A four compartment linear mammillary model

Studies are made for a four compartment model in which the central compartment is connected reversibly to three other compartments and the elimination occurs from the central compartment only. Identification of different distribution rate constants is made, with concentrations of drug in the central compartment at different times of observation being known. The solution depends on an optimization method in which the different unknowns are reduced to single variable with the help of Archimedes spiral. Thus, the solution requires the global minimum of a functional of single variable. Results are compared with those obtained by the generalized least square method.     

A four compartment model to study the kinetics of strontium metabolism in man

Many drugs confer upon the body the characteristics of a four compartment model. This paper deals with the estimation of pharmacokinetic parameters of a four compartment model to study the distribution of strontium in the organism. The central compartment (where the introduction of the material takes place) is connected to two other compartments (which represent the organic fluids) and one of them is connected to the fourth compartment (which represents the fraction that can be exchanged in the bone). The elimination from the central compartment is through urine and the elimination from the third compartment is in the form of a non-exchangeable deposit. The method of solution involves an optimization method which provides the global minimum of δ, a single variable function. The model is tested for different sets of data and the results are compared with those obtained by the generalized leasr square method.     

A multicompartment model of carboxyhemoglobin and carboxymyoglobin responses to inhalation of carbon monoxide.

We have developed a model that predicts the distribution of carbon monoxide (CO) in the body resulting from acute inhalation exposures to CO. The model includes a lung compartment, arterial and venous blood compartments, and muscle and nonmuscle soft tissues with both vascular and nonvascular subcompartments. In the model, CO is allowed to diffuse between the vascular and nonvascular subcompartments of the tissues and to combine with myoglobin in the nonvascular subcompartment of muscle tissue. The oxyhemoglobin dissociation curve is represented by a modified Hill equation whose parameters are functions of the carboxyhemoglobin (HbCO) level. Values for skeletal muscle mass and cardiac output are calculated from prediction formulas based on age, weight, and height of individual subjects. We demonstrate that the model fits data from CO rebreathing studies when diffusion of CO into the muscle compartment is considered. The model also fits responses of HbCO to single or multiple exposures to CO lasting for a few minutes each. In addition, the model reproduces reported differences between arterial and venous HbCO levels and replicates predictions from the Coburn-Forster-Kane equation for CO exposures of a 1- to 83-h duration. In contrast to approaches based on the Coburn-Forster-Kane equation, the present model predicts uptake and distribution of CO in both vascular and tissue compartments during inhalation of either constant or variable levels of CO.     

Parameter identification in N-compartment mamillary models

We consider a general mamillary model with a central compartment (compartment 1) and n?1 peripheral compartments, each bidirectionally connected to the first. Elimination is allowed from any compartment and effectively occurs from the system. With input introduced into an arbitrary compartment and measurement performed in an arbitrary compartment, explicit equations are given to derive the parameters of the model from the input-output procedure. The calculations include essentially the determination of the roots of a polynomial plus some elementary algebra. If input and measurement are performed in the same compartment, then a set of 2n elementary combinations of the model parameters can be uniquely determined. However, the model parameters themselves can only be localized, each within an interval. These intervals are explicitly calculated and their width discussed.     

Comparison of different methods of interpretation for the prediction of body water by heavy water dilution method: application in the male goat

Deuterium oxide dilution space (DS) predicted by a 1 or 2 compartment kinetic model was used to estimate total body water in male kids. Empty body water (EBW), total body water at slaughter (TBW) and total body water calculated in the middle of day of injection (TBWM) were predicted with more accuracy by 2 compartment models. Residual standard deviation for EBW, TBW and TBWM estimated from a 2 open compartment model was 939 g, 464 g and 450 g respectively. Measurement of DS provides an accurate method to determine body water content and body composition.     

On the stochastic theory of compartments: II. Multi-compartment systems

A stochastic model is developed for a system of interconnected compartments. The generating function of the random variable of any compartment can be constructed from a flow graph involving the expectations of the random variables of all compartments of the system.     

A three compartment open model with two time lags

The present study deals with the identification of exchange parameters involved in a three-compartment open model with two time lags in which elimination occurs from the central compartment. Two different optimization methods have been used which involve the reduction of different unknowns to a single variable θ, with the help of Archimedes Spiral. Thus, the solution requires the global minimum of a functional of single variable θ. Results are compared with those obtained by the generalized least square method.     

Modeling of lipid and protein depletion during total starvation

This study presents a model describing lipid and protein depletion of an individual facing total starvation. The model distinguishes two compartments of body mass: a metabolic compartment and a structural compartment. It is considered that the lipids and the proteins of the metabolic compartment ensure the totality of physiological functions. The main assumptions of the model lie in the definitions of lipid mass and protein mass of the metabolic compartment, which are related to total lipid mass and total body mass, respectively. Under these assumptions, for a given individual, the ratio of lipid and protein utilization rates is proportional to the adiposity. The model accounts for the protein sparing observed at high adiposity levels and enables us to discuss the individual's survival in relation to the levels of lipid and protein depletion. The time course of changes in lipid and protein depletion rates can be calculated by introducing the energy expenditure of the individual. In simulations, it was assumed that specific energy expenditure was constant during starvation and that mortality occurred at a critical level of protein depletion. The most characteristic results derived from these simulations concern the kinetics of protein depletion, which depend markedly on initial adiposity. Accordingly, in obese subjects, the rate of protein losses remains fairly constant during fasting, whereas it increases from the onset of the fast in lean subjects, in agreement with experimental observations. In the model, protein and lipid depletion rates are both proportional to energy expenditure, which needs to be confirmed from complementary data.     

Permeability of iodide in multilamellar liposomes modeled by two compartments and a reservoir

A previously published rate law for the diffusion of iodide from multilamellar egg phosphatidylcholine liposomes (Schullery, S.E. (1975) Chem. Phys. Lipids 49–58) is fitted to the relatively simple mathematical model of two compartments in series with a reservoir. All of the inner liposome compartments are assumed to behave as effectively one compartment in series with the liposome's outermost compartment. Based on this model, reasonable values are calculated for the fraction of the total solution trapped by liposomes which is in the outermost liposome compartment, 17%, and the permeability coefficient of iodide against isotonic, mixed iodide-chloride solution, $\text{2 · 10}{}^{\mathrm{?9}}\text{cm/s}$.     

State-Dependent Effects of Na Channel Noise on Neuronal Burst Generation

We explore the effects of stochastic sodium (Na) channel activation on the variability and dynamics of spiking and bursting in a model neuron. The complete model segregates Hodgin-Huxley-type currents into two compartments, and undergoes applied current-dependent bifurcations between regimes of periodic bursting, chaotic bursting, and tonic spiking. Noise is added to simulate variable, finite sizes of the population of Na channels in the fast spiking compartment.During tonic firing, Na channel noise causes variability in interspike intervals (ISIs). The variance, as well as the sensitivity to noise, depend on the model's biophysical complexity. They are smallest in an isolated spiking compartment; increase significantly upon coupling to a passive compartment; and increase again when the second compartment also includes slow-acting currents. In this full model, sufficient noise can convert tonic firing into bursting.During bursting, the actions of Na channel noise are state-dependent. The higher the noise level, the greater the jitter in spike timing within bursts. The noise makes the burst durations of periodic regimes variable, while decreasing burst length duration and variance in a chaotic regime. Na channel noise blurs the sharp transitions of spike time and burst length seen at the bifurcations of the noise-free model. Close to such a bifurcation, the burst behaviors of previously periodic and chaotic regimes become essentially indistinguishable.We discuss biophysical mechanisms, dynamical interpretations and physiological implications. We suggest that noise associated with finite populations of Na channels could evoke very different effects on the intrinsic variability of spiking and bursting discharges, depending on a biological neuron's complexity and applied current-dependent state. We find that simulated channel noise in the model neuron qualitatively replicates the observed variability in burst length and interburst interval in an isolated biological bursting neuron.     

Dopamine Uptake by Rat Striatal Synaptosomes: A Compartmental Analysis

Abstract: Dopamine (DA) uptake into synaptosomes from rat corpus striatum was studied in the presence of a monoamine oxidase (MAO) inhibitor and dithiothreitol, by means of a filtration technique. Under these conditions a steady state develops rapidly in which the synaptosomal DA content remains constant while the continuing DA uptake is counterbalanced by DA efflux from the synaptosome. Exchange of synaptosomal [³H]DA and [¹⁴C]DA was measured under these conditions. In timecourse experiments it was found that exchange could be described significantly better by a three-compartment model than by a two-compartment model. However, if synaptosomes from reserpine-pretreated animals were used, analysis according to a three-compartment model did not result in a significantly better fit compared with a two-compartment model. Subsequently, kinetic transfer parameters describing DA fluxes between compartments at different DA concentrations were calculated from the fitted exchange curves. A Michaelis-Menten kinetic analysis indicated that only the in-series three-compartment configuration, in which DA is taken up from the medium into one synaptosomal compartment, from which it can subsequently be transferred to a second compartment without direct access to the medium, gave kinetically acceptable results. Transfer parameters in synaptosomes from reserpine-treated rats were comparable to those parameters describing DA transport between the medium and the first intrasynaptosomal compartment as measured under control conditions. Morover, it was found that potassium depolarization of synaptosomes resulted in a release of DA in a quantity similar to that found in the second intrasynaptosomal compartment. It is suggested that the two intrasynaptosomal compartments found correspond to a cytoplasmatic and vesicular DA pool, respectively. The functional significance of these findings is discussed in terms of the regulation of DA levels within the nerve terminal.     

A simple model for cell volume and developmental compartments in nutrient limited cyclostat cultures of algae

Daily light-dark cycles can entrain cell growth and division cycles in populations of algae growing in nutrient limited continuous cultures, or cyclostats. In this study a simple model for the flux of cells between discrete developmental stages is formulated for periodic cyclostat cultures of algae. Cell growth, in terms of volume, was set as being constant within a given developmental compartment, but variable between compartments. Growth within a given compartment or transition between compartments was restricted to specific intervals of the subjective day. The model was calibrated to phosphate limited cyclostat growth of Euglena gracilis, with the intervals for transition between compartments fixed at the times relative to the subjective dawn corresponding to critical transition points in the phased cell cycle of this organism. The model output for mean population volume per cell agreed well with experimental data. Although greatly simplified, the periodic behavior of the model volume frequency distributions for the discrete compartments provide reasonable approximation of experimentally determined distributions.     

A kinetic analysis of the release of acidic amino acids from rat cortical synaptosomes following pre-loading with [14C]glutamic acid

The kinetics of the release of acidic amino acids have been studied in rat cortical synaptosomes. After pre-loading for 30 minutes in labeled glutamate, labeled glutamate and aspartate appear to be totally releasable. However, extra-synaptosomal Ca does not facilitate release. When elevated [K]₀ was used to depolarize, release was unaffected by removal of Ca from the incubation medium. When veratridine was used as a depolarizing agent, presence of Ca in the incubation medium inhibited release. In all solutions, semi-log plots of synaptosomal label content as a function of time were non-linear, which is incompatible with release from a single compartment. Previous studies of the effect of membrane potential on transport led to the development of a carrier model which should participate in depolarization induced release (19). Under the conditions used in the present studies, this carrier should be saturated. When the data were fitted to a two compartment model, with release from compartment A linear with compartment size and release from compartment B via a saturated carrier, an excellent fit was obtained. Under control conditions, about 90% of the labeled amino acid is in compartment B and about 70% of the total release is from this compartment. Rate of release is greatly accelerated in depolarizing solutions. Under depolarizing conditions, there is a large shift of labeled amino acid from compartment B to compartment A and release from compartment A predominates. Analysis of the results under the several depolarizing conditions used shows that the present results are consistent with the predictions of the carrier model which has been developed from previous studies of the Na and membrane potential dependence of glutamate transport.     

Vegetative crop growth model incorporating leaf area expansion and senescence, and applied to grass

Abstract. A crop growth model incorporating leaf area expansion and senescence is constructed. Leaf area is treated as an independent state variable with the incremental specific leaf area a function of the storage/structure ratio. The vegetative grass crop, which usually has three green leaves per tiller, is particularly considered; the above-ground dry matter is assumed to occupy four compartments: growing leaves, first fully expanded leaves, second fully expanded leaves, and senescing leaves. Each compartment is described by two state variables—structural weight and leaf area index. Newly synthesized structural material comprises leaf, sheath and stem in fixed proportions, although defoliation can alter these proportions in the standing crop. Photosynthesis and respiration are calculated in the usual way. Root growth, root: shoot partitioning, soil water and nutrients are assumed to be relatively unimportant for an established vegetative grass crop grown under favourable conditions. The model is used to simulate the time course of dry matter and leaf area development for crops that are exposed to a constant environment, a seasonally varying environment, and are defoliated.     

Molecular anatomy of a trafficking organelle

Membrane traffic in eukaryotic cells involves transport of vesicles that bud from a donor compartment and fuse with an acceptor compartment. Common principles of budding and fusion have emerged, and many of the proteins involved in these events are now known. However, a detailed picture of an entire trafficking organelle is not yet available. Using synaptic vesicles as a model, we have now determined the protein and lipid composition; measured vesicle size, density, and mass; calculated the average protein and lipid mass per vesicle; and determined the copy number of more than a dozen major constituents. A model has been constructed that integrates all quantitative data and includes structural models of abundant proteins. Synaptic vesicles are dominated by proteins, possess a surprising diversity of trafficking proteins, and, with the exception of the V-ATPase that is present in only one to two copies, contain numerous copies of proteins essential for membrane traffic and neurotransmitter uptake.     

A novel multi-coaxial hollow fiber bioreactor for adherent cell types. Part 1: hydrodynamic studies.

A novel multi-coaxial bioreactor for three-dimensional cultures of adherent cell types, such as liver, is described. It is composed of four tubes of increasing diameter placed one inside the other, creating four spatially isolated compartments. Liver acinar structure and physiological parameters are mimicked by sandwiching cells in the space between the two innermost semi-permeable tubes, or hollows fibers, and creating a radial flow of media from an outer compartment (ECC), through the cell mass compartment, and to an inner compartment (ICC). The outermost compartment is created by gas-permeable tubing, and the housing is used to oxygenate the perfusion media to periportal levels in the ECC. Experiments were performed using distilled water to correlate the radial flow rate (Q(r)) with (1) the pressure drop (DeltaP) between the media compartments that sandwich the cell compartment and (2) the pressure in the cell compartment (P(c)). These results were compared with the theoretical profile calculated based on the hydraulic permeability of the two innermost fibers. Phase-contrast velocity-encoded magnetic resonance imaging was used to visualize directly the axial velocities inside the bioreactor and confirm the assumptions of laminar flow and zero axial velocity at the boundaries of each compartment in the bioreactor. Axial flow rates were calculated from the magnetic resonance imaging results and were similar to the measured axial flow rates for the previously described experiments.     

Asymmetry of the viscoelastic properties of the skin and muscle compartments of the left and right hands

The aim of this research was to discriminate and categorize isolateral stress-strain characteristics contained within the musculocutaneous compartment (MCC) using the model of the first dorsal interosseous muscle (FDI) in vivo. In our approach, the musculocutaneous compartment of the dorsal interosseous muscle was progressively isokinetically compressed by a solid vertical bar with a 0.25 mm incremental step. During each step, the force and deflection were measured and recorded electronically. The subject maintained a constantly relaxed position. Twenty-two strongly right-handed young males returned three data acquisition sequences from each hand. From the sequences, the elastic modulus and the specific energy of deformation were determined for both the total musculocutaneous compartment structure and separately for the discrete cutaneous and muscular compartments. No unilateral pattern of dominance was interpreted from the analysis of the range of indices. There was a highly variable individual pattern of bilateral dominance with no specific indication or predictability represented by the data: only one subject illustrated a data profile confirming the classical approach to right-handed dominance. As the muscle was relaxed and the integument layers were under minimal cortical influence, we suggest that the classical theory of primary cortical influence in motor lateralization does not adequately explain our recorded patterns of mechanical response of the musculocutaneous compartment analyzed in this study.     

Mathematical models of the kinetics of glucose and insulin in plasma

On the assumption that plasma glucose and IRI curves are essentially non-periodic in character, two simple, linear, lumped-parameter mathematical models have been investigated, one consisting of a single compartment and the other of two compartments between which glucose exchanges. The two-compartment model has the stronger appeal in that it admits more readily of a variable hepatic output of glucose. Estimation of many of the rate constants involved has been effected by conforming the theoretical functions to data from intravenous glucose tolerance tests. Numerical values obtained for the rate constants associated with the two-compartment model are satisfactory, but some confusion still remains concerning the turnover time of insulin in plasma.     

Estimation of compartmentation of lysine inside the cells of Yarrowia lipolytica

We studied the compartmentation of lysine in vivo by the tracer method of Subramanian et al. (J. Bacteriol. 115 (1973) 284-290). To calculate the size of the different lysine pools and lysine fluxes inside the cell, a mathematical model was designed enabling quantitative estimation of these data from experimental measurements. This technique was applied to a lysine-accumulating strain, 15901.7, and to its low lysine pool derivatives, ply-1, ply-4 and ply-9, which were selected for their low polyphosphate pools. In the mother strain, 15901.7, it appeared that lysine was stored mainly in a non-cytoplasmic compartment. In the mutants, the efflux from this compartment was higher and accounted for the higher percentage of lysine in the cytoplasm of these strains. Simulation with calculated parameters fitted the experimental curves very well. This was good evidence for the pertinence of the model. The biological significance of these results are discussed.     

Group selection of early replicators and the origin of life

A major problem of the origin of life has been that of information integration. As Eigen (1971) has shown, a mutant distribution of RNAs replicating without the aid of a replicase cannot integrate sufficient information for the functioning of a higher-level unit utilizing several types of encoded enzymes. He proposed the hypercycle model to bridge this gap in prebiology. It can be shown by a nonlinear game model, incorporating mutation of a hypercycle, that the selection properties of hypercycles make them inefficient information integrators as they cannot compete favourably with all kinds of less efficient information carriers or mutationally coupled hypercycles. The stochastic corrector model is presented as an alternative resolution of Eigen's paradox. It assumes that replicative templates are competing within replicative compartments, whose selective values depend on the internal template composition via a catalytic acid in replication and "metabolism". The dynamics of template replication are analyzed by numerical simulation of master equations. Due to the stochasticity in replication and compartment fission the best compartment types recur. An Eigen equation at the compartment level is set up and calculated. Even selfish template mutants cannot destroy the system though they make it less efficient. The genetic information of templates is evaluated at both levels, and the higher (compartment) level successfully constrains the lower (template) one. Compartmentation together with stochastic effects is sufficient to integrate information dispersed in competitive replicators. Compartment selection is considered to be group selection of replicators. Implications for the origin of life are discussed.