Symposium:
Application of Models to Determination of Nutrient Requirements
Application of Models to the Determination of Nutrient Requirements: An Overview1 STEPHEN P. COBURH2 Biochemistry Department, Fort Wayne State Developmental Center, Fort Wayne, IN 46835 modeling are available, in the preface to Mathematical Modeling of Biological Systems, Harvey Gold notes that few of them allow the reader to understand fully the relationship between the mathematics being dis cussed and the biological realities (4). Modeling is ba sically a technique for using mathematics to describe the relationship between two or more parameters. Recognizing that, anyone who has performed linear regression or correlation analysis has already gained some experience in modeling. Notice that this defi nition of a model does not require that the model have any physiological reality. Sometimes simply describing the relationship between the parameters is all that is needed or possible. However, the real challenge and excitement arises when we try to relate the model to the physiological and metabolic processes in the body. As we use modeling techniques, it is essential to be constantly aware of the fundamental differences be tween the mathematical and physical sciences. Math ematics is based on logic. If the underlying assump tions are correct and the intermediate expressions are developed properly, the final mathematical expressions are logically correct. However, it is not always obvious what the underlying assumptions are. Many of the major advances in science have resulted from restating some of the fundamental assumptions. It is important in developing a model to identify the assumptions. For example, two common assumptions in tracer studies are that the amount of tracer is so small that
ABSTRACT The events leading up to this symposium are reviewed. The importance of recognizing the inher ent differences between mathematics, a logical science, and nutrition, an empirical science, are emphasized. The role of modeling leading to the proposal that vi tamin B-6 requirements for growth can be estimated by multiplying 15 nmol/g times the grams of daily gain is discussed. The goals and organization of the sym posium are summarized. J. Nutr. 122:687-689,1992. INDEXING KEY WORDS:
•nutrient requirements
•mathematical modeling
This symposium on Application of Models to De termination of Nutrient Requirements was presented at the 75th annual meeting of the Federation of Amer ican Societies for Experimental Biology (FASEB)in At lanta, Georgia on April 23, 1991. The idea for this program originated about 2 years ago. A small group of scientists interested in applying models to nutrition has been meeting informally at FASEB for several years. Members of this group have organized three workshops on use of models in nutrition independent of the FASEB meetings (1-3). A fourth one on trace elements is tentatively planned for 1992. It was felt that a symposium at FASEB might encourage more scientists to use these powerful techniques in their own nutrition research. Although many nutritionists may have a feeling that modeling might be useful, it is often hard to get started, particularly if no one has previously applied modeling to that particular nutrient. It is difficult to identify the literature on modeling because the word, model, may not appear in the title. Other key words that may be associated with models are kinetics, compartmental analysis, flux, turnover, utilization, tracers, isotope or labeled. Although a number of texts on 0022-3166/92
1 Presented as part of a symposium: Application of Models to Determination of Nutrient Requirements, given at the 75th Annual Meeting of the Federation of American Societies for Experimental Biology, Atlanta, GA, April 23, 1991. The symposium was sponsored by the American Institute of Nutrition. Guest editor for this sym posium was S. P. Coburn, Biochemistry Department, Fort Wayne Developmental Center, Fort Wayne, IN. 1 To whom correspondence should be addressed: Fort Wayne State Developmental 46835.
S3.00 ©1992 American Institute of Nutrition.
687 Downloaded from https://academic.oup.com/jn/article-abstract/122/suppl_3/687/4755311 by Washington University in St. Louis user on 26 March 2018
Center, 4900 St. Joe Road, Fort Wayne, IN
688
COBURN
it will not perturb the system and that the exogenous tracer will be metabolized exactly like the endogenous tracée.These assumptions are not always valid. The second caveat is to remember that the physical and life sciences are empirical. That is, they are based on observation, not logic. Because of this it is logically impossible to prove that a hypothesis is true, but it is possible to prove a hypothesis false. Therefore, perhaps the single most important comment in the subsequent papers is the reminder from Ramberg et al. (5) that "... genuinely new information is provided only by experiments designed to challenge and reject a putative hypothesis (model)." As a result, every model of met abolic processes should be viewed only as a working hypothesis that can be used productively until new observations require modification or perhaps com pletely invalidate the original model. I became interested in modeling because of indi cations that people with Down syndrome have altered vitamin B-6 metabolism. Because Down syndrome is characterized by an extra chromosome, it seemed likely that the rate of metabolism might be altered. One of the best ways to study rates is to use isotope tracer techniques. Whereas classical nutrient balance studies can demonstrate whether excretion of a par ticular nutrient equals intake, tracer studies can help to determine where the ingested molecules go, how they get there and how long they stay before they are excreted. Therefore, one of the major benefits of the modeling approach is that it forces detailed consid eration of what happens to a nutrient in the body. It is often assumed that water-soluble vitamins are readily flushed out of the body and must be continu ously replaced. Our very first tracer experiments sug gested that this was not the case with vitamin B-6 (6). We have since found that vitamin B-6 is very efficiently conserved and have evidence that, when vitamin B-6 intake is restricted, the half-life for the major vitamin B-6 pool in man may be several years (7). The fact that existing tissues could conserve their supplies suggested to us that the major vitamin B-6 requirement in grow ing animals might be to supply new tissue. Because the average whole-body vitamin B-6 content of several species is ~ 15 nmol/g, we proposed that the vitamin B-6 requirement for normal growth might be estimated by multiplying 15 nmol/g times the grams of daily gain (8). This calculation provides a reasonable ap proximation of the observed vitamin B-6 requirements for maximum growth of a variety of species from fish (9) to humans (8). If this calculation is valid, animals with the maximum feed efficiency of 1 g gain/g feed should require 15 nmol available vitamin B-6/g feed, and no animal should have a requirement higher than that for normal growth. Also, the original model pro posed to describe vitamin B-6 metabolism consisted of a small pool in equilibrium with a large pool, with excretion only from the small pool (10). This model Downloaded from https://academic.oup.com/jn/article-abstract/122/suppl_3/687/4755311 by Washington University in St. Louis user on 26 March 2018
was used with oral and intravenous administration of tracer with marked differences in the calculated body pool (10, 11) because most of an intravenous dose ini tially by-passes the liver and therefore exhibits differ ent kinetics than an oral dose. Based on our observa tions, we have modified that model for orally admin istered tracer to eliminate the equilibrium and to allow excretion from both pools (7). Even though our model has not reached the sophistication of some of the work to be discussed later, it is clear that the use of these techniques has had a profound effect on our thinking about vitamin B-6 requirements. Like many other areas of research, modeling efforts often raise more questions than they answer. However, a model can provide a useful working hypothesis for describing a particular system and for designing further studies of the system. The goal of this symposium was to provide enough information and support to encourage greater appli cation of modeling techniques in nutrition research. The first three papers introduce modeling. Michael Green discusses some of the general characteristics of modeling. Jerry Collins discusses some of the com puter software and resource facilities which are avail able, often at little cost. Charles Ramberg reviews the relative merits of various experimental approaches for gathering kinetic data. The final two papers present two specific examples for applying modeling tech niques to nutritional problems. Preston Mercer discuss his saturation kinetics approach to assessing nutrient requirements. Blossom Patterson describes the devel opment of her model of selenium metabolism with emphasis on the modeling process. We hope that this information will encourage wider application of mod eling techniques to nutrition research.
LITERATURE CITED 1. Canolty, N. L. & Cain, T. P., eds. (1985) Proceedings of 1985 Conference on Mathematical Models in Experimental Nutrition. pp. 1-139, University of Georgia, Athens, GA. 2. (1988) Proceedings of 1987 conference on mathematical models in experimental nutrition. Prog. Food Nutr. Sci. 12: 211-338. 3. Proceedings of 1989 conference on mathematical models in ex perimental nutrition: advances in amino acid and carbohydrate metabolism. J. Parenter. Enterai Nutr. (in press). 4. Gold, H. J. (1977) Preface In: Mathematical Modeling of Bio logical Systems-An Introductory Guidebook, pp. v-vii, Wiley, New York, NY. 5. Ramberg, C. F., Krishnamurti, C. R., Peter, D., Wolff, J. E. &. Boston, R. C. (1991) Application of models to determination of nutrient requirements: Experimental techniques employing tracers. J. Nutr. 122(suppl.): 000-000. 6. Coburn, S. P., Mahuren, J. D., Erbelding, W. F., Townsend, D. W., Hachey, D. L. & Klein, P. D. (1984) Measurement of vitamin B-6 kinetics in vivo using chronic administration of labelled pyridoxine. In: Chemical and Biological Aspects of Vi tamin B-6 Catalysis (Evangelopoulos, A. E., ed.) Part A, pp. 4354, Liss, New York, NY.
SYMPOSIUM: APPLICATION OF MODELS 7. Pauly, T., Szadkowska, Z., Coburn, S., Mahuren, D., Schal tenbrand, W., Booth, L., Hachey, D., Ziegler, P., Costili, D., Fink, W., Pearson, D., Townsend, D., Micelli, R. & Guilarte, T. (1991) Kinetics of deuterated vitamin B-6 metabolism in men on a marginal vitamin B-6 intake. FASEB J 5: 1660|abs). 8. Coburn, S. P. (1990) Location and turnover of vitamin B-6 pools and vitamin B-6 requirements of humans. Ann NY Acad Sci. 585: 76-85. 9. Coburn, S. P. (1991) Vitamin B-6. In: Comparative Animal
Downloaded from https://academic.oup.com/jn/article-abstract/122/suppl_3/687/4755311 by Washington University in St. Louis user on 26 March 2018
689
Nutrition of the Vitamins (Beynen, A. C. & West, C. E., eds.), Karger, Basel, Switzerland (in press). 10. Johansson, S., Lindstedt, S., Register, U. & Wadstrom, L. (1966) Studies on the metabolism of labeled pyridoxine in man. Am. J. Clin. Nutr. 18: 185-196. 11. Tillotson, J. A., Sauberlich, H. E., Baker, E. M. & Canham, J. E. (1966) Use of carbon-14 labeled vitamins in human nutrition studies: Pyridoxine. 7th Internat Congr Nutr, vol. 5, pp. 554557, Verlag Friedr. Vieweg & Sohn Gmbh, Braunschweig, Ger many.
Application of Models to Determination of Nutrient Requirements
Application of Models to the Determination of Nutrient Requirements: An Overview1 STEPHEN P. COBURH2 Biochemistry Department, Fort Wayne State Developmental Center, Fort Wayne, IN 46835 modeling are available, in the preface to Mathematical Modeling of Biological Systems, Harvey Gold notes that few of them allow the reader to understand fully the relationship between the mathematics being dis cussed and the biological realities (4). Modeling is ba sically a technique for using mathematics to describe the relationship between two or more parameters. Recognizing that, anyone who has performed linear regression or correlation analysis has already gained some experience in modeling. Notice that this defi nition of a model does not require that the model have any physiological reality. Sometimes simply describing the relationship between the parameters is all that is needed or possible. However, the real challenge and excitement arises when we try to relate the model to the physiological and metabolic processes in the body. As we use modeling techniques, it is essential to be constantly aware of the fundamental differences be tween the mathematical and physical sciences. Math ematics is based on logic. If the underlying assump tions are correct and the intermediate expressions are developed properly, the final mathematical expressions are logically correct. However, it is not always obvious what the underlying assumptions are. Many of the major advances in science have resulted from restating some of the fundamental assumptions. It is important in developing a model to identify the assumptions. For example, two common assumptions in tracer studies are that the amount of tracer is so small that
ABSTRACT The events leading up to this symposium are reviewed. The importance of recognizing the inher ent differences between mathematics, a logical science, and nutrition, an empirical science, are emphasized. The role of modeling leading to the proposal that vi tamin B-6 requirements for growth can be estimated by multiplying 15 nmol/g times the grams of daily gain is discussed. The goals and organization of the sym posium are summarized. J. Nutr. 122:687-689,1992. INDEXING KEY WORDS:
•nutrient requirements
•mathematical modeling
This symposium on Application of Models to De termination of Nutrient Requirements was presented at the 75th annual meeting of the Federation of Amer ican Societies for Experimental Biology (FASEB)in At lanta, Georgia on April 23, 1991. The idea for this program originated about 2 years ago. A small group of scientists interested in applying models to nutrition has been meeting informally at FASEB for several years. Members of this group have organized three workshops on use of models in nutrition independent of the FASEB meetings (1-3). A fourth one on trace elements is tentatively planned for 1992. It was felt that a symposium at FASEB might encourage more scientists to use these powerful techniques in their own nutrition research. Although many nutritionists may have a feeling that modeling might be useful, it is often hard to get started, particularly if no one has previously applied modeling to that particular nutrient. It is difficult to identify the literature on modeling because the word, model, may not appear in the title. Other key words that may be associated with models are kinetics, compartmental analysis, flux, turnover, utilization, tracers, isotope or labeled. Although a number of texts on 0022-3166/92
1 Presented as part of a symposium: Application of Models to Determination of Nutrient Requirements, given at the 75th Annual Meeting of the Federation of American Societies for Experimental Biology, Atlanta, GA, April 23, 1991. The symposium was sponsored by the American Institute of Nutrition. Guest editor for this sym posium was S. P. Coburn, Biochemistry Department, Fort Wayne Developmental Center, Fort Wayne, IN. 1 To whom correspondence should be addressed: Fort Wayne State Developmental 46835.
S3.00 ©1992 American Institute of Nutrition.
687 Downloaded from https://academic.oup.com/jn/article-abstract/122/suppl_3/687/4755311 by Washington University in St. Louis user on 26 March 2018
Center, 4900 St. Joe Road, Fort Wayne, IN
688
COBURN
it will not perturb the system and that the exogenous tracer will be metabolized exactly like the endogenous tracée.These assumptions are not always valid. The second caveat is to remember that the physical and life sciences are empirical. That is, they are based on observation, not logic. Because of this it is logically impossible to prove that a hypothesis is true, but it is possible to prove a hypothesis false. Therefore, perhaps the single most important comment in the subsequent papers is the reminder from Ramberg et al. (5) that "... genuinely new information is provided only by experiments designed to challenge and reject a putative hypothesis (model)." As a result, every model of met abolic processes should be viewed only as a working hypothesis that can be used productively until new observations require modification or perhaps com pletely invalidate the original model. I became interested in modeling because of indi cations that people with Down syndrome have altered vitamin B-6 metabolism. Because Down syndrome is characterized by an extra chromosome, it seemed likely that the rate of metabolism might be altered. One of the best ways to study rates is to use isotope tracer techniques. Whereas classical nutrient balance studies can demonstrate whether excretion of a par ticular nutrient equals intake, tracer studies can help to determine where the ingested molecules go, how they get there and how long they stay before they are excreted. Therefore, one of the major benefits of the modeling approach is that it forces detailed consid eration of what happens to a nutrient in the body. It is often assumed that water-soluble vitamins are readily flushed out of the body and must be continu ously replaced. Our very first tracer experiments sug gested that this was not the case with vitamin B-6 (6). We have since found that vitamin B-6 is very efficiently conserved and have evidence that, when vitamin B-6 intake is restricted, the half-life for the major vitamin B-6 pool in man may be several years (7). The fact that existing tissues could conserve their supplies suggested to us that the major vitamin B-6 requirement in grow ing animals might be to supply new tissue. Because the average whole-body vitamin B-6 content of several species is ~ 15 nmol/g, we proposed that the vitamin B-6 requirement for normal growth might be estimated by multiplying 15 nmol/g times the grams of daily gain (8). This calculation provides a reasonable ap proximation of the observed vitamin B-6 requirements for maximum growth of a variety of species from fish (9) to humans (8). If this calculation is valid, animals with the maximum feed efficiency of 1 g gain/g feed should require 15 nmol available vitamin B-6/g feed, and no animal should have a requirement higher than that for normal growth. Also, the original model pro posed to describe vitamin B-6 metabolism consisted of a small pool in equilibrium with a large pool, with excretion only from the small pool (10). This model Downloaded from https://academic.oup.com/jn/article-abstract/122/suppl_3/687/4755311 by Washington University in St. Louis user on 26 March 2018
was used with oral and intravenous administration of tracer with marked differences in the calculated body pool (10, 11) because most of an intravenous dose ini tially by-passes the liver and therefore exhibits differ ent kinetics than an oral dose. Based on our observa tions, we have modified that model for orally admin istered tracer to eliminate the equilibrium and to allow excretion from both pools (7). Even though our model has not reached the sophistication of some of the work to be discussed later, it is clear that the use of these techniques has had a profound effect on our thinking about vitamin B-6 requirements. Like many other areas of research, modeling efforts often raise more questions than they answer. However, a model can provide a useful working hypothesis for describing a particular system and for designing further studies of the system. The goal of this symposium was to provide enough information and support to encourage greater appli cation of modeling techniques in nutrition research. The first three papers introduce modeling. Michael Green discusses some of the general characteristics of modeling. Jerry Collins discusses some of the com puter software and resource facilities which are avail able, often at little cost. Charles Ramberg reviews the relative merits of various experimental approaches for gathering kinetic data. The final two papers present two specific examples for applying modeling tech niques to nutritional problems. Preston Mercer discuss his saturation kinetics approach to assessing nutrient requirements. Blossom Patterson describes the devel opment of her model of selenium metabolism with emphasis on the modeling process. We hope that this information will encourage wider application of mod eling techniques to nutrition research.
LITERATURE CITED 1. Canolty, N. L. & Cain, T. P., eds. (1985) Proceedings of 1985 Conference on Mathematical Models in Experimental Nutrition. pp. 1-139, University of Georgia, Athens, GA. 2. (1988) Proceedings of 1987 conference on mathematical models in experimental nutrition. Prog. Food Nutr. Sci. 12: 211-338. 3. Proceedings of 1989 conference on mathematical models in ex perimental nutrition: advances in amino acid and carbohydrate metabolism. J. Parenter. Enterai Nutr. (in press). 4. Gold, H. J. (1977) Preface In: Mathematical Modeling of Bio logical Systems-An Introductory Guidebook, pp. v-vii, Wiley, New York, NY. 5. Ramberg, C. F., Krishnamurti, C. R., Peter, D., Wolff, J. E. &. Boston, R. C. (1991) Application of models to determination of nutrient requirements: Experimental techniques employing tracers. J. Nutr. 122(suppl.): 000-000. 6. Coburn, S. P., Mahuren, J. D., Erbelding, W. F., Townsend, D. W., Hachey, D. L. & Klein, P. D. (1984) Measurement of vitamin B-6 kinetics in vivo using chronic administration of labelled pyridoxine. In: Chemical and Biological Aspects of Vi tamin B-6 Catalysis (Evangelopoulos, A. E., ed.) Part A, pp. 4354, Liss, New York, NY.
SYMPOSIUM: APPLICATION OF MODELS 7. Pauly, T., Szadkowska, Z., Coburn, S., Mahuren, D., Schal tenbrand, W., Booth, L., Hachey, D., Ziegler, P., Costili, D., Fink, W., Pearson, D., Townsend, D., Micelli, R. & Guilarte, T. (1991) Kinetics of deuterated vitamin B-6 metabolism in men on a marginal vitamin B-6 intake. FASEB J 5: 1660|abs). 8. Coburn, S. P. (1990) Location and turnover of vitamin B-6 pools and vitamin B-6 requirements of humans. Ann NY Acad Sci. 585: 76-85. 9. Coburn, S. P. (1991) Vitamin B-6. In: Comparative Animal
Downloaded from https://academic.oup.com/jn/article-abstract/122/suppl_3/687/4755311 by Washington University in St. Louis user on 26 March 2018
689
Nutrition of the Vitamins (Beynen, A. C. & West, C. E., eds.), Karger, Basel, Switzerland (in press). 10. Johansson, S., Lindstedt, S., Register, U. & Wadstrom, L. (1966) Studies on the metabolism of labeled pyridoxine in man. Am. J. Clin. Nutr. 18: 185-196. 11. Tillotson, J. A., Sauberlich, H. E., Baker, E. M. & Canham, J. E. (1966) Use of carbon-14 labeled vitamins in human nutrition studies: Pyridoxine. 7th Internat Congr Nutr, vol. 5, pp. 554557, Verlag Friedr. Vieweg & Sohn Gmbh, Braunschweig, Ger many.
