Ansätze zur quantitativen Analyse der Nachrichtenaufnahme und -verarbeitung in biologischen Rezeptoren

The flux equilibrium theory, used for interpretating active and passive ion transport, can explain the generation of receptor potentials. In a model, driving forces and velocity coefficients are represented by the parameters of electric circuits. From these membrane models ionic fluxes can be calculated quantitatively on the basis of transport equations. These equations are derived from the theory of irreversible thermodynamic processes. Receptor models allow a simulation and prediction of the bioelectric potentials which were recorded by other authors in neuro-physiological experiments under various stimulus conditions. The information capacity of a single receptor channel is determined by the ionic flux and the stimulus parameters. In combination with the network of neuron models, receptor models can be used in a perception. The problems of on-off-activation and lateral inhibition were investigated with such a network.     

An equation for flow in the renal proximal tubule

Approximate equations for epithelial solute and water transport have been combined with the relations of mass conservation to yield a single differential equation representing volume flow along the proximal tubule. This flow equation is first order, quasilinear and may be integrated directly. For the steady state, the result is an implicit relation between volume flow and distance along the tubule. For two time-dependent problems (step change of tubule inlet velocity or osmolality) the trajectories (distance as a function of transit time) of a fluid element starting at the inlet are obtained. Differentiation of the steady-state relation with respect to the inlet velocity yields a first-order differential equation relating inlet and outlet velocity. This equation is considered in detail, particularly with regard to the influence of solute-linked water reabsorption. Model calculations with parameters representing rat proximal tubule indicate that it will be difficult to discern coupled water flux in this epithelium from only outlet and inlet flows. Calculations using lower transport rates and lower permeabilities suggest that this equation may be useful in quantifying coupled water flow in proximal tubules from other species.     

Osmotic Pumping and Salt Rejection by Polyelectrolyte Hydrogel for Continuous Solar Desalination

Efficient mass transport and selective salt rejection are highly desirable for solar or thermally driven seawater desalination, but its realization is challenging. Here a new liquid supply mechanism is proposed, i.e., ionic pumping effect, using a polyelectrolyte hydrogel foam (PHF), demonstrated with poly(sodium acrylate) [P(SA)] embedded in a microporous carbon foam (CF). The PHF simultaneously possesses high osmotic pressure for liquid transport and a strong salt‐rejection effect. The PHF is able to sustain high flux of ≈24 L per m² per hour (LMH), comparable to the evaporative flux under 15 suns, and a salt rejection ratio over 80%. Compared to the porous carbon foam without the polyelectrolyte hydrogel, i.e., with only the capillary pumping effect, the PHF yields a 42.4% higher evaporative flux, at ≈1.6 LMH with DI water and ≈1.3 LMH with simulated seawater under one‐sun condition due to the more efficient ionic liquid pumping. More importantly, thanks to the strong salt‐rejection effect, the PHF shows a continuous and stable solar‐driven desalination flux of ≈1.3 LMH under one‐sun over 72 h, which has not been achieved before. The successful demonstration of both efficient ionic pumping and strong salt rejection effects makes the PHF an attractive platform for sustainable solar‐driven desalination.     

Effect of calcium on the potassium flux into the exudate of excised maize roots

Summary The effect of varying calcium concentration in the medium on the potassium flux into the exudate has been studied. In media of low ionic strength (o.1 mM KCl) the potassium flux, J _K, was significantly increased by increasing the calcium concentration of the medium. But in higher ionic strength media (10 mM) KCl) there was no increase in J _K as the calcium concentration of the medium was increased. The effect of external sodium concentration on J _K was also studied. These results are discussed in relation to present theories of salt and water movement into the plant root. It is concluded that two pathways potentially exist for movement of salts to the exudate stream: firstly, via a symplasm and secondly, through the cell wall pathway. But is is further concluded that the cell wall pathway, at normal physiological ionic strengths, is not available for salt transport due to co-ion exclusion by the fixed negative charges.     

Analysis of the Components of Ionic Flux across a Membrane

The unidirectional flux of an ionic species may occur because of several mechanisms such as active transport, passive diffusion, exchange diffusion, etc. The contribution of such mechanisms to the total unidirectional flux across a membrane cannot be determined by only measuring that flux. It is shown that if the pertinent experimental data (the opposite unidirectional fluxes and the composite phenomenological resistance coefficient of the ionic species for a given electrochemical potential difference) obey a certain inequality, then the parameters of a model consisting of parallel, independent, active transport, and passive processes may be determined. Although the existence of "additional" processes including exchange diffusion, single-file pore diffusion, isotope interaction, etc. is not disproved, their existence is unnecessary if the inequality is satisfied. Two types of violations of the inequality may occur: (a) if the upper limit is disobeyed the presence of another substance contributing to the measured resistance and/or a constant affinity of the active transport process may be indicated; (b) if the lower limit is disobeyed it is necessary to postulate the existence of an additional process. For the latter type of violation, exchange diffusion is chosen as an example. Methods are given for determining the contribution of exchange diffusion, active transport, and passive diffusion to the unidirectional flux for some special cases.     

MRI of long-distance water transport: a comparison of the phloem and xylem flow characteristics and dynamics in poplar, castor bean, tomato and tobacco

We used dedicated magnetic resonance imaging (MRI) equipment and methods to study phloem and xylem transport in large potted plants. Quantitative flow profiles were obtained on a per-pixel basis, giving parameter maps of velocity, flow-conducting area and volume flow (flux). The diurnal xylem and phloem flow dynamics in poplar, castor bean, tomato and tobacco were compared. In poplar, clear diurnal differences in phloem flow profile were found, but phloem flux remained constant. In tomato, only small diurnal differences in flow profile were observed. In castor bean and tobacco, phloem flow remained unchanged. In all plants, xylem flow profiles showed large diurnal variation. Decreases in xylem flux were accompanied by a decrease in velocity and flow-conducting area. The diurnal changes in flow-conducting area of phloem and xylem could not be explained by pressure-dependent elastic changes in conduit diameter. The phloem to xylem flux ratio reflects what fraction of xylem water is used for phloem transport (Münch's counterflow). This ratio was large at night for poplar (0.19), castor bean (0.37) and tobacco (0.55), but low in tomato (0.04). The differences in phloem flow velocity between the four species, as well as within a diurnal cycle, were remarkably small (0.25-0.40 mm s(-1)). We hypothesize that upper and lower bounds for phloem flow velocity may exist: when phloem flow velocity is too high, parietal organelles may be stripped away from sieve tube walls; when sap flow is too slow or is highly variable, phloem-borne signalling could become unpredictable.     

Blade motion and nutrient flux to the kelp,Eisenia arborea

Marine algae rely on currents and waves to replenish the nutrients required for photosynthesis. The interaction of algal blades with flow often involves dynamic reorientations of the blade surface (pitching and flapping) that may in turn affect nutrient flux. As a first step toward understanding the consequences of blade motion, we explore the effect of oscillatory pitching on the flux to a flat plate and to two morphologies of the kelp Eisenia arborea. In slow flow (equivalent to a water velocity of 2.7 cm s(-1)), pitching increases the time-averaged flux to both kelp morphologies, but not to the plate. In fast flow (equivalent to 20 cm s(-1) in water), pitching has negligible effect on flux regardless of shape. For many aspects of flux, the flat plate is a reliable model for the flow-protected algal blade, but predictions made from the plate would substantially underestimate the flux to the flow-exposed blade. These measurements highlight the complexities of flow-related nutrient transport and the need to understand better the dynamic interactions among nutrient flux, blade motion, blade morphology, and water flow.     

Nonlinear generalizations of the Kedem-Katachalsky equations for ionic fluxes

The transport equation of Kedem and Katchalsky for the flux of ions through a membrane is generalized to demonstrate explicitly the role of impermeant ions in determining its mathematical form. Whereas the Kedem-Katchalsky equation is linear in the salt concentrations in the bathing solutions, the more general equation is bilinear (and symmetric) in the ionic concentrations of the permeant species. The Kedem-Katchalsky flux equation is further generalized to include explicitly a term for ion-exchange in systems having more than a single permeant salt. This additional term is also bilinear (and antisymmetric) in the concentrations of the exchanging ionic species. Flux equations are derived for systems having (1) a single mono-monovalent salt, (2) two mono-monovalent salts and (3) an arbitrary number of salts with no restriction upon the valencies of the ionic components. Since it has no effect upon the form of concentration-dependent terms in the flux equations, coupling to volume flow is neglected.     

Derivation of the equations that describe the effects of unstirred water layers on the kinetic parameters of active transport processes in the intestine

Unidirectional flux of solutes into the intestinal mucosal cells is determined by the rate of movement of these molecules across both an unstirred water layer and the microvillus membrane of the epithelial cell. Therefore, an equation is derived in this paper that describes the velocity of active transport as a function of the characteristics of both the transport carrier in the membrane and the resistance of the overlying unstirred water layer. Using this equation a series of curves are presented that depict the effect on the kinetics of active transport of varying the thickness (d) or surface area (S_w) of the unstirred water layer, the free diffusion coefficient (D) of the solute, the distribution of active transport sites along the villus ($\text{?}{}_{\mathrm{<mtext>n</mtext>}}$), the maximal transport velocity (J^m_d) and the true Michaelis constant (K_m). These theoretical curves illustrate the serious limitations inherent in interpretation of previously published data dealing with active transport processes in the intestine.     

Nonvascular,Symplasmic Diffusion of Sucrose Cannot Satisfy the Carbon Demands of Growth in the Primary Root Tip of Zea mays L

Nonvascular, symplasmic transport of sucrose (Suc) was investigated theoretically in the primary root tip of maize (Zea mays L. cv WF9 x Mo 17) seedlings. Symplasmic diffusion has been assumed to be the mechanism of transport of Suc to cells in the root apical meristem (R.T. Giaquinta, W. Lin, N.L. Sadler, V.R. Franceschi [1983] Plant Physiol 72: 362-367), which grow apical to the end of the phloem and must build all biomass with carbon supplied from the shoot or kernel. We derived an expression for the growth-sustaining Suc flux, which is the minimum longitudinal flux that would be required to meet the carbon demands of growth in the root apical meristem. We calculated this flux from data on root growth velocity, area, and biomass density, taking into account construction and maintenance respiration and the production of mucilage by the root cap. We then calculated the conductivity of the symplasmic pathway for diffusion, from anatomical data on cellular dimensions and the frequency and dimensions of plasmodesmata, and from two estimates of the diffusive conductance of a plasmodesma, derived from independent data. Then, the concentration gradients required to drive a growth-sustaining Suc flux by diffusion alone were calculated but were found not to be physiologically reasonable. We also calculated the hydraulic conductivity of the plasmodesmatal pathway and found that mass flow of Suc solution through plasmodesmata would also be insufficient, by itself, to satisfy the carbon demands of growth. However, much of the demand for water to cause cell expansion could be met by the water unloaded from the phloem while unloading Suc to satisfy the carbon demands of growth, and the hydraulic conductivity of plasmodesmata is high enough that much of that water could move symplasmically. Either our current understanding of plasmodesmatal ultrastructure and function is flawed, or alternative transport mechanisms must exist for Suc transport to the meristem.     

Ion transport across transmembrane pores

To study the pore-mediated transport of ionic species across a lipid membrane, a series of molecular dynamics simulations have been performed of a dipalmitoyl-phosphatidyl-choline bilayer containing a preformed water pore in the presence of sodium and chloride ions. It is found that the stability of the transient water pores is greatly reduced in the presence of the ions. Specifically, the binding of sodium cations at the lipid/water interface increases the pore line tension, resulting in a destabilization of the pore. However, the application of mechanical stress opposes this effect. The flux of ions through these mechanically stabilized pores has been analyzed. Simulations indicate that the transport of the ions through the pores depends strongly on the size of the water channel. In the presence of small pores (radius <1.5 nm) permeation is slow, with both sodium and chloride permeating at similar rates. In the case in which the pores are larger (radius >1.5 nm), a crossover is observed to a regime where the anion flux is greatly enhanced. Based on these observations, a mechanism for the basal membrane permeability of ions is discussed.     

The relationship between active transport and the exchange diffusion effect

Dependences of unidirectional ionic fluxes across biological membranes on the trans concentrations of the same ion, commonly described as exchange diffusion, and the association of this phenomenon with active transport, are noted. It is suggested that this effect could arise as a result of energetic coupling between the movement of ions conveyed in each direction by the pump if the latter operates near thermodynamic equilibrium and if the rate of the energizing reactions are restricted. This hypothesis is supported by an analysis in which the transport step and the energizing reactions are separated and described according to the laws of chemical kinetics. A likely cause for such restriction of the maximum rate of energy supply is shown to lie in evolutionary optimization of the efficiency of active transport if the energizing reaction is not perfectly coupled. Similar optimization will produce gross ionic fluxes large compared with the net flux, especially if the transport step approaches perfect coupling, when restriction of the rate of energy supply will cause a large exchange diffusion effect. The range of validity of the analysis is examined with particular reference to the ionic exchanges between osmoregulating animals and their surroundings.     

A mathematical model of solute coupled water transport in toad intestine incorporating recirculation of the actively transported solute

A mathematical model of an absorbing leaky epithelium is developed for analysis of solute coupled water transport. The non-charged driving solute diffuses into cells and is pumped from cells into the lateral intercellular space (lis). All membranes contain water channels with the solute passing those of tight junction and interspace basement membrane by convection-diffusion. With solute permeability of paracellular pathway large relative to paracellular water flow, the paracellular flux ratio of the solute (influx/outflux) is small (2-4) in agreement with experiments. The virtual solute concentration of fluid emerging from lis is then significantly larger than the concentration in lis. Thus, in absence of external driving forces the model generates isotonic transport provided a component of the solute flux emerging downstream lis is taken up by cells through the serosal membrane and pumped back into lis, i.e., the solute would have to be recirculated. With input variables from toad intestine (Nedergaard, S., E.H. Larsen, and H.H. Ussing, J. Membr. Biol. 168:241-251), computations predict that 60-80% of the pumped flux stems from serosal bath in agreement with the experimental estimate of the recirculation flux. Robust solutions are obtained with realistic concentrations and pressures of lis, and with the following features. Rate of fluid absorption is governed by the solute permeability of mucosal membrane. Maximum fluid flow is governed by density of pumps on lis-membranes. Energetic efficiency increases with hydraulic conductance of the pathway carrying water from mucosal solution into lis. Uphill water transport is accomplished, but with high hydraulic conductance of cell membranes strength of transport is obscured by water flow through cells. Anomalous solvent drag occurs when back flux of water through cells exceeds inward water flux between cells. Molecules moving along the paracellular pathway are driven by a translateral flow of water, i.e., the model generates pseudo-solvent drag. The associated flux-ratio equation is derived.     

Calcium in Xylem Sap and the Regulation of its Delivery to the Shoot

Amounts of total and free calcium in root and shoot xylem sapwere quantified for a number of species grown in comparableenvironments and in a rooting medium not deficient in calcium.The potential for the shoot to sequester calcium was also examined,along with the ability for ABA to regulate calcium flux to theleaf. Xylem sap calcium showed considerable interspecific and diurnalvariation, even though the plants were grown with similar rhizosphericcalcium concentrations. The potential for the shoot to sequesterxylem sap calcium was also highly variable between species andimplied an ability, at least in some species, to regulate thecalcium reaching the shoot in the transpiration stream. Long distance transport of calcium in the xylem was not primarilyby mass flow, because neither calcium uptake nor distributionwere closely related to water uptake or transpiration. The diurnalchanges in xylem sap total ion concentration appeared to benegatively correlated with transpiration while, in contrast,the calcium ion concentration showed two peaks, one occurringin the dark and the other in the light period. The application of ABA to roots caused an increase in the rateof exudation from the xylem of detopped well-watered plants.These experiments suggest that changes in root water relationsdriven by ionic fluxes were the likely cause for enhanced sapexudation from ABA-treated roots. The steady-state concentrationof calcium in the xylem sap was unaffected by ABA when exudationrate increased and, consequently, the flux of calcium must alsohave increased. Key words: Abscisic acid, calcium, xylem sap, ionic fluxes     

Can numerical modeling help understand the fate of tau protein in the axon terminal?

In this paper, we used mathematical modeling to investigate the fate of tau protein in the axon terminal. We developed a comprehensive model of tau transport that accounts for transport of cytosolic tau by diffusion, diffusion transport of microtubule (MT)-bound tau along the MT lattice, active motor-driven transport of MT-bound tau via slow axonal transport mechanism, and degradation of tau in the axon due to tau's finite half-life. We investigated the effect of different assumptions concerning the fate of tau in the terminal on steady-state transport of tau in the axon. In particular, we studied two possible scenarios: (i) tau is destroyed in the terminal and (ii) there is no tau destruction in the terminal, and to avoid tau accumulation we postulated zero flux of tau at the terminal. We found that the tau concentration and percentage of MT-bound tau are not very sensitive to the assumption concerning the fate of tau in the terminal, but the tau's flux and average velocity of tau transport are very sensitive to this assumption. This suggests that measuring the velocity of tau transport and comparing it with the results of mathematical modeling for different assumptions concerning tau's fate in the terminal can provide information concerning what happens to tau in the terminal.     

Nonequilibrium thermodynamic model of the rat proximal tubule epithelium.

The rat proximal tubule epithelium is represented as well-stirred, compliant cellular and paracellular compartments bounded by mucosal and serosal bathing solutions. With a uniform pCO2 throughout the epithelium, the model variables include the concentrations of Na, K, Cl, HCO3, H2PO4, HPO4, and H, as well as hydrostatic pressure and electrical potential. Except for a metabolically driven Na-K exchanger at the basolateral cell membrane, all membrane transport within the epithelium is passive and is represented by the linear equations of nonequilibrium thermodynamics. In particular, this includes the cotransport of Na-Cl and Na-H2PO4 and countertransport of Na-H at the apical cell membrane. Experimental constraints on the choice of ionic conductivities are satisfied by allowing K-Cl cotransport at the basolateral membrane. The model equations include those for mass balance of the nonreacting species, as well as chemical equilibrium for the acidification reactions. Time-dependent terms are retained to permit the study of transient phenomena. In the steady state the energy dissipation is computed and verified equal to the sum of input from the Na-K exchanger plus the Gibbs free energy of mass addition to the system. The parameter dependence of coupled water transport is studied and shown to be consistent with the predictions of previous analytical models of the lateral intercellular space. Water transport in the presence of an end-proximal (HCO3-depleted) luminal solution is investigated. Here the lower permeability and higher reflection coefficient of HCO3 enhance net sodium and water transport. Due to enhanced flux across the tight junction, this process may permit proximal tubule Na transport to proceed with diminished energy dissipation.     

Differential suppression of axoplasmic transport: Effects of light irradiation to the growth cone of cultured dorsal root ganglion neurons

Summary 1. Growth cones of cultured dorsal root ganglion neurons from mice were irradiated using a mercury lamp.2. The flux of particles of fast retrograde axoplasmic transport decreased promptly after light irradiation without a change in velocity.3. That of anterograde transport decreased as well, but with a significant latency. The decrease in the anterograde flux was attributed to decreased velocity of particles.4. Video-enhanced contrast microscopy of growth cones revealed transient swelling of growth cones and transient stagnation of particles in growth cones.5. The longer the neurite, the larger the latency of the change of the anterograde transport; peripheral information was calculated to be conveyed to the cell body at a speed of 6 µm/min.6. The mechanism of this information conveyance and the export of materials from the cell body are discussed.     

Glutamate, water and ion transport through a charged nanosize pore

The transport of transmitter, ions and water through a positively-charged nanopore was investigated through computer simulations. The physics of the problem is described by a coupled set of Poisson-Nernst-Planck and Navier-Stokes equations in a computational domain consisting a cylindrical pore, whose radius ranged from 1 to 8 nm and which was flanked by two compartments representing the vesicular interior and extra-cellular space. The concentration of co-ions is suppressed and of counter-ions enhanced, especially near the pore wall owing to electrostatic interactions. Glutamate (i.e. the transmitter considered) is negatively charged and is simulated as a counter-ion. The electro-kinetically induced pressure due to the movement of ions is negative and very pronounced near the pore wall where the concentration and flux of counter-ions is very high. The water velocity peaks in the pore center, diminishes to zero at the pore wall, but is constant along the pore axis. The mean velocity of the water/fluid is proportional to the vesicular pressure and pore cross-sectional area. Interestingly it is inversely related to the vesicular glutamate concentration. The factors determining the glutamate flux are complex. The diffusive flux generally predominates for narrow pore, and convective flux may dominate for wide pore if the vesicular pressure is high. Surprisingly at low vesicular pressure the mean total glutamate flux per unit cross-sectional pore area is higher for narrow pores. Higher flux is probably due to the rise of glutamate concentration in the nanopore, which is much more pronounced for narrow nanopores, due to the maintenance of approximate neutrality of charges in the pore and on the pore wall. In conclusion intra-vesicular pressure helps 'flushing-out' the transmitter, but the induced pressure 'drags-out' the water into the extra-cellular space.     

Glutamate, water and ion transport through a charged nanosize pore

The transport of transmitter, ions and water through a positively-charged nanopore was investigated through computer simulations. The physics of the problem is described by a coupled set of Poisson-Nernst-Planck and Navier-Stokes equations in a computational domain consisting a cylindrical pore, whose radius ranged from 1 to 8 nm and which was flanked by two compartments representing the vesicular interior and extra-cellular space. The concentration of co-ions is suppressed and of counter-ions enhanced, especially near the pore wall owing to electrostatic interactions. Glutamate (i.e. the transmitter considered) is negatively charged and is simulated as a counter-ion. The electro-kinetically induced pressure due to the movement of ions is negative and very pronounced near the pore wall where the concentration and flux of counter-ions is very high. The water velocity peaks in the pore center, diminishes to zero at the pore wall, but is constant along the pore axis. The mean velocity of the water/fluid is proportional to the vesicular pressure and pore cross-sectional area. Interestingly it is inversely related to the vesicular glutamate concentration. The factors determining the glutamate flux are complex. The diffusive flux generally predominates for narrow pore, and convective flux may dominate for wide pore if the vesicular pressure is high. Surprisingly at low vesicular pressure the mean total glutamate flux per unit cross-sectional pore area is higher for narrow pores. Higher flux is probably due to the rise of glutamate concentration in the nanopore, which is much more pronounced for narrow nanopores, due to the maintenance of approximate neutrality of charges in the pore and on the pore wall. In conclusion intra-vesicular pressure helps ‘flushing-out’ the transmitter, but the induced pressure ‘drags-out’ the water into the extra-cellular space.     

The Effect of Water and Salt Fluxes on the Trans-root Potential in Helianthus annuus

The effect of an artificially imposed water flux on the trans-rootelectrical potential difference has been studied in excisedsunflower roots. It was found that the potential of the xylemsap became more negative with respect to the external mediumas the rate of water flow was increased. This change appearedto be related to an accompanying increase in the flux of ions. The effect of increasing the water flux on the vacuolar potentialdifference of the epidermal cells was also investigated. Italso became more negative with increasing water flux. Both potentialswere measured simultaneously in the same root. On increasingthe water flux it was found that the trans-root potential beganto rise immediately but there was a time lag of approximately2 min before the vacuolar potential began to change. The relevance of these potential changes to the mechanism andpathway of ion transport across the root is discussed.