Cell kinetics in the erythroid compartment of guinea pig bone marrow: a model based on 3H-TdR studies

A model of steady-state erythropoiesis in the guinea pig is described. The model incorporates an unidentified progenitor compartment, as well as compartments representing proerythroblasts, basophilic, polychromatic and orthochromatic cells. A computer representation of the model permits a simulation of the labeling curves obtained in pulse and intermittent labeling regimes. It was found that a reasonable fit to the data can be achieved when the parameters for the various compartments are essentially identical. The results of a preliminary sensitivity analysis, carried out by perturbing the duration of S phase from the best fit value, are reported. The fit achieved to the data supports the hypothesis underlying the model that each compartment corresponds to one generation and that the flux within and between compartments is sequential.     

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.     

Quantification of entry into and exit from the cell cycle in human lymphocyte cultures

A mathematical model is presented for the analysis of transition between cycling and non-cycling compartments by cells responding to a growth stimulus. The cellular age distribution as a function of time is derived from sequential [3H]thymidine pulse labeling indices. Rates of entry into and exit from the cycling compartment are determined on the basis of labeling indices obtained after instantaneous and long duration [3H]thymidine pulses. Analysis of an experiment involving sequential measurements over the whole lifespan of a human lymphocyte culture stimulated by phytohemagglutinin is presented as an example of the application of this method.     

Chylomicron metabolism in rats: kinetic modeling indicates that the particles remain at endothelial sites for minutes

Chylomicrons labeled in vivo with ¹⁴C-oleic acid (primarily in triglycerides, providing a tracer for lipolysis) and ³H-retinol (primarily in ester form, providing a tracer for the core lipids) were injected into rats. Radioactivity in tissues was followed at a series of times up to 40 min and the data were analyzed by compartmental modeling. For heart-like tissues it was necessary to allow the chylomicrons to enter into a compartment where lipolysis is rapid and then transfer to a second compartment where lipolysis is slower. The particles remained in these compartments for minutes and when they returned to blood they had reduced affinity for binding in the tissue. In contrast, the data for liver could readily be fitted with a single compartment for native and lipolyzed chylomicrons in blood, and there was no need for a pathway back to blood. A composite model was built from the individual tissue models. This whole-body model could simultaneously fit all data for both fed and fasted rats and allowed estimation of fluxes and residence times in the four compartments; native and lipolyzed chylomicrons (“remnants”) in blood, and particles in the tissue compartments where lipolysis is rapid and slow, respectively.     

A compartmental model of carbon allocation in the vegetative barley plant

Abstract. The allocation of carbon in a vegetative barley plant is described as an open, three-compartment model; the three compartments are soluble (which exchanges material with the environment), storage, and structure (both of which exchange material with the soluble compartment). The model shows a good fit with data on ¹⁴C kinetics following ¹⁴CO₂ feeding and some of its assumptions, properties and implications are discussed.     

Modeling Fusion/Fission‐Dependent Intracellular Transport of Fluid Phase Markers

A fundamental feature of eukaryotic cells is the presence of distinct membrane‐bound compartments having unique protein and lipid composition. These compartments are interconnected by active trafficking mechanisms that must direct macromolecules to defined locations, and at the same time maintain the protein and lipid composition of each organelle. It is well accepted that Rab proteins play a central role in intracellular transport regulating the recognition, fusion and fission of organelles. However, how the transport is achieved is not completely understood. We propose a model whereby a soluble component in the luminal compartment is transported along different Rab‐containing organelles that interact according to the following simple principles: (i) only organelles with the same or compatible Rab membrane domains can fuse; (ii) after fusion, an asymmetric fission occurs producing a tubule and a round‐shaped vesicle; and (iii) Rab membrane domains distribute asymmetrically between the two resulting organelles. When this model was tested in a simulation, efficient unidirectional transport was observed, while the compartment identity was preserved. All three principles were absolutely necessary for transport. The model is compatible with Rab association/dissociation dynamics and with Rab conversion. In simulations mimicking a simplified endocytic pathway, soluble and membrane‐associated markers were efficiently transported preserving the identity of the interacting compartments.     

Evaluation of quantitative models of the effect of insulin on lipolysis and glucose disposal

The effects of insulin on the suppression of lipolysis are neither fully understood nor quantified. We examined a variety of mathematical models analogous to the minimal model of glucose disposal (MMG) to quantify the combined influence of insulin on lipolysis and glucose disposal during an insulin-modified frequently sampled intravenous glucose tolerance test. The tested models, which include two previously published ones, consisted of separate compartments for plasma free fatty acids (FFA), glucose, and insulin. They differed in the number of compartments and in the action of insulin to suppress lipolysis that decreased the plasma FFA level. In one category of models, a single insulin compartment acted on both glucose and FFA simultaneously. In a second category, there were two insulin compartments, each acting on FFA and glucose independently. For each of these two categories, we tested 11 variations of how insulin suppressed lipolysis. We also tested a model with an additional glucose compartment that acted on FFA. These 23 models were fit to the plasma FFA and glucose concentrations of 102 subjects individually. Using Bayesian model comparison methods, we selected the model that best balanced fit and minimized model complexity. In the best model, insulin suppressed lipolysis via a Hill function through a remote compartment that acted on both glucose and FFA simultaneously, and glucose dynamics obeyed the classic MMG.     

Kinetics of C-14 Translocation in Soybean: II. Kinetics in the Leaf

The kinetics of ¹⁴C-assimilates in the soybean leaf were studied in pulse labeling and steady state labeling experiments. ¹⁴C-Sucrose apparently served as the ultimate source, at least, of translocated ¹⁴C-sucrose. However, since the specific activity of leaf sucrose reached a maximum within 5 minutes after pulse labeling, whereas that of exported sucrose did not reach a maximum until at least 20 minutes, it appeared that there were two sucrose compartments in the leaf. A possible physical basis for the two compartments may be the mesophyll (a photosynthetic compartment) and a specialized “paraveinal mesophyll” (a nonphotosynthetic compartment), through which photosynthate must pass on its way to the veins.     

In vivo imaging of retrogradely transported synaptic vesicle proteins in Caenorhabditis elegans neurons

Axonal transport is an essential process that carries cargoes in the anterograde direction to the synapse and in the retrograde direction back to the cell body. We have developed a novel in vivo method to exclusively mark and dynamically track retrogradely moving compartments carrying specific endogenous synaptic vesicle proteins in the Caenorhabditis elegans model. Our method is based on the uptake of a fluorescently labeled anti-green fluorescent protein (GFP) antibody delivered in an animal expressing the synaptic vesicle protein synaptobrevin-1::GFP in neurons. We show that this method largely labels retrogradely moving compartments. Very little labeling is observed upon blocking vesicle exocytosis or if the synapse is physically separated from the cell body. The extent of labeling is also dependent on the dyenin-dynactin complex. These data support the interpretation that the labeling of synaptobrevin-1::GFP largely occurs after vesicle fusion and the major labeling likely takes place at the synapse. Further, we observe that the retrograde compartment carrying synaptobrevin contains synaptotagmin but lacks the endosomal marker RAB-5. This labeling method is very general and can be readily adapted to any transmembrane protein on synaptic vesicles with a GFP tag inside the vesicle and can also be extended to other model systems.     

QUANTIFICATION OF ENTRY INTO AND EXIT FROM THE CELL CYCLE IN HUMAN LYMPHOCYTE CULTURES

A mathematical model is presented for the analysis of transition between cycling and non-cycling compartments by cells responding to a growth stimulus. the cellular age distribution as a function of time is derived from sequential [³H]thymidine pulse labeling indices. Rates of entry into and exit from the cycling compartment are determined on the basis of labeling indices obtained after instantaneous and long duration [³H]thymidine pulses. Analysis of an experiment involving sequential measurements over the whole lifespan of a human lymphocyte culture stimulated by phytohemagglutinin is presented as an example of the application of this method.     

Determining the number of specific proteins in cellular compartments by quantitative microscopy

This protocol describes a method for determining both the average number and variance of proteins, in the few to tens of copies, in isolated cellular compartments such as organelles and protein complexes. Other currently available protein quantification techniques either provide an average number, but lack information on the variance, or they are not suitable for reliably counting proteins present in the few to tens of copies. This protocol entails labeling of the cellular compartment with fluorescent primary-secondary antibody complexes, total internal reflection fluorescence microscopic imaging of the cellular compartment, digital image analysis and deconvolution of the fluorescence intensity data. A minimum of 2.5 d is required to complete the labeling, imaging and analysis of a set of samples. As an illustrative example, we describe in detail the procedure used to determine the copy number of proteins in synaptic vesicles. The same procedure can be applied to other organelles or signaling complexes.     

Compartmental models for human iodine metabolism

Compartmental models for the various aspects of human iodine metabolism are reviewed, emphasizing the role of Mones Berman in the development of this field. The review first presents published submodels for the peripheral distribution of inorganic iodine, for the thyroidal iodide trapping function, and for the peripheral distribution and metabolism of the thyroid hormones. Approaches to improving understanding of the physiology of the thyroid gland itself through compartmental modeling techniques are then discussed in more detail. The three submodels described above are incorporated into overall models of thyroid iodine metabolism after being simplified to various degrees. Previously published models for thyroid-gland radioiodine metabolism, as well as current work in progress, are illustrated by attempting to fit the models to data from a single (previously unpublished) detailed prolonged ¹²⁵I feeding experiment in a normal human subject. Published thyroid gland models reviewed include: (1) the usual presentation, where the thyroid is a single homogeneous iodine compartment; (2) the model of DeGroot and colleagues, where thyroidal iodine is presented as MIT, DIT, T3, and T4, each with an active and linked storage compartment; (3) the thyroid model developed by Berman and colleagues, with less chemical subcategorization but incorporating a delay compartment, in which a fraction of the iodinated material in the thyroid is partially or completely inaccessible to secretion during the delay; and the later updating of Berman's model to include a thyroidal iodide recirculation pool. The experimental data presented fits most of these models for the first 1–2 weeks, but the fit could not be extended to longer data collection times. To overcome this shortcoming, a new thyroid gland model is introduced. It is based on the latest Berman model but describes thyroglobulin metabolism as incorporating multiple delay compartments of various time periods. The overall fit of the long term data is better with this model construct than with any of the published models. It appears that a complex thyroidal substructure, such as that of the multidelay model under development, will be required to account for overall thyroid iodine metabolism as isotopic equilibrium in man is approached.     

A kinetic model of coronary reactive hyperemic response to transient ischemia

A kinetic model is proposed to delineate the factors that determine the coronary reactive hyperemic response (RHR) to transient ischemia. The model comprises of myocardial-interstitial (M) and vascular (V) compartments. Vasodilator metabolites (VM) are produced in the M compartment during the interval of coronary occlusion. The rate of VM production is dependent on the flow rate during the ischemic period, the ratio of excess flow above the control level (R) to the loss of flow during occlusion period (D), the amount of oxygen stored and the degree of vasodilation in the V compartment prior to occlusion. Following a complete release of occlusion, VM are transported from the M to V compartment and are washed out or degraded with time. The time course of RHR is determined by the coronary patency which is proportional to VM concentration in the V compartment. Based on a set of numerical constants, the model is tested by simulating RHR to the various occlusion manoeuvres: a pair of 10 sec occlusions separated by brief release, a 15 sec release followed by a second brief occlusion, a brief release of an occlusion followed by restriced inflow and a period of restricted inflow after occlusion. The simulated results fit the experimental R/D and RH durations data of canine hearts. Factors that determine the impairment of RH capacity in coronary stenosis are suggested in terms of the model scheme.     

A simple centrifugal dehydration force method to characterize water compartments in fresh and post-mortem fish muscle

A centrifugal dehydration force (CDF) method to quantify changes in tissue hydration in fresh and in post-mortem muscular fish tail tissue is presented. The data obtained were used to assess fluid flow rate from tissues and the size of hydration compartments expressed in g water/g dry mass (DM). Curve fit analysis demonstrated that muscle tissue has three detectable water compartments. Application of the method to the fresh fish indicated the presence of a large non-bulk water compartment (3.14 g water/g DM) with a much smaller (0.11 g water/g DM) inner non-bulk water sub-compartment in addition to a comparatively small bulk water compartment (0.99 g water/g DM). At 10 min and at 4h post-mortem, no significant change in size or flow rate of the water compartments was observed. At 24h post-mortem the muscular fish tissue, stored in water, swelled with statistically significant increase in total water and in the bulk water compartment but no significant change in the size of the non-bulk water compartments. The water flow rate from the non-bulk water compartment was, however, increased significantly in the 24h dead tissue. This simple CDF method has application for quantization of bulk and non-bulk water compartments in other biological and non-biological systems.     

Nucleolar morphology and cell proliferation kinetics of thymic lymphocytes

Proliferation kinetics of cells of the lymphocytic series were studied in mouse thymuses using ³H-methyl-thymidine (³H-TdR) as a tracer of DNA synthesis and employing autoradiographic technique. Cells were allocated arbitrarily to several compartments according to their degree of maturity and nucleolar morphology. Serial sampling after continuous ³H-TdR injection showed that thymic cells of the lymphocytic series constitute a small highly proliferating pool that feeds into a large nonproliferating pool. Lymphoblasts with dense and trabeculate nucleoli and prolymphocytes with trabeculate nucleoli represent multiplicative compartments and belong to the proliferating pool. A fraction of multiplicative precursors enters a ‘dormant’ state and these immature lymphocytes are morphologically characterized by ring-shaped nucleoli. Multiplicative compartments and non-dividing compartments of immature lymphocytes differ significantly in labeling indices, kinetics of labeling in serial samples and in other kinetic parameters, namely in the efflux from the unlabeled pool, labeling increment and efflux from the labeled pool. Serially connected compartments of lymphoblasts with dense and trabeculate nucleoli, prolymphocytes with trabeculate nucleoli and mature lymphocytes, represent the main stream of cell differentiation and maturation. At least a portion of mature lymphocytes proceeds during maturation from the compartment of cells with trabeculate nucleoli to the compartment of cells with ring-shaped nucleoli. The presence of proliferating and ‘dormant’ precursors suggests that lymphopoiesis in thymuses may correspond to the advantaged logarithmic system of multiplication.     

THE DISCRETE–TIME KINETIC MODEL ANALYSIS OF DNA CONTENT DISTRIBUTIONS IN EXPERIMENTAL TUMOUR CELLS

A method was developed to analyse and characterize FMF measurements of DNA content distribution, utilizing the discrete time kinetic (DTK) model for cell kinetics analysis. The DTK model determines the time sequence of the cell age distribution during the proliferation of a tumor cell population and simulates the distribution pattern of the DNA content of cells in each age compartment of the cell cycle. The cells in one age compartment are distributed and spread into several compartments of the DNA content distribution to allow for different rates of DNA synthesis and instrument dispersion effects. It is assumed that the DNA content of cells in each age compartment has a Gaussian distribution. Thus, for a given cell age distribution the DNA content distribution depends on two parameters of the cells in each age compartment: the average DNA content and its coefficient of variation. As the DTK model generates the best fit DNA content distribution to the FMF measurement data, it enables one to estimate specific values of these two parameters in each stage of the cell cycle and to determine the fraction of cells in each cycle phase. The method was utilized to fit FMF measurements of DNA content distributions and to analyse their relationship to the cell kinetic parameters, namely cell loss rate, cell cycle times and growth fraction of exponentially growing Chinese hamster ovary cells in vitro and, also, with a wide range of coefficients of variation, of the L1210 ascites tumour during the growth period.     

The discrete-time kinetic model analysis of DNA content distributions in experimental tumour cells.

A method was developed to analyse and characterize FMF measurements of DNA content distribution, utilizing the discrete time kinetic (DTK) model for cell kinetics analysis. The DTK model determines the time sequence of the cell age distribution during the proliferation of a tumor cell population and simulates the distribution pattern of the DNA content of cells in each age compartment of the cell cycle. The cells in one age compartment are distributed and spread into several compartments of the DNA content distribution to allow for different rates of DNA synthesis and instrument dispersion effects. It is assumed that the DNA content of cells in each age compartment has a Gaussian distribution. Thus, for a given cell age distribution the DNA content distribution depends on two parameters of the cells in each age compartment: the average DNA content and its coefficient of variation. As the DTK model generates the best fit DNA content distribution to the FMF measurement data, it enables one to estimate specific values of these two parameters in each stage of the cell cycle and to determine the fraction of cells in each cycle phase. The method was utilized to fit FMf measurements of DNA content distributions and to analyse their relationship tothe cell kinetic parameters, namely cell loss rate, cell cycle times and grwoth graction of exponentially growing Chinese hamster ovary cells in vitro and, also, with a wide range of coeffficients of variation, of the L1210 ascites tumour during the growth period.     

Pathway of ammonia assimilation in illuminated Lemna minor

Plants of duckweed (Lemna minor) were grown under constant illumination and with a controlled supply of ammonium-N so as to maintain a constant low concentration. In two kinetic experiments (differing in illumination and N level) with ¹⁵N-ammonia, plants were periodically harvested and their free amino acids analysed for ¹⁵N abundance. Attempts were then made to fit the data by computer simulation models. Only models which had at least two or more intracellular compartments gave adequate fits. Two two-compartment models were tested fully. Both had in compartment 1 the glutamine synthetase-glutamate synthase cycle and in compartment 2 a second site of glutamine synthesis. In one model the glutamate for compartment 2 was derived by transport from compartment 1; in the second model it was synthesized from ammonia by glutamate dehydrogenase at a rate equivalent to 10% of the total N uptake. This second model was rejected after it was found that plants previously treated with methionine sulphoximine and aza-serine (inhibitors of the glutamate synthase cycle) were unable to incorporate ¹⁵N. In spite of wide differences in labelling pattern between the two experiments the first model gave acceptable fits to both when different pool sizes were allowed for. Operation of the glutamate synthase cycle was confirmed by the correspondence between model and data for labelling of glutamine amide, glutamine amino and glutamic acid. Consideration of enzyme distributions suggested that compartment 1 (the glutamate synthase system) is the chloroplasts and compartment 2 the cytosol. Analysis of asparagine and neutral amino acids made it possible to construct balance sheets for N uptake in the two experiments. They suggest that all glutamine synthesized in the chloroplast is used for glutamate and asparagine synthesis and that the cytosol enzyme meets the need of the cell for glutamine per se. The high turnover rates for asparagine indicate that this compound is an important intermediate even under steady state conditions, and carries between 20 and 50% of the products of N assimilation.     

A rapid method for assessing the distribution of gold labeling on thin sections.

Particulate gold labeling on ultrathin sections is in widespread use for antigen localization at the EM level. To extend the usefulness of gold labeling technology, we are evaluating different methods for sampling and estimating quantities of gold labeling. Here we present a simple, rapid, and unbiased method for assessing the relative pool sizes of immunogold labeling distributed over different cell compartments. The method uses a sampling approach developed for stereology in which a regular array of microscopic fields or linear scans is positioned randomly on labeled sections. From these readouts, gold particles are counted and assigned to identifiable cell structures to construct a gold labeling frequency distribution of those labeled compartments. Here we use ultrathin cryosections labeled for a range of different proteins and for a signaling lipid. We show by scanning labeled sections at the electron microscope that counting 100-200 particles on each of two grids is sufficient to obtain a reproducible and rapid assessment of the pattern of labeling proportions over 10-16 compartments. If more precise estimates of labeling proportions over individual compartments are required (e.g., to achieve coefficients of error of 10-20%), then 100-200 particles need to be counted over each compartment of interest.     

Co-localization of an endocytic marker and acid phosphatase in a tubular/reticular compartment in macrophages.

Cultured resident murine macrophages are incubated in the continuous presence of the fluorescent endocytic marker Lucifer Yellow and a phorbol ester that activates protein kinase C. Under these steady-state labeling conditions the fluorescent tracer was, for the most part, in a tubular/reticular compartment. Enzyme cytochemical localization of acid phosphatase in the same cells showed essentially a one-to-one correlation between the Lucifer Yellow- and acid phosphatase-containing compartments. Procedures for epifluorescence observation and subsequent enzyme cytochemical examination of the same whole mount cells are described. In addition, chemical fixation methods for the preservation of this labile tubular/reticular compartment are presented.