Clustering of the K⁺ channel GORK of Arabidopsis parallels its gating by extracellular K⁺

GORK is the only outward-rectifying Kv-like K<sup>+</sup> channel expressed in guard cells. Its activity is tightly regulated to facilitate K<sup>+</sup> efflux for stomatal closure and is elevated in ABA in parallel with suppression of the activity of the inward-rectifying K<sup>+</sup> channel KAT1. Whereas the population of KAT1 is subject to regulated traffic to and from the plasma membrane, nothing is known about GORK, its distribution and traffic in vivo. We have used transformations with fluorescently-tagged GORK to explore its characteristics in tobacco epidermis and Arabidopsis guard cells. These studies showed that GORK assembles in puncta that reversibly dissociated as a function of the external K<sup>+</sup> concentration. Puncta dissociation parallelled the gating dependence of GORK, the speed of response consistent with the rapidity of channel gating response to changes in the external ionic conditions. Dissociation was also suppressed by the K<sup>+</sup> channel blocker Ba<sup>2+</sup>. By contrast, confocal and protein biochemical analysis failed to uncover substantial exo- and endocytotic traffic of the channel. Gating of GORK is displaced to more positive voltages with external K<sup>+</sup>, a characteristic that ensures the channel facilitates only K<sup>+</sup> efflux regardless of the external cation concentration. GORK conductance is also enhanced by external K<sup>+</sup> above 1 mM. We suggest that GORK clustering in puncta is related to its gating and conductance, and reflects associated conformational changes and (de)stabilisation of the channel protein, possibly as a platform for transmission and coordination of channel gating in response to external K<sup>+</sup>

Exploring emergent properties in cellular homeostasis using OnGuard to model K+ and other ion transport in guard cells

It is widely recognized that the nature and characteristics of transport across eukaryotic membranes are so complex as to defy intuitive understanding. In these circumstances, quantitative mathematical modeling is an essential tool, both to integrate detailed knowledge of individual transporters and to extract the properties emergent from their interactions. As the first, fully integrated and quantitative modeling environment for the study of ion transport dynamics in a plant cell, OnGuard offers a unique tool for exploring homeostatic properties emerging from the interactions of ion transport, both at the plasma membrane and tonoplast in the guard cell. OnGuard has already yielded detail sufficient to guide phenotypic and mutational studies, and it represents a key step toward ‘reverse engineering’ of stomatal guard cell physiology, based on rational design and testing in simulation, to improve water use efficiency and carbon assimilation. Its construction from the HoTSig libraries enables translation of the software to other cell types, including growing root hairs and pollen. The problems inherent to transport are nonetheless challenging, and are compounded for those unfamiliar with conceptual ‘mindset’ of the modeler. Here we set out guidelines for the use of OnGuard and outline a standardized approach that will enable users to advance quickly to its application both in the classroom and laboratory. We also highlight the uncanny and emergent property of OnGuard models to reproduce the ‘communication’ evident between the plasma membrane and tonoplast of the guard cell

The Gradient Flow of O'Hara's Knot Energies

Jun O'Hara invented a family of knot energies $E^{j,p}$, $j,p \in (0, \infty)$. We study the negative gradient flow of the sum of one of the energies $E^\alpha = E^{\alpha,1}$, $\alpha \in (2,3)$, and a positive multiple of the length. Showing that the gradients of these knot energies can be written as the normal part of a quasilinear operator, we derive short time existence results for these flows. We then prove long time existence and convergence to critical points.Comment: 45 page

Anion channel sensitivity to cytosolic organic acids implicates a central role for oxaloacetate in integrating ion flux with metabolism in stomatal guard cells

Stomatal guard cells play a key role in gas exchange for photosynthesis and in minimizing transpirational water loss from plants by opening and closing the stomatal pore. The bulk of the osmotic content driving stomatal movements depends on ionic fluxes across both the plasma membrane and tonoplast, the metabolism of organic acids, primarily Mal (Imitate), and its accumulation and loss. Anion channels at the plasma membrane are thought to comprise a major pathway for Mal efflux during stomatal closure, implicating their key role in linking solute flux with metabolism. Nonetheless, little is known of the regulation of anion channel current (I(Cl)) by cytosolic Mal or its immediate metabolite OAA (oxaloacetate). In the present study, we have examined the impact of Mal, OAA and of the monocarboxylic acid anion acetate in guard cells of Vicia faba L. and report that all three organic acids affect I(Cl), but with markedly different characteristics and sidedness to their activities. Most prominent was a suppression of I(Cl) by OAA within the physiological range of concentrations found in vivo. These findings indicate a capacity for OAA to co-ordinate organic acid metabolism with I(Cl), through the direct effect of organic acid pool size. The findings of the present study also add perspective to in vivo recordings using acetate-based electrolytes

Stationary Points of O'Hara's Knot Energies

In this article we study the regularity of stationary points of the knot energies $E^\alpha$ introduced by O'Hara in the range $\alpha \in (2,3)$. In a first step we prove that $E^\alpha$ is $C^1$ on the set of all regular embedded closed curves belonging to $H^{(\alpha +1)/2,2}$ and calculate its derivative. After that we use the structure of the Euler-Lagrange equation to study the regularity of stationary points of $E^\alpha$ plus a positive multiple of the length. We show that stationary points of finite energy are of class $C^\infty$ - so especially all local minimizers of $E^\alpha$ among curves with fixed length are smooth.Comment: Corrected typo