Compartmental models: theory and practice using the SAAM II software system

A puzzling case of contamination with 241Am

Two people were exposed to and contaminated with ²⁴¹Am. In vivo determinations of the incorporated ²⁴¹Am were performed using a whole-body counter and two partial-body counters for the skull and lung, respectively. Additionally, urine samples were analysed to estimate the systemic activity removed from the body. To improve the geometry of the skull measurements, an optimised detector configuration was used, a calibration with three physical phantoms of the human head was conducted, and the morphological variability between the individuals was also considered. The results of the measurements indicate that activity is not deposited in the deep tissues, rather in the skin tissues close to the body surface. Unfortunately, the many open questions relating to the actual circumstances during and after the incident make the interpretation of this case difficult if at all possible.

PET-based compartmental modeling of (124)I-A33 antibody: quantitative characterization of patient-specific tumor targeting in colorectal cancer

PURPOSE

The molecular specificity of monoclonal antibodies (mAbs) directed against tumor antigens has proven effective for targeted therapy of human cancers, as shown by a growing list of successful antibody-based drug products. We describe a novel, nonlinear compartmental model using PET-derived data to determine the "best-fit" parameters and model-derived quantities for optimizing biodistribution of intravenously injected (124)I-labeled antitumor antibodies.

METHODS

As an example of this paradigm, quantitative image and kinetic analyses of anti-A33 humanized mAb (also known as "A33") were performed in 11 colorectal cancer patients. Serial whole-body PET scans of (124)I-labeled A33 and blood samples were acquired and the resulting tissue time-activity data for each patient were fit to a nonlinear compartmental model using the SAAM II computer code.

RESULTS

Excellent agreement was observed between fitted and measured parameters of tumor uptake, "off-target" uptake in bowel mucosa, blood clearance, tumor antigen levels, and percent antigen occupancy.

CONCLUSION

This approach should be generally applicable to antibody-antigen systems in human tumors for which the masses of antigen-expressing tumor and of normal tissues can be estimated and for which antibody kinetics can be measured with PET. Ultimately, based on each patient's resulting "best-fit" nonlinear model, a patient-specific optimum mAb dose (in micromoles, for example) may be derived.

Pharmacokinetics and safety of intravenous cidofovir for life-threatening viral infections in pediatric hematopoietic stem cell transplant recipients

Children undergoing hematopoietic stem cell transplantation (HSCT) are at risk for life-threatening viral infections. Cidofovir is often used as a first-line agent for adenovirus infections, despite the absence of randomized controlled trials with HSCT patients, and as a second-line agent for resistant herpesvirus infections. The frequency and severity of adverse effects, particularly nephrotoxicity, in pediatric HSCT recipients are unclear, and pharmacokinetics (PK) of cidofovir in children have not previously been reported. This study was an open-label, nonrandomized, single-dose pilot study to determine the safety and PK of cidofovir in pediatric HSCT recipients with symptomatic adenovirus, nucleoside-resistant cytomegalovirus (CMV) or herpes simplex virus (HSV), and/or human papovavirus infections. Subsequent dosing and frequency were determined by clinical response and side effects, as assessed by the treating physician. Blood and urine samples were obtained from patients for PK studies and assessment of toxicity and virologic response. Twelve patients were enrolled (median age, 9 years; 33.5 days posttransplantation). Four of seven patients with adenovirus infection were successfully treated and eventually cleared their infections. Four of twelve patients died of disseminated viral disease and multiorgan failure. Two of twelve patients had evidence of acute kidney injury after the first dose, and one of these patients developed chronic kidney disease; two other patients developed late nephrotoxicity. The mean drug half-life was 9.5 h. There was no correlation between nephrotoxicity and plasma maximum concentration, clearance, or half-life. PK were similar to those reported for adults, although the drug half-life was significantly longer than that for adults. Cidofovir was well tolerated in the majority of patients. However, effective therapeutic strategies are urgently needed to support patients until immune reconstitution is achieved.

Considerations on the ICRP model predictions of the transfer of (137)Cs from food to the milk and urine of lactating mothers

A recent work has shown that the current ICRP biokinetic model for the transfer of caesium radionuclides from food to human breast milk was able to describe with satisfactory accuracy (137)Cs activity concentrations in human breast samples collected a few weeks after the Chernobyl accident as well as in samples collected some years later. However, systematic discrepancies were observed for the predictions of the activity concentrations in urine samples. In the present work, modifications to the model were investigated with the aim of improving the agreement between model predictions and data. It turned out that the disagreement for the urine data was ascribable to the mathematical simplifications used by the ICRP to describe urinary excretion in the first few days after delivery. However, the predictive performances of the model remained unchanged even when differences in the bioavailability of caesium from the ingested food types were considered or metabolic interactions between caesium and potassium were introduced into the model formulation.

The pharmacokinetics and pharmacodynamics of zaleplon delivered as a thermally generated aerosol in a single breath to volunteers

Pharmacokinetics, pharmacodynamics, safety, and tolerability of inhaled zaleplon were assessed in healthy volunteers. Forty participants received 0.5, 1, 2, or 4 mg zaleplon or placebo as a thermally generated aerosol in a randomized, double-blind, parallel-group, dose escalation study. Blood was collected up to 24 hours after dosing, and sedation was assessed up to 8 hours. Following inhalation, the observed median time to maximum plasma concentrations (25%, 75%) was 1.89 (1.45, 3.08) minutes and the mean (SD) elimination half-life was 1.24 (0.24) hours. The equilibration half-life for sedation (t(1/2) k(e0) ) was 1.16 (0.62, 2.17) minutes. The zaleplon AUC was dose proportional across doses, with a slope (90% confidence interval) of log-AUC versus log-dose of 0.92 (0.82, 1.02). No clinically significant changes were noted in laboratory values, vital signs, or spirometry. The most common adverse events were dizziness, somnolence, euphoria, headache, and visual disturbance. Zaleplon inhalation represents a safe, well-tolerated means of rapidly achieving effective plasma concentrations.

Insulin activation of plasma nonesterified fatty acid uptake in metabolic syndrome

OBJECTIVE

Insulin control of fatty acid metabolism has long been deemed dominated by suppression of adipose lipolysis. The goal of the present study was to test the hypothesis that this single role of insulin is insufficient to explain observed fatty acid dynamics.

METHODS AND RESULTS

Fatty acid kinetics were measured during a meal tolerance test and insulin sensitivity assessed by intravenous glucose tolerance test in overweight human subjects (n=15; body mass index, 35.8 ± 7.1 kg/m(2)). Non-steady state tracer kinetic models were formulated and tested using ProcessDB software. Suppression of adipose fatty acid release, by itself, could not account for postprandial nonesterified fatty acid concentration changes, but adipose suppression combined with insulin activation of fatty acid uptake was consistent with the measured data. The observed insulin K(m) for nonesterified fatty acid uptake was inversely correlated with both insulin sensitivity of glucose uptake (intravenous glucose tolerance test insulin sensitivity; r=-0.626; P=0.01) and whole body fat oxidation after the meal (r=-0.538; P=0.05).

CONCLUSIONS

These results support insulin regulation of fatty acid turnover by both release and uptake mechanisms. Activation of fatty acid uptake is consistent with the human data, has mechanistic precedent in cell culture, and highlights a new potential target for therapies aimed at improving the control of fatty acid metabolism in insulin-resistant disease states.

Kinetic studies to investigate lipoprotein metabolism

To develop novel strategies for the prevention and treatment of dyslipidaemia, it is essential to understand the pathophysiology of dyslipoproteinaemia in humans. Lipoprotein metabolism is a complex system in which abnormal concentrations of various lipoprotein particles can result from alterations in their rates of production, conversion and/or catabolism. Traditional methods that measure plasma lipoprotein concentrations only provide static estimates of lipoprotein metabolism and hence limited mechanistic information. By contrast, the use of tracers labelled with stable isotopes and mathematical modelling provides a powerful tool for probing lipid and lipoprotein kinetics in vivo and furthering understanding of the pathogenesis of dyslipoproteinaemia.

Parameter estimation for linear compartmental models--a sensitivity analysis approach

Linear compartmental models are useful, explanatory tools, that have been widely used to represent the dynamic behavior of complex biological systems. This paper addresses the problem of the numerical identification of such models, i.e., the estimation of the parameter values that will generate predictions closest to experimental observations. Traditional local optimization techniques find it difficult to arrive at satisfactory solutions to such a parameter estimation problem, especially when the number of parameters is large and/or few data are available from experiments. We present herewith a method based on a prior sensitivity analysis, which enables division of a large optimization problem into several smaller and simpler subproblems, on which only sensitive parameters are estimated, before the whole optimization problem is tackled from starting points that are already close to the optimum values. This method has been applied successfully to a linear 13-compartment, 21-parameter model describing the postprandial metabolism of dietary nitrogen in humans. The effectiveness of the method has been demonstrated using simulated and real data obtained in the intestine, blood and urine of healthy humans after the ingestion of a [(15)N]-labeled protein meal.

The pharmacokinetics and bioavailability of prochlorperazine delivered as a thermally generated aerosol in a single breath to volunteers

A thermally generated aerosol (TGA) system can effect reliable delivery of excipient-free drug to alveoli, resulting in rapid systemic drug absorption. We developed a pharmacokinetic model of prochlorperazine, administered by inhalation and as a rapid intravenous infusion, and we determined absolute TGA bioavailability in eight healthy volunteers in this institutional review board-approved, two-period crossover study. After the drug was administered as either a 5-s intravenous infusion or a TGA single-breath inhalation, blood was collected at various times for up to 24 h. Plasma prochlorperazine concentrations were measured using liquid chromatography-tandem mass spectrometry. Inhalation and rapid intravenous administration produced similar plasma prochlorperazine concentration profiles. Intravenous and inhalation pharmacokinetics were well characterized by a simultaneous two-compartment model with multiple absorption delays. Prochlorperazine pharmacokinetic parameters were similar to those reported for single intravenous doses. The geometric mean bioavailability after TGA delivery was 1.10. The administration of prochlorperazine by inhalation resulted in pharmacokinetics similar to that seen after intravenous administration, in terms of speed, extent, and consistency of absorption.

Using mass measurements in tracer studies--a systematic approach to efficient modeling

Tracer enrichment data are fitted by multicompartmental models to estimate rate constants and fluxes or transport rates. In apolipoprotein turnover studies, mass measurements are also available, for example, apolipoprotein B levels in very low-density lipoprotein, intermediate-density lipoprotein, and low-density lipoprotein, and are often essential to calculate some of the rate constants. The usual method to use mass measurements is to estimate pool masses along with rate constants. A systematic alternative approach is developed to use flux balances around pools to express some rate constants in terms of the other rate constants and the measured masses. The resulting reduction in the number of parameters to be estimated makes the modeling more efficient. In models that would be unidentifiable without mass measurements, the usual approach and the proposed approach yield identical results. In a simple two-pool model, the number of unknown parameters is reduced from 4 to 2. In a published five-pool model for apolipoprotein B kinetics with three mass measurements, the number of parameters is reduced from 12 to 9. With m mass measurements, the number of responses to be fitted and the number of parameters to be estimated are each reduced by m, a simplification by 1/4 to 1/3 in a typical pool model. Besides a proportionate reduction in computational effort, there is a further benefit because the dimensionality of the problem is also decreased significantly, which means ease of convergence and a smaller likelihood of suboptimal solutions. Although our approach is conceptually straightforward, the dependencies get considerably more complex with increasing model size. To generate dependency definitions automatically, a Web-accessible program is available at http://biomath.info/poolfit/constraints.

Neural network based glucose - insulin metabolism models for children with Type 1 diabetes

In this paper two models for the simulation of glucose-insulin metabolism of children with Type 1 diabetes are presented. The models are based on the combined use of Compartmental Models (CMs) and artificial Neural Networks (NNs). Data from children with Type 1 diabetes, stored in a database, have been used as input to the models. The data are taken from four children with Type 1 diabetes and contain information about glucose levels taken from continuous glucose monitoring system, insulin intake and food intake, along with corresponding time. The influences of taken insulin on plasma insulin concentration, as well as the effect of food intake on glucose input into the blood from the gut, are estimated from the CMs. The outputs of CMs, along with previous glucose measurements, are fed to a NN, which provides short-term prediction of glucose values. For comparative reasons two different NN architectures have been tested: a Feed-Forward NN (FFNN) trained with the back-propagation algorithm with adaptive learning rate and momentum, and a Recurrent NN (RNN), trained with the Real Time Recurrent Learning (RTRL) algorithm. The results indicate that the best prediction performance can be achieved by the use of RNN.

Increasing habitual protein intake results in reduced postprandial efficiency of peripheral, anabolic wheat protein nitrogen use in humans

BACKGROUND

The postprandial retention of dietary protein decreases when the prevailing protein intake increases.

OBJECTIVE

We investigated the influence of the prevailing protein intake on the regional utilization and anabolic use of wheat protein during the postprandial non-steady state in humans.

DESIGN

Healthy adults (n = 8) were adapted for 7 d, first to a normal-protein diet (NP: 1 g x kg(-1) x d(-1)) and then to a high-protein diet (HP: 2 g x kg(-1) x d(-1)). After each adaptation period, the subjects received the same single, solid mixed meal containing [15N]-labeled wheat protein. The postprandial kinetics of dietary nitrogen were then measured for 8 h in blood and urine. These data were further analyzed by using a multicompartmental model to predict the postprandial kinetics of dietary nitrogen in unsampled pools.

RESULTS

The postprandial whole-body retention of wheat protein nitrogen, measured 8 h after meal ingestion, decreased by 10% when the subjects switched from the NP diet to the HP diet. According to modeling results, this resulted from an increased splanchnic utilization of dietary nitrogen for urea production, whereas its incorporation into splanchnic proteins was unchanged, leading to a 20-30% decrease in peripheral availability and anabolic use in HP-adapted compared with NP-adapted subjects having ingested the same protein load.

CONCLUSIONS

By combining clinical experimentation with compartmental modeling, we provide a global overview of postprandial dietary protein metabolism. Increasing prior protein intake was shown to reduce the postprandial retention of wheat protein nitrogen, mainly by diminishing the efficiency of its peripheral availability and anabolic use.

A real time simulation model of glucose-insulin metabolism for type 1 diabetes patients

In this paper, a simulation model of glucose-insulin metabolism for Type 1 diabetes patients is presented. The proposed system is based on the combination of Compartmental Models (CMs) and artificial Neural Networks (NNs). This model aims at the development of an accurate system, in order to assist Type 1 diabetes patients to handle their blood glucose profile and recognize dangerous metabolic states. Data from a Type 1 diabetes patient, stored in a database, have been used as input to the hybrid system. The data contain information about measured blood glucose levels, insulin intake, and description of food intake, along with the corresponding time. The data are passed to three separate CMs, which produce estimations about (i) the effect of Short Acting (SA) insulin intake on blood insulin concentration, (ii) the effect of Intermediate Acting (IA) insulin intake on blood insulin concentration, and (iii) the effect of carbohydrate intake on blood glucose absorption from the gut. The outputs of the three CMs are passed to a Recurrent NN (RNN) in order to predict subsequent blood glucose levels. The RNN is trained with the Real Time Recurrent Learning (RTRL) algorithm. The resulted blood glucose predictions are promising for the use of the proposed model for blood glucose level estimation for Type 1 diabetes patients.

Conceptual, methodological and computational issues concerning the compartmental modeling of a complex biological system: Postprandial inter-organ metabolism of dietary nitrogen in humans

A multi-compartmental model has been developed to describe dietary nitrogen (N) postprandial distribution and metabolism in humans. This paper details the entire process of model development, including the successive steps of its construction, parameter estimation and validation. The model was built using experimental data on dietary N kinetics in certain accessible pools of the intestine, blood and urine in healthy adults fed a [15N]-labeled protein meal. A 13-compartment, 21-parameter model was selected from candidate models of increasing order as being the minimum structure able to properly fit experimental data for all sampled compartments. Problems of theoretical identifiability and numerical identification of the model both constituted mathematical challenges that were difficult to solve because of the large number of unknown parameters and the few experimental data available. For this reason, new robust and reliable methods were applied, which enabled (i) a check that all model parameters could theoretically uniquely be determined and (ii) an estimation of their numerical values with satisfactory precision from the experimental data. Finally, model validation was completed by first verifying its a posteriori identifiability and then carrying out external validation.

Studying apolipoprotein turnover with stable isotope tracers: correct analysis is by modeling enrichments

Lipoprotein kinetic parameters are determined from mass spectrometry data after administering mass isotopes of amino acids, which label proteins endogenously. The standard procedure is to model the isotopic content of the labeled precursor amino acid and of proteins of interest as tracer-to-tracee ratio (TTR). It is shown here that even though the administered tracer alters amino acid mass and turnover, apolipoprotein synthesis is unaltered and hence the apolipoprotein system is in a steady state, with the total (labeled plus unlabeled) masses and fluxes remaining constant. The correct model formulation for apolipoprotein kinetics is shown to be in terms of tracer enrichment, not of TTR. The needed mathematical equations are derived. A theoretical error analysis is carried out to calculate the magnitude of error in published results using TTR modeling. It is shown that TTR modeling leads to a consistent underestimation of the fractional synthetic rate. In constant-infusion studies, the bias error percent is shown to equal approximately the plateau enrichment, generally <10%. It is shown that, in bolus studies, the underestimation error can be larger. Thus, for mass isotope studies with endogenous tracers, apolipoproteins are in a steady state and the data should be fitted by modeling enrichments.

Thematic review series: Patient-Oriented Research. Design and analysis of lipoprotein tracer kinetics studies in humans

Lipoprotein tracer kinetics studies have for many years provided new and important knowledge of the metabolism of lipoproteins. Our understanding of kinetics defects in lipoprotein metabolism has resulted from the use of tracer kinetics studies and mathematical modeling. This review discusses all aspects of the performance of kinetics studies, including the development of hypotheses, experimental design, statistical considerations, tracer administration and sampling schedule, and the development of compartmental models for the interpretation of tracer data. In addition to providing insight into new metabolic pathways, such models provide quantitative information on the effect of interventions on lipoprotein metabolism. Compartment models are useful tools to describe experimental data but can also be used to aid in experimental design and hypothesis generation. The SAAM II program provides an easy-to-use interface with which to develop and test compartmental models against experimental models. The development of a model requires that certain checks be performed to ensure that the model describes the experimental data and that the model parameters can be estimated with precision. In addition to methodologic aspects, several compartment models of apoprotein and lipid metabolism are reviewed.

Global nature of dynamic protein-chromatin interactions in vivo: three-dimensional genome scanning and dynamic interaction networks of chromatin proteins

Genome structure and gene expression depend on a multitude of chromatin-binding proteins. The binding properties of these proteins to native chromatin in intact cells are largely unknown. Here, we describe an approach based on combined in vivo photobleaching microscopy and kinetic modeling to analyze globally the dynamics of binding of chromatin-associated proteins in living cells. We have quantitatively determined basic biophysical properties, such as off rate constants, residence time, and bound fraction, of a wide range of chromatin proteins of diverse functions in vivo. We demonstrate that most chromatin proteins have a high turnover on chromatin with a residence time on the order of seconds, that the major fraction of each protein is bound to chromatin at steady state, and that transient binding is a common property of chromatin-associated proteins. Our results indicate that chromatin-binding proteins find their binding sites by three-dimensional scanning of the genome space and our data are consistent with a model in which chromatin-associated proteins form dynamic interaction networks in vivo. We suggest that these properties are crucial for generating high plasticity in genome expression.

Quantitation of in vivo human folate metabolism

BACKGROUND

A quantitative understanding of human folate metabolism is needed.

OBJECTIVE

The objective was to quantify and interpret human folate metabolism as it might occur in vivo.

DESIGN

Adults (n = 13) received 0.5 nmol [(14)C]pteroylmonoglutamate (100 nCi radioactivity) plus 79.5 nmol pteroylmonoglutamate in water orally. (14)C was measured in plasma, erythrocytes, urine, and feces for >/=40 d. Kinetic modeling was used to analyze and interpret the data.

RESULTS

According to the data, the population was healthy and had a mean dietary folate intake of 1046 nmol/d, and the apparent dose absorption of (14)C was 79%. The model predictions showed that only 0.25% of plasma folate was destined for marrow, mean bile folate flux was 5351 nmol/d, and the digestibility of the mix (1046 + 5351 nmol/d) was 92%. About 33% of visceral pteroylmonoglutamate was converted to the polyglutamate form, most of the body folate was visceral (>99%), most of the visceral folate was pteroylpolyglutamate (>98%), total body folate was 225 micromol, and pteroylpolyglutamate synthesis, recycling, and catabolism were 1985, 1429, and 556 nmol/d, respectively. Mean residence times were 0.525 d as visceral pteroylmonoglutamate, 119 d as visceral pteroylpolyglutamate, 0.0086 d as plasma folate, and 0.1 d as gastrointestinal folate.

CONCLUSIONS

Across subjects, folate absorption, bile folate flux, and body folate stores were larger than prior estimates. Marrow folate uptake and pteroylpolyglutamate synthesis, recycling, and catabolism are saturable processes. Visceral pteroylpolyglutamate was an immediate precursor of plasma p-aminobenzoylglutamate. The model is a working hypothesis with derived features that are explicitly model-dependent. It successfully quantitated folate metabolism, encouraging further rigorous testing.

Lipoprotein transport in the metabolic syndrome: methodological aspects of stable isotope kinetic studies

The metabolic syndrome encapsulates visceral obesity, insulin resistance, diabetes, hypertension and dyslipidaemia. Dyslipidaemia is a cardinal feature of the metabolic syndrome that accelerates the risk of cardiovascular disease. It is usually characterized by high plasma concentrations of triacylglycerol (triglyceride)-rich and apoB (apolipoprotein B)-containing lipoproteins, with depressed concentrations of HDL (high-density lipoprotein). However, lipoprotein metabolism is complex and abnormal plasma concentrations can result from alterations in the rates of production and/or catabolism of these lipoprotein particles. Our in vivo understanding of kinetic defects in lipoprotein metabolism in the metabolic syndrome has been achieved chiefly by ongoing developments in the use of stable isotope tracers and mathematical modelling. This review deals with the methodological aspects of stable isotope kinetic studies. The design of in vivo turnover studies requires considerations related to stable isotope tracer administration, duration of sampling protocol and interpretation of tracer data, all of which are critically dependent on the kinetic properties of the lipoproteins under investigation. Such models provide novel insight that further understanding of metabolic disorders and effects of treatments. Future investigations of the pathophysiology and therapy of the dyslipoproteinaemia of the metabolic syndrome will require the development of novel kinetic methodologies. Specifically, new stable isotope techniques are required for investigating in vivo the turnover of the HDL subpopulation of particles, as well as the cellular efflux of cholesterol into the extracellular space and its subsequent transport in plasma and metabolic fate in the liver.

Comparative multiple dose plasma kinetics of lycopene administered in tomato juice, tomato soup or lycopene tablets

BACKGROUND

Lycopene is mainly provided in tomato and tomato products in Western diet. Among other factors the systemic availability of lycopene from natural sources is dependent on release from the cell matrix as achieved by food processing.

AIMS OF THE STUDY

The purpose of this study was to compare plasma concentration responses of total lycopene and its major isomers to dosing of the carotenoid as tomato juice, tomato soup or tablets containing synthetic lycopene.

METHODS

Intake of lycopene rich food products was restricted throughout this randomized, parallel group study, including 6 volunteers per group. Following a 14 day lycopene depletion phase subjects ingested 20 mg of lycopene daily for 8 days as tomato juice, soup prepared from tomato paste or lycopene tablets. Lycopene plasma concentrations were monitored throughout the depletion and dosing phases and for 22 days post-dosing and kinetics were evaluated using both empirical and compartmental modelling.

RESULTS

Irrespective of the lycopene treatment all-E lycopene was the predominant lycopene isomer, whereas 5-Z lycopene was the most abundant Z isomer. Plasma concentration response of total and all-E lycopene to dosing of the carotenoid in tablets and tomato soup was comparable but exceeded that of intake in tomato juice. No differences were noted in dose normalized 5-Z lycopene concentrations between groups. The estimates of efficient half-life were approximately 5 and 9 days for all-E and 5-Z lycopene, respectively.

CONCLUSIONS

The systemic availability of synthetic lycopene from a tablet formulation is comparable to that observed from processed tomatoes (soup from tomato paste) and superior to that from tomato juice. No differences were observed in disposition kinetics of natural and synthetic lycopene. The synthetic lycopene tablet formulation used in this investigation may be of value for future clinical investigations.

GLUT4 is retained by an intracellular cycle of vesicle formation and fusion with endosomes

The intracellularly stored GLUT4 glucose transporter is rapidly translocated to the cell surface upon insulin stimulation. Regulation of GLUT4 distribution is key for the maintenance of whole body glucose homeostasis. We find that GLUT4 is excluded from the plasma membrane of adipocytes by a dynamic retention/retrieval mechanism. Our kinetic studies indicate that GLUT4-containing vesicles continually bud and fuse with endosomes in the absence of insulin and that these GLUT4 vesicles are 5 times as likely to fuse with an endosome as with the plasma membrane. We hypothesize that this intracellular cycle of vesicle budding and fusion is an element of the active mechanism by which GLUT4 is retained. The GLUT4 trafficking pathway does not extensively overlap with that of furin, indicating that the trans-Golgi network, a compartment in which furin accumulates, is not a significant storage reservoir of GLUT4. An intact microtubule cytoskeleton is required for insulin-stimulated recruitment to the cell surface, although it is not required for the basal budding/fusion cycle. Nocodazole disruption of the microtubule cytoskeleton reduces the insulin-stimulated exocytosis of GLUT4, accounting for the reduced insulin-stimulated translocation of GLUT4 to the cell surface.

Modeling ionic hydrogels swelling: characterization of the non-steady state

Ionic hydrogels can be used as controlled release systems that respond to an external substrate or trigger by swelling or de-swelling. One example is a glucose-sensitive system for insulin-controlled release based on pH-sensitive hydrogel. To enhance understanding of non-steady state swelling, and to facilitate design of specifications (e.g., glucose-sensitivity) of the pH-sensitive ionic hydrogel based on the copolymer poly (2-hydroxyethyl methacrylate-co-N, N-dimethylaminoethyl methacrylate) (poly (HEMA-co-DMAEMA)), we developed a mathematical compartmental model using the software SAAM II. Current analytical and computational methods focus on equilibrium swelling of hydrogels; although for many stimuli-responsive hydrogel applications, the dynamic process is significant. We now report, using a combination of experimental data and kinetic analysis that in the poly (HEMA-co-DMAEMA) the rate of proton entry is governed by a different rate coefficient than water entry rate. The transport coefficient governing water uptake is dependent upon three variables: pH of external media, amine groups incorporated into the polymer, and crosslinking density of the polymer. An additional result is that swelling equilibrium is reached when all the amine groups are protonated. In this study we also demonstrate the predictive capability of the model for both interpolated and extrapolated data, and its use in design of future bench experiments. Uncovering these fundamental properties of pH-sensitive hydrogels with the aid of a kinetic model suggests that the complexities of hydrogel research and development can be overcome by combining experimental and computational approaches.

A nonlinear compartmental model of Sr metabolism. I. Non-steady-state kinetics and model building

A model of Sr metabolism was developed by using plasma and urinary Sr kinetic data obtained in groups of postmenopausal women who received four different oral doses of Sr and collected during the Sr administration period (25 days) and for 28 days after cessation of treatment. A nonlinear compartmental formalism that is appropriate for study of non-steady-state kinetics and allows dissociation of variables pertaining to Sr metabolism (system 1) from those indirectly operating on it (system 2) was used. At each stage of model development, the dose-dependent model response was fitted to the four sets of data considered simultaneously (1 set per dose). A seven-compartment model with internal Sr distribution and intestinal, urinary, and bone metabolic pathways was selected. It includes two kinds of nonlinearities: those accounting for saturable intestinal and bone processes, which behave as intrinsic nonlinearities because they are directly dependent on Sr, and extrinsic nonlinearities (dependent on system 2), which suggest the cooperative involvement of plasma Sr changes in modulating some intestinal and bone mineral metabolic pathways. With the set of identified parameter values, the initial steady-state model predictions are relevant to known physiology, and some peculiarities of model behavior for long-term Sr administration were simulated.

Measurement of dynamic protein binding to chromatin in vivo, using photobleaching microscopy

We have described procedures for collecting, processing, and analyzing kinetic data obtained by photobleaching microscopy of GFP-tagged chromatin proteins in nuclei of cultured living cells. These procedures are useful for characterizing the in vivo binding of chromatin proteins to their natural template--unperturbed, native chromatin in an intact cell nucleus. These techniques have revealed several generalizations that significantly change our view of the nucleus. At the qualitative level, it has become clear that almost all chromatin proteins bind only transiently to their targets. More importantly, the combined use of in vivo microscopy and kinetic, computational analysis allows analysis of the kinetics of protein binding in vivo. These methods should prove useful in the further in vivo investigation of the molecular mechanisms involved in genome organization and expression.

The concordance of early antipyrine and thiopental distribution kinetics

Studies of factors affecting the initial disposition of drugs with a rapid onset of effect following i.v. administration have used antipyrine as a surrogate for lipophilic drugs because it lacks cardiovascular effects. The present study tested the assumption that antipyrine is a useful surrogate for the flow-dependent tissue distribution of the lipophilic drug thiopental by comparing the recirculatory pharmacokinetic models of antipyrine and thiopental disposition after concomitant administration to five dogs anesthetized with 1.5% halothane. The pharmacokinetics of indocyanine green, a marker of the intravascular behavior of antipyrine and thiopental, and antipyrine in these dogs was nearly identical to that described previously in dogs anesthetized with 1.5% halothane but not given thiopental. The total volume of distribution of the highly lipophilic drug thiopental was more than 60% larger than that of antipyrine, 53 versus 33 liters, respectively. Nonetheless, the initial distribution kinetics of the two drugs, including the pulmonary tissue volume and the volume of the nondistributive pathway as well as the clearance to it, were nearly identical. As a result, the fraction of cardiac output involved in distribution of the two drugs to peripheral tissues was similarly identical, although the distribution of cardiac output between clearance to the rapidly equilibrating tissues and clearance to the slowly equilibrating tissues differed slightly. This study validates the assumption that antipyrine is a useful surrogate for lipophilic drugs in pharmacokinetic studies in which physiologic stability is desirable to meet the assumption of system stationarity.

Age-stratified pharmacokinetics of ketorolac tromethamine in pediatric surgical patients

Published data suggest that ketorolac pharmacokinetics are different in children than in adults. We sought to better characterize ketorolac pharmacokinetics in children. Thirty-six children, aged 1-16 yr, were stratified into four age groups: 1-3 yr, 4-7 yr, 8-11 yr, and 12-16 yr. Each child received 0.5 mg/kg of ketorolac tromethamine IV after completion of elective surgery. A maximum of 16 venous blood samples (mean, 13 +/- 2) were collected at predetermined times up to 10 h after drug administration. Plasma ketorolac concentrations were measured by high-performance liquid chromatography after solid-phase extraction. Individual concentration-versus-time relationships were best fit to a two-compartment pharmacokinetic model by using SAAM II. Body weight-normalized pharmacokinetic variables did not differ among the age groups and were similar to those reported for adults, including a volume of distribution at steady state of 113 +/- 33 mL/kg (mean +/- SD) and an elimination clearance of 0.57 +/- 0.17 mL x min(-1) x kg(-1). Our study demonstrates that a single dose of ketorolac (0.5 mg/kg) results in plasma concentrations in the adult therapeutic concentration range for 6 h in most children. Our data provide no evidence that children require either larger weight-adjusted doses or shorter dosing intervals than adults to provide similar plasma drug concentrations.

IMPLICATIONS

The literature suggests that ketorolac disposition differs between children and adults. We characterized ketorolac pharmacokinetics in 36 children. Body weight-normalized two-compartment pharmacokinetic variables did not differ among pediatric patients <17 yr old and were similar to adult values.

Peripheral and splanchnic metabolism of dietary nitrogen are differently affected by the protein source in humans as assessed by compartmental modeling

We used a previously developed compartmental model to assess the postprandial distribution and metabolism of dietary nitrogen (N) in the splanchnic and peripheral areas after the ingestion of a single mixed meal containing either (15)N-labeled milk or soy purified protein. Although the lower whole-body retention of dietary N from soy protein was measured experimentally, the splanchnic retention of dietary N was predicted by the model not to be affected by the protein source, and its incorporation into splanchnic proteins was predicted to reach approximately 35% of ingested N at 8 h after both meals. However, dietary N intestinal absorption and its appearance in splanchnic free amino acids were predicted to be more rapid from soy protein and were associated with a higher deamination, concomitant with a higher efficiency of incorporation of dietary N into proteins in the splanchnic bed. In contrast, soy protein was predicted to cause a reduction in peripheral dietary N uptake, as a consequence of both similar splanchnic retention and increased oxidation compared with milk protein. In addition, protein synthesis efficiency was reduced in the peripheral area after soy protein intake, leading to dietary N incorporation in peripheral proteins that fell from 26 to 19% of ingested N 8 h after milk and soy protein ingestion, respectively. Such a model thus enables a description of the processes involved in the differential metabolic utilization of dietary proteins and constitutes a valuable tool for further definition of the notion of protein quality during the period of protein gain.

The pharmacokinetics of dexmedetomidine in volunteers with severe renal impairment

Dexmedetomidine, an alpha2-adrenergic agonist with sedative and analgesic properties, is mainly cleared by hepatic metabolism. Because the pharmacokinetics of dexmedetomidine have not been determined in humans with impaired renal function, we studied them in volunteers with severe renal disease and in control volunteers. Six volunteers with severe renal disease and six matched volunteers with normal renal function received dexmedetomidine, 0.6 microg/kg, over 10 min. Venous blood samples for the measurement of plasma dexmedetomidine concentrations were drawn before, during, and up to 12 h after the infusion. Two-compartmental pharmacokinetic models were fit to the drug concentration versus time data. We also determined its hemodynamic, respiratory, and sedative effects. There was no difference between Renal Disease and Control groups in either volume of distribution at steady state (1.81 +/- 0.55 and 1.54 +/- 0.08 L/kg, respectively; mean +/- SD) or elimination clearance (12.5 +/- 4.6 and 8.9 +/- 0.7 mL x min(-1) x kg(-1), respectively). However, elimination half-life was shortened in the Renal Disease group (113.4 +/- 11.3 vs 136.5 +/- 13.0 min; P < 0.05). A mild reduction in blood pressure occurred in most volunteers. Although most volunteers were sedated by dexmedetomidine, renal disease volunteers were sedated for a longer period of time.

IMPLICATIONS

The pharmacokinetics of dexmedetomidine in volunteers with severe renal impairment differed little from those in volunteers with normal renal function. In addition, there were no clinically significant differences in the hemodynamic responses to dexmedetomidine. However, dexmedetomidine resulted in more prolonged sedation in subjects with renal disease.

Energy nutrients modulate the splanchnic sequestration of dietary nitrogen in humans: a compartmental analysis

We used a previously developed compartmental model to assess the postprandial distribution and metabolism of dietary nitrogen (N) in the splanchnic and peripheral areas after the ingestion of a single meal containing milk protein either alone (MP) or with additional sucrose (SMP) or fat (FMP). The addition of fat was predicted to enhance splanchnic dietary N anabolism only transiently, without significantly affecting the global kinetics of splanchnic retention and peripheral uptake. In contrast, the addition of sucrose, which induced hyperinsulinemia, was predicted to enhance dietary N retention and anabolism in the splanchnic bed, thus leading to reduced peripheral dietary amino acid availability and anabolism. The incorporation of dietary N into splanchnic proteins was thus predicted to reach 18, 24, and 35% of ingested N 8 h after MP, FMP, and SMP, respectively. Such a model provides insight into the dynamics of the system in the nonsteady postprandial state and constitutes a useful, explanatory tool to determine the region-specific utilization of dietary N under different nutritional conditions.

A basis for a visual language for describing, archiving and analyzing functional models of complex biological systems

BACKGROUND

We propose that a computerized, internet-based graphical description language for systems biology will be essential for describing, archiving and analyzing complex problems of biological function in health and disease.

RESULTS

We outline here a conceptual basis for designing such a language and describe BioD, a prototype language that we have used to explore the utility and feasibility of this approach to functional biology. Using example models, we demonstrate that a rather limited lexicon of icons and arrows suffices to describe complex cell-biological systems as discrete models that can be posted and linked on the internet.

CONCLUSIONS

Given available computer and internet technology, BioD may be implemented as an extensible, multidisciplinary language that can be used to archive functional systems knowledge and be extended to support both qualitative and quantitative functional analysis.

Compartmental modeling of postprandial dietary nitrogen distribution in humans

A linear 11-compartment model was developed to describe and simulate the postprandial distribution of dietary nitrogen. The values of its 15 constant diffusion coefficients were estimated from the experimental measurement of (15)N nitrogen kinetics in the intestine, blood, and urine after the oral administration of (15)N-labeled milk protein in humans. Model structure development, parameter estimation, and sensibility analysis were achieved using SAAM II and SIMUSOLV softwares. The model was validated at each stage of its development by testing successively its a priori and a posteriori identifiability. The model predicted that, 8 h after a meal, the dietary nitrogen retained in the body comprised 28% free amino acids and 72% protein, approximately 30% being recovered in the splanchnic bed vs. 70% in the peripheral area. Twelve hours after the meal, these values had decreased to 18 and 23% for the free amino acid fraction and splanchnic nitrogen, respectively. Such a model constitutes a useful, explanatory tool to describe the processes involved in the metabolic utilization of dietary proteins.

Object-oriented biomedical system modeling--the rationale

A short tutorial and a rationale for Object-Oriented Biomedical (Continuous) System Modelling (OOBSM) are given. The paper investigates and defines what is needed in order to make the work with complex bio-medical and pathophysiological models easier, less error prone and conceptually clearer than is possible by using the existing modelling techniques. It also contains a specification of what is required in order to make such models and corresponding knowledge communicable among different research groups and in order to use such models as components in even more complex models. The work shows that hitherto available continuous system modelling languages and tools are less suitable for the construction of complex, interdisciplinary, multilevel, hierarchical models and model components and that those modelling languages do not allow for easy exchange and communication of the model knowledge between different research groups and sites. It concludes that object-oriented and distributed objects methodologies are both feasible and suitable for such modelling.