Unidirectional Fluxes Research Articles

Fundamental diagrams for pedestrian flows in a channel via an extended social force model

In this paper, an extended social force model was applied to investigate fundamental diagrams of pedestrian flows. In the presented model, both the static floor field and the view field were taken into account. Then each pedestrian can determine his/her desired walking directions according to both global and local information. The fundamental diagrams were obtained numerically under periodic boundary condition. It was found that the fundamental diagrams show good agreement with the measured data in the case of unidirectional flow, especially in the medium density range. However, the fundamental diagram for the case of bidirectional flow gave larger values than the measured data. Furthermore, the bidirectional flux is larger than the unidirectional flux in a certain density range. It is indicated that the bidirectional flow may be more efficient than the unidirectional flow in some cases. The process of lane formation is quite quick in the model. Typical flow patterns in three scenarios were given to show some realistic applications.

Lipid transfer proteins rectify inter-organelle flux and accurately deliver lipids at membrane contact sites

The endoplasmic reticulum (ER) is the main center for the synthesis of various lipid types in cells, and newly synthesized lipids are delivered from the ER to other organelles. In the past decade, various lipid transfer proteins (LTPs) have been recognized as mediators of lipid transport from the ER to other organelles; inter-organelle transport occurs at membrane contact sites (MCSs) and in a nonvesicular manner. Although the intermembrane transfer reaction catalyzed by LTPs is an equilibrium reaction, various types of newly synthesized lipids are transported unidirectionally in cells. This review provides a brief history of the inter-organelle trafficking of lipids and summarizes the structural and biochemical characteristics of the ceramide transport protein (CERT) as a typical LTP acting at MCSs. In addition, this review compares several LTP-mediated inter-organelle lipid trafficking systems and proposes that LTPs generate unidirectional fluxes of specific lipids between different organelles by indirect coupling with the metabolic reactions that occur in specific organelles. Moreover, the available data also suggest that the major advantage of LTP-mediated lipid transport at MCSs may be the accuracy of delivery. Finally, how cholesterol is enriched in the plasma membrane is discussed from a thermodynamic perspective.

A dynamic method for the measurement of pyroelectric properties of materials

This study introduces a novel experimental set-up to measure the pyroelectric coefficient of materials at variable frequencies of temperature change. In this method, temperature changes are periodically applied through a mechanical set-up moving the sample between a hot and cold thermal reservoir in order to measure the current obtained from the sample’s pyroelectric conversion effect. For low frequencies of temperature change, an exponential equation is suggested for the temperature change in the sample based on a unidirectional heat flux through the sample. The pyroelectric coefficient can be determined from this model by fitting an exponential decay function to the pyroelectric current obtained from a single heating cycle. In comparison to other approaches for the measurement of the pyroelectric effect, the described method exhibits some advantages concerning flexibility, accuracy and simplicity, e.g. an almost deliberate adjustment of the rate of temperature change, the avoidance of electrical noise induced by continuously temperature-modulated heat stages and furnaces, a high accuracy of temperature control and the acceptance of samples made from different materials or with different sizes. The method is verified by pyroelectric coefficient measurements on a commercial PZT ceramic and on triglycine sulfate (TGS) single crystals, which have been grown by a temperature-lowering technique in our laboratory. Pyroelectric measurements were conducted at different temperature differences for samples with different thicknesses and contact areas. The measurement results for PZT M202 (427 ± 1 μC m–2 K–1) are close to the datasheet value, which is 430 μC m–2 K–1. An average pyroelectric coefficient of 306 ± 2 μC m–2 K–1) is measured for the single crystal of TGS over multiple trials. The measurement results depend on the quality of the crystal and the process for the preparation of the sample. The results show internal consistency between the measurements, which are also in agreement with literature values.

Communication: Transition-path velocity as an experimental measure of barrier crossing dynamics.

Experimental observation of transition paths-short events when the system of interest crosses the free energy barrier separating reactants from products-provides an opportunity to probe the dynamics of barrier crossing. Yet limitations in the experimental time resolution usually result in observing trajectories that are smoothed out, recross the transition state fewer times, and exhibit apparent velocities that are much lower than the instantaneous ones. Here we show that it is possible to define (and measure) an effective transition-path velocity which preserves exact information about barrier crossing dynamics in the following sense: the exact transition rate can be written in a form resembling that given by transition-state theory, with the mean thermal velocity replaced by the transition-path velocity. In addition, the transition-path velocity (i) ensures the exact local value of the unidirectional reactive flux at equilibrium and (ii) leads to the exact mean transition-path time required for the system to cross the barrier region separating reactants from products. We discuss the coordinate dependence of the transition path velocity and derive analytical expressions for it in the case of diffusive dynamics. These results can be used to discriminate among models of barrier crossing dynamics in single-molecule force spectroscopy studies.

Coexpression of proximal tubule claudins‐2 and ‐10a increases conductance and decreases permselectivity in a renal epithelial cell line

The mammalian nephron is composed of a series of tubule segments with distinct patterns of tight junction morphology, ion selectivity, and protein expression. Paracellular permeability of epithelial tissues is determined in part by claudins, a family of tight junction membrane proteins. The most abundantly expressed claudins in the proximal tubule (PT) are claudin‐2 and ‐10a. In general, claudin‐2 is expressed in leaky epithelia and functions as a cation‐permeable paracellular channel, whereas claudin‐10a has been shown to form anion‐selective pores. We hypothesized that coexpression of these PT claudins leads to distinct paracellular permeability properties, and contribute to ion transport in this segment.We established a double‐inducible, titratable gene expression system using Madin‐Darby canine kidney cells (MDCK I). Utilizing tetracycline‐controlled transcriptional activation (Tet‐Off), we developed stable cell lines which expressed claudin‐2 in the absence of tetracycline antibiotics. From this parent line, we generated stable transfectants expressing claudin‐10a under the control of a cumate‐inducible switch (SBI). Induction of claudin‐2, ‐10a, or both isoforms, all reduced TER compared to cells with no claudin overexpression (p<0.0001 using 2‐way ANOVA). We found a marked increase in PCl in cells induced to express claudin‐10a alone (17.4 ± 1.7 * 106 cm/s vs. 0.55 ± 0.06 * 106 cm/s with no induction), and a marked increase in PNa in cells induced to express claudin‐2 alone (12.2 ± 0.6 * 106 cm/s vs. 0.59 ± 0.07 * 106 cm/s with no induction). When both claudin‐2 and ‐10a were expressed, PCl and PNa were both increased (to 9.5 ± 1.5 * 106 cm/s and 6.2 ± 0.4 * 106 cm/s, respectively) and PNa/PCl was unchanged (0.76 ± 0.10 vs. 1.07 ± 0.05 with no induction). Calcium transport is believed to occur via a paracellular route in the PT, and so we measured the effect of PT claudin overexpression on unidirectional 45calcium radiotracer flux. Claudin‐2 expression increased calcium flux by over 7‐fold (p<0.0001), while claudin‐10a had no effect compared with no expression (p=0.99). No difference was detected in calcium flux between claudin‐2 expression and claudin‐2 and ‐10a in combination (p=0.89). These results further support claudin‐2 as the mediator of calcium reabsorption in the PT, and suggest that an interaction between PT claudin isoforms reduces the permselectivity of the PT to sodium and chloride.Support or Funding InformationSupported in part by NIH grant F30DK109605This abstract is from the Experimental Biology 2018 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.

Oscillatory dissipative conjugate heat and mass transfer in chemically reacting micropolar flow with wall couple stress: A finite element numerical study

High temperature non-Newtonian materials processing provides a stimulating area for process engineering simulation. Motivated by emerging applications in this area, the present article studies time-dependent free convective flow of a chemically reacting micropolar fluid from a vertical plate oscillating in its own plane adjacent to a porous medium. Thermal radiative, viscous dissipation and wall couple stress effects are included. The Rosseland diffusion approximation is used to model uni-directional radiative heat flux in energy equation. Darcy’s model is adopted to mimic porous medium drag force effect. The governing two-dimensional conservation equations are normalized with appropriate variables and transformed into a dimensionless, coupled, nonlinear system of partial differential equations under the assumption of low Reynolds number. The governing boundary value problem is then solved under physically viable boundary conditions numerically with a finite element method based on the weighted residual approach. Graphical illustrations for velocity, micro-rotation (angular velocity), temperature, and concentration are obtained as functions of the emerging physical parameters, i.e. thermal radiation, viscous dissipation, first-order chemical reaction parameter, etc. Furthermore, friction factor (skin friction), surface heat transfer and mass transfer rates have been tabulated quantitatively for selected thermo-physical parameters. A comparison with previously published article is made to check the validity and accuracy of the present finite element solutions under some limiting cases and excellent agreement is attained. Additionally, a mesh independence study is conducted. The model is relevant to reactive polymeric materials processing simulation.

Permeation of acetate across sheep ruminal epithelium is partly mediated by an anion channel

The present study pursued the question if an anion channel could be partly responsible for the transport of acetate in the isolated ovine ruminal epithelium. Using the Ussing chamber technique, changes of short-circuit current (Isc) induced by mucosal or serosal addition of acetate was investigated. To further evaluate the Isc changes induced by acetate the epithelia were preincubated with ouabain or 4,4′-diisothiocyano-2,2′-stilbenedisulfonic acid (DIDS). In addition, unidirectional flux rates of 14C-acetate were measured at different transepithelial potential difference (Vt). At Vt=0mV, acetate addition to the mucosal side of epithelia incubated in ouabain/DIDS free solution resulted in an Isc decrease, whereas application to the serosal side induced an Isc increase. Absolute Isc changes were significantly larger after serosal than after mucosal acetate addition. Ouabain pre-incubation abolished these side-specific differences. Pre-incubation with DIDS on the mucosal side inhibited the current induced by subsequent mucosal acetate addition in a voltage dependent manner, whereas serosal DIDS pre-incubation had no effect on acetate-induced changes of Isc. Mucosal-to-serosal acetate flux was partly voltage-dependent. The serosal-to-mucosal flux of acetate was not influenced by Vt. The asymmetric changes of Isc after acetate application and the Vt dependence of the DIDS inhibition on the mucosal side indicate a partly electrogenic transcellular permeation of acetate which includes an apically located acetate conductance. It is suggested that this conductance may be important for epithelial cell homeostasis.

Flow-boiling canopy wick for extreme heat transfer

The maximum theoretical boiling heat transfer rate qmax is set by interface unidirectional thermal vapor flux, and quest continues for achieving a high fraction of it under saturated liquid flow. We introduce the flow-boiling canopy wick (FBCW) employing film (meniscus) evaporation and perforated screenlayer separating the liquid stream from the underlying vapor space. The vapor vents continuously through periodic perforations, in contrast to plain surface which becomes completely covered by vapor at high heat flux. The FBCW allows streamwise liquid tracks on the screenlayer between perforations providing capillary liquid flow toward heated surface and evaporation on high-effective-conductivity monolayer wick. Under extreme heat flux, various hydrodynamic limits prevent liquid supply and vapor removal, i.e., the capillary-viscous, wick superheat, perforation pressure drop and chocking and liquid-vapor stability limits. The liquid and vapor inertiae control the streamwise continuous liquid track (with isolated and/or merged vapor track) and for saturated water at 1 atm CFD and wick pressure drop predict heat flux up to 0.1qmax = 20 MW/m2, an order-of-magnitude larger than the nucleate flow-boiling limit. The concept of replacing the chaotic nucleated bubbles with the structured, continuous vapor venting in the periodic FBCW transforms boiling heat transfer and its upper limit.

Shock‐Induced Disappearance and Subsequent Recovery of Plasmaspheric Hiss: Coordinated Observations of RBSP, THEMIS, and POES Satellites

AbstractPlasmaspheric hiss is an extremely low frequency whistler‐mode emission contributing significantly to the loss of radiation belt electrons. There are two main competing mechanisms for the generation of plasmaspheric hiss: excitation by local instability in the outer plasmasphere and origination from chorus outside the plasmasphere. Here on the basis of the analysis of an event of shock‐induced disappearance and subsequent recovery of plasmaspheric hiss observed by RBSP, THEMIS, and POES missions, we attempt to identify its dominant generation mechanism. In the preshock plasmasphere, the local electron instability was relatively weak and the hiss waves with bidirectional Poynting fluxes mainly originated from the dayside chorus waves. On arrival of the shock, the removal of preexisting dayside chorus and the insignificant variation of low‐frequency wave instability caused the prompt disappearance of hiss waves. In the next few hours, the local instability in the plasmasphere was greatly enhanced due to the substorm injection of hot electrons. The enhancement of local instability likely played a dominant role in the temporary recovery of hiss with unidirectional Poynting fluxes. These temporarily recovered hiss waves were generated near the equator and then propagated toward higher latitudes. In contrast, both the enhancement of local instability and the recurrence of prenoon chorus contributed to the substantial recovery of hiss with bidirectional Poynting fluxes.

Flux Ratios and Channel Structures

We investigate Ussing's unidirectional fluxes and flux ratios of charged tracers motivated particularly by the insightful proposal of Hodgkin and Keynes on a relation between flux ratios and channel structure. Our study is based on analysis of quasi-one-dimensional Poisson-Nernst-Planck type models for ionic flows through membrane channels. This class of models includes the Poisson equation that determines the electrical potential from the charges present and is in that sense consistent. Ussing's flux ratios generally depend on all physical parameters involved in ionic flows, particularly, on bulk conditions and channel structures. Certain setups of ion channel experiments result in flux ratios that are universal in the sense that their values depend on bulk conditions but not on channel structures; other setups lead to flux ratios that are specific in the sense that their values depend on channel structures too. Universal flux ratios could serve some purposes better than specific flux ratios in some circumstances and worse in other circumstances. We focus on two treatments of tracer flux measurements that serve as estimators of important properties of ion channels. The first estimator determines the flux of the main ion species from measurements of the flux of its tracer. Our analysis suggests a better experimental design so that the flux ratio of the tracer flux and the main ion flux is universal. The second treatment of tracer fluxes concerns ratios of fluxes and experimental setups that try to determine some properties of channel structure. We analyze the two widely used experimental designs of estimating flux ratios and show that the most widely used method depends on the spatial distribution of permanent charge so this flux ratio is specific and thus allows estimation of (some of) the properties of that permanent charge, even with ideal ionic solutions. ...

Bryophyte gas-exchange dynamics along varying hydration status reveal a significant carbonyl sulphide (COS) sink in the dark and COS source in the light.

Summary Carbonyl sulphide (COS) is a potential tracer of gross primary productivity (GPP), assuming a unidirectional COS flux into the vegetation that scales with GPP. However, carbonic anhydrase (CA), the enzyme that hydrolyses COS, is expected to be light independent, and thus plants without stomata should continue to take up COS in the dark.We measured net CO 2 (AC) and COS (AS) uptake rates from two astomatous bryophytes at different relative water contents (RWCs), COS concentrations, temperatures and light intensities.We found large AS in the dark, indicating that CA activity continues without photosynthesis. More surprisingly, we found a nonzero COS compensation point in light and dark conditions, indicating a temperature‐driven COS source with a Q 10 (fractional change for a 10°C temperature increase) of 3.7. This resulted in greater AS in the dark than in the light at similar RWC. The processes underlying such COS emissions remain unknown.Our results suggest that ecosystems dominated by bryophytes might be strong atmospheric sinks of COS at night and weaker sinks or even sources of COS during daytime. Biotic COS production in bryophytes could result from symbiotic fungal and bacterial partners that could also be found on vascular plants.

Porcine milk induces a strengthening of barrier function in porcine jejunal epithelium in vitro.

Milk contains a variety of components that have been shown to affect the expression and localization of epithelial tight junction proteins and therefore the intestinal barrier. Thus, we hypothesized that milk would have an effect on intestinal barrier properties, owing to effects on the tight junction in an intraspecies porcine intestinal in vitro model. Jejunal samples of piglets derived from different age groups were analyzed. Transepithelial electrical resistance was recorded employing the Ussing chamber technique. Porcine milk or predigested milk in buffer solution was added to the apical side, and effects were compared to untreated controls. Unidirectional paracellular flux measurements were performed using sodium fluorescein. Tight junction protein expression and localization were analyzed by immunoblotting and immunofluorescence microscopy. Incubation with milk or predigested milk led to an increase in transepithelial electrical resistance, while paracellular permeability for sodium fluorescein did not result in significant changes. Densitometric analysis of immunoblot signals did not show significant alterations in claudin expression, but a reduction of claudin signals in apicolateral membrane compartments in both approaches became apparent via immunohistology. The functional effect might reflect a physiological protective mechanism, when offspring exclusively rely on their mother's milk and are exposed to a plethora of potentially barrier-perturbing factors.

Forskolin (cAMP) Promotes Insertion of Large Conductance Potassium (KCa1.1) Channels into Apical Membranes of Rat Distal Colon

Mammalian colon contributes significantly to overall K+ homeostasis. Under normal conditions, the proximal colon secretes and distal colon absorbs K+. Distal colon also has a secretory capacity, which becomes important to K+ homeostasis under pathological conditions, such as end‐stage renal failure. K+ secretion in the distal colon is primarily mediated through apical large conductance (BK) channels. We hypothesized that the BK opener BMS‐204352 (BMS) and the adenylate cyclase activator forskolin (FSK) induce K+ secretion through separate mechanisms. K+ flux studies were performed in distal colonic mucosal tissues obtained from male Sprague‐Dawley rats (200–225g). Unidirectional 86Rb fluxes (K+ surrogate), and short‐circuit current (ISC) were measured under voltage‐clamped conditions in an Ussing chamber setup. Fluxes were performed in the presence of amiloride (10 mM) to inhibit ENaC‐mediated ISC, as well as VO4 (1mM) to inhibit apical H+/K+ ATPase and unmask BK‐mediated K+ secretion. Results indicate that BMS (10mM) and FSK (10mM) induced a net K+ secretion of 0.083 ± 0.04 and 0.274 ± 0.05 mEq/cm2·hr, respectively (n=4, p<0.05). FSK, but not BMS, increased ISC compared to baseline (220.5 ± 30.5 vs 132.2 ± 18.7 uA/cm2). Immunofluorescence studies performed on the same tissues used in flux experiments showed markedly increased apical BK staining in tissues exposed to FSK, but not in those exposed to only BMS. Taken together, these data suggest that while BMS may only open BK channels already present on apical membranes, FSK may cause further K+ secretion by triggering the insertion of more BK channels into the apical membrane.Support or Funding Information• R01 DK104791/DK/NIDDK NIH HHS/United States

Segmental diversity of phosphate transport along the intestinal axis in horses.

For horses, distinct differences in intestinal phosphate transport have been postulated to account for the unique features of hind gut fermentation compared to other monogastric animals and ruminants. So far published data on mechanisms and underlying transport proteins involved in intestinal phosphate transport in the horse are still missing. Therefore we investigated intestinal phosphate transport in horses at both functional and molecular levels. Segmental diversity of intestinal phosphate transport along the intestinal axis was documented using the Ussing chamber technique. A transcellular phosphate secretion in the jejunum was confirmed. Furthermore, 2 sodium-dependent phosphate cotransporters, NaPiIIb and PiT1, were first detected in the equine intestine at mRNA level with PiT1 being expressed in both the small and large intestine, and NaPiIIb being solely expressed in the large intestine. In the colon, unidirectional net flux rates of phosphate were significantly greater compared to flux rates in other segments ( < 0.005) suggesting the colon as a major site for phosphate absorption in horses. Phosphate transport in the colon was mainly transcellular and mediated by a sodium-gradient as documented by Ussing chamber experiments and uptake of phosphate into colonic brush border membrane vesicles. In summary, the present study demonstrated mechanisms and transporters of intestinal phosphate transport in equine intestinal tissues with distinct differences between intestinal segments providing a new basis for a better understanding of intestinal phosphate transport in horses.

Experimental stydy of chloride transport into double layered components with concrete and rendering mortar

This work studied the influence of rendering mortar layer on chloride transport into concrete structures. Concrete specimens rendered with three different mortar mixtures and two rendering thickness were used. Five of the six faces of the specimens were coated with epoxy resin to simulate unidirectional flux. The specimens were subjected to weekly wetting and drying cycles in a sodium chloride solution for 49 days. At the end, total chloride profiles were obtained. Results show that rendering mortars influence chloride transport into concrete and this is more accentuated for less porous mortars and with higher cement content. There is also a chloride accumulation close to the interface mortar-concrete region, which is explained by the differences on chloride transport ability between mortar and concrete. Although mortars are more porous than concrete, they can represent an additional protection against chloride penetration into concrete.

Brillouin cooling in a linear waveguide

Brillouin scattering is not usually considered as a mechanism that can cause cooling of a material due to the thermodynamic dominance of Stokes scattering in most practical systems. However, it has been shown in experiments on resonators that net phonon annihilation through anti-Stokes Brillouin scattering can be enabled by means of a suitable set of optical and acoustic states. The cooling of traveling phonons in a linear waveguide, on the other hand, could lead to the exciting future prospect of manipulating unidirectional phonon fluxes and even the nonreciprocal transport of quantum information via phonons. In this work, we present an analysis of the conditions under which Brillouin cooling of phonons of both low and high group velocities may be achieved in a linear waveguide. We analyze the three-wave mixing interaction between the optical and traveling acoustic modes that participate in forward Brillouin scattering, and reveal the key regimes of operation for the process. Our calculations indicate that measurable cooling may occur in a system having phonons with spatial loss rate that is of the same order as the spatial optical loss rate. If the Brillouin gain in such a waveguide reaches the order of 105 m−1 W−1, appreciable cooling of phonon modes may be observed with modest pump power of a few mW.

Asymmetry in inward- and outward-affinity constant of transport explain unidirectional lysine flux in Saccharomyces cerevisiae

The import of basic amino acids in Saccharomyces cerevisiae has been reported to be unidirectional, which is not typical of how secondary transporters work. Since studies of energy coupling and transport kinetics are complicated in vivo, we purified the major lysine transporter (Lyp1) of yeast and reconstituted the protein into lipid vesicles. We show that the Michaelis constant (KM) of transport from out-to-in is well in the millimolar range and at least 3 to 4-orders of magnitude higher than that of transport in the opposite direction, disfavoring the efflux of solute via Lyp1. We also find that at low values of the proton motive force, the transport by Lyp1 is comparatively slow. We benchmarked the properties of eukaryotic Lyp1 to that of the prokaryotic homologue LysP and find that LysP has a similar KM for transport from in-to-out and out-to-in, consistent with rapid influx and efflux. We thus explain the previously described unidirectional nature of lysine transport in S. cerevisiae by the extraordinary kinetics of Lyp1 and provide a mechanism and rationale for previous observations. The high asymmetry in transport together with secondary storage in the vacuole allow the cell to accumulate basic amino acids to very high levels.

Conditions for duality between fluxes and concentrations in biochemical networks

Mathematical and computational modelling of biochemical networks is often done in terms of either the concentrations of molecular species or the fluxes of biochemical reactions. When is mathematical modelling from either perspective equivalent to the other? Mathematical duality translates concepts, theorems or mathematical structures into other concepts, theorems or structures, in a one-to-one manner. We present a novel stoichiometric condition that is necessary and sufficient for duality between unidirectional fluxes and concentrations. Our numerical experiments, with computational models derived from a range of genome-scale biochemical networks, suggest that this flux-concentration duality is a pervasive property of biochemical networks. We also provide a combinatorial characterisation that is sufficient to ensure flux-concentration duality.The condition prescribes that, for every two disjoint sets of molecular species, there is at least one reaction complex that involves species from only one of the two sets. When unidirectional fluxes and molecular species concentrations are dual vectors, this implies that the behaviour of the corresponding biochemical network can be described entirely in terms of either concentrations or unidirectional fluxes.

Unidirectional Flux Balance of Monovalent Ions in Cells with Na/Na and Li/Na Exchange: Experimental and Computational Studies on Lymphoid U937 Cells.

Monovalent ion traffic across the cell membrane occurs via various pathways. Evaluation of individual fluxes in whole cell is hampered by their strong interdependence. This difficulty can be overcome by computational analysis of the whole cell flux balance. However, the previous computational studies disregarded ion movement of the self-exchange type. We have taken this exchange into account. The developed software allows determination of unidirectional fluxes of all monovalent ions via the major pathways both under the balanced state and during transient processes. We show how the problem of finding the rate coefficients can be solved by measurement of monovalent ion concentrations and some of the fluxes. Interdependence of fluxes due to the mandatory conditions of electroneutrality and osmotic balance and due to specific effects can be discriminated, enabling one to identify specific changes in ion transfer machinery under varied conditions. To test the effectiveness of the developed approach we made use of the fact that Li/Na exchange is known to be an analogue of the coupled Na/Na exchange. Thus, we compared the predicted and experimental data obtained on U937 cells under varied Li+ concentrations and following inhibition of the sodium pump with ouabain. We found that the coupled Na/Na exchange in U937 cells comprises a significant portion of the entire Na+ turnover. The data showed that the loading of the sodium pump by Li/Na exchange involved in the secondary active Li+ transport at 1–10 mM external Li+ is small. This result may be extrapolated to similar Li+ and Na+ flux relationships in erythrocytes and other cells in patients treated with Li+ in therapeutic doses. The developed computational approach is applicable for studying various cells and can be useful in education for demonstrating the effects of individual transporters and channels on ion gradients, cell water content and membrane potential.

Energy-Based Magnetization and Magnetostriction Modeling of Grain-Oriented Silicon Steel Under Vectorial Excitations

The assembled domain structure model (ADSM) is an energy-based macroscopic magnetization model of a core material. In this paper, we used the ADSM to simulate the magnetization curves and magnetostriction of a grain-oriented (GO) silicon steel sheet under vectorial excitations, and we measured the same sheet using the rotational single-sheet tester with a three-element strain gage rosette. In the simulation, the target value of the average magnetization vector representing unidirectional or rotational magnetic flux is given as a known parameter. We obtained the magnetization state by finding the external magnetic field vector and state vectors, satisfying the criteria that the average magnetization vector equals the target value and that the total magnetic energy is locally minimized. The simulation reconstructed the magnetostriction produced by the 90° domain-wall motion under unidirectional magnetization as well as the vectorial contraction and extension under rotational magnetization.