reaction-diffusion model of the boat evolution used in the above-mentioned paper.

Complexity and bifurcations in the motion of a self-propelled rectangle confined in a circular water chamber

We consider the motion of a self-propelled object of rectangular shape inside a circular water chamber. The mathematical model of self-motion includes equations for the orientation and location of the rectangle and reaction-diffusion equation with an effective diffusion coefficient for the time evolution of the surface concentration of active molecules. Numerical simulations of motion were performed for different values of the ratio between the supply rate S and the evaporation rate a of active molecules. Treating S₀ = S/a as a control parameter, we found the critical behavior in variables characterizing the trajectory and identified different types of motion. If the value of S₀ is small, the rectangle rests at the chamber center. For larger S₀, a reciprocal motion during which the rectangle passes through the center is observed. At yet higher supply rates, the star-polygonal motion appears, and the trajectory remains at a distance from the chamber center. In the experiments with a rectangle made of camphor-camphene-polypropylene plastic moving in a Petri dish, we observed the transition from the star-polygonal motion to the reciprocal motion in time. This transition can be understood on the basis of the developed model if we assume that the supply rate decreases in time.

Anomalous diffusion and transport by a reciprocal convective flow

Under low-Reynolds-number conditions, dynamics of convection and diffusion are usually considered separately because their dominant spatial and temporal scales are different, but cooperative effects of convection and diffusion can cause diffusion enhancement [Koyano et al., Phys. Rev. E 102, 033109 (2020)2470-004510.1103/PhysRevE.102.033109]. In this paper, such cooperative effects are investigated in detail. Numerical simulations based on the convection-diffusion equation revealed that anisotropic diffusion and net shift as well as diffusion enhancement occur under a reciprocal flow. Such anomalous diffusion and transport are theoretically derived by the analyses of the Langevin dynamics.

Pairing-induced motion of source and inert particles driven by surface tension

We experimentally and theoretically investigate systems with a pair of source and inert particles that interact through a concentration field. The experimental system comprises a camphor disk as the source particle and a metal washer as the inert particle. Both are floated on an aqueous solution of glycerol at various concentrations, where the glycerol modifies the viscosity of the aqueous phase. The particles form a pair owing to the attractive lateral capillary force. As the camphor disk spreads surface-active molecules at the aqueous surface, the camphor disk and metal washer move together, driven by the surface tension gradient. The washer is situated in the front of the camphor disk, keeping the distance constant during their motion, which we call a pairing-induced motion. The pairing-induced motion exhibited a transition between circular and straight motions as the glycerol concentration in the aqueous phase changed. Numerical calculations using a model that considers forces caused by the surface tension gradient and lateral capillary interaction reproduced the observed transition in the pairing-induced motion. Moreover, this transition agrees with the result of the linear stability analysis on the reduced dynamical system obtained by the expansion with respect to the particle velocity. Our results reveal that the effect of the particle velocity cannot be overlooked to describe the interaction through the concentration field.

Imperfect bifurcation in the rotation of a propeller-shaped camphor rotor

We investigated the bifurcation structure on the self-propelled motion of a camphor rotor at a water surface. The center of the camphor rotor was fixed by the axis, and it showed rotational motion around it. Due to the chiral asymmetry of its shape, the absolute values of the angular velocities in clockwise and counterclockwise directions were different. This asymmetry in the angular velocities implies an imperfect bifurcation. From the numerical simulation results, we discuss the condition for the occurrence of the imperfect bifurcation.

Diffusion enhancement in a levitated droplet via oscillatory deformation

Recent experimental results indicate that mixing is enhanced by a reciprocal flow induced inside a levitated droplet with an oscillatory deformation [T. Watanabe et al., Sci. Rep. 8, 10221 (2018)2045-232210.1038/s41598-018-28451-5]. Generally, reciprocal flow cannot convect the solutes in time average, and agitation cannot take place. In the present paper, we focus on the diffusion process coupled with the reciprocal flow. We theoretically derive that the diffusion process can be enhanced by the reciprocal flow, and the results are confirmed via numerical calculation of the over-damped Langevin equation with a reciprocal flow.

On a simple model that explains inversion of a self-propelled rotor under periodic stop-and-release-operations

We propose a simple mathematical model that describes the time evolution of a self-propelled object on a liquid surface using variables such as object location, surface concentration of active molecules, and hydrodynamic surface flow. The model is applied to simulate the time evolution of a rotor composed of a polygonal plate with camphor pills at its corners. We have qualitatively reproduced results of experiments, in which the inversion of rotational direction under periodic stop-and-release-operations was investigated. The model correctly describes the probability of the inversion as a function of the duration of the phase when the rotor is stopped. Moreover, the model allows to introduce the rotor asymmetry unavoidable in real experiments and study its influence on the studied phenomenon. Our numerical simulations have revealed that the probability of the inversion of rotational direction is determined by the competition among the transport of the camphor molecules by the flow, the intrinsic asymmetry of the rotor, and the noise amplitude.

Start of Micrometer-Sized Oil Droplet Motion through Generation of Surfactants

Self-propelled motion of micrometer-sized oil droplets in surfactant solution has drawn much attention as an example of nonlinear life-like dynamics under far-from-equilibrium conditions. The driving force of this motion is thought to be induced by Marangoni convection based on heterogeneity in the interfacial tension at the droplet surface. Here, to clarify the required conditions for the self-propelled motion of oil droplets, we have constructed a chemical system, where oil droplet motion is induced by the production of 1,2,3-triazole-containing surfactants through the Cu-catalyzed azide-alkyne cycloaddition reaction. From the results of the visualization and analysis of flow fields around the droplet, the motion of the droplets could be attributed to the formation of flow fields, which achieved sufficient strength caused by the in situ production of surfactants at the droplet surface.

Rotational motion of a camphor disk in a circular region

In a two-dimensional axisymmetric system, the system symmetry allows rotational or oscillatory motion as stable stationary motion for a symmetric self-propelled particle. In the present paper, we studied the motion of a camphor disk confined in a two-dimensional circular region. By reducing the mathematical model describing the dynamics of the motion of a camphor disk and the concentration field of camphor molecules on a water surface, we analyzed the reduced equations around a bifurcation point where the rest state at the center of the system becomes unstable. As a result, we found that rotational motion is stably realized through the double-Hopf bifurcation from the rest state. The theoretical results were confirmed by numerical calculation and corresponded well to the experimental results.

Bifurcation in the angular velocity of a circular disk propelled by symmetrically distributed camphor pills

We studied rotation of a disk propelled by a number of camphor pills symmetrically distributed at its edge. The disk was put on a water surface so that it could rotate around a vertical axis located at the disk center. In such a system, the driving torque originates from surface tension difference resulting from inhomogeneous surface concentration of camphor molecules released from the pills. Here, we investigated the dependence of the stationary angular velocity on the disk radius and on the number of pills. The work extends our previous study on a linear rotor propelled by two camphor pills [Y. Koyano et al., Phys. Rev. E 96, 012609 (2017)]. It was observed that the angular velocity dropped to zero after a critical number of pills was exceeded. Such behavior was confirmed by a numerical model of time evolution of the rotor. The model predicts that, for a fixed friction coefficient, the speed of pills can be accurately represented by a function of the linear number density of pills. We also present bifurcation analysis of the conditions at which the transition between a standing and a rotating disk appears.

Publisher's Note: Oscillatory motion of a camphor grain in a one-dimensional finite region [Phys. Rev. E 94, 042215 (2016)]

This corrects the article DOI: 10.1103/PhysRevE.94.042215.

Relationship between the size of a camphor-driven rotor and its angular velocity

We consider a rotor made of two camphor disks glued below the ends of a plastic stripe. The disks are floating on a water surface and the plastic stripe does not touch the surface. The system can rotate around a vertical axis located at the center of the stripe. The disks dissipate camphor molecules. The driving momentum comes from the nonuniformity of surface tension resulting from inhomogeneous surface concentration of camphor molecules around the disks. We investigate the stationary angular velocity as a function of rotor radius ℓ. For large ℓ the angular velocity decreases for increasing ℓ. At a specific value of ℓ the angular velocity reaches its maximum and, for short ℓ it rapidly decreases. Such behavior is confirmed by a simple numerical model. The model also predicts that there is a critical rotor size below which it does not rotate. Within the introduced model we analyze the type of this bifurcation.

Unidirectional motion of a camphor disk on water forced by interactions between surface camphor concentration and dynamically changing boundaries

Dynamically changing boundaries induce unidirectional motion of a camphor disk on water, which is regarded as a signal diode.

Oscillatory motion of a camphor grain in a one-dimensional finite region

The motion of a self-propelled particle is affected by its surroundings, such as boundaries or external fields. In this paper, we investigated the bifurcation of the motion of a camphor grain, as a simple actual self-propelled system, confined in a one-dimensional finite region. A camphor grain exhibits oscillatory motion or remains at rest around the center position in a one-dimensional finite water channel, depending on the length of the water channel and the resistance coefficient. A mathematical model including the boundary effect is analytically reduced to an ordinary differential equation. Linear stability analysis reveals that the Hopf bifurcation occurs, reflecting the symmetry of the system.

Hydrodynamic collective effects of active proteins in biological membranes

Lipid bilayers forming biological membranes are known to behave as viscous two-dimensional fluids on submicrometer scales; usually they contain a large number of active protein inclusions. Recently, it was shown [A. S. Mikhailov and R. Kapral, Proc. Natl. Acad. Sci. USA 112, E3639 (2015)PNASA60027-842410.1073/pnas.1506825112] that such active proteins should induce nonthermal fluctuating lipid flows leading to diffusion enhancement and chemotaxislike drift for passive inclusions in biomembranes. Here, a detailed analytical and numerical investigation of such effects is performed. The attention is focused on the situations when proteins are concentrated within lipid rafts. We demonstrate that passive particles tend to become attracted by active rafts and are accumulated inside them.

Oscillation of a rotating levitated droplet: Analysis with a mechanical model

A droplet of millimeter-to-centimeter scale can exhibit electrostatic levitation, and such levitated droplets can be used for the measurement of the surface tension of the liquids by observing the characteristic frequency of oscillatory deformation. In the present study, a simple mechanical model is proposed by considering a single mode of oscillation in the ellipsoidal deformation of a levitated rotating droplet. By measuring the oscillation frequency with respect to the rotational speed and oscillation amplitude, it is expected that the accuracy of the surface tension measurement could be improved. Using the proposed model, the dependences of the characteristic frequency of oscillatory deformation and the averaged aspect ratio are calculated with respect to the rotational angular velocity of a rotating droplet. These dependences are found to be consistent with the experimental observations.

Chondrocyte-derived ezrin-like domain containing protein (CDEP), a rho guanine nucleotide exchange factor, is inducible in chondrocytes by parathyroid hormone and cyclic AMP and has transforming activity in NIH3T3 cells

OBJECTIVE

The purpose of this study is to investigate stage- and hormone-dependent expression of chondrocyte-derived ezrin-like domain containing protein (CDEP), a putative guanine nucleotide exchange factor (GEF) for Rho in chondrocytes, and demonstrate the guanine nucleotide exchange activity of this protein in vitro, as well as the transforming activity in NIH3T3 cells.

METHODS

The expression of CDEP mRNA in growth plate chondrocytes in vivo and in vitro was examined by RT-PCR Southern analysis. The guanine nucleotide exchange activity was determined using a recombinant CDEP peptide containing the DH and PH domains in Sf9 cell lysates. The transforming activity was examined using NIH3T3 cells transiently transfected with a truncated CDEP cDNA.

RESULTS

CDEP mRNA was expressed at the highest level in the hypertrophic (terminal) stage of chondrocytes in vivoand in vitro. Parathyroid hormone (PTH) elicited a biphasic increase of CDEP mRNA in chondrocytes. The CDEP mRNA level increased within 1 h, then decreased nearly to the control level at 3 h. Thereafter the mRNA level started to increase at 6 h, reaching a plateau at 24 h. Dibutyryl cyclic AMP had a similar effect on CDEP expression in chondrocytes. The dissociation of [3H]GDP from RhoA was stimulated dose-dependently by Sf9 cell lysates containing the CDEP peptide. Furthermore, transfection of a truncated CDEP cDNA induced focus formation in NIH3T3 cultures.

CONCLUSIONS

CDEP is a novel GEF for Rho family GTPases with the transforming activity. CDEP may play a role in mediating or modulating the action of cAMP-elevating hormones on maturing chondrocytes.

Temperature dependence of chromatic dispersion in various types of optical fiber

The temperature dependence of chromatic dispersion is examined for various types of fiber. Its coefficient is found to depend strongly on the dispersion slope. Dispersion-flattened fiber has a significantly low coefficient of -0.0005(ps/nm/km)/ degrees C , compared with -0.0038(ps/nm/km)/ degrees C for large-core nonzero dispersion-shifted fiber. Transmission lines with low dispersion slopes consisting of pure silica core fiber and dispersion-compensating fiber also exhibit low coefficients of less than -0.001(ps/nm/km)/ degrees C because of their compensating effects.

Surgical management of congenital permanent dislocation of the patella in nail patella syndrome by Stanisavljevic procedure

We report a patient with nail patella syndrome associated with congenital permanent dislocation of the patella successfully operated on using a modified Stanisavljevic method. The patient, a 26-year-old woman, complained of inability to completely extend her right knee joint. She had occasionally experienced the "giving way" phenomenon since childhood, but she had not received any treatment since birth. Physical examination showed that all fingernails were deformed, with longitudinal striations, while the lunules were of an abnormal triangular shape or were missing. Both patellae were palpably hypoplastic, with the right patella dislocated laterally, and the knee had an extension lag of 90 degrees. Thigh and leg muscle were slightly underdeveloped, but quadriceps muscle contraction was good. Several radiographs were taken and they showed bilateral iliac horns and hypoplasia of the bilateral humero-radial joints and of both patellae, and complete dislocation of the right patella. We employed the Stanisavljevic procedure for the reduction of the patella, with Z-lengthening of the rectus femoris and medial translocation of the tibial tuberosity. Four years after the operation, a 30-degree extension lag still exists in the right knee, but the treatment resulted in stable alignment of the quadriceps mechanism, and notably improved gait appearance.

Molecular cloning and characterization of CDEP, a novel human protein containing the ezrin-like domain of the band 4.1 superfamily and the Dbl homology domain of Rho guanine nucleotide exchange factors

A cDNA for a novel human protein named CDEP was cloned using the subtractive hybridization method between dedifferentiated cartilage cells and overtly differentiated cartilage cells. CDEP cDNA contained an open reading frame encoding 1,045 amino acids in a total length of 3.4 kb. The deduced amino acid sequence revealed that a single polypeptide contained the ezrin-like domain, which is found in cytoskeleton-associated proteins of the band 4.1 superfamily, and the Dbl homology (DH) and pleckstrin homology (PH) domains, which are conserved in the Rho GEF (guanine nucleotide exchange factor) family. Northern blot analysis demonstrated that CDEP mRNA was expressed not only in the differentiated chondrocytes but also in various fetal and adult tissues. Since members of the band 4.1 superfamily and the Rho GEF family are crucial for microfilament organization, the novel protein CDEP may be involved in the adhesion, proliferation, and differentiation of some cell types including chondrocytes via changes in the cytoskeleton.

Molecular characterization of the novel basic helix-loop-helix protein DEC1 expressed in differentiated human embryo chondrocytes

The differentiation of human embryo chondrocytes was markedly induced by the addition of Bt2cAMP to the culture medium. Using this culture system, a novel human cDNA for a basic helix-loop-helix (bHLH) protein (named DEC1) expressed primarily in the chondrocytes in response to Bt2cAMP was cloned by the subtractive hybridization method. DEC1 protein consists of 412 amino acids and exhibits structural similarities to the mammalian HES family, Drosophila hairy, and Enhancer of split m7 in the bHLH region. Northern blot analysis showed that DEC1 mRNA was expressed in various tissues including the cartilage, lung, spleen, and intestine, but not in the brain. These findings suggest that the bHLH factor DEC is involved in the control of cell differentiation in several tissues including cartilage.

Analysis of 3H-proline-labeled protein by rapid filtration in multiwell plates for the study of collagen metabolism

Quantitative and qualitative analysis of cell cultures labeled with 3H-proline for monitoring collagen synthesis is time-consuming and occasionally generates large quantities of radioactive waste. This present work describes the application of a microwell filtration system for the analysis of collagen metabolism in chondrocytes. It is based on trichloroacetic acid (TCA) precipitation of 3H-proline-labeled proteins onto polyvinylidene difluoride membranes fitted in a 96-well plate and subsequent analysis of precipitated proteins by liquid scintillation counting, amino acid analysis and sodium dodecyl sulfate (SDS) gel electrophoresis. This method allows for the initial processing of 96 samples within 2 h, has high sensitivity and accuracy (linearity > or = 200 cpm/sample) for quantitative measurements and a capacity of up to 10 micrograms collagen/microwell. The ratio of the radioactive protein collected by this filtration assay compared to that collected by molecular sieve chromatography on Sephadex G-25 was linear over a broad range, indicating full compatibility of data and a high reproducibility for both assay systems. The quality of protein separation by SDS-polyacrylamide gel electrophoresis (PAGE) from samples obtained by the filtration assay and by dialysis was virtually identical. These features make the assay particularly suited for pulse-chase experiments and for monitoring protein degradation.

[Do calcium and zinc ions influence matrix molecule synthesis of chondrocytes?]

The experiments described here tested the effect of various calcium (Ca) and Zinc (Zn) concentrations on cell proliferation and matrix molecule synthesis of fetal and adult bovine chondrocytes in monolayer cultures. Levels of Ca < 0.2 mM in a culture medium or the addition of Zn (0.1-50 microM) selectively promoted the production of collagen but did not affect significantly synthesis of proteoglycans. No change in proliferation of fetal and adult chondrocytes could be observed. In contrast 10 mM Ca promoted the hypertrophic differentiation of chondrocytes (e.g. expression of collagen type X). The results are related to calcium channel configurations in chondrocytes in the discussion.

Collagen and proteoglycan production by bovine fetal and adult chondrocytes under low levels of calcium and zinc ions

The experiments described herein tested the effects of CaCl2 and ZnCl2, added at various concentrations in the culture medium, upon the synthesis of collagen and proteoglycan by adult and fetal (articular, epiphyseal and hypertrophic) bovine chondrocytes maintained in high density multilayer cultures. CaCl2 concentrations below 0.5 mM or the addition of 1-50 microM ZnCl2 to the medium selectively promoted the production of collagen by all four populations of chondrocytes but had no effect on fibroblasts. Further, these changes had no statistically significant effect on the incorporation of 35S-sulfate into macromolecules or on the synthesis of gelatinase A, measured by gelatin zymography. The addition of CaCl2 and ZnCl2 at these concentrations did not result in a change in the relative proportion of non-crosslinked 3H-collagen molecules (synthesized in the presence of beta-aminopropionitrile) partitioning in the cell layer and medium compartments, and did not appreciably alter the pattern of collagens synthesized by any of the cell populations. The hypertrophic cells synthesized high levels of collagen type X in the presence as well as absence of exogenously added cations. However, CaCl2 at 10 mM caused a marked upregulation of collagen type X synthesis by a preparation of chondrocytes derived from the entire growth plate, consistent with the view that calcium at that concentration stimulated the differentiation of some of the cells into hypertrophic chondrocytes.