Modeling the parameters for plasmodesmal sugar filtering in active symplasmic phloem loaders

Parallel auxin transport via PINs and plasmodesmata during the Arabidopsis leaf hyponasty response

KEY MESSAGE

The leaf hyponasty response depends on tip-to-petiole auxin transport. This transport can happen through two parallel pathways: active trans-membrane transport mediated by PIN proteins and passive diffusion through plasmodesmata. A plant's ability to counteract potential shading by neighboring plants depends on transport of the hormone auxin. Neighbor sensing at the leaf tip triggers auxin production. Once this auxin reaches the abaxial petiole epidermis, it causes cell elongation, which leads to leaf hyponasty. Two pathways are known to contribute to this intercellular tip-to-petiole auxin movement: (i) transport facilitated by plasma membrane-localized PIN auxin transporters and (ii) diffusion enabled by plasmodesmata. We tested if these two modes of transport are arranged sequentially or in parallel. Moreover, we investigated if they are functionally linked. Mutants in which one of the two pathways is disrupted indicated that both pathways are necessary for a full hyponasty response. Visualization of PIN3-GFP and PIN7-GFP localization indicated PIN-mediated transport in parallel to plasmodesmata-mediated transport along abaxial midrib epidermis cells. We found plasmodesmata-mediated cell coupling in the pin3pin4pin7 mutant to match wild-type levels, indicating no redundancy between pathways. Similarly, PIN3, PIN4 and PIN7 mRNA levels were unaffected in a mutant with disrupted plasmodesmata pathway. Our results provide mechanistic insight on leaf hyponasty, which might facilitate the manipulation of the shade avoidance response in crops.

Diversity of funnel plasmodesmata in angiosperms: the impact of geometry on plasmodesmal resistance

In most plant tissues, threads of cytoplasm, or plasmodesmata, connect the protoplasts via pores in the cell walls. This enables symplasmic transport, for instance in phloem loading, transport and unloading. Importantly, the geometry of the wall pore limits the size of the particles that may be transported, and also (co-)defines plasmodesmal resistance to diffusion and convective flow. However, quantitative information on transport through plasmodesmata in non-cylindrical cell wall pores is scarce. We have found conical, funnel-shaped cell wall pores in the phloem-unloading zone in growing root tips of five eudicot and two monocot species, specifically between protophloem sieve elements and phloem pole pericycle cells. 3D reconstructions by electron tomography suggested that funnel plasmodesmata possess a desmotubule but lack tethers to fix it in a central position. Model calculations showed that both diffusive and hydraulic resistance decrease drastically in conical and trumpet-shaped cell wall pores compared with cylindrical channels, even at very small opening angles. Notably, the effect on hydraulic resistance was relatively larger. We conclude that funnel plasmodesmata generally are present in specific cell-cell interfaces in angiosperm roots, where they appear to facilitate symplasmic phloem unloading. Interestingly, cytosolic sleeves of most plasmodesmata reported in the literature do not resemble annuli of constant diameter but possess variously shaped widenings. Our evaluations suggest that widenings too small for unambiguous identification on electron micrographs may drastically reduce the hydraulic and diffusional resistance of these pores. Consequently, theoretical models assuming cylindrical symmetries will underestimate plasmodesmal conductivities.

Coordination Between Phloem Loading and Structure Maintains Carbon Transport Under Drought

Maintaining phloem transport under water stress is expected to be crucial to whole-plant drought tolerance, but the traits that benefit phloem function under drought are poorly understood. Nearly half of surveyed angiosperm species, including important crops, use sucrose transporter proteins to actively load sugar into the phloem. Plants can alter transporter abundance in response to stress, providing a potential mechanism for active-loading species to closely regulate phloem loading rates to avoid drought-induced reductions or failures in phloem transport. We developed an integrated xylem-phloem-stomatal model to test this hypothesis by quantifying the joint impacts of transporter kinetics, phloem anatomy, and plant water status on sucrose export to sinks. We parameterized the model with phloem hydraulic resistances and sucrose transporter kinetic parameters compiled from the literature, and simulated loading regulation by allowing loading rates to decline exponentially with phloem pressure to prevent excessive sucrose concentrations from inducing viscosity limitations. In the absence of loading regulation, where loading rates were independent of phloem pressure, most resistance values produced unrealistic phloem pressures owing to viscosity effects, even under well-watered conditions. Conversely, pressure-regulated loading helped to control viscosity buildup and improved export to sinks for both lower and higher resistant phloem pathways, while maintaining realistic phloem pressures. Regulation also allowed for rapid loading and export in wet conditions while maintaining export and viable phloem pressures during drought. Therefore, we expect feedbacks between phloem pressure and loading to be critical to carbon transport in active-loading species, especially under drought, and for transporter kinetics to be strongly coordinated with phloem architecture and plant water status. This work provides an important and underexplored physiological framework to understand the ecophysiology of phloem transport under drought and to enhance the genetic engineering of crop plants.

More Insights from Ultrastructural and Functional Plasmodesmata Data Using PDinsight

PDinsight is a Python-based tool for computing effective wall permeability for symplasmic transport based on plasmodesma (PD) size and distribution data. PDinsight can be used for direct computation of such permeabilities if full data is available, as well as in an explorative way if some data is either not available or considered unreliable. In this chapter, we briefly describe the basic model underlying the PDinsight calculations and discuss how the different modes of PDinsight can be used in relation to typical research questions. We also offer advice on choosing appropriate values for diffusion coefficients and particle size based on the currently most used experimental probes.

Sugar export from Arabidopsis leaves: actors and regulatory strategies

Plant acclimation and stress responses depend on the dynamic optimization of carbon balance between source and sink organs. This optimization also applies to the leaf export rate of photosynthetically produced sugars. So far, investigations into the molecular mechanisms of how the rate is controlled have focused on sugar transporters responsible for loading sucrose into the phloem sieve element-companion cell complex of leaf veins. Here, we take a broader view of the various proteins with potential direct influence on the leaf sugar export rate in the model plant Arabidopsis thaliana, helped by the cell type-specific transcriptome data that have recently become available. Furthermore, we integrate current information on the regulation of these potential target proteins. Our analysis identifies putative control points and units of transcriptionally and post-transcriptionally co-regulated genes. Most notable is the potential regulatory unit of sucrose transporters (SUC2, SWEET11, SWEET12, and SUC4) and proton pumps (AHA3 and AVP1). Our analysis can guide future research aimed at understanding the regulatory network controlling leaf sugar export by providing starting points for characterizing regulatory strategies and identifying regulatory factors that link sugar export rate to the major signaling pathways.

Computational Tools for Serial Block Electron Microscopy Reveal Plasmodesmata Distributions and Wall Environments

Plasmodesmata are small channels that connect plant cells. While recent technological advances have facilitated analysis of the ultrastructure of these channels, there are limitations to efficiently addressing their presence over an entire cellular interface. Here, we highlight the value of serial block electron microscopy for this purpose. We developed a computational pipeline to study plasmodesmata distributions and detect the presence/absence of plasmodesmata clusters, or pit fields, at the phloem unloading interfaces of Arabidopsis (Arabidopsis thaliana) roots. Pit fields were visualized and quantified. As the wall environment of plasmodesmata is highly specialized, we also designed a tool to extract the thickness of the extracellular matrix at and outside of plasmodesmata positions. We detected and quantified clear wall thinning around plasmodesmata with differences between genotypes, including the recently published plm-2 sphingolipid mutant. Our tools open avenues for quantitative approaches in the analysis of symplastic trafficking.

GM1 Oligosaccharide Crosses the Human Blood-Brain Barrier In Vitro by a Paracellular Route

Ganglioside GM1 (GM1) has been reported to functionally recover degenerated nervous system in vitro and in vivo, but the possibility to translate GM1′s potential in clinical settings is counteracted by its low ability to overcome the blood–brain barrier (BBB) due to its amphiphilic nature. Interestingly, the soluble and hydrophilic GM1-oligosaccharide (OligoGM1) is able to punctually replace GM1 neurotrophic functions alone, both in vitro and in vivo. In order to take advantage of OligoGM1 properties, which overcome GM1′s pharmacological limitations, here we characterize the OligoGM1 brain transport by using a human in vitro BBB model. OligoGM1 showed a 20-fold higher crossing rate than GM1 and time–concentration-dependent transport. Additionally, OligoGM1 crossed the barrier at 4 °C and in inverse transport experiments, allowing consideration of the passive paracellular route. This was confirmed by the exclusion of a direct interaction with the active ATP-binding cassette (ABC) transporters using the “pump out” system. Finally, after barrier crossing, OligoGM1 remained intact and able to induce Neuro2a cell neuritogenesis by activating the TrkA pathway. Importantly, these in vitro data demonstrated that OligoGM1, lacking the hydrophobic ceramide, can advantageously cross the BBB in comparison with GM1, while maintaining its neuroproperties. This study has improved the knowledge about OligoGM1′s pharmacological potential, offering a tangible therapeutic strategy.

From plasmodesma geometry to effective symplasmic permeability through biophysical modelling

Regulation of molecular transport via intercellular channels called plasmodesmata (PDs) is important for both coordinating developmental and environmental responses among neighbouring cells, and isolating (groups of) cells to execute distinct programs. Cell-to-cell mobility of fluorescent molecules and PD dimensions (measured from electron micrographs) are both used as methods to predict PD transport capacity (i.e., effective symplasmic permeability), but often yield very different values. Here, we build a theoretical bridge between both experimental approaches by calculating the effective symplasmic permeability from a geometrical description of individual PDs and considering the flow towards them. We find that a dilated central region has the strongest impact in thick cell walls and that clustering of PDs into pit fields strongly reduces predicted permeabilities. Moreover, our open source multi-level model allows to predict PD dimensions matching measured permeabilities and add a functional interpretation to structural differences observed between PDs in different cell walls.

Quantification of Symplasmic Phloem Loading Capacity with Live-Cell Microscopy

Sugars produced by photosynthesis in leaves get transported to other organs in the phloem vascular tissue. Three general mechanisms have been proposed for the loading of sugars into the phloem. These differ in the involvement of active transport across the phloem cell's membrane and their capacity for passive intercellular transport through plasmodesmata. This capacity for diffusion from the mesophyll into the phloem cells can be quantified by live-cell microscopy. Instead of sugar molecules, the movement of fluorescent tracers of similar size can be observed. In this chapter, a simple method is described that allows quantification of plasmodesmata-mediated intercellular diffusion across the mesophyll-bundle sheath interface and the bundle sheath-phloem cell interfaces. The fluorescent tracer carboxyfluorescein is loaded into intact leaves and its diffusion monitored with confocal microscopy after photobleaching of a bundle sheath cell.

Cyclosis-mediated intercellular transmission of photosynthetic metabolites in Chara revealed with chlorophyll microfluorometry

Symplastic interconnections of plant cells via perforations in adjoining cell walls (plasmodesmata) enable long-distance transport of photoassimilates and signaling substances required for growth and development. The pathways and features of intercellular movement of assimilates are often examined with fluorescent tracers whose molecular dimensions are similar to natural metabolites produced in photosynthesis. Chlorophyll fluorescence was recently found to be a sensitive noninvasive indicator of long-distance intracellular transport of physiologically produced photometabolites in characean internodes. The present work shows that the chlorophyll microfluorometry has a potential for studying the cell-to-cell transport of reducing substances released by local illumination of one internode and detected as the fluorescence increase in the neighbor internode. The method provides temporal resolution in the time frame of seconds and can be used to evaluate permeability of plasmodesmata to natural components released by illuminated chloroplasts. The results show that approximately one third of the amount of photometabolites released into the streaming cytoplasm during a 30-s pulse of local light permeates across the nodal complex with the characteristic time of ~ 10 s. The intercellular transport was highly sensitive to moderate elevations of osmolarity in the bath solution (150 mM sorbitol), which contrasts to the view that only transnodal gradients in osmolarity (and internal hydrostatic pressure) have an appreciable influence on plasmodesmal conductance. The inhibition of cell-to-cell transport was reversible and specific; the sorbitol addition had no influence on photosynthetic electron transport and the velocity of cytoplasmic streaming. The conductance of transcellular pores increased in the presence of the actin inhibitor cytochalasin D but the cell-to-cell transport was eventually suppressed due to the deceleration and cessation of cytoplasmic streaming. The results show that the permeability of plasmodesmata to low-molecular photometabolites is subject to upregulation and downregulation.

Direct Comparison of Leaf Plasmodesma Structure and Function in Relation to Phloem-Loading Type

The export of photosynthetically produced sugars from leaves depends on plasmodesmatal transport of sugar molecules from mesophyll to phloem. Traditionally, the density of plasmodesmata (PD) along this phloem-loading pathway has been used as a defining feature of different phloem-loading types, with species proposed to have either many or few PD between the phloem and surrounding cells of the leaf. However, quantitative determination of PD density has rarely been performed. Moreover, the structure of PD has not been considered, even though it could impact permeability, and functional data are only available for very few species. Here, a comparison of PD density, structure, and function using data from transmission electron microscopy and live-cell microscopy was conducted for all relevant cell-cell interfaces in leaves of nine species. These species represent the three principal phloem-loading types currently discussed in literature. Results show that relative PD density among the different cell-cell interfaces in one species, but not absolute PD density, is indicative of phloem-loading type. PD density data of single interfaces, even combined with PD diameter and length data, did not correlate with the intercellular diffusion capacity measured by the fluorescence loss in photobleaching method. This means that PD substructure not visible on standard transmission electron micrographs may have a strong influence on permeability. Furthermore, the results support a proposed passive symplasmic loading mechanism in the tree species horse chestnut (Aesculus hippocastanum), white birch (Betula pubescens), orchard apple (Malus domestica), and gray poplar (Populus x canescens) as functional cell coupling and PD structure differed from active symplasmic and apoplasmic phloem-loading species.

Ratio of sugar concentrations in the phloem sap and the cytosol of mesophyll cells in different tree species as an indicator of the phloem loading mechanism

Sucrose concentration in phloem sap was several times higher than in the cytosol of mesophyll cells. The results suggest that phloem loading involves active steps in the analyzed tree species. Phloem loading in source leaves is a key step for carbon partitioning and passive symplastic loading has been proposed for several tree species. However, experimental evidence to prove the potential for sucrose diffusion from mesophyll to phloem is rare. Here, we analyzed three tree species (two angiosperms, Fagus sylvatica, Magnolia kobus, and one gymnosperm, Gnetum gnemon) to investigate the proposed phloem loading mechanism. For this purpose, the minor vein structure and the sugar concentrations in phloem sap as well as in the subcellular compartments of mesophyll cells were investigated. The analyzed tree species belong to the open type minor vein subcategory. The sucrose concentration in the cytosol of mesophyll cells ranged between 75 and 165 mM and was almost equal to the vacuolar concentration. Phloem sap could be collected from F. sylvatica and M. kobus and the concentration of sucrose in phloem sap was about five- and 11-fold higher, respectively, than in the cytosol of mesophyll cells. Sugar exudation of cut leaves was decreased by p-chloromercuribenzenesulfonic acid, an inhibitor of sucrose-proton transporter. The results suggest that phloem loading of sucrose in the analyzed tree species involves active steps, and apoplastic phloem loading seems more likely.

Photoinducible DRONPA-s: a new tool for investigating cell-cell connectivity

The development of multicellular plants relies on the ability of their cells to exchange solutes, proteins and signalling compounds through plasmodesmata, symplasmic pores in the plant cell wall. The aperture of plasmodesmata is regulated in response to developmental cues or external factors such as pathogen attack. This regulation enables tight control of symplasmic cell-to-cell transport. Here we report on an elegant non-invasive method to quantify the passive movement of protein between selected cells even in deeper tissue layers. The system is based on the fluorescent protein DRONPA-s, which can be switched on and off repeatedly by illumination with different light qualities. Using transgenic 35S::DRONPA-s Arabidopsis thaliana and a confocal microscope it was possible to activate DRONPA-s fluorescence in selected cells of the root meristem. This enabled us to compare movement of DRONPA-s from the activated cells into the respective neighbouring cells. Our analyses showed that pericycle cells display the highest efflux capacity with a good lateral connectivity. In contrast, root cap cells showed the lowest efflux of DRONPA-s. Plasmodesmata of quiescent centre cells mediated a stronger efflux into columella cells than into stele initials. To simplify measurements of fluorescence intensity in a complex tissue we developed software that allows simultaneous analyses of fluorescence intensities of several neighbouring cells. Our DRONPA-s system generates reproducible data and is a valuable tool for studying symplasmic connectivity.

Phloem networks in leaves

The survival of all vascular plants depends on phloem and xylem, which comprise a hydraulically coupled tissue system that transports photosynthates, water, and a variety of other molecules and ions. Although xylem hydraulics has been extensively studied, until recently, comparatively little is known quantitatively about the phloem hydraulic network and how it is functionally coupled to the xylem network, particularly in photosynthetic leaves. Here, we summarize recent advances in quantifying phloem hydraulics in fully expanded mature leaves with different vascular architectures and show that (1) the size of phloem conducting cells across phylogenetically different taxa scales isometrically with respect to xylem conducting cell size, (2) cell transport areas and lengths increase along phloem transport pathways in a manner that can be used to model Münch's pressure-flow hypothesis, and (3) report observations that invalidate da Vinci's and Murray's hydraulic models as plausible constructs for understanding photosynthate transport in the leaf lamina.

Mechanisms of phloem loading

The complex form of higher plants requires continuous, balanced transport of nutrients in the phloem. The initial step of transferring sugars, amino acids, and other materials from photosynthetic cells to the conducting sieve tubes is known as phloem loading. Three phloem loading mechanisms have been described. The first involves release of sucrose into the apoplast and subsequent retrieval by the phloem. The initial release step in this process is now known to be mediated by a new class of transporters, the SWEET proteins. In the other two loading mechanisms, polymer trapping and diffusion, sucrose passes into the phloem through cytoplasmic channels, the plasmodesmata. Recent models have shed additional light on these mechanisms and their ability to sustain the growth of even the tallest trees.

An update on phloem transport: a simple bulk flow under complex regulation

The phloem plays a central role in transporting resources and signalling molecules from fully expanded leaves to provide precursors for, and to direct development of, heterotrophic organs located throughout the plant body. We review recent advances in understanding mechanisms regulating loading and unloading of resources into, and from, the phloem network; highlight unresolved questions regarding the physiological significance of the vast array of proteins and RNAs found in phloem saps; and evaluate proposed structure/function relationships considered to account for bulk flow of sap, sustained at high rates and over long distances, through the transport phloem.

Phloem Loading through Plasmodesmata: A Biophysical Analysis

In many species, Suc en route out of the leaf migrates from photosynthetically active mesophyll cells into the phloem down its concentration gradient via plasmodesmata, i.e. symplastically. In some of these plants, the process is entirely passive, but in others phloem Suc is actively converted into larger sugars, raffinose and stachyose, and segregated (trapped), thus raising total phloem sugar concentration to a level higher than in the mesophyll. Questions remain regarding the mechanisms and selective advantages conferred by both of these symplastic-loading processes. Here, we present an integrated model-including local and global transport and kinetics of polymerization-for passive and active symplastic loading. We also propose a physical model of transport through the plasmodesmata. With these models, we predict that (1) relative to passive loading, polymerization of Suc in the phloem, even in the absence of segregation, lowers the sugar content in the leaf required to achieve a given export rate and accelerates export for a given concentration of Suc in the mesophyll and (2) segregation of oligomers and the inverted gradient of total sugar content can be achieved for physiologically reasonable parameter values, but even higher export rates can be accessed in scenarios in which polymers are allowed to diffuse back into the mesophyll. We discuss these predictions in relation to further studies aimed at the clarification of loading mechanisms, fitness of active and passive symplastic loading, and potential targets for engineering improved rates of export.

Sucrose transporters and plasmodesmal regulation in passive phloem loading

An essential step for the distribution of carbon throughout the whole plant is the loading of sugars into the phloem in source organs. In many plants, accumulation of sugars in the sieve element-companion cell (SE-CC) complex is mediated and regulated by active processes. However, for poplar and many other tree species, a passive symplasmic mechanism of phloem loading has been proposed, characterized by symplasmic continuity along the pre-phloem pathway and the absence of active sugar accumulation in the SE-CC complex. A high overall leaf sugar concentration is thought to enable diffusion of sucrose into the phloem. In this review, we critically evaluate current evidence regarding the mechanism of passive symplasmic phloem loading, with a focus on the potential influence of active sugar transport and plasmodesmal regulation. The limited experimental data, combined with theoretical considerations, suggest that a concomitant operation of passive symplasmic and active phloem loading in the same minor vein is unlikely. However, active sugar transport could well play an important role in how passively loading plants might modulate the rate of sugar export from leaves. Insights into the operation of this mechanism has direct implications for our understanding of how these plants utilize assimilated carbon.

Characterization, localization, and seasonal changes of the sucrose transporter FeSUT1 in the phloem of Fraxinus excelsior

Trees are generally assumed to be symplastic phloem loaders. A typical feature for most wooden species is an open minor vein structure with symplastic connections between mesophyll cells and phloem cells, which allow sucrose to move cell-to-cell through the plasmodesmata into the phloem. Fraxinus excelsior (Oleaceae) also translocates raffinose family oligosaccharides in addition to sucrose. Sucrose concentration was recently shown to be higher in the phloem sap than in the mesophyll cells. This suggests the involvement of apoplastic steps and the activity of sucrose transporters in addition to symplastic phloem-loading processes. In this study, the sucrose transporter FeSUT1 from F. excelsior was analysed. Heterologous expression in baker's yeast showed that FeSUT1 mediates the uptake of sucrose. Immunohistochemical analyses revealed that FeSUT1 was exclusively located in phloem cells of minor veins and in the transport phloem of F. excelsior. Further characterization identified these cells as sieve elements and possibly ordinary companion cells but not as intermediary cells. The localization and expression pattern point towards functions of FeSUT1 in phloem loading of sucrose as well as in sucrose retrieval. FeSUT1 is most likely responsible for the observed sucrose gradient between mesophyll and phloem. The elevated expression level of FeSUT1 indicated an increased apoplastic carbon export activity from the leaves during spring and late autumn. It is hypothesized that the importance of apoplastic loading is high under low-sucrose conditions and that the availability of two different phloem-loading mechanisms confers advantages for temperate woody species like F. excelsior.

Quantification of plant cell coupling with live-cell microscopy

Movement of nutrients and signaling compounds from cell to cell is an essential process for plant growth and development. To understand processes such as carbon allocation, cell communication, and reaction to pathogen attack it is important to know a specific molecule's capacity to pass a specific cell wall interface. Transport through plasmodesmata, the cell wall channels that directly connect plant cells, is regulated not only by a fixed size exclusion limit, but also by physiological and pathological adaptation. The noninvasive approach described here offers the possibility of precisely determining the plasmodesmata-mediated cell wall permeability for small molecules in living cells.The method is based on photoactivation of the fluorescent tracer caged fluorescein. Non-fluorescent caged fluorescein is applied to a target tissue, where it is taken up passively into all cells. Imaged by confocal microscopy, loaded tracer is activated by UV illumination in a target cell and its spread to neighboring cells monitored. When combined with high-speed acquisition by resonant scanning or spinning disc confocal microscopy, the high signal-to-noise ratio of photoactivation allows collection of three-dimensional (3D) time series. These contain all necessary functional and anatomical data to measure cell coupling in complex tissues noninvasively.

Diffusion or bulk flow: how plasmodesmata facilitate pre-phloem transport of assimilates

Assimilates synthesized in the mesophyll of mature leaves move along the pre-phloem transport pathway to the bundle sheath of the minor veins from which they are loaded into the phloem. The present review discusses the most probable driving force(s) for the pre-phloem pathway, diffusion down the concentration gradient or bulk flow along a pressure gradient. The driving force seems to depend on the mode of phloem loading. In a majority of plant species phloem loading is a thermodynamically active process, involving the activity of membrane transporters in the sieve-element companion cell complex. Since assimilate movement includes an apoplasmic step, this mode is called apoplasmic loading. Well established is also the polymer-trap loading mode, where the phloem-transport sugars are raffinose-family oligomers in herbaceous plants. Also this mode depends on the investment of energy, here for sugar oligomerization, and leads to a high sugar accumulation in the phloem, even though the phloem is not symplasmically isolated, but well coupled by plasmodesmata (PD). Hence the mode polymer-trap mode is also designated active symplasmic loading. For woody angiosperms and gymnosperms an alternate loading mode is currently matter of discussion, called passive symplasmic loading. Based on the limited material available, this review compares the different loading modes and suggests that diffusion is the driving force in apoplasmic loaders, while bulk flow plays an increasing role in plants having a continuous symplasmic pathway from mesophyll to sieve elements. Crucial for the driving force is the question where water enters the pre-phloem pathway. Surprisingly, the role of PD in water movement has not been addressed so far appropriately. Modeling of assimilate and water fluxes indicates that in symplasmic loaders a considerable part of water flux happens through the PD between bundle sheath and phloem.

Mobility of signaling molecules: the key to deciphering plant organogenesis

Signaling molecules move between cells to form a characteristic distribution pattern within a developing organ; thereafter, they spatiotemporally regulate organ development. A key question in this process is how the signaling molecules robustly form the precise distribution on a tissue scale in a reproducible manner. Despite of an increasing number of quantitative studies regarding the mobility of signaling molecules, the detail mechanism of organogenesis via intercellular signaling is still unclear. We here review the potential advantages of plant development to address this question, focusing on the cytoplasmic continuity of plant cells through the plasmodesmata. The plant system would provide a unique opportunity to define the simple transportation mode of diffusion process, and, hence, the mechanism of organogenesis via intercellular signaling. Based on the advances in the understanding of intercellular signaling at the molecular level and in the quantitative imaging techniques, we discuss our current challenges in measuring the mobility of signaling molecules for deciphering plant organogenesis.

Diffusion and bulk flow in phloem loading: a theoretical analysis of the polymer trap mechanism for sugar transport in plants

Plants create sugar in the mesophyll cells of their leaves by photosynthesis. This sugar, mostly sucrose, has to be loaded via the bundle sheath into the phloem vascular system (the sieve elements), where it is distributed to growing parts of the plant. We analyze the feasibility of a particular loading mechanism, active symplasmic loading, also called the polymer trap mechanism, where sucrose is transformed into heavier sugars, such as raffinose and stachyose, in the intermediary-type companion cells bordering the sieve elements in the minor veins of the phloem. Keeping the heavier sugars from diffusing back requires that the plasmodesmata connecting the bundle sheath with the intermediary cell act as extremely precise filters, which are able to distinguish between molecules that differ by less than 20% in size. In our modeling, we take into account the coupled water and sugar movement across the relevant interfaces, without explicitly considering the chemical reactions transforming the sucrose into the heavier sugars. Based on the available data for plasmodesmata geometry, sugar concentrations, and flux rates, we conclude that this mechanism can in principle function, but that it requires pores of molecular sizes. Comparing with the somewhat uncertain experimental values for sugar export rates, we expect the pores to be only 5%-10% larger than the hydraulic radius of the sucrose molecules. We find that the water flow through the plasmodesmata, which has not been quantified before, contributes only 10%-20% to the sucrose flux into the intermediary cells, while the main part is transported by diffusion. On the other hand, the subsequent sugar translocation into the sieve elements would very likely be carried predominantly by bulk water flow through the plasmodesmata. Thus, in contrast to apoplasmic loaders, all the necessary water for phloem translocation would be supplied in this way with no need for additional water uptake across the plasma membranes of the phloem.

Dual-porosity model of solute diffusion in biological tissue modified by electroporation

In many electroporation applications mass transport in biological tissue is of primary concern. This paper presents a theoretical advancement in the field and gives some examples of model use in electroporation applications. The study focuses on post-treatment solute diffusion. We use a dual-porosity approach to describe solute diffusion in electroporated biological tissue. The cellular membrane presents a hindrance to solute transport into the extracellular space and is modeled as electroporation-dependent porosity, assigned to the intracellular space (the finite rate of mass transfer within an individual cell is not accounted for, for reasons that we elaborate on). The second porosity is that of the extracellular space, through which solute vacates a block of tissue. The model can be used to study extraction out of or introduction of solutes into tissue, and we give three examples of application, a full account of model construction, validation with experiments, and a parametrical analysis. To facilitate easy implementation and experimentation by the reader, the complete derivation of the analytical solution for a simplified example is presented. Validation is done by comparing model results to experimentally-obtained data; we modeled kinetics of sucrose extraction by diffusion from sugar beet tissue in laboratory-scale experiments. The parametrical analysis demonstrates the importance of selected physicochemical and geometrical properties of the system, illustrating possible outcomes of applying the model to different electroporation applications. The proposed model is a new platform that supports rapid extension by state-of-the-art models of electroporation phenomena, developed as latest achievements in the field of electroporation.