Kaare Hartvig Jensen

Polygons on a Rotating Fluid Surface

We report a novel and spectacular instability of a fluid surface in a rotating system. In a flow driven by rotating the bottom plate of a partially filled, stationary cylindrical container, the shape of the free surface can spontaneously break the axial symmetry and assume the form of a polygon rotating rigidly with a speed different from that of the plate. With water, we have observed polygons with up to 6 corners. It has been known for many years that such flows are prone to symmetry breaking, but apparently the polygonal surface shapes have never been observed. The creation of rotating internal waves in a similar setup was observed for much lower rotation rates, where the free surface remains essentially flat [J. M. Lopez, J. Fluid Mech. 502, 99 (2004). We speculate that the instability is caused by the strong azimuthal shear due to the stationary walls and that it is triggered by minute wobbling of the rotating plate.

Testing the Münch hypothesis of long distance phloem transport in plants

Long distance transport in plants occurs in sieve tubes of the phloem. The pressure flow hypothesis introduced by Ernst Münch in 1930 describes a mechanism of osmotically generated pressure differentials that are supposed to drive the movement of sugars and other solutes in the phloem, but this hypothesis has long faced major challenges. The key issue is whether the conductance of sieve tubes, including sieve plate pores, is sufficient to allow pressure flow. We show that with increasing distance between source and sink, sieve tube conductivity and turgor increases dramatically in Ipomoea nil. Our results provide strong support for the Münch hypothesis, while providing new tools for the investigation of one of the least understood plant tissues. DOI: http://dx.doi.org/10.7554/eLife.15341.001

Phloem unloading in Arabidopsis roots is convective and regulated by the phloem-pole pericycle.

In plants, a complex mixture of solutes and macromolecules is transported by the phloem. Here, we examined how solutes and macromolecules are separated when they exit the phloem during the unloading process. We used a combination of approaches (non-invasive imaging, 3D-electron microscopy, and mathematical modelling) to show that phloem unloading of solutes in Arabidopsis roots occurs through plasmodesmata by a combination of mass flow and diffusion (convective phloem unloading). During unloading, solutes and proteins are diverted into the phloem-pole pericycle, a tissue connected to the protophloem by a unique class of ‘funnel plasmodesmata’. While solutes are unloaded without restriction, large proteins are released through funnel plasmodesmata in discrete pulses, a phenomenon we refer to as ‘batch unloading’. Unlike solutes, these proteins remain restricted to the phloem-pole pericycle. Our data demonstrate a major role for the phloem-pole pericycle in regulating phloem unloading in roots. DOI: http://dx.doi.org/10.7554/eLife.24125.001

Slower phloem transport in gymnosperm trees can be attributed to higher sieve element resistance

In trees, carbohydrates produced in photosynthesizing leaves are transported to roots and other sink organs over distances of up to 100 m inside a specialized transport tissue, the phloem. Angiosperm and gymnosperm trees have a fundamentally different phloem anatomy with respect to cell size, shape and connectivity. Whether these differences have an effect on the physiology of carbohydrate transport, however, is not clear. A meta-analysis of the experimental data on phloem transport speed in trees yielded average speeds of 56 cm h(-1) for angiosperm trees and 22 cm h(-1) for gymnosperm trees. Similar values resulted from theoretical modeling using a simple transport resistance model. Analysis of the model parameters clearly identified sieve element (SE) anatomy as the main factor for the significantly slower carbohydrate transport speed inside the phloem in gymnosperm compared with angiosperm trees. In order to investigate the influence of SE anatomy on the hydraulic resistance, anatomical data on SEs and sieve pores were collected by transmission electron microscopy analysis and from the literature for 18 tree species. Calculations showed that the hydraulic resistance is significantly higher in the gymnosperm than in angiosperm trees. The higher resistance is only partially offset by the considerably longer SEs of gymnosperms.

Passive phloem loading and long-distance transport in a synthetic tree-on-a-chip

Vascular plants rely on differences in osmotic pressure to export sugars from regions of synthesis (mature leaves) to sugar sinks (roots, fruits). In this process, known as Münch pressure flow, the loading of sugars from photosynthetic cells to the export conduit (the phloem) is crucial, as it sets the pressure head necessary to power long-distance transport. Whereas most herbaceous plants use active mechanisms to increase phloem sugar concentration above that of the photosynthetic cells, in most tree species, for which transport distances are largest, loading seems, counterintuitively, to occur by means of passive symplastic diffusion from the mesophyll to the phloem. Here, we use a synthetic microfluidic model of a passive loader to explore the non-linear dynamics that arise during export and determine the ability of passive loading to drive long-distance transport. We first demonstrate that in our device, the phloem concentration is set by the balance between the resistances to diffusive loading from the source and convective export through the phloem. Convection-limited export corresponds to classical models of Münch transport, where the phloem concentration is close to that of the source; in contrast, diffusion-limited export leads to small phloem concentrations and weak scaling of flow rates with hydraulic resistance. We then show that the effective regime of convection-limited export is predominant in plants with large transport resistances and low xylem pressures. Moreover, hydrostatic pressures developed in our synthetic passive loader can reach botanically relevant values as high as 10 bars. We conclude that passive loading is sufficient to drive long-distance transport in large plants, and that trees are well suited to take full advantage of passive phloem loading strategies.

Measurement of flow velocity and inference of liquid viscosity in a microfluidic channel by fluorescence photobleaching.

We present a simple, noninvasive method for simultaneous measurement of flow velocity and inference of liquid viscosity in a microfluidic channel. We track the dynamics of a sharp front of photobleached fluorescent dye using a confocal microscope and measure the intensity at a single point downstream of the initial front position. We fit an exact solution of the advection diffusion equation to the fluorescence intensity recovery curve to determine the average flow velocity and the diffusion coefficient of the tracer dye. The dye diffusivity is correlated to solute concentration to infer rheological properties of the liquid. This technique provides a simple method for simultaneous elucidation of flow velocity and liquid viscosity in microchannels.

Stomatal design principles in synthetic and real leaves

Stomata are portals in plant leaves that control gas exchange for photosynthesis, a process fundamental to life on Earth. Gas fluxes and plant productivity depend on external factors such as light, water and CO2 availability and on the geometrical properties of the stoma pores. The link between stoma geometry and environmental factors has informed a wide range of scientific fields—from agriculture to climate science, where observed variations in stoma size and density are used to infer prehistoric atmospheric CO2 content. However, the physical mechanisms and design principles responsible for major trends in stomatal patterning are not well understood. Here, we use a combination of biomimetic experiments and theory to rationalize the observed changes in stoma geometry. We show that the observed correlations between stoma size and density are consistent with the hypothesis that plants favour efficient use of space and maximum control of dynamic gas conductivity, and that the capacity for gas exchange in plants has remained constant over at least the last 325 Myr. Our analysis provides a new measure to gauge the relative performance of species based on their stomatal characteristics.

Maintenance of carbohydrate transport in tall trees

Trees present a critical challenge to long-distance transport because as a tree grows in height and the transport pathway increases in length, the hydraulic resistance of the vascular tissue should increase. This has led many to question whether trees can rely on a passive transport mechanism to move carbohydrates from their leaves to their roots. Although species that actively load sugars into their phloem, such as vines and herbs, can increase the driving force for transport as they elongate, it is possible that many trees cannot generate high turgor pressures because they do not use transporters to load sugar into the phloem. Here, we examine how trees can maintain efficient carbohydrate transport as they grow taller by analysing sieve tube anatomy, including sieve plate geometry, using recently developed preparation and imaging techniques, and by measuring the turgor pressures in the leaves of a tall tree in situ. Across nine deciduous species, we find that hydraulic resistance in the phloem scales inversely with plant height because of a shift in sieve element structure along the length of individual trees. This scaling relationship seems robust across multiple species despite large differences in plate anatomy. The importance of this scaling becomes clear when phloem transport is modelled using turgor pressures measured in the leaves of a mature red oak tree. These pressures are of sufficient magnitude to drive phloem transport only in concert with structural changes in the phloem that reduce transport resistance. As a result, the key to the long-standing mystery of how trees maintain phloem transport as they increase in size lies in the structure of the phloem and its ability to change hydraulic properties with plant height.The phloem is the system of ‘blood vessels’ that translocates carbohydrates from the leaves to different plant organs. Here, using new structural imaging and pressure measuring tools, the researchers show interesting phloem structural changes that ensure a passive transport mechanism in tall trees.

Convergent evolution of vascular optimization in kelp (Laminariales)

Terrestrial plants and mammals, although separated by a great evolutionary distance, have each arrived at a highly conserved body plan in which universal allometric scaling relationships govern the anatomy of vascular networks and key functional metabolic traits. The universality of allometric scaling suggests that these phyla have each evolved an ‘optimal’ transport strategy that has been overwhelmingly adopted by extant species. To truly evaluate the dominance and universality of vascular optimization, however, it is critical to examine other, lesser-known, vascularized phyla. The brown algae (Phaeophyceae) are one such group—as distantly related to plants as mammals, they have convergently evolved a plant-like body plan and a specialized phloem-like transport network. To evaluate possible scaling and optimization in the kelp vascular system, we developed a model of optimized transport anatomy and tested it with measurements of the giant kelp, Macrocystis pyrifera, which is among the largest and most successful of macroalgae. We also evaluated three classical allometric relationships pertaining to plant vascular tissues with a diverse sampling of kelp species. Macrocystis pyrifera displays strong scaling relationships between all tested vascular parameters and agrees with our model; other species within the Laminariales display weak or inconsistent vascular allometries. The lack of universal scaling in the kelps and the presence of optimized transport anatomy in M. pyrifera raises important questions about the evolution of optimization and the possible competitive advantage conferred by optimized vascular systems to multicellular phyla.

Sugar export limits size of conifer needles

Plant leaf size varies by more than three orders of magnitude, from a few millimeters to over one meter. Conifer leaves, however, are relatively short and the majority of needles are no longer than 6 cm. The reason for the strong confinement of the trait-space is unknown. We show that sugars produced near the tip of long needles cannot be exported efficiently, because the pressure required to drive vascular flow would exceed the greatest available pressure (the osmotic pressure). This basic constraint leads to the formation of an inactive region of stagnant fluid near the needle tip, which does not contribute to sugar flow. Remarkably, we find that the size of the active part does not scale with needle length. We predict a single maximum needle size of 5 cm, in accord with data from 519 conifer species. This could help rationalize the recent observation that conifers have significantly smaller leaves than angiosperms, and provide a biophysical explanation for this intriguing difference between the two largest groups of plants.