Linking phloem function to structure: Analysis with a coupled xylem-phloem transport model

We carried out a theoretical analysis of phloem transport based on Münch hypothesis by developing a coupled xylem-phloem transport model. Results showed that the maximum sugar transport rate of the phloem was limited by solution viscosity and that transport requirements were strongly affected by prevailing xylem water potential. The minimum number of xylem and phloem conduits required to sustain transpiration and assimilation, respectively, were calculated. At its maximum sugar transport rate, the phloem functioned with a high turgor pressure difference between the sugar sources and sinks but the turgor pressure difference was reduced if additional parallel conduits were added or solute relays were introduced. Solute relays were shown to decrease the number of parallel sieve tubes needed for phloem transport, leading to a more uniform turgor pressure and allowing faster information transmission within the phloem. Because xylem water potential affected both xylem and phloem transport, the conductance of the two systems was found to be coupled such that large structural investments in the xylem reduced the need for investment in the phloem and vice versa.     

Convective gas transport in the pulmonary acinus: Comparing roles of convective and diffusive lengths

To investigate the relative importance of convection and diffusion in the transport of oxygen in the pulmonary acinus, it is often useful to locate the transition from convection-dominated to diffusion-dominated transport. Traditionally, this is done by estimating the values of a Peclet number. This dimensionless number compares the bulk ductal flow velocity at an acinar generation with a diffusion velocity over a characteristic length scale. Here, we revisit the convection–diffusion transition by comparing the relative importance of convective and diffusive lengths. We introduce the ratio of such lengths (L_conv/L_diff) to quantify the extent of convective transport in the acinus over an inhalation phase. We distinguish between convection along the acinar airways and within alveoli, respectively. Results for L_conv/L_diff suggest that convection in acinar ducts may play a potential role in more peripheral airways compared with values obtained for a Peclet number. Within alveoli, however, independent of acinar depth, oxygen transport is governed by diffusion as soon as molecules enter within alveolar cavities.     

Solute convection in dynamically compressed cartilage

Chondrocytes depend upon solute transport within the avascular extracellular matrix of articular cartilage for many of their biological activities. Alterations to solute transport parameters may therefore mediate the cell response to tissue compression. While interstitial solute transport may be supplemented by convection during dynamic tissue compression, matrix compression is also associated with decreased diffusivities. Such trade-offs between increased convection and decreased diffusivities of solutes in dynamically compressed cartilage remain largely unexplored. We measured diffusion and convection coefficients of a wide range of solutes in mature bovine cartilage explant disks subjected to radially unconfined axial ramp compression and release. Solutes included approximately 500 Da fluorophores bearing positive and negative charges, and 10 kDa dextrans bearing positive, neutral, and negative charges. Significantly positive values of convection coefficients were measured for several different solutes. Findings therefore support a role for solute convection in mediating the cartilage biological response to dynamic compression.     

Validation of theoretical framework explaining active solute uptake in dynamically loaded porous media

Solute transport in biological tissues is a fundamental process necessary for cell metabolism. In connective soft tissues, such as articular cartilage, cells are embedded within a dense extracellular matrix that hinders the transport of solutes. However, according to a recent theoretical study (Mauck et al., 2003, J. Biomech. Eng. 125, 602–614), the convective motion of a dynamically loaded porous solid matrix can also impart momentum to solutes, pumping them into the tissue and giving rise to concentrations which exceed those achived under passive diffusion alone. In this study, the theoretical predictions of this model are verified against experimental measurements. The mechanical and transport properties of an agarose–dextran model system were characterized from independent measurements and substituted into the theory to predict solute uptake or desorption under dynamic mechanical loading for various agarose concentrations and dextran molecular weights, as well as different boundary and initial conditions. In every tested case, agreement was observed between experiments and theoretical predictions as assessed by coefficients of determination ranging from R²=0.61 to 0.95. These results provide strong support for the hypothesis that dynamic loading of a deformable porous tissue can produce active transport of solutes via a pumping mechanisms mediated by momentum exchange between the solute and solid matrix.     

The Kinetics of Osmotic Transport through Pores of Molecular Dimensions

This paper presents a theoretical analysis of the kinetics of osmotic transport across a semipermeable membrane. There is a thermodynamic connection between the rate of flow under a hydrostatic pressure difference and the rate of flow due to a difference in solute concentration on the two sides. One might therefore attempt to calculate the osmotic transport coefficient by applying Poiseuille's equation to the flow produced by a difference in hydrostatic pressure. Such a procedure is, however, inappropriate if the pores in the membrane are too small to allow molecules to “overtake.” It then becomes necessary to perform a statistical calculation of the transport coefficient, and such a calculation is described in this paper. The resulting expression for the number of solvent molecules passing through a pore per second is J = m D₁ δn₁/l² where m is the number of solvent molecules in the pore, l is the length of the pore, D₁ is the self-diffusion coefficient of the solute, and δn₁ the difference in solvent mole fraction on the two sides of the membrane. This equation is used for estimating the number of pores per unit area of the squid axon membrane; the result is 6 × 10⁹ pores/cm².     

Effects of dynamic loading on solute transport through the human cartilage endplate

Nutrient and metabolite transport through the cartilage endplate (CEP) is important for maintaining proper disc nutrition, but the mechanisms of solute transport remain unclear. One unresolved issue is the role of dynamic loading. In comparison to static loading, dynamic loading is thought to enhance transport by increasing convection. However, the CEP has a high resistance to fluid flow, which could limit solute convection. Here we measure solute transport through site-matched cadaveric human lumbar CEP tissues under static vs. dynamic loading, and we determine how the degree of transport enhancement from dynamic loading depends on CEP porosity and solute size. We found that dynamic loading significantly increased small and large solute transport through the CEP: on average, dynamic loading increased the transport of sodium fluorescein (376 Da) by a factor of 1.85 ± 0.64 and the transport of a large dextran (4000 Da) by a factor of 4.97 ± 3.05. Importantly, CEP porosity (0.65 ± 0.07; range: 0.47–0.76) strongly influenced the degree of transport enhancement. Specifically, for both solutes, transport enhancement was greater for CEPs with low porosity than for CEPs with high porosity. This is because the CEPs with low porosity were susceptible to larger improvements in fluid flow under dynamic loading. The CEP becomes less porous and less hydrated with aging and as disc degeneration progresses. Together, these findings suggest that as those changes occur, dynamic loading has a greater effect on solute transport through the CEP compared to static loading, and thus may play a larger role in disc nutrition.     

The biophysics of differential growth

The intrinsic control of uniform and differential growth of plant cells can be traced to a small number of physical parameters. These are cell wall rheology, membrane and tissue hydraulic conductivity, and membrane and tissue solute transport. Water and solute effects are manifested as alterations in turgor pressure. Environmental and biochemical processes always channel their effects through one or more of these parameters. Technical developments such as the pressure probe and Instron tensiometer, together with a reappraisal of older techniques, are beginning to allow assessment of the relative roles of these factors. Although the importance of cell wall rheology is becoming increasingly apparent, there is still insufficient information to allow generalized conclusions regarding the role of turgor pressure in differential growth. This review considers attempts to correlate these parameters with observed anatomical growth patterns.     

Analysis of coupled intra- and extraluminal flows for single and multiple capillaries

Matched asymptotic expansions are used to study a model of the coupled fluid flow in the capillaries and tissue of the microcirculation. These capillaries are long, narrow cylindrical tubes embedded in a uniform tissue space. The capillary, or intraluminal, flow is assumed to be that of an incompressible Navier-Stokes fluid wherein colloids are represented as dilute solute; the extraluminal flow in the tissue is according to Darcy's law. Central to this fluid exchange is the boundary condition on the fluid radial velocity at the semipermeable wall of the capillary. This boundary condition, involving the local hydrostatic and colloidal osmotic pressures in both the capillary and the tissue, together with the radial gradient of the tissue hydrostatic pressure, couples the intra- and extraluminal flow fields. With this model we investigate the relationship between transport properties, hydrostatic pressures, and flow exchange for a single capillary, and describe the fluid transport in the tissue space produced by an array of such capillaries.     

Preservation and analysis of nonequilibrium solute concentration distributions within mechanically compressed cartilage explants

Solute transport within articular cartilage is of central importance to tissue physiology, and may mediate effects of mechanical compression on cell metabolism. We therefore developed and applied a freeze-substitution method for fixation of cartilage explant disks which had been compressed axially during radial solute desorption. Dextrans were used as model solutes. Explant morphology was well preserved and nonequilibrium solute concentration distributions were stable for several hours at room temperature. For desorption from explants compressed statically to 0-46% strain, analysis of laser confocal images and comparison to a theoretical model permitted measurement of effective diffusivities. Results were consistent with previous studies suggesting a role for transport limitations in mediating the decreases of chondrocyte metabolic rates associated with static compression. In explants compressed dynamically (23+/-5% strain at 0.001 Hz), evidence was obtained for the augmentation of effective transport rate of 3 kDa dextrans by oscillatory interstitial fluid flows. This suggests that augmented solute transport may play a role in mediating the increases of chondrocyte metabolic rates associated with dynamic compression. Methods appear suitable for quantitative studies of transport within mechanically compressed cartilage-like tissues, and may be valuable for identification of loading environments which optimize solute transport in tissue engineering applications.     

Effect of tumor shape,size, and tissue transport properties on drug delivery to solid tumors

Background

The computational methods provide condition for investigation related to the process of drug delivery, such as convection and diffusion of drug in extracellular matrices, drug extravasation from microvessels or to lymphatic vessels. The information of this process clarifies the mechanisms of drug delivery from the injection site to absorption by a solid tumor. In this study, an advanced numerical method is used to solve fluid flow and solute transport equations simultaneously to investigate the effect of tumor shape and size on drug delivery to solid tumor.

Methods

The advanced mathematical model used in our previous work is further developed by adding solute transport equation to the governing equations. After applying appropriate boundary and initial conditions on tumor and surrounding tissue geometry, the element-based finite volume method is used for solving governing equations of drug delivery in solid tumor. Also, the effects of size and shape of tumor and some of tissue transport parameters such as effective pressure and hydraulic conductivity on interstitial fluid flow and drug delivery are investigated.

Results

Sensitivity analysis shows that drug delivery in prolate shape is significantly better than other tumor shapes. Considering size effect, increasing tumor size decreases drug concentration in interstitial fluid. This study shows that dependency of drug concentration in interstitial fluid to osmotic and intravascular pressure is negligible.

Conclusions

This study shows that among diffusion and convection mechanisms of drug transport, diffusion is dominant in most different tumor shapes and sizes. In tumors in which the convection has considerable effect, the drug concentration is larger than that of other tumors at the same time post injection.

     

Tie-dyed1 encodes a novel, phloem-expressed transmembrane protein that functions in carbohydrate partitioning

Carbon is partitioned between export from the leaf and retention within the leaf, and this process is essential for all aspects of plant growth and development. In most plants, sucrose is loaded into the phloem of carbon-exporting leaves (sources), transported through the veins, and unloaded into carbon-importing tissues (sinks). We have taken a genetic approach to identify genes regulating carbon partitioning in maize (Zea mays). We identified a collection of mutants, called the tie-dyed (tdy) loci, that hyperaccumulate carbohydrates in regions of their leaves. To understand the molecular function of Tdy1, we cloned the gene. Tdy1 encodes a novel transmembrane protein present only in grasses, although two protein domains are conserved across angiosperms. We found that Tdy1 is expressed exclusively in phloem cells of both source and sink tissues, suggesting that Tdy1 may play a role in phloem loading and unloading processes. In addition, Tdy1 RNA accumulates in protophloem cells upon differentiation, suggesting that Tdy1 may function as soon as phloem cells become competent to transport assimilates. Monitoring the movement of a fluorescent, soluble dye showed that tdy1 leaves have retarded phloem loading. However, once the dye entered into the phloem, solute transport appeared equal in wild-type and tdy1 mutant plants, suggesting that tdy1 plants are not defective in phloem unloading. Therefore, even though Tdy1 RNA accumulates in source and sink tissues, we propose that TDY1 functions in carbon partitioning by promoting phloem loading. Possible roles for TDY1 are discussed.     

On the volume-flow mechanism of phloem transport

Summary A steady-state model of solution flow in a tubular semipermeable membrane is developed for an arbitrary distribution of solute sources and sinks along the translocation path. It is demonstrated that the volume-flow mechanism of phloem transport depends only on the two assumptions: 1. that the plasmalemma of the sieve tube is a differentially permeable membrane, and 2. that sugars are actively secreted into and absorbed from the lumen of the sieve tube. It is shown that in the absence of a pressure gradient, there is a negligible concentration gradient over most of the translocation path. However, in the presence of a pressure gradient a small concentration gradient develops as a result of the continually changing chemical potential of water along the direction of solution flow. For Poiseuille flow the concentration gradient is approximately proportional to the mean stream velocity.     

Flux Ratio and Driving Forces in a Model of Active Transport

In order to analyze the energetics of active transport, a hypothetical carrier model is considered in which the active transport process is reduced to a minimal number of elementary steps. The relation between the following three quantities is examined: The affinity of the reaction driving the active transport, the ratio of isotope fluxes between identical solutions (“short-circuit”), and the maximal chemical potential difference which the active transport system can maintain. The interdependence of isotopeinteraction and the degree of coupling between transport and chemical reaction is shown explicitly: when the transport and chemical reaction are completely coupled, there is marked isotope interaction. In general, the logarithm of the short-circuit flux ratio (multiplied by RT) and the maximal chemical potential are not equal. The two quantities are approximately equal, when coupling between metabolism and transport is very loose, or when the reaction step is much faster than the transfer of the adsorbed solute across the barrier. Without prior knowledge of the kinetic parameters of the carrier, the maximal potential and the dependence of the metabolic reaction on solute flow have to be measured in order to derive the affinity of the driving reaction. Measurement of the flux ratio in the same system will then yield independent information on the carrier mechanism.     

Are plant growth substances involved in the partitioning of assimilate to developing reproductive sinks?

The possible involvement of plant growth substances in assimilate production in source leaves, loading into phloem and unloading in sink tissues is discussed in relation to their sites of formation and transport characteristics. The relative importance and possible functions of imported and locally-synthesised plant growth substances in postfertilisation development of reproductive sinks is briefly reviewed.Abbreviations ABA Abscisic acid - PA Phaseic acid - DPA Dihydrophaseic acid - GA Gibberellin - IAA Indole-3-acetic acid     

A theory of membrane permeability: II. Diffusion in the presence of water-flow

The author's earlier treatment of diffusion through a membrane is extended to include the case in which there is a mass motion of water through the membrane. Water flows through the membrane in the direction from lower to higher concentrations of the solute. This water carries a part of the solute by convection. Thus in this general case there is a transport of solute through the membrane both in the direction from higher to lower concentration, and in the opposite direction. If the latter effect prevails, the net result is a flow of solute from lower to higher concentrations. Mathematically this corresponds to negative values of the permeability. The effect of hydrostatic pressure is considered also.     

Factors influencing arterial wall mass transport

Arterial wall mass transport has particularly attracted attention because it may be implicated in the development of arterial disease, including arteriosclerosis. A short review is presented of the structure of the arterial wall and of studies of mass transport within it. Recent findings confirm that mass transport occurs across the entire arterial wall apparently from the lumen to the adventitial lymphatics. Evidence has emerged of inhomogeneity of the distribution volume for extracellular tracers in different layers of the wall. An attempt is made to interpret results which indicate that distension per se of arteries and increase of medial smooth muscle tone tend to compact the medial interstitium whereas pressure driven convection across the wall tends to expand that tissue. These findings imply a potentially important role of endothelial permeability, smooth muscle tone and luminal pressure in influencing solute transport in the wall and wall transport properties.     

Signaling in morphogenesis: transport cues in morphogenesis

Extracellular transport processes play critical roles in morphogenesis. While diffusive transport effects on morphogenesis are well illustrated in examples like blood capillary architecture and in cell morphogenetic responses to the local extracellular protein environment, the effects of fluid convection, although important in many developing and regenerating tissues, are not well understood. Convective forces are present whenever a hydrated tissue undergoes dynamic mechanical strain, and so convection could not only dominate the transport of large molecules like proteins, but might also serve as a mechanism for mechanosensing. The complex interdependence of mechanical forces, protein transport and extracellular morphogen gradients needs to be elucidated in a comprehensive way in order for the importance of transport on morphogenesis to be fully appreciated.     

Dynamic compression augments interstitial transport of a glucose-like solute in articular cartilage

Solute transport through the extracellular matrix is essential for cellular activities in articular cartilage. Increased solute transport via fluid convection may be a mechanism by which dynamic compression stimulates chondrocyte metabolism. However, loading conditions that optimally augment transport likely vary for different solutes. To investigate effects of dynamic loading on transport of a bioactive solute, triangular mechanical loading waveforms were applied to cartilage explants disks while interstitial transport of a fluorescent glucose analog was monitored. Peak-to-peak compression amplitudes varied from 5-50% and frequencies varied from 0.0006-0.1 Hz to alter the spatial distribution and magnitude of oscillatory fluid flow. Solute transport was quantified by monitoring accumulation of fluorescence in a saline bath circulated around the explant. Individual explants were subjected to a series of compression protocols, so that effects of loading on solute desorption could be observed directly. Maximum increases in solute transport were obtained with 10-20% compression amplitudes at 0.1 Hz; similar loading protocols were previously found to stimulate chondrocyte metabolism in vitro. Results therefore support hypotheses relating to increased solute transport as a mediator of the cartilage biological response to dynamic compression, and may have application in mechanical conditioning of cartilage constructs for tissue engineering.     

Direct measurement of turgor and osmotic potential in individual epidermal cells : independent confirmation of leaf water potential as determined by in situ psychrometry

The pressure probe, which is routinely used to measure the turgor potential (Ψ_p) of individual epidermal cells in Tradescantia virginiana (L.), has also been used to sample small volumes of vacuolar fluid from these same cells (as low as 0.02 nl) for measurement of cellular solute (osmotic) potential (Ψ_s) in a micro freezing point osmometer. The water potential components Ψ_p and Ψ_o have been used to calculate the total water potential of individual epidermal cells (Ψ_cell) which has then been directly compared to the total leaf water potential (Ψ_leaf) measured psychrometrically. The relation of Ψ_leaf and Ψ_cell to leaf transpiration indicates that in T. virginiana, a relatively straightforward relation exists between the level of water flow through the leaf tissue, and the ΔΨ within the leaf, between two points along the water flow pathway. Substantial agreement was found between the two independent, in situ methods of measuring Ψ when extrapolated to zero transpiration conditions. These results are discussed with respect to the thermodynamics of water transport in plant tissues.     

Modeling and analysis of radial flow mammalian cell culture

A model for radial flow mammalian cell culture has been developed. Two situations, one with permeable hollow fibers and the other with a porous matrix in the annulus, were considered. The hollow fibers were modeled as continuously distributed sinks. Numerical solutions are presented for the complete model as well as limiting analytical solutions. The analysis identified the importance of various kinetic, transport, and design dimensionless groups for maintenance of radial flow cell culture systems under uniform conditions. The important design parameter was the depth of the bed and the important operating parameter was a modified Damkohler number, both of which should be maintained low for gradient free systems. Dispersion was included in the analysis but substrate consumption was relatively independent of dispersion. Preliminary separation of a low-and high-molecular-weight product was also modeled, and shown to be strongly dependent on the permeability of the fibers, as well as the aspect ratio and the magnitude of the transmembrane flux.