A two-compartment model for zinc in humans.

The oral absorption of zinc, from a test meal of minced beef, mashed potatoes and peas, have been measured in 19 healthy adults using the radiotracer 65Zn. The oral absorption, expressed as a percentage of the administered dose, was 20 +/- 5% (mean +/- 1 SD) in good agreement with previous results. In a subset of 9 subjects, tracer retention in whole body and whole blood was followed out to one year. The data were fitted to a simple two compartment model yielding total body zinc (TBZn), the zinc content in each of the 2 compartments and zinc turnover. The TBZn values ranged from 15.5 to 35.9 mmol while zinc turnover ranged from 0.043 to 0.073 mmol/d in keeping with results reported for significantly more complicated compartmental models applied to more comprehensive 65Zn tracer data sets. Additionally, TBZn correlated well with total body potassium, a measure of lean body mass, measured by whole body counting of the naturally-occurring potassium radioisotope, 40K. The zinc content of the more rapidly turning over compartment ranged from 3.2 to 5.6 mmol in reasonable agreement with exchangeable zinc pool estimations reported for short term studies using stable zinc isotopes. Therefore, the simple dataset and model employed in the present study yielded information on the short- and long-term behaviour of zinc compatible with both more complex radiotracer studies and analytically more demanding stable isotope studies.     

A two-compartment phenomenological model of a dopaminergic neuron

A two-compartment model of a dopaminergic neuron based on modified FitzHugh-Nagumo oscillators for each compartment has been built. The compartments correspond to the soma and dendrites and differ in the values of small parameters. The influence of stimuli (imposed current for the soma compartment and synaptic activation for the dendrite compartment) on the model has been studied. Activation of AMPA and NMDA synaptic currents is shown to cause generation of high-frequency bursts by the neuron. The mechanisms underlying burst generation are considered.     

A two-compartment model of osmotic lysis in Plasmodium falciparum-infected erythrocytes

We recently identified a voltage-dependent anion channel on the surface of human red blood cells (RBCs) infected with the malaria parasite, Plasmodium falciparum. This channel, the plasmodial erythrocyte surface anion channel (PESAC), likely accounts for the increased permeability of infected RBCs to various small solutes, as assessed quantitatively with radioisotope flux and patch-clamp studies. Whereas this increased permeability has also been studied by following osmotic lysis of infected cells in permeant solutes, these experiments have been limited to qualitative comparisons of lysis rates. To permit more quantitative examination of lysis rates, we have developed a mathematical model for osmotic fragility of infected cells based on diffusional uptake via PESAC and the two-compartment geometry of infected RBCs. This model, combined with a simple light scattering assay designed to track osmotic lysis precisely, produced permeability coefficients that match both previous isotope flux and patch-clamp estimates. Our model and light scattering assay also revealed Michaelian kinetics for inhibition of PESAC by furosemide, suggesting a 1:1 stoichiometry for their interaction.     

A stochstic model for a two-compartment reversible system

This paper discusses a general stochastic model for a two-compartment reversible system with non-homogeneous Poisson inputs, arbitrary residence times at each of the compartments and time-dependent transition probabilities. The probability distributions of the number of particles in each compartment and in the system are obtained together with the number of particles which depart from the system. In addition, various covariance functions with a time lag are obtained. Some of the above obtained results are deduced for time-independent arrivals, exponential residence times and time-independent transition probabilities. Fluctuations of the particles present in the system are also analysed. Similar analysis is provided for the model into which some particles are initially introduced at the system. Some possible applications are discussed at the end.     

A two-compartment model of pulmonary nitric oxide exchange dynamics

The relativelyrecent detection of nitric oxide (NO) in the exhaled breath hasprompted a great deal of experimentation in an effort to understand thepulmonary exchange dynamics. There has been very little progress intheoretical studies to assist in the interpretation of the experimentalresults. We have developed a two-compartment model of the lungs in aneffort to explain several fundamental experimental observations. Themodel consists of a nonexpansile compartment representing theconducting airways and an expansile compartment representing thealveolar region of the lungs. Each compartment is surrounded by a layerof tissue that is capable of producing and consuming NO. Beyond thetissue barrier in each compartment is a layer of blood representing thebronchial circulation or the pulmonary circulation, which are bothconsidered an infinite sink for NO. All parameters were estimated fromdata in the literature, including the production rates of NO in the tissue layers, which were estimated from experimental plots of theelimination rate of NO at end exhalation (E_NO) vs. theexhalation flow rate (_E). The modelis able to simulate the shape of the NO exhalation profile and tosuccessfully simulate the following experimental features of endogenousNO exchange: 1) an inverse relationship between exhaled NOconcentration and _E, 2) the dynamic relationship between the phase III slope and_E, and 3) the positiverelationship between E_NO and_E. The model predicts that theserelationships can be explained by significant contributions of NO inthe exhaled breath from the nonexpansile airways and the expansilealveoli. In addition, the model predicts that the relationship betweenE_NO and _E can be used as anindex of the relative contributions of the airways and the alveoli toexhaled NO.

     

Impact of protein binding on receptor occupancy: A two-compartment model

In this paper we analyse the impact of protein-, lipid- and receptor-binding on receptor occupancy in a two-compartment system, with proteins in both compartments and lipids and receptors in the peripheral compartment only. We do this for two manners of drug administration: a bolus administration and a constant rate infusion, both into the central compartment. We derive explicit approximations for the time-curves of the different compounds valid for a wide range of realistic values of rate constants and initial concentrations of proteins, lipids, receptors and the drug. These approximations are used to obtain both qualitative and quantitative insight into such critical properties as the distribution of the drug over the two compartments, the maximum receptor occupancy and the area under the drug-receptor complex curve. In particular we focus on assessing the impact of the dissociation constants, K_P, K_L and K_R of the drug with, respectively, the proteins, the lipids and the receptors, the permeability and the surface area of the membrane between compartments, and the rate the drug is eliminated from the system.     

Bifurcation analysis of a two-compartment hippocampal pyramidal cell model

The Pinsky-Rinzel model is a non-smooth 2-compartmental CA3 pyramidal cell model that has been used widely within the field of neuroscience. Here we propose a modified (smooth) system that captures the qualitative behaviour of the original model, while allowing the use of available, numerical continuation methods to perform full-system bifurcation and fast-slow analysis. We study the bifurcation structure of the full system as a function of the applied current and the maximal calcium conductance. We identify the bifurcations that shape the transitions between resting, bursting and spiking behaviours, and which lead to the disappearance of bursting when the calcium conductance is reduced. Insights gained from this analysis, are then used to firstly illustrate how the irregular spiking activity found between bursting and stable spiking states, can be influenced by phase differences in the calcium and dendritic voltage, which lead to corresponding changes in the calcium-sensitive potassium current. Furthermore, we use fast-slow analysis to investigate the mechanisms of bursting and show that bursting in the model is dependent on the intermediately slow variable, calcium, while the other slow variable, the activation gate of the afterhyperpolarisation current, does not contribute to setting the intraburst dynamics but participates in setting the interburst interval. Finally, we discuss how some of the described bifurcations affect spiking behaviour, during sharp-wave ripples, in a larger network of Pinsky-Rinzel cells.     

Emergence of stochastic resonance in a two-compartment hippocampal pyramidal neuron model

Journal of Computational Neuroscience - In vitro studies have shown that hippocampal pyramidal neurons employ a mechanism similar to stochastic resonance (SR) to enhance the detection and...     

The hot IVGTT two-compartment minimal model: an improved version

The two-compartment minimal model (2CMM) interpretation of a labeled intravenous glucose tolerance test (IVGTT) is a powerful tool to assess glucose metabolism in a single individual. It has been reported that a derived 2CMM parameter describing the proportional effect of glucose on insulin-independent glucose disposal can take physiologically unplausible negative values. In addition, precision of 2CMM parameter estimates is sometimes not satisfactory. Here we resolve the above issues by presenting an improved version of 2CMM that relies on a new assumption on the constant component R(d0) of insulin-independent glucose disposal. Here R(d0) is not fixed to 1 mg x kg(-1) x min(-1) but instead is expressed as a fraction of steady-state glucose disposal. The new 2CMM is identified on the same stable labeled IVGTT data base on which the original 2CMM was formulated. A more reliable insulin-independent glucose disposal portrait is obtained while that of insulin action remains unchanged. The new 2CMM also improves the precision with which model parameters and metabolic indexes are estimated.     

On the two-compartment model for estimating the rate and extent of feed degradation in the rumen

An analysis of the compartmental scheme used to determine the rate and extent of ruminal degradation of feeds is presented. Attention is given to the kinetic representation of the degradation of the potentially degradable fraction. Changing the kinetic order of the rate, and introducing indigestible substrate inhibition and microbial activity into its representation, are investigated. This leads to response functions such as the Gompertz and logistic for describing the cumulative disappearance of potentially degradable substrate during in-sacco and in-vitro incubation.     

A comprehensive model of hyaluronan turnover in the mouse

The metabolism of hyaluronan (HA), especially its catabolism, is still far from being elucidated. Although several studies suggest that HA is degraded locally in tissues and through the lymphatic or circulatory systems, much needs to be learned about the enzymes, receptors and cell types that support this dynamic process. In the current work, the clearance of exogenously administered HA was examined in a C57BL/6 mouse model. Hyaluronidase-sensitive fluorescein-labeled 1.2MDa hyaluronan (flHA) was administered either intravenously (i.v.) or subcutaneously (s.c.) into wild type C57BL/6 mice. Plasma was sampled for pharmacokinetic analysis and tissues were harvested for histological examination of the cell types responsible for uptake using immunofluorescent localization and for size exclusion chromatography analysis. We observed that flHA could be degraded locally in the skin or be taken up by sinusoidal cells in lymph nodes, liver and spleen. I.v. administration of flHA revealed non-linear Michaelis-Menten pharmacokinetics compatible with a saturable, receptor-mediated clearance system (K(m)=11.6μg/ml±46.0%, V(max)=1.69μg/ml/min±59.7%). Through a combination of immunofluorescence microscopy, pharmacokinetic, and chromatographic analyses of labeled substrate in vivo, our results shed additional light on the mechanisms by which HA is catabolized in mammals, and serve as a basis for future studies.     

A novel in vitro pharmacokinetic/pharmacodynamic model based on two-compartment open model used to simulate serum drug concentration-time profiles

An in vitro pharmacokinetic/pharmacodynamic perfusion model that simulates a two-compartment open model of serum drug concentration-time profiles following intravenous bolus injection and infusion was developed and mathematically described. In the present apparatus model, flow was kept in a one-way mode to avoid liquid traffic, and the washout effect seen in dilution models was overcome by embedding the tested bacteria in low melting point agarose gel. The validity of the equations and the reproducibility of the apparatus model were ascertained by simulating the concentration-time profiles of cefazolin and fosfomycin by substitution of their pharmacokinetic parameters obtained from humans for the equations. An empirical regimen 1X(q24h) of 1 g with cefazolin administered by intravenous infusion effectively killed a Staphylococcus aureus strain. The same regimen with fosfomycin produced a marked kill-curve with a fosfomycin-susceptible enterohaemorrhagic Escherichia coli O157:H7, whereas considerable regrowth was observed with a resistant strain. These results indicated that the present model was able to provide a convenient and reliable method for evaluating the efficacy of antimicrobial agents administered by intravenous infusion.     

A new model of pacing in the mouse intestine

A simple model of pacing in mouse intestine to longitudinal (LM) as well as circular muscle (CM) has been developed. Undissected segments of LM or CM from mouse ileum or jejunum were prepared to record contractions, nerve functions were inhibited, and regular spontaneous contractions were recorded. These had the properties expected of interstitial cells of Cajal (ICC) paced contractions: ileum slower than jejunum, inhibited but not abolished by nicardipine, reduced in frequency by cyclopiazonic acid, abolished by Ca(2+)-free media, and high temperature dependence (Q10 approximately 2.6-3.2). Nicardipine significantly reduced the pacing frequency in LM and CM. Intestinal segments from W/W(V) mice had few irregular contractions in CM but had regular contractions in LM. Other differences were found between LM and CM that suggest that the control of pacing of LM differed from pacing of CM. Moreover, both LM and CM segments in wild-type and W/W(V) and after cyclopiazonic acid responded to electrical pacing (50 V/cm, 50 or 100 ms) at 1 pulse per second. Temperature <26 degrees C inhibited electrically paced contractions in CM. These findings suggest that the current models of ICC pacing need to be modified to apply to intact segments of mouse intestine.     

A compartmental model of iron regulation in the mouse

A simple compartmental model is developed for investigating the mechanism of iron homeostasis. In contrast to previous mathematical models of iron metabolism, the liver is included as a key site of iron regulation. Compartments for free iron in blood, diferric transferrin (Tf) in blood, hepatocytes, red blood cells, and macrophages are included, and their roles in iron regulation are explored. The function of hepcidin in regulating iron absorption is modeled through an inverse relationship between hepatocyte transferrin receptor 2 (TfR2) levels and the rate of iron export processes mediated by ferroportin (Fpn). Simulations of anemia and erythropoiesis stimulation support the idea that the iron demands of the erythroid compartment can be communicated through diferric Tf. The iron-responsive element of Fpn is found to be important for stabilizing intracellular iron stores in response to changing iron demands and allowing proper iron regulation through diferric Tf. The contribution of iron dysregulation to the pathogenesis of iron overload disorders is also investigated. It is shown that the characteristics of HFE hemochromatosis can be reproduced by increasing the setpoint of iron absorption in the duodenum to a level where the system cannot downregulate iron absorption to meet the iron excretion rate.     

Epinephrine effects on insulin-glucose dynamics: the labeled IVGTT two-compartment minimal model approach

The hyperglycemic effects of epinephrine (Epi) are established; however, the modulation of Epi-stimulated endogenous glucose production (EGP) by glucose and insulin in vivo in humans is less clear. Our aim was to determine the effect of exogenously increased plasma Epi concentrations on insulin and glucose dynamics. In six normal control subjects, we used the labeled intravenous glucose tolerance test (IVGTT) interpreted with the two-compartment minimal model, which provides not only glucose effectiveness (S(G)(2*)), insulin sensitivity (S(I)(2*)), and plasma clearance rate (PCR) at basal state, but also the time course of EGP. Subjects were randomly studied during either saline or Epi infusion (1.5 microg/min). Exogenous Epi infusion increased plasma Epi concentration to a mean value of 2,034 +/- 138 pmol/l. During the stable-label IVGTT, plasma glucose, tracer glucose, and insulin concentrations were significantly higher in the Epi study. The hormone caused a significant (P < 0.05) reduction in PCR in the Epi state when compared with the basal state. The administration of Epi has a striking effect on EGP profiles: the nadir of the EGP profiles occurs at 21 +/- 7 min in the basal state and at 55 +/- 13 min in the Epi state (P < 0.05). In conclusion, we have shown by use of a two-compartment minimal model of glucose kinetics that elevated plasma Epi concentrations have profound effects at both hepatic and tissue levels. In particular, at the liver site, this hormone deeply affects, in a time-dependent fashion, the inhibitory effect of insulin on glucose release. Our findings may explain how even a normal subject may have the propensity to develop glucose intolerance under the influence of small increments of Epi during physiological stress.     

Steady-state analysis of a two-compartment barrier-limited capillary-tissue model with michaelis-menten saturation kinetics

The steady-state solution of the equations governing substrate exchange between vascular and extravascular compartments separated by a membrane with finite, symmetrical substrate permeability is presented. Substrate removal from the extravascular compartment by Michaelis-Menten saturation type kinetics with negligible diffusion in the axial and instantaneous diffusion in the transverse directions in both compartments are assumed. It is shown that the solution degenerates into known expressions for special linearized and asymptotic cases. The method of solution is also applied to an extension of the original model incorporating autoregulatory feedback effects upon the process responsible for substrate removal.     

Pharmacokinetics and effects of intravenous infusion of somatostatin in normal subjects--a two-compartment open model

A direct radioimmunoassay of plasma somatostatin-like immunoreactivity (SRIF-LI) was developed and validated. The sensitivity was 16.0 pg/ml, and the specificity was good. The recovery of plasma SRIF-LI was 98.8 +/- 6.3%. The Scatchard plot of the antiserum binding data revealed a straight line, with a binding affinity of 3.52 X 10(-12) M and a binding capacity 4.06 X 10(-10) M. Synthetic SRIF (Stilamin), 250 micrograms, was infused intravenously over a 30-min period in 9 healthy volunteers. Plasma glucose, insulin (IRI), glucagon (IRG) and SRIF-LI were measured. A two-compartment open model was adopted to analyze the pharmacokinetic data of SRIF-LI. The results showed that plasma SRIF-LI rose from 192.2 +/- 16.2 pg/ml to a plateau of 2,129.8 +/- 288.2 pg/ml within 5-10 min after starting the infusion. The half disappearance time from plasma (Ta1/2) was 1.36 +/- 0.18 min, the half disappearance time from the 'remote' compartment (Tb1/2) was 49.6 +/- 10.9 min and the net half disappearance time from the two compartments together (Tn1/2) was 9.19 +/- 1.49 min. The metabolic clearance rate was 50.3 +/- 7.0 ml/kg/min. The plasma IRI, IRG and the IRI/IRG molar ratio were all suppressed during the infusion period. The recovery time of plasma IRG was mildly delayed in comparison to that of IRI. This indicates that there are dissociations between IRI and IRG in the extent and the duration of suppression caused by somatostatin infusion.