(27) 1 6 & 27 Nture Pulishing Group All rights reserved 37-565/7 $3. www.nture.com/ijo ORIGINAL ARTICLE How dpttions of sustrte utiliztion regulte ody composition KD Hll, HL Bin nd CC Chow Lortory of Biologicl Modeling, Ntionl Institute of Dietes & Digestive & Kidney Diseses, Ntionl Institutes of Helth, Bethesd, MD, USA Ojective: To elucidte the mthemticl reltionship etween longitudinl chnges of ody composition nd the dpttions of sustrte utiliztion required to produce those chnges. Design: We developed simple mthemticl model of mcronutrient lnce. By using n empiricl reltionship descriing len ody mss s function of ft mss, we derived mthemticl expression for how sustrte utiliztion dpts to chnges of diet, energy expenditure nd ody ft such tht energy imlnces produced the required chnges of ody composition. Results: The generl properties of our model implied tht short-term chnges of dietry ft lone hd little impct on either ft or non-ft oxidtion rtes, in greement with indirect clorimetry dt. In contrst, chnges of non-ft intke cused roust dpttions of oth ft nd non-ft oxidtion rtes. Without fitting ny model prmeters, the predicted ody composition chnges nd oxidtion rtes greed with experimentl studies of overfeeding nd underfeeding when the mesured food intke, energy expenditure nd initil ody composition were used s model inputs. Conclusion: This is the first report to define the quntittive connection etween longitudinl chnges of ody composition nd the required reltionship etween sustrte utiliztion, diet, energy expenditure nd ody ft mss. The mthemticl model predictions re in good greement with experimentl dt nd provide the sis for future study of how chnges of sustrte utiliztion impct ody composition regultion. dvnce online puliction, 13 Mrch 27; doi:1.138/sj.ijo.8368 Keywords: ody composition; weight loss; weight gin; mthemticl model; sustrte utiliztion Introduction Wht determines the reltive chnge of ody ft nd len mss during weight loss or weight gin? Answering this question hs importnt implictions for tretment of oesity s the desired gol is to decrese ody ft while preserving len mss. Alterntively, other conditions of ltered ody composition, such s norexi nervos nd cchexi, hve the chllenge of recovering len ody mss without excessive ccumultion of ft. The concept of mcronutrient lnce is now ccepted s the physiologicl sis for determining ody composition chnges. 1 4 However, it remins to e elucidted exctly how longitudinl ody composition chnges re quntittively relted to the properties of mcronutrient lnce. Here, we sked the following question: how must sustrte utiliztion Correspondence: Dr KD Hll, NIDDK/NIH, 12A South drive, Room 47, Bethesd, MD 2892-5621, USA. E-mil: kevinh@niddk.nih.gov Received 14 Octoer 26; revised 31 Jnury 27; ccepted 31 Jnury 27 quntittively dpt to given energy imlnce to produce the longitudinl ody composition chnges proposed y Fores 5? Addressing this question led to simple eqution tht elucidtes how interctions etween diet, energy expenditure nd sustrte utiliztion re quntittively connected to chnges of ody composition. Rther thn develop explicit mthemticl models of food intke nd energy expenditure, our gol ws to define the quntittive interctions etween these vriles, sustrte utiliztion nd the resulting chnges of ody composition. (For more generl model incorporting energy expenditure dynmics we refer the reder to more complex model of mcronutrient metolism y Hll 6 ). Thus, we only considered comprisons to experimentl studies, where energy expenditure nd food intke were mesured nd could e used s model inputs. The model then predicts chnges of ody composition nd sustrte utiliztion. This strtegy llowed for n explicit mthemticl connection to the Fores ody composition dt nd the resulting equtions contined no free prmeters therey voiding ny model fitting procedures. Remrkly, our simple equtions ccurtely predicted the chnges of ody composition nd
2 sustrte utiliztion rtes during oth experimentl underfeeding nd overfeeding when the mesured food intke nd totl energy expenditure were provided s inputs to the model. Methods Theory of sustrte utiliztion nd ody composition Fores found the following cross-sectionl curve of len ody mss (L) versus ft mss (F) nd hypothesized tht longitudinl chnges of ody composition during energy imlnce were descried y movement long the curve: L ¼ 1:4 Log e F þ 14:2 ð1þ with L nd F expressed in kg. 5 The following differentil reltionship ws therey derived for infinitesiml weight chnges: dl df ¼ 1:4 ð2þ F We egn y considering the following mcronutrient lnce equtions: df r F dt ¼ I F f F E ð3þ dl r L dt ¼ I L ð1 f F ÞE ð3þ where E is the totl energy expenditure rte, f F the frction of the energy expenditure rte ccounted for y ft oxidtion, I F the metolizle intke rte of ft, I L the sum of the metolizle intke rtes of protein nd crohydrte, nd r F ¼ 9.4 kcl/g nd r L ¼ 1.8 kcl/g re the energy densities of ody ft nd len mss chnges, respectively. 6 Eq. 3 simply sttes tht the rte of ody ft mss chnge, df/dt, results from differences of ft intke nd oxidtion rtes. This ssumes tht de novo lipogenesis is negligile, which is typiclly true in humns. 7 Eq. 3 is similr eqution for the comintion of crohydrte nd protein lnces nd their impct on the rte of len ody mss chnge, dl/dt. Fortuntely, comining crohydrte nd protein in this wy does not introduce serious errors ecuse oth of these mcronutrients hve similr energy densities. 8 nd re ssocited with similr mounts of wter. 9 To connect the simplified mcronutrient lnce equtions to Fores s theory, we divided Eq. 3 y 3 nd used Eq. 2 to derive the following expression for the ft oxidtion rte: FtOx f F E ¼ ðc=fþi F I L þ E ð4þ 1 þ C=F where C ¼ 1.4 r L /r F. Eq. 4 predicts how ft oxidtion rtes dpt to chnges of ft intke, non-ft intke, energy expenditure nd ody ft mss. These dpttions form the physiologicl sis of Fores s hypothesis for longitudinl ody composition regultion. To demonstrte the generl properties of Eqs. 3 nd 4, we considered n individul with n initil ody weight of 65 kg with 31% ody ft. The seline intke rtes of dietry ft nd non-ft were 9 nd 17 kcl/dy, respectively, nd the energy expenditure of 26 kcl/dy ws held constnt. These intke rtes were chosen so tht the seline ody ft nd len mss were constnt. To compre the model directly with experimentl overfeeding nd underfeeding studies, we ltered the initil ody composition to mtch the verge physicl chrcteristics of the study sujects nd used experimentl studies, where oth the dietry intke rtes s well s the totl energy expenditure were mesured so tht we could directly specify the time courses of I F, I L nd E nd predict the resulting chnges of ody composition s well s ft nd non-ft oxidtion rtes. Results Eqution (4) hs severl importnt physiologicl implictions. The first results from the fct tht C/F is typiclly smll. Therefore, ft oxidtion does not chnge significntly for short-term chnges of ft intke reltive to the sme increment of non-ft intke. This is shown in Figure 1 nd where we plotted the short-term chnge of ft nd non-ft oxidtion rtes s dietry ft nd non-ft were vried. Figure 1 shows tht when non-ft intke ws fixed t its lnced vlue of 17 kcl/dy, wide vritions of ft intke hd little impct on the sustrte utiliztion rtes nd therey resulted in sustntil ft imlnces. In contrst, Figure 1 shows tht ltertions of non-ft intke profoundly impcted sustrte utiliztion rtes when ft intke ws fixed t its lnced vlue. Agin, this resulted in energy imlnces primrily ccounted for y chnges of ody ft. Another importnt consequence of Eq. 4 results from the fct tht C/F chnges very little for modest weight chnges unless the ody ft is very low. This implies tht the ft oxidtion rte is only wekly influenced y ody ft chnges for modest weight chnges in norml or overweight sujects. Rther, the diet nd energy expenditure ply dominnt role in determining sustrte utiliztion rtes in such circumstnces. We pplied Eqs. 3 nd 4 to the overfeeding study of Diz et l., 1 where 1 sujects were overfed y 5% in excess of mintennce requirements for 42 dys. The sujects were young men with n verge ody weight of 73.4 kg nd 21.3% ody ft. The energy content of the diet consisted of 12% protein, 42% ft nd 46% crohydrte. Figure 2 demonstrtes tht the predicted ody weight nd ft mss chnges (lue nd red curves, respectively) closely mtched the dt (closed nd open oxes, respectively). Figure 2 illustrtes the predicted ft nd non-ft oxidtion rtes (solid lue nd red curves, respectively) long with the mesured metolizle dietry intke rtes (dshed curves) nd mesured oxidtion rtes (oxes). Wheres the predicted
Theory of sustrte utiliztion nd ody composition 25 8 3 2 15 1 5 25 2 15 1 5 5 1 15 2 25 Ft Intke (kcl/d) 5 1 15 2 25 Non-Ft Intke (kcl/d) Figure 1 Short-term dpttions of sustrte utiliztion required y Fores s logrithmic ody composition curve. () Chnges of dietry ft ove cuse insignificnt chnges of ft oxidtion (red curve) nd non-ft oxidtion (lue curve) resulting in lrge ft imlnces. () In contrst, chnges of non-ft intke cuse roust dpttions of oth ft nd non-ft oxidtion rtes tht gin result in energy imlnces to e primrily ccounted for y chnges of ody ft. non-ft oxidtion incresed to rech out 95% of the nonft intke, ft oxidtion ws suppressed nd ccounted for only out 5% of the ft intke. These model predictions gree with the experimentl mesurements of ft oxidtion (open oxes) s well s non-ft oxidtion clculted from the difference etween the mesured expenditure nd ft oxidtion rtes (closed oxes). It is importnt to emphsize tht no prmeter fitting ws performed to mke these comprisons. We lso simulted n underfeeding study y Je et l., 11 where three sujects spent 12 continuous dys in metolic chmer to ssess mcronutrient oxidtion rtes The sujects were mle with n verge ody weight of 73.7 kg nd 23% ody ft. The energy content of the diet consisted of 31% protein, 24% ft nd 45% crohydrte. Figure 3 shows tht the simulted chnges of ody weight nd ft Energy Rte (kcl/d) Mss Chnge (kg) 6 4 2 35 3 25 2 15 1 5 1 2 3 4 5 6 Time (weeks) 1 2 3 4 5 6 Time (weeks) Figure 2 Simultion of the overfeeding study y Diz et l. 1 () The predicted chnges of ody weight (lue curve) nd ft mss (red curve) closely mtched the dt (closed nd open oxes, respectively). () The predicted chnges of ft nd non-ft oxidtion (solid red nd lue curves, respectively) mtched the dt (open nd closed oxes, respectively) in response to the incresed rtes of ft nd non-ft intke (dshed red nd lue curves, respectively). mss closely mtched the ody composition dt. Figure 3 shows tht the underfeeding cused incresed ft oxidtion nd suppressed non-ft oxidtion in greement with the dt. However, the dpttions of ft nd non-ft oxidtion oserved y Je et l. occurred more slowly thn the predicted oxidtion rtes, proly reflecting the short-term influence of glycogen reduction, which likely required severl dys to rech stedy stte. As the present model does not directly include glycogen nd its impct on sustrte oxidtion rtes, this effect ws not predicted. Finlly, we simulted study y Rumpler et l. 12 where eight overweight men (verge 96.6 kg nd 28% ody ft) underwent 5% energy restriction on either high-ft (14% protein, 4% ft nd 46% crohydrte) or low-ft diet (14% protein, 2% ft nd 66% crohydrte) for 4 weeks followed y 1 week of the mintennce diet. Figure 4 shows tht the predicted chnges of ody weight (lue curve) nd ody ft mss (red curve) greed with the mesurements for the low ft diet (closed nd open oxes, respectively), nd Figure 4 shows the greement with ody composition dt
4 Energy Rte (kcl/d) Mss Chnge (kg) -1-2 -3 from the high-ft diet. Figure 4c shows tht the predicted ft nd non-ft oxidtion rtes (solid lue nd red curves, respectively) for the low-ft diet closely mtched the experimentl dt (open nd closed oxes, respectively), wheres the model slightly overestimted the ft oxidtion rte nd underestimted the non-ft oxidtion rte during the energy restriction phse of the high-ft diet. Discussion -4 2 4 6 8 1 12 2 16 12 8 4 Theory of sustrte utiliztion nd ody composition 2 4 6 8 1 12 Figure 3 Simultion of the underfeeding study y Je et l. 11 () The predicted ody weight nd ft mss chnges greed with the mesured chnges during 12 dys of continuous indirect clorimetry. () Aprt from the first few dys, the predicted oxidtion rtes mtched the dt. See Figure 2 for description of the symols. For the first time, we hve elucidted the mthemticl connection etween longitudinl chnges of ody composition nd the dpttions of sustrte utiliztion required to produce those chnges. We used Fores s logrithmic reltionship etween len nd ft mss to determine how sustrte utiliztion dpts to chnges of mcronutrient intke, ody ft nd energy expenditure. Without djusting ny model prmeters, the model ccurtely predicted the experimentl mesurements of mcronutrient oxidtion rtes nd ody composition chnges during oth overfeeding 1 nd underfeeding. 11,12 These model predictions were mde y using the mesured food intke, energy expenditure nd initil ody composition s model inputs. We hve not explicitly modeled the dpttions of energy expenditure tht contriute to determining the solute rtes of mcronutrient oxidtion. Hll s more complex model of mcronutrient metolism 6 includes detiled model of whole ody energy expenditure, s well s model of the individul mcronutrient lnces. For the present study we used mesured energy expenditure s model input nd lumped protein nd crohydrte together to minimize the numer of model prmeters. In fct, the model presented here contins no free prmeters ecuse sustrte utiliztion ws constrined y Fores s empiricl ody composition curve. The generl properties of our model imply tht there is hierrchy of sustrte utiliztion, with dietry ft hving little influence on ft nd non-ft oxidtion rtes in comprison with non-ft intke. This result is in generl greement with oservtions using indirect clorimetry showing tht ddition of excess dietry ft hd little impct on mcronutrient oxidtion rtes in comprison with dietry crohydrte or protein. 1,13,14 Glycogen chnges cn impct the mcronutrient oxidtion rtes, ut these effects re limited to only few dys fter which glycogen chieves new equilirium. Therefore, our model responds correctly fter tht time period s illustrted y comprisons with the mcronutrient oxidtion dt in Figures 3 nd 4. Inclusion of glycogen in the present model significntly complictes the mthemticl reltionship to ody composition chnges nd introduces dditionl model prmeters. There is much dete surrounding the weight loss potentil of diets differing in mcronutrient content. 15,16 When our model ws pplied to dt from weight loss study compring the effects of low-ft diet with high-ft diet, 12 the sustrte utiliztion rtes were quite different during weight loss despite the similr cloric contents of the diets. Becuse of the ility to dpt mcronutrient oxidtion to the diet composition, the two diets generted similr degrees of weight loss nd ody ft reduction. Whether this holds for other diets, such s low-crohydrte nd high-protein diets, is presently uncler ecuse relile estimtes of food intke, energy expenditure nd mcronutrient oxidtion hve yet to e mde during weight loss with such diets. Previous investigtors hve recognized the importnce of sustrte utiliztion dpttions s mjor determinnt of ody composition regultion. 1 4 Here, we extended these concepts to relte quntittively the longitudinl ody composition chnges with dpttions of sustrte utiliztion. Although Fores s logrithmic ody composition reltionship ws used for illustrtive purposes in the present study, the sme nlysis could e pplied to ny function relting longitudinl chnges of len mss to ft mss. In prticulr, different individuls or groups my e chrcterized y different ody composition curves. These differences will e reflected y how sustrte utiliztion dpts to dietry chnges s defined y our nlysis. It is intriguing to speculte tht the reverse might lso e true:
Theory of sustrte utiliztion nd ody composition 1 Low-ft diet 29 c 98 High-ft diet 32 5 Body Weight (kg) 98 96 94 27 25 23 Body Ft (kg) Body Weight (kg) 96 94 92 3 28 26 Body Ft (kg) 92 21 7 14 21 28 35 3 2 1 7 14 21 28 35 d 9 24 7 14 21 28 35 3 2 1 7 14 21 28 35 Figure 4 Simultion of the underfeeding study y Rumpler et l. 12 The predicted ody weight nd ft mss chnges greed with the mesured chnges during the low-ft diet () s well s the high-ft diet (). The predicted oxidtion rtes closely mtched the dt during the low-ft diet (c), ut the predicted ft oxidtion rte ws slightly higher thn the dt during the energy restriction phse of the high-ft diet (d). See Figure 2 for description of the symols. tht mesurement of sustrte utiliztion differences my predict differences in longitudinl ody composition chnges. In prticulr, if we ssume tht the generl form of Fores s curve is correct, ut tht different groups or individuls my e chrcterized y different vlues of the constnt C, then Eq. 4 cn e solved for the vlue of this constnt: C ¼ F½ð1 f FÞE I L Š ð6þ f F E I F Interestingly, the stte of mcronutrient lnce results in n undetermined vlue for C ecuse oth the numertor nd denomintor of Eq. 6 re zero. However, suitle short-term dietry perturtions long with mesurements of the resulting mcronutrient oxidtion rtes could result in n experimentl determintion of C nd therey predict n individul s longitudinl ody composition reltionship efore significnt chnges of ody composition hve occurred. Future work will ddress this possiility. Severl investigtors hve proposed mthemticl expressions tht descrie the interreltionships etween ody ft nd len mss. For exmple, Pyne nd Dugdle, 17 Christinsen nd Gry, 18 nd Krietzmn 19 proposed tht the composition of weight chnge is constnt for given individul. Dulloo nd Jcquet 2 suggested tht the composition of ody weight chnge depends on the initil ft mss, in greement with the oservtions of Fores. 5 Recently, Hll 21 showed tht Fores s theory of ody composition further implies tht the reltive chnge of ody ft nd len mss lso depends on the mgnitude nd direction of the weight chnge. Others hve proposed complex clcultions involving the degree of energy imlnce nd percent ody ft. 22 These theoreticl descriptions of the fctors impcting ft nd len mss interreltionships do not ddress the underlying mechnism of mcronutrient lnce. Our model hs tken step eyond previous descriptions of ody ft nd len mss interreltionships y connecting the ody composition chnges with dpttions of sustrte utiliztion. Although our model shows tht diet plys dominnt role in determining sustrte utiliztion rtes, we hve not modeled food intke regultion s there re insufficient dt in humns to construct ccurtely such model. Rther, we compred the model predictions with experimentl dt where the food intke ws controlled nd used s model input. Finlly, lthough our model predicts how sustrte utiliztion dpts to chnges of diet, energy expenditure nd ody ft, we hve not specified the physiologicl mechnisms for these dpttions. Clerly, diet nd ody ft impct mny metolic processes including, whole ody lipolysis, glucose disposl, de novo lipogenesis nd nitrogen lnce. 3,4,23 Future work will investigte more complex models of mcronutrient metolism 6 to etter understnd the physiologicl control of
6 sustrte utiliztion in the context of ody composition regultion. Acknowledgements This work ws supported y the Intrmurl Reserch Progrm of the NIH, NIDDK. References Theory of sustrte utiliztion nd ody composition 1 Fltt JP. Importnce of nutrient lnce in ody weight regultion. Dietes Met Rev 1988; 4: 571 581. 2 Schutz Y. The djustment of energy expenditure nd oxidtion to energy intke: the role of crohydrte nd ft lnce. Int J Oes Relt Met Disord 1993; 17 (Suppl 3): S23 S27 discussion S41 S42. 3 Schutz Y. Concept of ft lnce in humn oesity revisited with prticulr reference to de novo lipogenesis. Int J Oes Relt Met Disord 24; 28 (Suppl 4): S3 S11. 4 Schutz Y. Dietry ft, lipogenesis nd energy lnce. Physiol Behv 24; 83: 557 564. 5 Fores GB. Len ody mss-ody ft interreltionships in humns. Nutr Rev 1987; 45: 225 231. 6 Hll KD. Computtionl model of in vivo humn energy metolism during semistrvtion nd refeeding. Am J Physiol Endocrinol Met 26; 291: E23 E37. 7 Hellerstein M. No common energy currency: de novo lipogenesis s the rod less trveled. Am J Clin Nutr 21; 74: 77 78. 8 Livesey G, Eli M. Estimtion of energy expenditure, net crohydrte utiliztion, nd net ft oxidtion nd synthesis y indirect clorimetry: evlution of errors with specil reference to the detiled composition of fuels. Am J Clin Nutr 1988; 47: 68 628. 9 McBride J, Guest M, Scott E. The storge of the mjor liver components; emphsizing the reltionship of glycogen to wter in the liver nd the hydrtion of glycogen. J Biol Chem 1941; 139: 943 952. 1 Diz EO, Prentice AM, Golderg GR, Murgtroyd PR, Cowrd WA. Metolic response to experimentl overfeeding in len nd overweight helthy volunteers. Am J Clin Nutr 1992; 56: 641 655. 11 Je SA, Prentice AM, Golderg GR, Murgtroyd PR, Blck AE, Cowrd WA. Chnges in mcronutrient lnce during over- nd underfeeding ssessed y 12-d continuous whole-ody clorimetry. Am J Clin Nutr 1996; 64: 259 266. 12 Rumpler WV, Sele JL, Miles CW, Bodwell CE. Energy-intke restriction nd diet-composition effects on energy expenditure in men. Am J Clin Nutr 1991; 53: 43 436. 13 Horton TJ, Drougs H, Brchey A, Reed GW, Peters JC, Hill JO. Ft nd crohydrte overfeeding in humns: different effects on energy storge. Am J Clin Nutr 1995; 62: 19 29. 14 Schutz Y, Fltt JP, Jequier E. Filure of dietry ft intke to promote ft oxidtion: fctor fvoring the development of oesity. Am J Clin Nutr 1989; 5: 37 314. 15 Buchholz AC, Schoeller DA. Is clorie clorie? Am J Clin Nutr 24; 79: 899S 96S. 16 Feinmn RD, Fine EJ. Whtever hppened to the second lw of thermodynmics? Am J Clin Nutr 24; 8: 1445 1446 uthor reply 1446. 17 Pyne PR, Dugdle AE. A model for the prediction of energy lnce nd ody weight. Ann Hum Biol 1977; 4: 525 535. 18 Christinsen E, Gry L. Prediction of ody weight chnges cused y chnges in energy lnce. Eur J Clin Invest 22; 32: 826 83. 19 Kreitzmn SN. Fctors influencing ody composition during very-low-clorie diets. Am J Clin Nutr 1992; 56 (1 Suppl): 217S 223S. 2 Dulloo AG, Jcquet J. The control of prtitioning etween protein nd ft during humn strvtion: its internl determinnts nd iologicl significnce. Br J Nutr 1999; 82: 339 356. 21 Hll KD. Body ft nd ft-free mss interreltionships: Fores s theory revisited. Br J Nutr 27. In press. 22 Westerterp KR, Donkers JH, Fredrix EW, Boekhoudt P. Energy intke, physicl ctivity nd ody weight: simultion model. Br J Nutr 1995; 73: 337 347. 23 Fryn KN. Physiologicl regultion of mcronutrient lnce. Int J Oes Relt Met Disord 1995; 19 (Suppl 5): S4 1.