In this letter we present an experimental study of the collective dipole oscillation of a spin-orbit coupled Bose-Einstein condensate in a harmonic trap. Dynamics of the center-of-mass dipole oscillation is studied in a broad parameter region, as a function of spin-orbit coupling parameters as well as oscillation amplitude. Anharmonic properties beyond effective-mass approximation are revealed, such as amplitude-dependent frequency and finite oscillation frequency at place with divergent effective mass. These anharmonic behaviors agree quantitatively with variational wave-function calculations. Moreover, we experimentally demonstrate a unique feature of spin-orbit coupled system predicted by a sum-rule approach, stating that spin polarization susceptibility-a static physical quantity-can be measured via dynamics of dipole oscillation. The divergence of polarization susceptibility is observed at the quantum phase transition that separates magnetic nonzero-momentum condensate from nonmagnetic zero-momentum phase. The good agreement between the experimental and theoretical results provides a bench mark for recently developed theoretical approaches.Many interesting quantum phases can emerge in solid state materials when electrons are placed in a strong magnetic field or possess strong spin-orbit (SO) coupling, such as the fractional quantum Hall effect [1] and the topological insulator [2]. In cold atom systems, albeit neutral atoms have neither charges nor SO coupling, the recent exciting experimental progress demonstrates that artificial gauge potentials can be synthesized in laboratory by laser control technique [3][4][5][6][7][8][9][10]. Synthetic gauge potential is becoming a powerful tool for simulating real materials with cold atoms. Moreover, the system of SO coupled bosons does not have an analogy in conventional condensed matter systems, and can exhibit many novel phases [11] such as striped superfluid phase [12,13] and half vortex phase [14][15][16][17].Collective excitations play an important role in studying physical properties of trapped atomic Bose-Einstein condensates (BEC) and degenerate Fermi gases. Collective dipole oscillation is a center-of-mass motion of all atoms. For a conventional condensate, the dipole oscillation is trivial: the frequency is just the harmonictrap frequency, independent of oscillation amplitude and interatomic interaction. This is known as Kohn theorem [18,19]. For a SO coupled condensate, however, it was found [4] that the dipole-oscillation frequency deviates from the trap frequency and the experimental data thereby can be explained by effective-mass approximation. Recently, much theoretical effort has been taken to understand dynamics of a SO coupled BEC [20][21][22][23][24][25], and many predicted unconventional properties remain to be experimentally explored. In particular, the so-called sum-rule approach predicts [25] a unique feature of SO coupled condensate: spin polarization susceptibility-a static physical quantity-can be measured via dynamics of dipole oscillatio...

BackgroundLight plays a key role in multiple plant developmental processes. It has been shown that root development is modulated by shoot-localized light signaling and requires shoot-derived transport of the plant hormone, auxin. However, the mechanism by which light regulates root development is not largely understood. In plants, the endogenous auxin, indole-3-acetic acid, is directionally transported by plasma-membrane (PM)-localized auxin influx and efflux carriers in transporting cells. Remarkably, the auxin efflux carrier PIN proteins exhibit asymmetric PM localization, determining the polarity of auxin transport. Similar to PM-resident receptors and transporters in animal and yeast cells, PIN proteins undergo constitutive cycling between the PM and endosomal compartments. Auxin plays multiple roles in PIN protein intracellular trafficking, inhibiting PIN2 endocytosis at some concentrations and promoting PIN2 degradation at others. However, how PIN proteins are turned over in plant cells is yet to be addressed.Methodology and Principle FindingsUsing laser confocal scanning microscopy, and physiological and molecular genetic approaches, here, we show that in dark-grown seedlings, the PM localization of auxin efflux carrier PIN2 was largely reduced, and, in addition, PIN2 signal was detected in vacuolar compartments. This is in contrast to light-grown seedlings where PIN2 was predominantly PM-localized. In light-grown plants after shift to dark or to continuous red or far-red light, PIN2 also accumulated in vacuolar compartments. We show that PIN2 vacuolar targeting was derived from the PM via endocytic trafficking and inhibited by HY5-dependent light signaling. In addition, the ubiquitin 26S proteasome is involved in the process, since its inhibition by mutations in COP9 and a proteasome inhibitor MG132 impaired the process.Conclusions and SignificanceCollectively, our data indicate that light plays an essential role in PIN2 intracellular trafficking, promoting PM-localization in the presence of light and, on the other hand, vacuolar targeting for protein degradation in the absence of light. Based on these results, we postulate that light regulation of root development is mediated at least in part by changes in the intracellular distribution of auxin efflux carriers, PIN proteins, in response to the light environment.

Plant clathrin-mediated membrane trafficking is involved in many developmental processes as well as in responses to environmental cues. Previous studies have shown that clathrin-mediated endocytosis of the plasma membrane (PM) auxin transporter PIN-FORMED1 is regulated by the extracellular auxin receptor AUXIN BINDING PROTEIN1 (ABP1). However, the mechanisms by which ABP1 and other factors regulate clathrin-mediated trafficking are poorly understood. Here, we applied a genetic strategy and time-resolved imaging to dissect the role of clathrin light chains (CLCs) and ABP1 in auxin regulation of clathrin-mediated trafficking in Arabidopsis thaliana. Auxin was found to differentially regulate the PM and trans-Golgi network/early endosome (TGN/EE) association of CLCs and heavy chains (CHCs) in an ABP1-dependent but TRANSPORT INHIBITOR RESPONSE1/AUXIN-BINDING F-BOX PROTEIN (TIR1/AFB)-independent manner. Loss of CLC2 and CLC3 affected CHC membrane association, decreased both internalization and intracellular trafficking of PM proteins, and impaired auxin-regulated endocytosis. Consistent with these results, basipetal auxin transport, auxin sensitivity and distribution, and root gravitropism were also found to be dramatically altered in clc2 clc3 double mutants, resulting in pleiotropic defects in plant development. These results suggest that CLCs are key regulators in clathrin-mediated trafficking downstream of ABP1-mediated signaling and thus play a critical role in membrane trafficking from the TGN/EE and PM during plant development.

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The PIN family of auxin efflux transporters exhibit polar plasma membrane (PM) localization and play a key role in auxin gradient-mediated developmental processes. Auxin inhibits PIN2 endocytosis and promotes its PM localization. However, the underlying mechanisms remain elusive. Here, we show that the inhibitory effect of auxin on PIN2 endocytosis was impaired in SCF TIR1/AFB auxin signaling mutants. Similarly, reducing membrane sterols impaired auxin inhibition of PIN2 endocytosis. Gas chromatography-mass spectrometry analyses indicate that membrane sterols were significantly reduced in SCF TIR1/AFB mutants, supporting a link between membrane sterols and auxin signaling in regulating PIN2 endocytosis. We show that auxin promoted PIN2 recycling from endosomes to the PM and increased PIN2 steady state levels in the PM fraction. Furthermore, we show that the positive effect of auxin on PIN2 levels in the PM was impaired by inhibiting membrane sterols or auxin signaling. Consistent with this, the sterol biosynthetic mutant fk-J79 exhibited pronounced defects in primary root elongation and gravitropic response. Our data collectively indicate that, although there are distinct processes involved in endocytic regulation of specific PM-resident proteins, the SCF TIR1/AFB -dependent processes are required for auxin regulation of endocytosis, recycling, and PM accumulation of the auxin efflux transporter PIN2 in Arabidopsis thaliana.