Mathematical Models in Experimental Nutrition VI

University of California, Davis

Sunday August 17 through Wednesday August 20, 1997

Abstracts

Balancing needs, efficiency, and functionality in the provision of modeling software: a perspective of the NIH WinSAAM Project. Ray Boston¹, Peter Greif², Meryl Wastney³, and Oscar Linares⁴. Clinical Studies¹, NBC, University of Pennsylvania, Laboratory of Exptl. and Computational Biology², National Inst. of Health, Dept. of Neonatology³, Georgetown University Medical School, and Dept. of Geriatrics⁴, Medical School, University of Michigan

The development of new software or the refinement of existing software for new operating environments each calls for judicious balancing. On the one hand we strive for simplicity, predictability, and operational protection as it is well recognized that software with these attributes will attract an audience of satisfied users. But, on the other hand, these attributes do not conjure a sense of power, efficiency, or flexibility, and these properties are also appreciated by users, albeit a somewhat different group of users. The goal is to achieve a blend which isolates critical functionality, flexible control, and user support meeting the needs of the broadest collection of serious users. In this paper we discuss the issues impacting the migration of SAAM to the Windows environment, the NIH WinSAAM Project, and we outline the steps taken to ensure its feasibility. In addition we describe a new paradigm for software development and use ensuring the durability of software for modeling.

Approaches to compartmental population kinetics. P. Hugh R. Barrett¹, Bradley M. Bell², Claudio Cobelli³, David M. Foster¹, Alan Schumitzky^1,4 and Paolo Vicini¹, Department of Bioengineering¹, University of Washington, Seattle, WA, Applied Physics Laboratory², University of Washington, Seattle, WA, Department of Electronics and Informatics³, University of Padova, Italy, and Department of Mathematics⁴, University of Southern California, Los Angeles, CA.

Compartmental models [1] are widely used to estimate parameters of interest from a kinetic experiment performed in an individual. Their application to epidemiological studies is more and more frequent [2-4]. Applications of compartmental models to well-defined populations has commonly relied upon first fitting each individual’s data to a model, and then determining the average of the parameter estimates. This approach is suboptimal, since the individual estimates can be affected by poor precision and do not take into account the other subjects’ data.

More accurate estimates of the population parameters can be obtained using algorithms for population kinetic analysis of nonlinear mixed effects problems. There are basically two approaches, which in statistical terms are called: parametric and nonparametric. In the parametric approach (of which NONMEM [5] and the two-stage methods [6] are examples), the population distribution is assumed to be normal, in the nonparametric approach [7], no assumptions are made about the form of the population distribution.

We will discuss various two stage and other parametric [8] methods. We show how some of these methods, besides providing reliable estimates the population parameters and covariance matrix, also allow the estimation of individual parameters with very good precision even in a sparse data situation.

JA Jacquez, Compartmental analysis in biology and medicine, Ann Arbor 1996.

RL Lalonde et al., Pharm Res 13: 832-8, 1996.

VD Schmith et al., Pharm Res 14: 91-7, 1997.

MF Saad et al., Diabetes 43: 1114-1121, 1994.

SL Beal and LB Sheiner, CRC Critical reviews in Bioengineering 8: 195-222, 1982

JL Steimer et al., Drug Metabolism Reviews 15: 265-292, 1984

A Mallet, Biometrika 73: 645-656, 1986

MJ Lindstrom and DM Bates, Biometrics 46: 673-687, 1990

 

Statistical Models for Quantitative Bioassay. Matthew R. Facer¹, Hans-Georg Mueller¹, Andrew J. Clifford². Division of Statistics¹ and Department of Nutrition², University of California, Davis, CA.

We provide a survey of various statistical approaches for the analysis of dose-response data with continuous response. The emphasis is on the multivariate case with several predictors. The methods which will be discussed can be classified into three categories: (1) Parametric models, including change-point models; (2) Nonparametric models, using smoothing methods such as weighted local linear fitting; (3) Semiparametric models, combining nonparametric and parametric components. The methods will be illustrated with the analysis of data generated from a folate depletion-repletion bioassay experiment conducted on rats where the measured growth rate of the rats is the response variable. We also discuss the biological conclusions that can be drawn from applying the various statistical methods to this data set.

The mathematics behind modeling. Judah Rosenblatt, Metabolism Unit Shriners Burns Institute, Director of Biomathematics, University of Texas Medical Branch, Galveston, TX.

Many of the models used in applied fields such as metabolism and nutrition are developed from "local descriptions" - that is, descriptions obtained by examining typical, but very small portions of the systems under consideration, often over typical short time intervals. These descriptions lead to differential equations, usually considered technically advanced, and hence, inaccessible to many users. The computer packages available for analyzing these models allow users to solve these differential equations and obtain important quantitative properties of the systems being examined without requiring any mathematical understanding. Unfortunately, some users may feel uncomfortable using powerful packages without knowledge of the background on which they are based. However, by looking at them in a way which examines only the important concepts, not only can differential equations be understood quite easily, but important information about the system can readily be extracted from these equations without requiring any advanced mathematical background. This presentation will illustrate how this is done for several useful compartmental models.

Modeling the Dynamics of Vitamin A Metabolism in Men. Michael H. Green¹ and Doris von Reinersdorff², Pennsylvania State University¹, University Park, PA and Hoffmann-LaRoche², Basel, Switzerland and Nutley, NJ.

Data were recently presented (v. Reinersdorff, D. et al., J. Lipid Res. 37:1875-1885, 1996) on the kinetics of vitamin A in plasma for 1 week after administration of a single oral dose of 105 micromol of [8,9,19-¹³C]retinyl palmitate to 11 healthy adult males. Non-compartmental methods were used to calculate peak plasma concentrations of total retinyl esters, [¹²C]retinol, [8,9,19-¹³C]retinol, and total retinol; the times to reach these maxima; areas-under-the-curve versus time profiles; and half-times. Here we describe our application of model-based compartmental analysis to data for 1 representative subject and the resulting compartmental model developed to quantify the dynamic behavior of vitamin A. The large load of labeled vitamin A (tracer) perturbed the dynamic behavior of the unlabeled, endogenous vitamin A (tracee), and necessitated the development of parallel models for the tracer and tracee systems. We first present our postulated initial model and the rationale for choosing this model, and then describe the steps taken to develop final working models that are consistent with the data and with known physiology. Our purpose is to both explain the modeling process for novice modelers and to discuss some of the insights into vitamin A metabolism that have been derived from this work.

Modeling of vitamin A and beta-carotene metabolism. Betty Jane Burri and Jin-Young Kim Park, USDA/ARS/Western Human Nutrition Research Center, PO Box 29997, Presidio of San Francisco, CA.

We are developing kinetic models for retinol and beta-carotene metabolism in women living under controlled conditions on diets with known concentrations of vitamins and carotenoids. Twenty-five healthy adults were fed either tetradeuterated vitamin A (retinyl-d₄ acetate), or octadeuterated beta-carotene (beta-carotene-d₈) before breakfast. Natural and stable-isotopes of vitamin A and beta-carotene in serial serum specimens collected for up to 120 days after administrations were separated and measured from other components by GC-MS and HPLC, respectively. Kinetic modeling was done with SAAMII (RFKA, U. Washington, Seattle). Retinol-d₄ metabolism in all women tested can be described by a simple four-part compartmental kinetic model. The model includes compartments for stomach, serum, and other tissues (mostly liver), with a delay term representing the intestines. The model predicts a mean absorption of Retinol-d₄ of 7% and a steady-state turnover rate of four mmol/day; with high inter-individual variability. Dietary intakes of beta-carotene did not influence the absorption or turnover rate of retinol. However, it did result in changes (p < 0.05) of steady-state masses of retinol in all compartments but serum. Our working eight-compartment model of beta-carotene-d₈ predicts 2% absorption of the isotope and 34% conversion to retinol, with a negative association between absorption and conversion.

The dynamics of folate metabolism in an adult volunteer using ¹⁴C-accelerator mass spectrometry. Andrew J. Clifford¹, Ali Arjomand¹, Stephen R. Dueker¹, Heidi Johnson², A. Daniel Jones³, Philip D. Schneider⁴, Rebecca A. Zulim⁴, Bruce B. Buchholz⁵ and John S. Vogel⁵. Departments of Nutrition¹, and Animal Science² and Facility for Advanced Instrumentation³, University of California, Davis, CA, Cancer Center⁴, UCDMC, Sacramento, CA and Center for Accelerator Mass Spectrometry⁵, Lawrence Livermore National Laboratory, Livermore, CA.

Metabolism of a 0.08 micromol oral dose of pteroyl-¹⁴C(U)-glutamate in water was determined from the ¹⁴C-folate concentrations in serial plasma, erythrocyte, urine and feces by time since dose in a healthy adult male. The ¹⁴C-folate concentrations were measured using accelerator mass spectrometry. Plasma ¹⁴C-folate, urine ¹⁴C-folate and feces ¹⁴C-folate concentration-time curves were each described by a 3 term polyexponential equation, using an empirical description of folic acid metabolism. The erythrocyte ¹⁴C-folate concentration-time curves was described by a 2 term polyexponential equation that included a three day delay. A physiologic compartmental model of folic acid metabolism was also constructed and tested. This model suggests that 90% of the pteroyl-¹⁴C(U)-glutamate dose was rapidly absorbed as intact folic acid and that urinary losses of absorbed ¹⁴C-folate were ~5 times greater than the fecal losses. Also, it suggests that liver is important in converting folic acid to the reduced and methylated forms of this vitamin. Finally, it suggests that the mean residence time for folic acid is 150 days. The in vivo dynamics of folate metabolism in humans, its significance and the nutritional, physiological and environmental factors that affect it can now be studied using a combination of AMS that measures ¹⁴C concentrations to parts per 10^13-15 on miligram-sized samples, and mathematical modeling.

Human Zinc Metabolism: Advances in the Modeling of Stable Isotope Data. K. Michael Hambidge, Nancy F. Krebs, and Leland V. Miller. University of Colorado Center for Human Nutrition, Denver, CO.

Although zinc has been well-established as a micronutrient of vital, multifaceted importance, our understanding of how to prevent or to detect and treat human zinc deficiency continues to be hampered by our limited understanding of zinc metabolism under various dietary circumstances and host conditions. Central to our investigations of zinc in human nutrition, we have developed a compartmental model of zinc metabolism based on data from studies of adults in which multiple isotope tracers were simultaneously administered orally and intravenously and the resulting enrichment measured in plasma, erythrocytes, urine, and feces. These enrichment data have been fitted to a consistent compartmental model using SAAM/CONSAM. Additional information, including estimations of fundamental steady state parameters derived from non-compartmental calculations and measurements of tracee intake and excretion, was taken into account in the fitting process. After extensive manual fitting, we implemented more refined data, weighting schemes and other statistical constraints to facilitate computer fitting. In addition, model validation issues were examined. We have also used the Extended Multiple Studies Analysis facility of SAAM to produce an aggregate of the individual subject models and a single set of population statistics. With additional data from multiple aspiration sites in the small intestine, we are currently developing a more detailed model of the small intestine, site of important zinc homeostatic processes.

Key Features of Copper versus Molybdenum Metabolism in Humans. Judith R. Turnlund, USDA/ARS/Western Human Nutrition Research Center, PO Box 29997 Presidio of San Francisco, CA

Copper and molybdenum are essential nutrients for humans. Both trace elements are required in the diet in small amounts, are toxic in excess, and body stores are low, but there are major differences in their metabolism. Metabolic studies were conducted in the human nutrition suite of the Western Human Nutrition Research Center. Young men were confined to the unit for 2 to 90 days in studies of copper metabolism and for 120 days for studies of molybdenum metabolism. Stable isotopes were used as tracers to follow the metabolic fate of these elements. ⁶⁵Cu was administered orally and intravenously in the copper studies. ¹⁰⁰Mo was administered orally and ⁹⁷Mo was administered intravenously in the molybdenum studies. Kinetic models were developed to gain a better understanding of their metabolism. The long-term goals of the model development were to estimate pool sizes and rates of transfer between compartments which could not be sampled directly, to identify points of metabolic regulation, and then elucidate the mechanisms of regulation. Compartmental models were developed using CONSAM. A 5-compartment model with two delay components and two routes of excretion was developed for copper and a model with 7 compartments and two routes of excretion was developed for molybdenum. Key features of these models and differences between the metabolism of copper and molybdenum will be discussed.

Realistic models of calcium waves in living cells. John Wagner¹, Richard L. Nuccitelli² and Joel E. Keizer³, Institute and Graduate Group in Applied Mathematics¹, and Sections of Molecular and Cell Biology² and of Neurobiology, Physiology and Behavior³, Division of Biologic Sciences, University of California, Davis, CA.

Fontanilla and Nuccitelli (Mol. Biol. of the Cell, 1996,7:S484A) recently presented detailed measurements of the shape and speed of the fertilization Ca2+ wave in Xenopus laevis eggs. In order to help interpret their results, we have hypothesized that the physiological state of the egg is bistable, i.e. that the cytoplasm can support two alternative Ca2+ concentrations, a low concentration characteristic of the prefertilization state, and an elevated concentration characteristic of the state following the passage of the wave. We explore this hypothesis by assuming that the bistability is due to the release and reuptake properties of the endoplasmic reticulum as determined by the IP3 receptor/Ca2+ channels and SERCA type ATPases. Our simulations show that inhomogeneities in the Ca2+ release properties near the plasma membrane can explain the temporal and spatial dependences of the shape and speed of these waves. Our results are consistent with the hypothesis that a small gradient of IP3 exists near the plasma membrane and is essential for determining the shape of the wave front.

Calcium Kinetics During Extended Space Flight. Meryl E. Wastney¹, Scott M. Smith², Victor S. Oganov³, Boris V. Morukov³, Irina M. Larina³, Steven A. Abrams⁴, Laurence E. Nyquist², Chi-Yu Shih², and Helen W. Lane². Georgetown University Medical Center¹, Washington, DC; NASA Johnson Space Center², Houston, TX; Institute for Biomedical Problems³, Moscow, Russia and Baylor College of Medicine⁴, Houston, TX.

A major concern of extended space flight is bone loss of calcium. Calcium homeostasis is perturbed during space flight but the sites involved and the degree of perturbation at each site are not known. These studies were designed to examine calcium kinetics during a 115-day mission on board the Mir space station. The subjects (n=3 males) were studied seven times following administration of stable calcium isotopes as tracers (⁴³Ca orally and ⁴⁶Ca i.v.): three times before flight, flight day 115, on landing, 7 days after landing and 3 months after landing. Blood, urine and fecal samples were obtained for up to 5 days after tracer administration. As we had previously shown that isotope enrichment of saliva is proportional to serum (Smith SM et al, J Mass Spect 31, 1265, 1996) saliva was also sampled. Data were analyzed using a compartmental model and the SAAM software. All data from each subject were fitted simultaneously, and a minimal number of parameters were changed to fit the changes in kinetics between the studies. Compared to preflight values, absorption was decreased by 38% after 115 d in space, 56% on landing day, 29% 7 d after landing and 4% after 3 mo. Calcium intake decreased during space flight. Normally, fractional absorption increases when calcium intake is low. Results suggest that bone loss during space flight is associated with perturbed regulation of calcium absorption.

Insights into bone metabolism from calcium kinetic studies in children. Steven A. Abrams, USDA/ARS ChildrenÕs Nutrition Research Center, Baylor College of Medicine, Houston, TX.

Childhood is the primary time point for growth and mineralization of the skeleton. Changes in the mineralization rate during childhood are related to normal growth and pubertal development and may be effected by chronic illnesses. We have used multi-compartmental studies to examine calcium kinetics in children. These studies are performed using orally and intravenously administered stable isotopes of calcium. Dosing is determined based on the distribution volumes of the isotope, and is greater, on a body-weight basis, in pubertal children than in adults. Sample collection requires multiple blood samples to be obtained during the initial time period after isotope dosing. Twenty-four hours after dosing, however, urine enrichment of isotopes is comparable to serum enrichment and measurements may be made from urine samples.

We have found that the peak rate for both bone calcium deposition and removal occurs in girls during the year before menarche. Peak kinetic rates decrease in an exponential fashion post-menarche. Differences in calcium kinetics exist between Caucasian and Black girls. On a body-weight basis, the greatest rates of bone calcium deposition and removal are in infants, especially preterm infants. Children with chronic illnesses may have decreased rates of calcium absorption and bone calcium deposition which are not readily corrected by increasing calcium intake.

Development and application of a compartmental model of 3-methylhistidine metabolism in humans and domestic animals. John A. Rathmacher. Metabolic Technologies Inc. and Iowa State University, Ames, IA.

Measurement of urinary 3-methylhistidine (3MH) excretion is the primary in vivo method to measure skeletal muscle (myofibrillar) protein breakdown. This method requires quantitative collection of urine and is based on the assumption that no metabolism of 3MH occurs once released from actin and myosin. This is true in most species but in sheep and pigs a proportion is retained in muscle as a dipeptide, balenine. In none of these species does urine 3MH yield any data on the metabolism of 3MH. We have conducted studies that propose 3MH metabolism in sheep, cattle, pigs, dogs and humans can be defined from a single bolus infusion of a stable isotope 3-[methyl-2H3]-methylhistidine. Following the bolus dose of the stable isotope tracer serial blood samples and/or urine was collected over three to five days. A minimum of three exponentials was required to describe the plasma decay curve adequately. The kinetic linear-time-invariant models of 3MH metabolism in the whole animal were constructed by using the SAAM/CONSAM modeling program. Three different configurations of a three compartment model are described: A) A simple 3-compartment model for cattle, dogs and humans, in which plasma kinetics (3-[methyl-2H3]-MH/3MH) are described by compartment 1 and has one urinary exit from compartment 1; B) a plasma-urinary kinetic 3-compartment model with two exits was used for sheep ( a urinary exit out of compartment 1 and a balenine exit out of a tissue compartment 3; and C) a plasma 3-compartment model with an exit out of a tissue compartment 3 was used in pigs. The kinetic parameters reflect the differences in known physiology of cattle, dogs and humans compared to sheep and pigs that do not quantitatively excrete 3MH into the urine. Steady-state model calculations define masses and fluxes of 3MH between three compartments and importantly the de novo production of 3MH. The de novo production of 3MH for humans, cattle, dogs, sheep and pigs are 3.1, 6.0, 12.1, 10.3, and 7.2 fmol/kg/d.

The de novo production of 3MH as calculated by the compartmental model was not different when compared to 3MH production as calculated via traditional urinary collection. Additionally, data suggest that steady state compartment masses and mass transfer rates may be related to Fat Free Mass and muscle mass in humans and pigs, respectively. In conclusion, a model of 3MH metabolism has been developed in numerous species and these models can be used for the assessment of muscle proteolysis and 3MH kinetics without the collection of urine. This methodology is less evasive and will be useful in testing further experimental designs that alter myofibrillar protein breakdown.

A theoretical model of protein synthesis and degradation to identify appropriate experimental designs. Heidi A. Johnson, Chris C. Calvert and Ransom L. Baldwin. Animal Science Department, University of California, Davis, CA.

The measurement of fractional synthesis rate is based on the assumptions that amino acids for protein synthesis are supplied by an intracellular pool and amino acids from protein degradation are not recycled back to protein synthesis. In order to test these assumptions a mechanistic, theoretical model of protein turnover for a nongrowing 26g mouse was developed based on data from the literature. The model consists of three protein pools turning over at fast (102 micromoles leucine, t_1/2=11.5 h), medium (212 micromoles leucine, t_1/2=16.6 h) or slow (536 micromoles leucine t_1/2=71.5 h) rates and extracellular (1.69 micromoles leucine), leucyl-tRNA (0.0226 micromoles leucine) and intracellular (5.72 micromoles leucine) amino acid pools which exchange amino acids. The flow of amino acids from the protein pools to the leucyl tRNA pool determines the amount of recycling. The flow of amino acids from the extracellular pool to the small precursor pool determines the amount of channeling. Two flooding dose data sets are used to evaluate specific radioactivity changes predicted by the model. Data are generated from the model and fit to the model to determine the measurements necessary to estimate the percent recycling, channeling and protein synthesis.

Dynamics of glucose and lipid metabolism using mass isotopomer distribution analysis (MIDA). Mark K. Hellerstein, Nutritional Sciences, University of California, Berkeley, CA.

I will discuss recently developed non-invasive methods for gaining access to intracellular biochemical processes in vivo, mostly involving use of stable isotopes with mass spectrometry. These techniques include mass isotopomer distribution analysis (MIDA), a method for measuring polymerization biosynthesis; non-invasive secreted "probes", for sampling intracellular metabolites; intracellular dilution, for measuring absolute fluxes through intracellular pathways; and DNA synthesis, for measuring cell proliferation kinetics. MIDA considers biosynthesis as a combinatorial process (monomers into polymers); the mathematics of combinatorial probabilities (i.e. the binomial or multinomial expansion) can therefore be applied. By this strategy, the isotope enrichment of the true intracellular monomeric biosynthetic precursor pool (p) can be inferred. From p, kinetic parameters (fractional and absolute synthesis) can be calculated. Non-invasive probes use secreted metabolites to reflect the labelling of their intracellular precursors. Intracellular dilution allows absolute fluxes to be measured, by applying the dilution principle to intracellular metabolites. Finally, a new method for measuring DNA synthesis allows cell kinetics to be measured in vivo. In summary, new approaches permit intracellular metaboliic events to be measured quantitatively in vivo; from this, many new opportunities for modeling can be envisioned.

Modeling the depression in resting metabolic rate during energy deficit in humans. Janet A. Novotny and William V. Rumpler. Diet and Human Performance Laboratory, Beltsville Human Nutrition Research Center, USDA/ARS, Beltsville, MD.

Many researchers have observed a depression in resting energy expenditure per unit fat-free mass (REE/FFM) occurring with energy deficit in weight reducing individuals, and this depression in REE/FFM has been suggested to indicate metabolic adaptation. Because of the potential of metabolic adaptation to influence post-obese weight maintenance, the mechanism behind such a depression in REE/FFM is of great interest. Since fat-free mass is not of uniform composition, disproportionate changes in high activity tissues may lead to changes in REE/FFM without metabolic adaptation. For example, small decreases in organ masses may result in decreased REE/FFM with no detectable change in FFM. Such a phenomenon is in accord with animal studies showing a dependence of organ masses on level of food intake. To test the hypothesis that small reductions in organ masses may account for the reduction in REE/FFM observed during energy deficit, we have developed a mathematical model of human weight loss in which an energy deficit in the model causes a decrease in kidney, GI, and liver size. The model was assembled into a FORTRAN program, and simulations of body weight reduction were performed. Simulation results were compared to experimental data for overweight males who were subjected to an energy deficit for one month. Model results were in good agreement with experimental data. The model showed that the reduction in resting energy expenditure observed during energy deficit may result from a slight reduction in visceral organ size.

Statistical Perspectives on Assay Development. David M. Giltinan. Department of Biostatistics, Genentech Inc., South San Francisco, CA.

Recent technical advances in assay methodology afford enormous potential to deepen our understanding of fundamental biochemical and physiological processes by enabling measurement of key analytes in picomolar amounts and below. Poor understanding of key statistical characteristics of an assay can nullify any potential gains, however, by leading to inefficient use of the assay, or incorrect interpretation of results.

This talk will provide an overview of key statistical aspects of assay development and interpretation. A pragmatic approach will be taken, focusing on issues that are important in practice, as opposed to those that are more of a theoretical concern. I will discuss: (i) selected design aspects to consider during assay development, (ii) appropriate characterization of assay accuracy and precision, (iii) determination of the range of reliable calibration, (iv) definitions of sensitivity and lower limits of quantitation, (v) use and interpretation of control samples in monitoring assay performance

These issues will be addressed within the context of HPLC assays (linear standard curve and generally good precision) and immunoassays (nonlinear standard curve and intermediate precision). The importance of intelligent replication strategies in submitting samples for assay will be emphasized.

Preparation and Analysis of Biological Materials for Stable Isotopes by Plasma Source Mass Spectrometry. Ramon M. Barnes, Yves GŽlinas, and Antoneta Krushevska, Department of Chemistry, Lederle Graduate Research Center, University of Massachusetts, Amherst, MA

The development and commercial availability of plasma source, specifically inductively coupled plasma, mass spectrometers (ICP-MS) have significantly extended the potential application of stable isotopes for nutritional modeling. The status of research and commercial ICP-MS instruments, and their applications and limitations for stable isotopic studies will be reviewed. The consequences of mass spectroscopic resolution and measurement sensitivity obtainable with quadrupole, sector, time-of-flight, and trap instruments on stable isotope analysis will be examined. Requirements for reliable measurements with practical biological samples including tissues and fluids will be considered for calcium, chromium, lead, and zinc isotopes. Sample preparation often is critical. The possibilities for stable isotope analysis in chemically separated compounds (speciation) also will be explored. On-line compound separations by chromatography or electrophoresis, for example, have been combined instrumentally with ICP-MS. Some possibilities and requirements will be described for stable isotope speciation analysis.

Protocol development for tracer studies; considerations and perspectives. Stephen R. Dueker¹, A. Daniel Jones² and Andrew J. Clifford¹. Nutrition Department¹ and Facility for Advanced Instrumentation, University of California, Davis, CA.

Stable (non radioactive) isotopes allow a compound to be distinguished from endogenous chemicals and are particularly useful for in vivo human studies. Success with stable isotope tracer studies on organic molecules requires several considerations beyond prerequisite good analytical practices. Prior to any study, questions need to be addressed concerning the type and position of the label, the degree of enrichment necessary for a desired level of sensitivity, the lability of the heavy nuclide both under biological conditions and during subsequent isolation and derivitization (if necessary) prior to mass spectral analysis, possibility for biological discrimination, and the expected catabolic products. Bracketed by these concerns, I will discuss my experiences with stable isotope labeled experimentation using tagged micronutrients in humans subjects. An evaluation of mass spectral techniques and instrumentation suitable for stable isotope analysis will also be discussed.

Accelerator MS as a Bioanalytical Tool. John S. Vogel. Center for Accelerator MS, Lawrence Livermore National Laboratory, 7000 East Avenue, L-397, Livermore, CA

The sensitivity of AMS was primarily developed in the 1980's for radiocarbon dating of archaeological artifacts and isotope tracing in oceanographic, atmospheric, or geologic science. Through intense intercomparisons of previous and concurrent decay-counting data, AMS is well validated and has a proven sensitivity to parts in 10¹⁵. AMS has been more recently used in tracing labeled chemical compounds through biological systems, including humans. The 10⁶ factor in sensitivity over decay counting for detecting long-lived isotopes such as radiocarbon can be applied to reducing specific activity of the labeled compound, to tracing the compound to more exquisitely defined biochemical fractions, to lowering the administered radiative dose to levels that are not legally radioactive, or a combination of all three benefits. Data from LLNL's research are used to quantitate and validate properties of ¹⁴C-AMS that are relevant to its use in biochemical research. The sensitivity, precision, specificity, and stability of AMS are discussed in comparison to liquid scintillation counting and stable isotope IRMS tracing. (Work was performed under the auspices of the U.S. Department of Energy at Lawrence Livermore National Laboratory under contract W-7405-ENG-48).

Poster Abstracts

Modelling of Mortality Data by Means of Poisson Regression with Error in Variables. Paul Jordan and U. Moser. F. Hoffmann-La Roche LTD, Human Nutrition Research, CH, 4070 Basel, Switzerland.

Death rates of particular categories in epidemiological studies are often based on a small number of occurrences which can be well described by a Poisson distribution. We applied this model for the analysis of a multi-center study in five Japanese counties where the death rates of stomach cancer (ICD-9 code 151) in 4 age groups are known. In our example
some covariates of the cases (e.g. plasma lycopene levels) are unknown values and are estimated from a randomly chosen collective. Therefore, these values are subject to a sampling error. The inclusion of errors in variables (e-i-v ) into the statistical model can adequately describe such a situation. The model is estimated in a Bayesian framework by means of resampling techniques. Based on the posterior distribution of the parameters the relative risk of stomach cancer is 0.46 (95% credible interval 0.23 - 0.79) comparing the maximum of the population medians of lycopene with the minimum. The estimated overdispersion is close to zero indicating only minor interference with other possible explanatory variables. In addition, we show that inclusion of e-i-v can give more accurate estimates of the parameters even from small sample sizes.

A Mechanism for Distributing Working Versions of Published Models via the Internet. Meryl E. Wastney¹, D. Yang², D. F. Andretta¹, J. Blumenthal³, J. Hylton³, N. Canolty⁴, J. Collins⁵ and R. C. Boston⁶. Departments of Pediatrics¹ and Chemistry², and the Dahlgren Memorial Library³, Georgetown University Medical Center, Washington, D.C., Department of Foods and Nutrition⁴, University of Georgia, Athens, GA, Department of Medicine⁵, Vanderbilt University School of Medicine, Nashville, TN, and Biomathematics Unit⁶, School of Veterinary Medicine, University of Pennsylvania, Kennett Square, Philadelphia, PA

Mathematical models are useful tools for investigating complex systems. By representing physiological systems as models, theories can be tested quantitatively against data from the system. Models can be used to explore new theories prior to experimentation and to design studies to optimize experimental resources. They can also be used as teaching tools to illustrate physiochemical principles. In spite of their usefulness and the time invested in developing models, published models are often underused due to the difficulty in obtaining working versions of the model. To address this problem we have designed a library for mathematical models of biological systems on the Internet. The library contains published models and chemical models in formats compatible with several modeling packages. The models can be viewed graphically, model solutions can be viewed as plots against data, and models can be downloaded to be run with software on the user's own system. The address of the library is:

http://biomodel.georgetown.edu/model/

Investigators are invited to submit working versions of published models to the library. Models can be submitted electronically at the time a manuscript is accepted for publication. As journals go online articles containing models can be linked to working versions of the models in the library. By increasing access to working versions of models, more of the investment in kinetic studies and model development can be realized.

Intermediate Steps in Model Development: Decision-Making Processes for Beginning Modelers. Nancy L. Canolty¹, H. B. Everts¹, H. K. Jang¹ and Ray C. Boston². Department of Foods and Nutrtion¹, University of Georgia, Athens, GA and Biomathematics Unit², School of Veterinary Medicine, University of Pennsylvania, Kennet Square, PA.

Mathematical models describing biological systems usually evolve by evaluating many intermediate models, but other modelers are seldom able to analyze such steps. In this study, all intermediate steps during the development of a published model for lithium metabolism in rats (Everts et al., J. Nutr. 1996. 126:1445-1454) were documented. The model was developed as follows: a) lithium was forced into the model via the QO mechanism that puts an amount into the gut compartment each day that is equivalent to the measured mean daily lithium intake for that day; b) the gut compartment is emptied just before a new amount of lithium is added; c) lithium moves to the blood compartment, then to either the tissue or urine compartments; d) the tissues measured (brain, heart, kidney, liver, spleen and tibia) were combined into one compartment by summing their total lithium contents (in mg). All four compartments are supported by data, obtained either daily (gut and urine) or on day 17 (serum and tissues). This 4-compartment preliminary model (Model 1) was sequentially revised (Models 2-9) until a 6-compartment model (Model 10) met acceptance criteria. Each model was evaluated and, when necessary, revised. A simplified accept/reject decision-making protocol was developed to evaluate model acceptance. Initially, intermediate steps included altering the number of compartments and changing adjustable parameter ranges. When this did not work, it was realized that this was a dynamic model that changed with time. In subsequent steps various time interrupts and dependency functions were tried until one was found that fit the data and could be explained in physiological terms. An understanding of intermediate steps in model development could enhance decision-making skills of beginning modelers.

Ion trap mass spectrometry for kinetics of stable-isotope labeled vitamin A at low concentrations. Stephen R. Dueker¹, Roger S. Mercer², A. Daniel Jones² and Andrew J. Clifford¹. Department of Nutrition¹ and Facility for Advanced Instrumentation², University of California, Davis, CA.

The role of §-carotene in chemoprevention of cancers and other chronic diseases generated controversy when subpopulations taking §-carotene supplements showed increased mortality in clinical trails. Determination of the dynamics of §-carotene in individual human subjects has emerged as a high priority. Stable isotope labeled §-carotene tracers can be employed to determine rates of conversion to retinol (vitamin A), but tracer doses must be small to minimize perturbation of endogenous retinoid and carotenoid pools. In such cases, ratios of labeled tracer to endogenous retinol are often low, and quantitative analysis at enrichments < 1 mol % are unreliable owing to ion-molecule reactions which generate ions at the same mass as the labeled tracer even when no tracer is present. The current study demonstrates improved gas chromatography/mass spectrometry quantification of retinol-d₄ and unlabeled retinol, as their tert-butyldimethylsilyl ethers, at low enrichments using an ion trap mass spectrometer operated in selected ion storage mode. Electron ionization of analyte takes place in the ion trap using conditions that eject ions outside the range m/z 390-420, and molecular ions at m/z 400 and 404 from retinol and retinol-d₄ are quantified. Using this approach, unlabeled retinol yields a signal close to values calculated from natural isotopic abundances (~ 0.2%), whereas several quadrupole instruments operated using selected ion monitoring yielded 2-5times greater signal when no labeled retinol was present.

Distribution of ¹⁴C-PhIP in Lactating Female Rats and Their Suckling Pups at Low Doses Using Accelerator Mass Spectrometry. Robert J. Mauthe¹, Elizabeth G. Snyderwine², Amit Ghoshal², John S. Vogel³ and Kenneth W. Turteltaub¹. Molecular and Structural Biology Division¹, and Center for Accelerator Mass Spectrometry³ Lawrence Livermore National Laboratory, Livermore, CA, and Laboratory of Experimental Carcinogenesis², National Cancer Institute, NIH, Bethesda, MD.

2-Amino-1-methyl-6-phenylimidazo-[4,5-b]pyridine (PhIP) is a mammary carcinogen in female rats and is present in a wide variety of cooked meats. Lactating female F344 rats with suckling pups were gavaged with doses ranging from 50-1000 ng/kg ¹⁴C-PhIP. The excretion of the ¹⁴C-PhIP in the milk and distribution of ¹⁴C-PhIP into the dam and their suckling pups were measured using accelerator mass spectrometry (AMS). ¹⁴C-PhIP-derived radioactivity increased in a dose-dependent manner in the milk as well as in other dam and pup tissues. Cotreatment of lactating female rats with 500 mg/kg chlorophyllin in conjunction with a 500 ng/kg ¹⁴C-PhIP dose caused increased levels of ¹⁴C-PhIP in the milk and stomach contents of the pup while decreasing levels in all other tissues measured. These data suggest that PhIP and PhIP metabolites are excreted into the breast milk and are absorbed by the newborn at dietary doses. Additionally, chlorophyllin may modulate the excretion patterns of PhIP. These findings raise the possibility that there is a carcinogenic risk to the newborn from exposure to low levels of PhIP via breast milk. This work performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract no. W-7405-ENG-48 and partially supported by NIH (CA55861) and USAMRDC (MM4559FLB).

Beta-carotene changes vitamin A kinetics in women: compartmental modeling of vitamin A. Jin-Young K. Park¹, Betty Jane Burri¹, Hugh Barrett², Stephen Dueker³ and Andrew J. Clifford³. Western Human Nutrition Research Center¹, U.S. Department of Agriculture, Agricultural Research Service, Presidio of San Francisco, CA 94129, Center for Bioengineering², University of Washington, Seattle, WA 98195, and Department of Nutrition³, University of California, Davis, CA 95616.

Beta-carotene is a precursor of vitamin A. We tested a hypothesis that changes in beta-carotene intake might have an important role on the kinetics of vitamin A metabolism in women. Nine young healthy women lived in a metabolic research unit for 100 days. They were given a diet of an adequate amount of vitamin A (1100 mg/d) but low in beta-carotene (60 mg/d) during the depletion period of the study. They were given the same diet plus 15 mg/d of beta-carotene supplement during the following repletion period. At the beginning of each period a 20 mg oral dose of deuterated retinyl acetate (retinyl-d₄ acetate) was given as a stable-isotope of vitamin A before breakfast. Natural and stable-isotopes of retinol were separated and measured in serum using gas chromatography-mass spectrometry. A four-compartmental model for retinol was developed. The model includes a delay term and three compartments, which may represent gastrointestinal tract, serum, and tissues. The model accurately describes the data on changes in deuterated serum retinol in response to beta-carotene intake. Changes of beta-carotene intake did not influence the turnover rate of retinol (4 mmol/d). However, it did result in changes (p < 0.05) of the mean bioavailability of retinyl-d₄ acetate, fractional transfer coefficients, steady-state masses, and residence times of retinol in several compartments including tissues. An equation-based and area under serum concentration curve analyses showed the same conclusions.

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For further information on the conference, please contact:

Andrew J. Clifford
ajclifford@ucdavis.edu
Department of Nutrition
3135 Meyer Hall
University of California, Davis
Davis, CA 95616-5270
Phone: (916) 752-3376
Fax: (916) 752-8966

or

Hans-Georg Mueller
hgmueller@ucdavis.edu