The Kinetics of Sodium Transport in the Toad Bladder : I. Determination of the transport pool

A compartmental model of toad bladder sodium content has been developed, whereby it is possible to measure the four unidirectional fluxes across the opposite faces of the transport compartment, as well as the amount of sodium in the compartment. ²⁴Na is added to the mucosal medium of a short-circuited bladder mounted between halves of a chamber in which the fluid is stirred by rotating impellers. After a steady state is reached, nonradioactive medium is flushed through both sides of the chamber, collected, and counted. The data from each chamber are fitted to sums of exponentials and interpreted in terms of conventional compartmental analysis. Three exponentials are required, with half-times of 0.2, 2.2, and 14.0 min. It is shown that the first of these represents chamber washout, the second the transport pool, and the third a tissue compartment which is not involved in active sodium transport and which does not communicate with the transport pool. The second compartment contains 10.5 µEq of sodium per 100 mg dry weight, an amount equal to approximately 30% of total tissue sodium. The results also indicate, as expected from electrophysiological data, that the mucosal-facing side of the transport compartment is over 10 times as permeable to sodium as the serosal, or pump, side.     

The role of endosomal traffic in the transendothelial transport of ceruloplasmin in the liver

Through a process resembling receptor-mediated endocytosis, liver endothelium binds and internalizes the plasma glycoprotein ceruloplasmin (CP) on the luminal side. The protein is then transported via a vesicular system to the albuminal side where it is externalized to the space of Disse. In its path, the glycoprotein is fully desialylated. To determine if the endosomal compartment is involved in this transport, we used endosomal inhibitors NH4Cl, ethylamine as well as monensin to quantitatively measure the magnitude of radiolabeled CP transport across purified liver endothelial cells. All three reagents inhibited the transport of CP and its discharge by endothelium. The magnitude of inhibition was dose-related for all three reagents. We conclude that the endosomal compartment is involved in the transendothelial transport of CP across the liver endothelium.     

A two-barrier compartment model for volume flow across amphibian skin

The amphibian skin has long been used as a model tissue for the study of ion transport and osmotic water movement across tight epithelia. To understand the mechanism of water uptake across amphibian skin, we model the skin as a well-stirred compartment bounded by an apical barrier and a tissue barrier. The compartment represents the lateral intercellular space between cells in the stratum granulosum. The apical barrier represents the stratum corneum, the principal/mitochondria-rich cells, and the junctional area between cells. This barrier is hypothesized to have the ability to actively transport solutes through Na+-K+-ATPase. The actively transported solute flux is assumed to satisfy the Michaelis-Menten relationship. The tissue barrier represents a composite barrier comprising the stratum spinosum, the stratum germinativum, the basal lamina, and the dermis. Our model shows that 1) the predicted rehydration rates from apical bathing solutions are in good agreement with the experiment results in Hillyard and Larsen (J Comp Physiol 171: 283-292, 2001); 2) under their experimental conditions, there is a substantial volume flux coupled to the active solute flux and this coupled volume flux is nearly constant when the osmolality of the apical bathing solution is >100 mosmol/kgH2O; 3) the molar ratio of the actively transported solute flux to the coupled water flux is about 1:160, which is the same as that reported in Nielsen (J Membr Biol 159: 61-69, 1997).     

Nonsteady-State Three Compartment Tracer Kinetics: II. Sodium Flux Transients in the Toad Urinary Bladder in Response to Short Circuit

The theoretical approach presented in the previous paper provides an analytical method for determining the unidirectional, nonsteady-state fluxes in a three compartment system. Based on this a study was made of the sodium flux transients in the toad urinary bladder. A transient time-dependent state was generated by suddenly short-circuiting a bladder previously maintained in an open-circuited steady state. The sequence of experiments suggested by the theory provided the data required for the analysis. The results of these tracer experiments were consistent with the complex non-three compartmental structure of this tissue. As a result both of the inadequacy of the three compartment model in representing the tissue and of certain experimental difficulties, attempts at a quantitative solution were not entirely successful. Useful information was nevertheless obtained through a careful use of this model, and a qualitative analysis implied that the sodium influxes into the tissue at both of its surfaces are sensitive to changes in electrical potential while both effluxes are insensitive to this change. This suggests that both of the effluxes result from active processes while both influxes are associated with passive processes. The net transepithelial transport of sodium would then necessarily result from a more complex polarization than that proposed by Koefoed-Johnsen and Ussing.     

Transport of heterocyclic acids across rat small intestinein Vitro

Summary A study has been made of the steady-state fluxes of barbituric acid, six of its substituted derivatives, and 5,5-dimethyloxazolidinedione (DMO) across the wall of rat jejunumin vitro. For each of the compounds tested the mucosal (M) to serosal (S) flux was significantly larger than theS toM flux. BothM toS andS toM fluxes increased linearly with concentration, and the transport of one acid was not influenced by the presence of a tenfold greater concentration of a second heterocyclic acid. The fluxes decreased as the pH of the incubation saline was increased, but neither theM toS, nor theS toM fluxes could be described in terms of simple nonionic diffusion. It was found that the relation between the flux ratios of the transported acids and their pK _a values could be described by an equation derived from consideration of the transport of a weak acid in a series three compartment system, and it has been concluded that the three compartment system provides a good working hypothesis for the mechanism of heterocyclic acid transport across rat jejunum. It was found that the best fit of the theoretical curve to the experimental data was obtained when the ratio of permeabilities to the ionized and nonionized forms of a weak acid at one of the barriers was assigned the value 5×10^–1. It is suggested that this value may be characteristic of a noncellular restriction to diffusion, such as a layer of connective tissue, and substantiates previous suggestion that the intermediate compartment of the intestinal three compartment system is a component of the sub-epithelial extracellular space.     

Substrate supply for calcite precipitation in Emiliania huxleyi: assessment of different model approaches

Over the last four decades, different hypotheses of Ca²⁺ and dissolved inorganic carbon transport to the intracellular site of calcite precipitation have been put forth for Emiliania huxleyi (Lohmann) Hay & Mohler. The objective of this study was to assess these hypotheses by means of mathematical models. It is shown that a vesicle‐based Ca²⁺ transport would require very high intravesicular Ca²⁺ concentrations, high vesicle fusion frequencies as well as a fast membrane recycling inside the cell. Furthermore, a kinetic model for the calcification compartment is presented that describes the internal chemical environment in terms of carbonate chemistry including calcite precipitation. Substrates for calcite precipitation are transported with different stoichiometries across the compartment membrane. As a result, the carbonate chemistry inside the compartment changes and hence influences the calcification rate. Moreover, the effect of carbonic anhydrase (CA) activity within the compartment is analyzed. One very promising model version is based on a Ca²⁺/H⁺ antiport, CO₂ diffusion, and a CA inside the calcification compartment. Another promising model version is based on an import of Ca²⁺ and HCO₃^? and an export of H⁺.     

用胆固醇代谢的房室模型速率系数来分析动脉粥样硬化程度

理论上认为胆固醇逆向转运的速率与动脉粥样硬化程序呈负相关。但目前尚无完善的测试血浆脂蛋白－胆固醇体内代谢的方法。我们运用同位素＾３Ｈ－胆固醇示踪方法,建立房室模型,选取健康兔与ＡＳ兔对照,研究血浆脂蛋白转运胆固醇能力的差异,并结合ＡＳ兔主动脉斑块程度对比,结果验证了上述理论,此法如改用短半衰期同位素或稳定性同位素标记的胆固醇,就可用于人体,这可为临床判断ＡＳ程度提供一种无创性的新方法。     

A mixture theory model of fluid and solute transport in the microvasculature of normal and malignant tissues. I. Theory

In order to better understand the mechanisms governing transport of drugs, nanoparticle-based treatments, and therapeutic biomolecules, and the role of the various physiological parameters, a number of mathematical models have previously been proposed. The limitations of the existing transport models indicate the need for a comprehensive model that includes transport in the vessel lumen, the vessel wall, and the interstitial space and considers the effects of the solute concentration on fluid flow. In this study, a general model to describe the transient distribution of fluid and multiple solutes at the microvascular level was developed using mixture theory. The model captures the experimentally observed dependence of the hydraulic permeability coefficient of the capillary wall on the concentration of solutes present in the capillary wall and the surrounding tissue. Additionally, the model demonstrates that transport phenomena across the capillary wall and in the interstitium are related to the solute concentration as well as the hydrostatic pressure. The model is used in a companion paper to examine fluid and solute transport for the simplified case of an axisymmetric geometry with no solid deformation or interconversion of mass.     

The Kinetics of Sodium Transport in the Toad Bladder : II. Dual effects of vasopressin

In the accompanying paper, a compartmental model for the toad bladder sodium transport system was developed. In the present paper, the model is tested by determining the effects of antidiuretic hormone on the pools and fluxes. It is shown that this hormone affects only that sodium pool previously designated as the transport pool, and that the effects are on two separate sites. In the first place, the hormone stimulates entry at the mucosal side of the transport compartment, and by this means brings about an increase in the amount of sodium contained in the compartment. Second, the hormone has a distinct stimulatory effect on the rate coefficient for efflux across the serosal boundary, the pump rate coefficient. Evidence is presented that under control conditions, the pump rate coefficient is a decreasing function of the pool size, a characteristic feature of a saturating system. Therefore, the effect of vasopressin in increasing both the pool size and the pump rate coefficient must be construed as a direct effect on the pump, and not one which is secondary to the increase in the pool size. Furthermore, it is shown that the effect of the hormone on the sodium pump is not dependent on the presence of sodium in the serosal medium.     

Stochastic Dynamic Model for Estimation of Rate Constants and Their Variances from Noisy and Heterogeneous PET Measurements

Tissue heterogeneity, radioactive decay and measurement noise are the main error sources in compartmental modeling used to estimate the physiologic rate constants of various radiopharmaceuticals from a dynamic PET study. We introduce a new approach to this problem by modeling the tissue heterogeneity with random rate constants in compartment models. In addition, the Poisson nature of the radioactive decay is included as a Poisson random variable in the measurement equations. The estimation problem will be carried out using the maximum likelihood estimation. With this approach, we do not only get accurate mean estimates for the rate constants, but also estimates for tissue heterogeneity within the region of interest and other possibly unknown model parameters, e.g. instrument noise variance, as well. We also avoid the problem of the optimal weighting of the data related to the conventionally used weighted least-squares method. The new approach was tested with simulated time–activity curves from the conventional three compartment – three rate constants model with normally distributed rate constants and with a noise mixture of Poisson and normally distributed random variables. Our simulation results showed that this new model gave accurate estimates for the mean of the rate constants, the measurement noise parameter and also for the tissue heterogeneity, i.e. for the variance of the rate constants within the region of interest.     

Physiologically based pharmacokinetic models for the transport of trichloroethylene in adipose tissue

In this paper we present three physiologically based pharmacokinetic (PBPK) models for the systemic transport of trichloroethylene (TCE), with a focus on the adipose, or fat tissue. TCE is a widespread environmental contaminant, and has been shown to produce toxic effects in both animals and humans. A key characteristic of TCE is its tendency to accumulate in fat tissue, which has a major impact on the overall systemic disposition of TCE. Here we use PBPK models to predict the dynamics of TCE in the various tissues and organs, including the adipose tissue. The first model utilizes the standard ‘perfusion-limited’ compartmental model for the fat tissue, while the second model uses a ‘diffusion-limited’ model to describe the transport through the adipose tissue. Both of these ODE models are based on ‘well-mixed’ and rapid equilibrium assumptions, and do not take into account the specific and largely heterogeneous physiology of adipose tissue. The third model we discuss is a PBPK hybrid model with an axial-dispersion type model for the adipose tissue. This PDE-based model is designed to capture key physiological heterogeneities of fat tissue, including widely varying fat cell sizes, lipid distribution, and blood flow properties. Model simulations demonstrate that this model may be well-suited to predict the experimental behavior of TCE in adipose tissue using parameter estimation techniques.     

Calcium transport and distribution in Ehrlich mouse ascites tumor cells

Data from isotopic uptake experiments were used to measure calcium fluxes and compartment sizes in ascites tumor cells. The data were analyzed with two kinetic models, A and B. In 80% of the experiments model A, which is based on one exchangeable calcium compartment, was rejected in favor of Model B, which predicts two exchangeable compartments. A statistical evaluation of the model's performance, when fit to the experimental data was used to select between the two models. The results show that calcium was distributed between three cellular compartments in the ratio, non-exchangeable (88%): rapidly exchanging (7%): slowly exchanging (5%). The undirectional fluxes suggested that calcium transport could be described as a series system with the temporal sequence: environment ? rapidly exchanging ? slowly exchanging.     

A morphometric analysis of the phloem-unloading pathway in developing tobacco leaves

A morphometric analysis of developing leaves of Nicotiana tabacum L. was conducted to determine whether imported photoassimilates could be unloaded by symplastic transport and whether interruption of symplastic transport could account for termination of import. Five classes of veins were recognized, based on numbers of cells in transverse section. Photoassimilate is unloaded primarily from Class III veins in tissue nearing the end of the sink phase of development. Smaller veins (Class IV and V) do not transport or unload photoassimilate in sink tissue because the sieve elements of these veins are immature until after the tissue stops importing. In Class III veins the sieve element-companion cell (SE-CC) complexes are surrounded by phloem parenchyma which abuts the bundle sheath. Along the most obvious unloading route, from SE-CC complex to phloem parenchyma to bundle sheath to mesophyll cells, the frequency of plasmodesmata at each interface increases. To determine whether this pattern of plasmodesmatal contact is consistent with symplastic unloading we first demonstrated, by derivation from Fick's law that the rate of diffusion from a compartment is proportional to a number N which is equal to the ratio of surface area to volume of the compartment multiplied by the frequency of pores (plasmodesmata) which connect it to the next compartment. N was calculated for each compartment within the vein which has the SE-CC complex as its center, and was shown to be statistically the same in all cases except one. These observations are consistent with a symplastic unloading route. As the leaf tissue matures and stops importing, plasmodesmatal frequency along the unloading route decreases and contact area between cells also decreases as intercellular spaces enlarge. As a result, the number of plasmodesmata between the SE-CC complex and the first layer of mesophyll cells declines in nonimporting tissue to 34% of the number found in importing tissue, indicating that loss of symplastic continuity between the phloem and surrounding cells plays a role in termination of photoassimilate unloading.Abbreviation SE-CC sieve element-companion cell     

Mathematical models for exchange of substances in regional vascular beds— Measurement of the rates within vivo counters

Sangren and Sheppard developed a mathematical model for first-order processes taking place in the regional circulation, applicable—for example—to tracer studies of potassium transport. It permits calculation of specific activity at any point along a “tube of flow” or in the cuff of tissue surrounding it as a function of time following a spike injection of tracer. In efforts to relate to the exchange a rate curves obtained within vivo counters pointed at the region of interest, we developed a compartment-system model of the process. In investigating the properties of the Sangren and Sheppard model integrated over an entire circulatory bed, as thein vivo counter would see it, we found that when the distribution of transit times of the “tubes of flow” can be approximated by an exponential sum, the solution reduces to that of the compartment system model. This results in an important simplification in the calculation, and insight into the assumptions underlying the two different models. A curve-fitting computer program for the compartment model has been written and applied to double-isotope studies of potassium transport in the hind leg of the dog.     

Volume Estimates by Imaging Methods: Model Comparisons with Visible Woman as the Reference

Objective: To compare the accuracy of four volume estimation models to actual tissue and organ volumes measured in the visible woman. Methods: Actual volumes were calculated from 1‐mm‐thick visible woman images that were segmented for five major components including subcutaneous and visceral adipose tissue across the 1730 available slices. Four available models resolved to two equations: truncated cone/truncated pyramid vs. two‐column/parallel trapezium. Between‐slice interval and initial slice were systematically varied when deriving component volumes using the two equations in four regions. Results: For each compartment and each between‐slice interval, the means of the two‐column model were always the same as the corresponding reference volumes, whereas those of the truncated cone model were smaller than the reference volumes. Similarly, the coefficient variation for the two‐column model was always smaller than for the truncated cone model. Discussion: The equation based on the parallel trapezium and the two‐column models is more accurate in estimating tissue volumes than the corresponding equation for truncated pyramid and truncated cone models. This finding has important implications for the volume calculations of imaging‐based body compartments such as adipose tissue.     

Modelling inert gas exchange in tissue and mixed-venous blood return to the lungs

Inert gas exchange in tissue has been almost exclusively modelled by using an ordinary differential equation. The mathematical model that is used to derive this ordinary differential equation assumes that the partial pressure of an inert gas (which is proportional to the content of that gas) is a function only of time. This mathematical model does not allow for spatial variations in inert gas partial pressure. This model is also dependent only on the ratio of blood flow to tissue volume, and so does not take account of the shape of the body compartment or of the density of the capillaries that supply blood to this tissue. The partial pressure of a given inert gas in mixed-venous blood flowing back to the lungs is calculated from this ordinary differential equation. In this study, we write down the partial differential equations that allow for spatial as well as temporal variations in inert gas partial pressure in tissue. We then solve these partial differential equations and compare them to the solution of the ordinary differential equations described above. It is found that the solution of the ordinary differential equation is very different from the solution of the partial differential equation, and so the ordinary differential equation should not be used if an accurate calculation of inert gas transport to tissue is required. Further, the solution of the PDE is dependent on the shape of the body compartment and on the density of the capillaries that supply blood to this tissue. As a result, techniques that are based on the ordinary differential equation to calculate the mixed-venous blood partial pressure may be in error.     

Dynamic Bayesian sensitivity analysis of a myocardial metabolic model

Dynamic compartmentalized metabolic models are identified by a large number of parameters, several of which are either non-physical or extremely difficult to measure. Typically, the available data and prior information is insufficient to fully identify the system. Since the models are used to predict the behavior of unobserved quantities, it is important to understand how sensitive the output of the system is to perturbations in the poorly identifiable parameters. Classically, it is the goal of sensitivity analysis to asses how much the output changes as a function of the parameters. In the case of dynamic models, the output is a function of time and therefore its sensitivity is a time dependent function. If the output is a differentiable function of the parameters, the sensitivity at one time instance can be computed from its partial derivatives with respect to the parameters. The time course of these partial derivatives describes how the sensitivity varies in time.When the model is not uniquely identifiable, or if the solution of the parameter identification problem is known only approximately, we may have not one, but a distribution of possible parameter values. This is always the case when the parameter identification problem is solved in a statistical framework. In that setting, the proper way to perform sensitivity analysis is to not rely on the values of the sensitivity functions corresponding to a single model, but to consider the distributed nature of the sensitivity functions, inherited from the distribution of the vector of the model parameters.In this paper we propose a methodology for analyzing the sensitivity of dynamic metabolic models which takes into account the variability of the sensitivity over time and across a sample. More specifically, we draw a representative sample from the posterior density of the vector of model parameters, viewed as a random variable. To interpret the output of this doubly varying sensitivity analysis, we propose visualization modalities particularly effective at displaying simultaneously variations over time and across a sample. We perform an analysis of the sensitivity of the concentrations of lactate and glycogen in cytosol, and of ATP, ADP, NAD⁺ and NADH in cytosol and mitochondria, to the parameters identifying a three compartment model for myocardial metabolism during ischemia.     

Sucrose transport at the tonoplast

Sucrose that leaked from maize scutellum slices upon transfer of slices from a hexose or hexitol solution to water or upon placing the slices in a buffered EDTA solution was considered to be cytoplasmic in origin; residual (after leakage) tissue sucrose was considered to be stored in the vacuoles. This paper presents a study of the movement of sucrose across the tonoplast between the vacuoles and the cytoplasmic compartment. It is concluded that; (a) sucrose transport into the vacuoles is directly linked to sucrose synthesis in such a way that free sucrose is not an intermediate in the coupled process, (b) cytoplasmic sucrose is not (cannot be?) stored, (c) sucrose transport out of the vacuoles is linked to the metabolic demand for sugar, and (d) the transport process removing sucrose from the vacuoles does not release free sucrose into the cytoplasm. The sucrose fluxes at the plasmalemma and at the tonoplast are calculated, and the transport processes at the two membranes are compared.