- Email: [email protected]
Kinetic analysis using specific radioactivity data
384
METABOLISM OF PLASMA LIPOPROTEINS
[23]
It probably appears to the casual observer that techniques exist for the continued expansion of the analysis through the use of compartmental models. However, this is not the case or was it ever the case over the past quarter decade as a theory developed for lipoprotein metabolism. The tools and techniques for the realization, identification, and analysis of a large system (such as the system of lipid and lipoprotein metabolism) are developed as the need presents itself. Even though some techniques can be borrowed from other disciplines they usually need to be modified according to the requirements of the specific topic under investigation. Furthermore, in the process of following the historical progression of the development of the theory of lipoprotein metabolism as represented by mathematical models, it becomes clear that the power of the methodology is derived from its ability to integrate many facts into a general theory. This provides a common framework for the development of a classification of lipoproteins based on the kinetics, and in the future, the dynamics of the interactions of these lipoproteins with the physiologic system under study. While the mathematical details have not been considered in the above discussion, they are important. These details are not as important to the building of models of large integrated systems such as the lipoprotein metabolic system, however, as the powerful technique of using the compartmental model as the test bed for diverse experimental outcomes. When used in this capacity the model allows the separation of these outcomes into a set which are alike and represent the physiologic system and a set which differ and represent the biophysical and mathematical methodology.
[23] Kinetic Analysis U s i n g S p e c i f i c R a d i o a c t i v i t y Data By
NGOC-ANH
LE, RAJASEKHAR RAMAKRISHNAN, RALPH
B.
DELL,
HENRY N. GINSSERG,and W. VmGIL BROWN Introduction In kinetic turnover studies a tracer amount of radiolabeled material is injected intravenously as a bolus. The biologic half-life and/or the in vivo metabolic fate of the material of interest can then be determined by analyzing the decay curve which describes the disappearance of the injected METHODS IN ENZYMOLOGY,VOL. 129
Copyright © 1986by Academic Press, Inc. All rights of reproduction in any form reserved.
[23]
ANALYSIS USING SPECIFIC RADIOACTIVITY
385
radioactivity. A general discussion of the use of compartmental analysis to derive metabolic parameters from the decay curves is presented in Chapter [22], this volume.l The data available for analysis may be in the form of either total radioactivity (TR) or specific radioactivity (specific activity, SA). An advantage of study protocols which permit the direct determination of SA data is that quantitative recovery of the material is not required. In other words, the SA will theoretically be the same whether 5 or 95% of the starting material is recovered following the procedure. Furthermore, while TR reflects only the fate of the injected tracer, SA data reflect the simultaneous fate of both the injected tracer and the unlabeled tracee. Available programs for compartmental analysis, however, are primarily designed for the analysis of TR data. Thus even if SA data are available experimentally a common practice has been to multiply these SA data by an estimate of the appropriate pool size to obtain the TR data used in the analysis. In this chapter we will define a number of relationships characteristic only of SA data which can be used to derive information regarding the tracee. The application of these relationships in the elucidation of pathways for the metabolism of apolipoproteins will be illustrated for two systems: (1) the precursor-product relationship between VLDL and IDL apoB, and (2) the instantaneous equilibration of apoC-III in plasma. Relationship in Precursor-Product Systems Kinetic Equations
Let us assume that a dose of radioactivity D1 is injected into pool 1 of the two-pool system shown in Fig. 1. In the present example, pool 1 would represent V L D L apoB, which is converted to IDL apoB represented by pool 2. We will now proceed to relate the parameters of the SA decay curves directly to the conversion process from pool 1 to pool 2. If we denote by y l ( t ) the amount of apoB radioactivity present in VLDL (pool 1) and y2(t) the apoB radioactivity in IDL (pool 2) at various time t, the kinetic equations for the transfer of radioactivity in this system can be written as: d dt yl = -(k01 + k21)Yl
yl(0) = D1
d d t Y2 = k21yl -- ko2Y2
(1) y2(0) = 0
i L. A. Zech, R. C. Boston, and D. M. Foster, this volume, [22].
386
[23]
METABOLISM OF PLASMA LIPOPROTEINS
>t-.I.0 ,< 0 (:3 <
D i ,~.,,.,._~
Ul = Rzf+R01=Rll
U~1 R ~ 2 1 Rm
rr
(.~
=0 ~ '
LL
Dz
(,S, ILl (3O3
UZ = 0 ~)--,~
R22=R21+U2 I
l I I HOURS
I
FIG. 1. A simple precursor-product relationship. (a) The precursor pool, pool 1, displays a simple monoexponential decay following the bolus injection of a dose of radioactivity, Dj. (b) Of the total flux Ut through pool 1, an amount R0~ is directly removed from the system and a flux R2~ is converted to the product pool, pool 2. Assuming that there is no initial injection of radioactivity directly into pool 2 and that all of the flux in pool 2 is derived from pool 1, then the specific activity in pool 2 will reach a maximum value exactly as it crosses the specific activity curve corresponding to the precursor pool, pool 1. Furthermore, the areas under the specific activity curves for pools 1 and 2 will be exactly equal to one another.
In other words, the rate of change of radioactivity in pool 1 is proportional to the amount of radioactivity yl. The fractional rate constant represents the combined effect of two metabolic processes : (1) k01 for direct irreversible removal from pool I and (2) k2~ for conversion to the product pool, pool 2. The rate of change of radioactivity in pool 2 is the net result of the input from pool 1, k21Yl, and the irreversible loss from pool 2, k02Y2. At the beginning of the turnover study, the injected dose DI is entirely in pool 1 and there is no radioactivity present in pool 2. If M1 and 3/2 represent the mass of apoB in VLDL and IDL, pool 1 and 2, respectively, we can represent the total radioactivity in Eq. (1) as the product of the mass by the corresponding specific radioactivity, i.e., d
d t MIS1 = -(kol + k2OMiSl
d M2S2 = k21M]S1 - kozMzS2 dt
S O = yl(O) M1
i
D1 Ml
So = 0
where $1 and Sz are the apoB SA in VLDL and IDL, respectively.
(2)
[23]
ANALYSIS USING SPECIFIC RADIOACTIVITY
387
In terms of the flux of apoB (mass per unit time) transferred between pools we have the following equations: d dt M I S I = - R I I S I
(3) d
dt MzS2 = R2ISI - R2zS2
where R u = (ko~ + kzOM~ is the total flux of apoB through VLDL, pool 1 R2j = k21Mj is the flux of apoB transferred from VLDL to IDL R22 = ko2M2 is the total flux of apoB through IDL, pool 2 Since the system is assumed to be in steady state, there should be no net change in the apoB mass within each pool, we can divide the rate equations through by the respective mass to obtain: d
Rll
d t $1 -
Ml
$1 = - L l l S l
(4)
d R21 Rzz d-~ Sz = ~ Sl - -~z Sz = LziS1 - L22S2
the rate constants Lij will be referred to as fractional flux rate constants to differentiate them from the fractional rate constants kij commonly used in rate equations relating total radioactivity data. The experimental SA decay curves can then be described by sums of exponentials: S l ( t ) = S ° e Lilt L2~ $2(/) -- Lzz - Ltl ( e - L i l t -- e-L22t)
(5)
Thus, using a sum of exponential terms to approximate the experimental SA data corresponding to pools 1 and 2, we can obtain estimates for the fractional flux rate constants L I~, L21, and L22. Furthermore, by examining the values estimated for L2~ and L22, certain conclusions regarding the source of flux in the product pool, pool 2, can be made without a priori knowledge of the pool sizes in either compartment. If L23 < L22, this would indicate that there is direct input of material into pool 2 from a source other than pool I. If L21 = L2z, this would indicate that all of the flux through pool 2 is derived entirely from pool 1. It should be pointed out that if TR data, defined as the product of the SA data by the appropriate pool size, were analyzed only estimates of the
388
METABOLISM OF PLASMA LIPOPROTEINS
[23]
fraction of the radioactivity initially in pool 1 which is converted to pool 2 could be obtained. Information regarding direct input into the product pool would be obtained only if the analysis indicated that the flux through pool 2 is greater than that through pool 1. These flux estimates, however, will be dependent on the accuracy of the determinations of the pool sizes.
Areas Under the Specific Activity Curves Another relationship of the fluxes which is unique to SA data can also be derived from the areas under the SA decay curves. If we denote by A~ the area under the SA curve for VLDL apoB (pool 1, in this example) and A2 the area under the IDL apoB SA curve as described in Eq. (5), then, s o
(6) L21 sO = L21 A2 = LIIL2-----~ "7-- Al LZ2
Thus for the simple precursor-product system depicted in Fig. 1, a number of relationships must be satisfied by the areas under the experimental SA curves and the steady-state fluxes, including the following: If pool 1 receives a dose D1 of radioactivity and has a total flux Rj~ of material then the area under the SA curve corresponding to pool 1 will be DI AI = RI---~ With respect to pool 2, if a flux R2~ of material from pool 1 is converted to pool 2 which receives a total flux R22 through it, then the area under the SA curve corresponding to pool 2 will be A2 =
(R21/R22)A1
or
A2/A1 = R21/R22
In other words, area under the product SA curve area under the precursor SA curve flux from the precursor to the product total flux through the product If all of the flux through the product is derived from the precursor, i.e., there is no direct input of material into pool 2 from sources other than pool 1 (R21 = R22), the ratio will be exactly equal to 1. If there is contribution into pool 2 from sources other than pool 1 (R22 > Rzl), the ratio will be less than 1. Two important concepts relating to the ratio of the areas
[23]
ANALYSIS USING SPECIFIC RADIOACTIVITY
389
under the SA curves must be emphasized: (1) this ratio of the areas does not depend on the fraction of the flux through pool 1 which is actually converted to pool 2. Thus the same ratio of the areas could be associated with a system in which there was conversion of 90% of the flux in pool I to pool 2 as well as with a system in which only 10% of the flux was converted; (2) this ratio of the areas can never exceed 1. Conversion o f A p o B f r o m V L D L to I D L
Following the bolus injection of radioiodinated VLDL, the apoB SA curve displays a typical initial flattening period followed by a biexponential decay. It is generally accepted that the slower terminal component of the VLDL apoB SA curve represents the direct catabolism of a subpopulation of VLDL particles without conversion to IDL and LDL. 2-5 The simplest approach to characterize the conversion of apoB from VLDL to IDL can be outlined as follows: 1. Approximate the VLDL apoB SA curve by a sum of two exponential terms either by using a nonlinear regression program or by graphical method using Matthews' curve-peeling procedure. 6 B j e -~l' + B z e -~2t
(ill > f12)
2. Estimate the area under the fast component of the VLDL apoB decay curve. This will correspond to the fraction of the VLDL apoB flux which serves as precursor for IDL apoB. Let this area be denoted as Av =
Bl/fll. 3. Approximate the IDL apoB SA curve to a sum of exponential terms. In general, at least three exponential terms will be required to describe the decay curve during the first 48 hr. Cle-~'lt + C2e-r2t - C3e-r3t
4. Estimate the a r e a AI under the IDL apoB SA curve, AI = C1/yl + C2/y2 - C3/y3 2 M, Berman, M. Hall, 111, R. 1. Levy, S. Eisenberg, D. W. Bilheimer, R. D. Phair, and R. H. Goebel, J. Lipid Res. 19, 38 (1978). s M. Berman, Prog, Biomed. Pharmacol. 15, 67 (1979). 4 N.-A. Le, H. N. Ginsberg, and W. V. Brown, in "Lipoprotein Kinetics and Modeling" (M. Berman, S. M. Grundy, and B. Howard, eds.), p. 121. Academic Press, New York, 1982. N.-A. Le, H. N. Ginsberg, R. Ramakrishnan, R. B. Dell, and W. V. Brown, Submitted (1985). 6 C. M. E. Matthews, Phys. Med. Biol. 2, 36 (1957).
390
METABOLISM OF PLASMA LIPOPROTEINS
[23]
Depending on the relationship between the two areas estimated from the precursor and product SA curves, three cases could be considered: C a s e I. If Av > AI, there is direct input or unlabeled apoB into IDL independent of plasma VLDL. This extent of independent apoB influx may be estimated from the ratio under the apoB SA curves: U2/R22 = 1 -
(At/Av)
where/-/2 is the direct influx and R22 is the total apoB flux through IDL. C a s e II. If Av = AI, there is a simple precursor-product between VLDL and IDL apoB and all of the flux in IDL is derived from VLDL. Note again that this does not necessarily imply that all of the VLDL apoB flux is converted to IDL. C a s e I l L If Av < AI, there is a theoretical contradiction in the analysis. Under the present assumption of simple precursor-product between VLDL and IDL apoB, it is impossible for the IDL fraction to have an area under the SA curve which is greater than the area under the VLDL apoB SA curve. In most apoB turnover studies completed by our group to date, however, it appears that the a r e a AI is significantly greater than the area Av with a ratio of the areas ranging from 1 to 4.5. 5,7 Even greater ratios of the areas have been reported by Reardon et al.,7 who used both exponential components of the VLDL apoB decay curve in the computation of the area of the precursor. Two possible explanations may be proposed: 1. The larger area under the IDL apoB SA curve is due to contamination of the injected radiolabeled VLDL preparation, which results in a portion of the injected dose appearing instantaneously in the IDL density range. In this situation we would expect the difference in the areas be proportional to the dose injected as IDL, i.e., to the initial apoB SA observed in IDL. Available data would suggest that at most, only 5-10% of the injected radioactivity is recovered in the IDL density fraction 5 min after the bolus injection. Most of this radioactivity, however, is associated with apolipoproteins other than apoB. Thus the measured apoB SA in IDL at 5 rain is usually low and not sufficient to account for the large difference in the areas observed. 2. The larger area under the IDL apoB SA curve may be indicative of kinetic heterogeneity of apoB within the VLDL density range. The simplest type of heterogeneity would be the situation in which plasma VLDL exist as distinct subpopulations of particles. These subpopulations are metabolically distinct in that one subpopulation can be converted to IDL in a single step while another subpopulation must undergo several transformations within the VLDL density range before becoming IDL. Since 7 M. Reardon, N. H. Fidge, and P. J. Nestel, J. Clin. Invest. 61, 850 (1978).
[231
ANALYSIS USING SPECIFIC RADIOACTIVITY
391
all of the subpopulations in the density less than 1.006 g/ml would be initially isolated and radiolabeled, there will be direct injection of radiolabeled V L D L apoB into each of the subpopulations. In such a system, the radioactivity in the IDL density fraction will represent the cumulative contribution of apoB radioactivity injected into each and every VLDL subpopulation. The SA for apoB in each VLDL subpopulation, on the other hand, will reflect only the radioactivity directly injected into it and that derived from the preceding subpopulations. Thus it can be shown that when VLDL is characterized by a series of pools connected in a cascade process, 2,3 The IDL apoB SA curve will have an area which is greater than that for the entire VLDL apoB cascade process. 5 The theoretical basis of the larger area for the IDL apoB SA curve when the VLDL apoB is represented by a cascade process is discussed in detail elsewhere .5 Stepwise Conversion o f ApoB from VLDL to IDL The conversion of apoB from VLDL to IDL has been analyzed using any of a number of approaches, including (1) deconvolution method using total apoB radioactivity data, 8 (2) difference method using a portion of the VLDL and IDL apoB SA curves, 7 (3) a simple two-pool model for VLDL with an extravascular delay pool between VLDL and IDL, 4 and (4) a fourpool cascade model for VLDL apoB.2.3 Except for the method by difference which does not actually fit the experimental curves, the other three approaches can produce theoretical curves which closely approximate the VLDL and IDL apoB TR decay curves. With respect to the areas under the apoB SA curves, however, none of these analyses can satisfy the experimental data. From the analysis of SA data, the two-pool model for VLDL apoB 4 would result in equality of the areas under the apoB SA curves for V L D L and IDL. The 4-pool cascade model, z,3 on the other hand, would predict an area for IDL apoB SA which will be exactly 1.6 times the area of the apoB SA curve corresponding to the VLDL cascade process. The simplest modification of the four-pool VLDL cascade process which can account for a wide range of ratios between the areas for VLDL and IDL apoB SA curves is to allow for a variable distribution of the total VLDL apoB mass among the four VLDL subpopulations. The basic assumption of this system is that newly secreted VLDL particles are associated with subpopulation 1 which will require, on the average, four metabolic steps to be converted to an IDL particle. The percentage of the total VLDL apoB mass which is associated with this subpopulation of newly 8 A. H. Kissebah, S. Alfarsi, P, W. Adams, and V. Wynn,
Diabetologia 12, 501 (1976).
392
METABOLISM OF PLASMA LIPOPROTEINS
[23]
secreted VLDL will depend directly on the relationship between the areas under the SA curves obtained experimentally for VLDL and IDL. Based on our own experimental SA data in normolipidemic and hypertriglyceridemic subjects, from 5 to as much as 45% of the VLDL apoB mass may be associated with the subpopulation of newly secreted VLDL particles. This distribution scheme for the VLDL apoB mass is a theoretical concept and further investigation would be needed to determine the physicochemical characteristics of these VLDL subpopulations. Although experimental data at this time is not available to further define the subpopulations proposed in our model for the conversion of VLDL apoB to IDL, several statements concerning the apoB flux from VLDL to IDL can be made, including the following: Direct Loss from Each Subpopulation. With influx of newly secreted VLDL only into the first subpopulation, direct loss of apoB flux from each subpopulation within the VLDL cascade will increase the ratio of the areas, i.e., the area under the IDL apoB SA curve will be greater. Direct Secretion into Each Subpopulation. With efflux of VLDL apoB only out of the last subpopulation, any direct input of newly synthesized apoB into the various subpopulations within the cascade will decrease the ratio of the areas. In some situations, the area under the IDL apoB SA curve could be less than that for the VLDL apoB cascade. Direct Conversion of Each VLDL Subpopulation to IDL. Direct conversion of apoB from any of the VLDL subpopulations to IDL will not affect the area under the IDL apoB SA curve to any significant degree. This is an important concept which illustrates the difference between the traditional analysis based on total radioactivity data and analysis using SA data. The area under the SA curve for a product is a weighted average of the areas of all contributing precursors. In this cascade process, since the last subpopulation reflects the apoB radioactivities injected into all of the subpopulations, it will have the largest area. Thus, while direct conversion of VLDL apoB from the first subpopulation to IDL is expected to increase the apoB radioactivity in IDL during the early time points, the larger area under the IDL apoB SA curve must still be explained by the large area generated in the last subpopulation by the cascades process. In fact, it can be shown that, if all of the subpopulations within the VLDL cascade can be directly converted to IDL, the ratio of the areas under the SA curves will be exactly 1. Relationship in Equilibrating Systems: Metabolism of ApoC-III Another class of metabolic systems in which specific radioactivity data can provide additional insight into the underlying kinetics is systems
[23]
ANALYSIS USING SPECIFIC RADIOACTIVITY
393
in which there is rapid equilibration among metabolically distinct pools. An example of such exchange systems is the dynamic equilibration of apoC among different VLDL particles as well as with lipoprotein particles of other density classes. This exchange of apoC radioactivity was first described by Bilheimer and co-workers. 9,1° Combining in vitro observations with in oivo data in animals, these investigators concluded that the equilibration of the C-apolipoproteins was instantaneous. They had no data, however, to demonstrate that this equilibration was complete. If the equilibration of apoC is supposed to be complete, the bolus injection of a dose D as apoC radioactivity should result in a uniform SA for plasma apoC, which depend only on the dose injected and the apoC pool size in plasma. In other words, the same initial SA will be obtained for apoC in VLDL, IDL, LDL, and HDL. Divergence in the SA curves after the initial time would reflect differences in the metabolism of apoC associated with the various lipoprotein classes. We recently described an immunoaffinity method for the direct determination of the SA of apoC-III in radiolabeled lipoproteins.l~,12 Following the injection of radiolabeled VLDL in a group of subjects we have noted the significant difference in the apoC-III SA in VLDL and HDL. Over a 75-hr period the two SA curves for VLDL and HDL apoC-III were parallel, as demonstrated elsewhere in this volume. ~2Thus, if the experimental SA data for the two curves were multiplied by the appropriate apoC-III pool sizes and expressed as a percentage of the injected dose, then the decay curves for VLDL and HDL apo C-Ill would be indistinguishable. However, by considering the specific activity data it must be concluded that the variability in the SA between VLDL and HDL apoC-III among subjects is indicative of the lack of complete equilibration of apoC-III in plasma. Experimental protocols can then be designed to specifically characterize the nature of this equilibration processes) 2'j3 These studies have demonstrated that portions of the apoC-III pools in both VLDL and HDL did not participate in the equilibration process in vitro. The lack of complete equilibration of apoC-III between VLDL and HDL can also be used to define a relationship between the exchangeable pools of apoC-III in VLDL and HDL. In particular, from the injection of 9 D. W. Bilheimer, S. Eisenberg, and R. 1. Levy, Biochim. Biophys. Acta 260, 361 (1972). l0 S. Eisenberg, D. W. Bilheimer, and R. I. Levy, Biochim. Biophys. Acta 326, 361 (1973). 11 p. R. Bukberg, N.-A. Le, J. C. Gibson, L. Goldman, H. N. Ginsberg, and W. V. Brown, J. Lipid Res. 24, 1251 (1983). 12 N.-A. Le, P. R. Bukberg, H. N. Ginsberg, J. C. Gibson, and W. V. Brown, This volume [27]. 13 p. R. Bukberg, N.-A. Le, H. N. Ginsberg, J. C. Gibson, and W. V. Brown, J. Lipid Res. 26, 1047 (1985).
394
METABOLISM OF PLASMALIPOPROTEINS
[23]
radiolabeled VLDL, it is expected that the SA of apoC-III in the whole VLDL fraction will be the same as the SA in the equilibrating and nonequilibrating components of VLDL apoC-III prior to equilibration, that is, Sv= Sve=Svn where Sv, Sw, and Sv. correspond to the apoC-III SA in whole, equilibrating, and nonequilibrating pools of VLDL apoC-III, respectively. Prior to equilibration, no apoC-III radioactivity is expected in HDL, or, S H = SHe = SHn ~--- 0
with SH, SHe, and SHn denoting the apoC-III SA in whole HDL, the equilibrating, and nonequilibrating pools in HDL, respectively. After the instantaneous equilibration, the SA in the nonequilibrating pools of VLDL and HDL should not be affected by the in vitro incubation. The SA for apoC-III in the exchangeable pools of VLDL and HDL will reach a new equilibrium value which reflects fPv, the fraction of the exchangeable mass of apoC-III which is associated with VLDL, i.e., SHe = Sve = fpvSve
The overall apoC-III SA in each lipoprotein class is a weighted average of the SA in the equilibrating and nonequilibrating pool. Sv = Svefv + SVn(1 - - f v )
SH = Saefn
where fv =
mass of equilibrating VLDL apoC-III total mass of apoC-III in VLDL
wherefH =
mass of equilibrating HDL apoC-III total mass of apoC-III in HDL
The ratio R of the apoC-III SA between VLDL and HDL as obtained from the decay curves is defined as R = Sv/S H
which is the ratio of the SA of VLDL apoC-III to that of HDL apoC-III observed in vivo following the tracer injection of radioiodinated VLDL. R = (Svefv + Svn(l - f v ) )
7,,v-- Ve or, (1 - fpv~
1
f n = - \ Rfpv / f v + R]pv
[24]
METABOLISM OF A p o B - C O N T A I N I N G LIPOPROTEINS
395
In other words, for a given ratio of the apoC-III specific activity between VLDL and HDL observed in vivo following the injection of radioiodinated VLDL, the fraction of apoC-III in VLDL which can participate in the equilibration process is negatively correlated to the fraction of equilibrating apoC-III in HDL. Any kinetic system proposed to explain the metabolism of apoC-III in man must address this relationship. Acknowledgments This w o r k w a s initiated u n d e r a postdoctoral training program from N H L B I (HL-07343). Dr. Le is currently s u p p o r t e d by a N e w Investigator A w a r d from N H L B I (HL-27170).
[24] M e t a b o l i s m o f t h e A p o l i p o p r o t e i n B - C o n t a i n i n g Lipoproteins By GEORGE STEINER, MARY E. POAPST, STEVEN L. DAVID M. F O S T E R
SHUMAK,
and
Introduction This chapter will describe, in general terms, the approaches that can be taken to study the kinetics of apoB-containing lipoproteins in vivo. These lipoproteins fall into the classes generally called chylomicrons, VLDL, IDL, and LDL. Unlike glucose, a lipoprotein is not a single molecule in solution in the plasma. Therefore, when describing its metabolism one must consider its various components. One focus here will be on apoB itself, as this is the key apolipoprotein in this family of lipoproteins, and as it appears to stay constant in amount with the particle during its lifetime in the circulation. The other focus will be on the triglyceride of these iipoproteins. This will be of particular importance because it is now recognized that, although the metabolism of the lipoprotein's protein and lipid moieties are related, they may still be independent of each other, t-3 For example, triglyceride in the VLDL particle is hydrolyzed by the repetitive interactions with lipoprotein lipase (LPL). The result is a succession of VLDL particles of increasing density. Furthermore, triglyci j. Melish, N. A. Le, H. Ginsberg, D. Steinberg, and W. V. Brown, Am. J. Physiol. 239, E354 (1980). -' G. Steiner and M. F. Reardon, in " L i p o p r o t e i n Kinetics and Modeling" (M. B e r m a n , S. M. G r u n d y and B. V. H o w a r d , eds.), p. 237. Academic Press, N e w York, 1982. 3 G. Steiner and M. F. Reardon, Metabolism 32, 342 (1983).
METHODS IN ENZYMOLOGY, VOL. 129
Copyright © 1986by AcademicPress, lnc. All rights of reproduction in any form reserved.
METABOLISM OF PLASMA LIPOPROTEINS
[23]
It probably appears to the casual observer that techniques exist for the continued expansion of the analysis through the use of compartmental models. However, this is not the case or was it ever the case over the past quarter decade as a theory developed for lipoprotein metabolism. The tools and techniques for the realization, identification, and analysis of a large system (such as the system of lipid and lipoprotein metabolism) are developed as the need presents itself. Even though some techniques can be borrowed from other disciplines they usually need to be modified according to the requirements of the specific topic under investigation. Furthermore, in the process of following the historical progression of the development of the theory of lipoprotein metabolism as represented by mathematical models, it becomes clear that the power of the methodology is derived from its ability to integrate many facts into a general theory. This provides a common framework for the development of a classification of lipoproteins based on the kinetics, and in the future, the dynamics of the interactions of these lipoproteins with the physiologic system under study. While the mathematical details have not been considered in the above discussion, they are important. These details are not as important to the building of models of large integrated systems such as the lipoprotein metabolic system, however, as the powerful technique of using the compartmental model as the test bed for diverse experimental outcomes. When used in this capacity the model allows the separation of these outcomes into a set which are alike and represent the physiologic system and a set which differ and represent the biophysical and mathematical methodology.
[23] Kinetic Analysis U s i n g S p e c i f i c R a d i o a c t i v i t y Data By
NGOC-ANH
LE, RAJASEKHAR RAMAKRISHNAN, RALPH
B.
DELL,
HENRY N. GINSSERG,and W. VmGIL BROWN Introduction In kinetic turnover studies a tracer amount of radiolabeled material is injected intravenously as a bolus. The biologic half-life and/or the in vivo metabolic fate of the material of interest can then be determined by analyzing the decay curve which describes the disappearance of the injected METHODS IN ENZYMOLOGY,VOL. 129
Copyright © 1986by Academic Press, Inc. All rights of reproduction in any form reserved.
[23]
ANALYSIS USING SPECIFIC RADIOACTIVITY
385
radioactivity. A general discussion of the use of compartmental analysis to derive metabolic parameters from the decay curves is presented in Chapter [22], this volume.l The data available for analysis may be in the form of either total radioactivity (TR) or specific radioactivity (specific activity, SA). An advantage of study protocols which permit the direct determination of SA data is that quantitative recovery of the material is not required. In other words, the SA will theoretically be the same whether 5 or 95% of the starting material is recovered following the procedure. Furthermore, while TR reflects only the fate of the injected tracer, SA data reflect the simultaneous fate of both the injected tracer and the unlabeled tracee. Available programs for compartmental analysis, however, are primarily designed for the analysis of TR data. Thus even if SA data are available experimentally a common practice has been to multiply these SA data by an estimate of the appropriate pool size to obtain the TR data used in the analysis. In this chapter we will define a number of relationships characteristic only of SA data which can be used to derive information regarding the tracee. The application of these relationships in the elucidation of pathways for the metabolism of apolipoproteins will be illustrated for two systems: (1) the precursor-product relationship between VLDL and IDL apoB, and (2) the instantaneous equilibration of apoC-III in plasma. Relationship in Precursor-Product Systems Kinetic Equations
Let us assume that a dose of radioactivity D1 is injected into pool 1 of the two-pool system shown in Fig. 1. In the present example, pool 1 would represent V L D L apoB, which is converted to IDL apoB represented by pool 2. We will now proceed to relate the parameters of the SA decay curves directly to the conversion process from pool 1 to pool 2. If we denote by y l ( t ) the amount of apoB radioactivity present in VLDL (pool 1) and y2(t) the apoB radioactivity in IDL (pool 2) at various time t, the kinetic equations for the transfer of radioactivity in this system can be written as: d dt yl = -(k01 + k21)Yl
yl(0) = D1
d d t Y2 = k21yl -- ko2Y2
(1) y2(0) = 0
i L. A. Zech, R. C. Boston, and D. M. Foster, this volume, [22].
386
[23]
METABOLISM OF PLASMA LIPOPROTEINS
>t-.I.0 ,< 0 (:3 <
D i ,~.,,.,._~
Ul = Rzf+R01=Rll
U~1 R ~ 2 1 Rm
rr
(.~
=0 ~ '
LL
Dz
(,S, ILl (3O3
UZ = 0 ~)--,~
R22=R21+U2 I
l I I HOURS
I
FIG. 1. A simple precursor-product relationship. (a) The precursor pool, pool 1, displays a simple monoexponential decay following the bolus injection of a dose of radioactivity, Dj. (b) Of the total flux Ut through pool 1, an amount R0~ is directly removed from the system and a flux R2~ is converted to the product pool, pool 2. Assuming that there is no initial injection of radioactivity directly into pool 2 and that all of the flux in pool 2 is derived from pool 1, then the specific activity in pool 2 will reach a maximum value exactly as it crosses the specific activity curve corresponding to the precursor pool, pool 1. Furthermore, the areas under the specific activity curves for pools 1 and 2 will be exactly equal to one another.
In other words, the rate of change of radioactivity in pool 1 is proportional to the amount of radioactivity yl. The fractional rate constant represents the combined effect of two metabolic processes : (1) k01 for direct irreversible removal from pool I and (2) k2~ for conversion to the product pool, pool 2. The rate of change of radioactivity in pool 2 is the net result of the input from pool 1, k21Yl, and the irreversible loss from pool 2, k02Y2. At the beginning of the turnover study, the injected dose DI is entirely in pool 1 and there is no radioactivity present in pool 2. If M1 and 3/2 represent the mass of apoB in VLDL and IDL, pool 1 and 2, respectively, we can represent the total radioactivity in Eq. (1) as the product of the mass by the corresponding specific radioactivity, i.e., d
d t MIS1 = -(kol + k2OMiSl
d M2S2 = k21M]S1 - kozMzS2 dt
S O = yl(O) M1
i
D1 Ml
So = 0
where $1 and Sz are the apoB SA in VLDL and IDL, respectively.
(2)
[23]
ANALYSIS USING SPECIFIC RADIOACTIVITY
387
In terms of the flux of apoB (mass per unit time) transferred between pools we have the following equations: d dt M I S I = - R I I S I
(3) d
dt MzS2 = R2ISI - R2zS2
where R u = (ko~ + kzOM~ is the total flux of apoB through VLDL, pool 1 R2j = k21Mj is the flux of apoB transferred from VLDL to IDL R22 = ko2M2 is the total flux of apoB through IDL, pool 2 Since the system is assumed to be in steady state, there should be no net change in the apoB mass within each pool, we can divide the rate equations through by the respective mass to obtain: d
Rll
d t $1 -
Ml
$1 = - L l l S l
(4)
d R21 Rzz d-~ Sz = ~ Sl - -~z Sz = LziS1 - L22S2
the rate constants Lij will be referred to as fractional flux rate constants to differentiate them from the fractional rate constants kij commonly used in rate equations relating total radioactivity data. The experimental SA decay curves can then be described by sums of exponentials: S l ( t ) = S ° e Lilt L2~ $2(/) -- Lzz - Ltl ( e - L i l t -- e-L22t)
(5)
Thus, using a sum of exponential terms to approximate the experimental SA data corresponding to pools 1 and 2, we can obtain estimates for the fractional flux rate constants L I~, L21, and L22. Furthermore, by examining the values estimated for L2~ and L22, certain conclusions regarding the source of flux in the product pool, pool 2, can be made without a priori knowledge of the pool sizes in either compartment. If L23 < L22, this would indicate that there is direct input of material into pool 2 from a source other than pool I. If L21 = L2z, this would indicate that all of the flux through pool 2 is derived entirely from pool 1. It should be pointed out that if TR data, defined as the product of the SA data by the appropriate pool size, were analyzed only estimates of the
388
METABOLISM OF PLASMA LIPOPROTEINS
[23]
fraction of the radioactivity initially in pool 1 which is converted to pool 2 could be obtained. Information regarding direct input into the product pool would be obtained only if the analysis indicated that the flux through pool 2 is greater than that through pool 1. These flux estimates, however, will be dependent on the accuracy of the determinations of the pool sizes.
Areas Under the Specific Activity Curves Another relationship of the fluxes which is unique to SA data can also be derived from the areas under the SA decay curves. If we denote by A~ the area under the SA curve for VLDL apoB (pool 1, in this example) and A2 the area under the IDL apoB SA curve as described in Eq. (5), then, s o
(6) L21 sO = L21 A2 = LIIL2-----~ "7-- Al LZ2
Thus for the simple precursor-product system depicted in Fig. 1, a number of relationships must be satisfied by the areas under the experimental SA curves and the steady-state fluxes, including the following: If pool 1 receives a dose D1 of radioactivity and has a total flux Rj~ of material then the area under the SA curve corresponding to pool 1 will be DI AI = RI---~ With respect to pool 2, if a flux R2~ of material from pool 1 is converted to pool 2 which receives a total flux R22 through it, then the area under the SA curve corresponding to pool 2 will be A2 =
(R21/R22)A1
or
A2/A1 = R21/R22
In other words, area under the product SA curve area under the precursor SA curve flux from the precursor to the product total flux through the product If all of the flux through the product is derived from the precursor, i.e., there is no direct input of material into pool 2 from sources other than pool 1 (R21 = R22), the ratio will be exactly equal to 1. If there is contribution into pool 2 from sources other than pool 1 (R22 > Rzl), the ratio will be less than 1. Two important concepts relating to the ratio of the areas
[23]
ANALYSIS USING SPECIFIC RADIOACTIVITY
389
under the SA curves must be emphasized: (1) this ratio of the areas does not depend on the fraction of the flux through pool 1 which is actually converted to pool 2. Thus the same ratio of the areas could be associated with a system in which there was conversion of 90% of the flux in pool I to pool 2 as well as with a system in which only 10% of the flux was converted; (2) this ratio of the areas can never exceed 1. Conversion o f A p o B f r o m V L D L to I D L
Following the bolus injection of radioiodinated VLDL, the apoB SA curve displays a typical initial flattening period followed by a biexponential decay. It is generally accepted that the slower terminal component of the VLDL apoB SA curve represents the direct catabolism of a subpopulation of VLDL particles without conversion to IDL and LDL. 2-5 The simplest approach to characterize the conversion of apoB from VLDL to IDL can be outlined as follows: 1. Approximate the VLDL apoB SA curve by a sum of two exponential terms either by using a nonlinear regression program or by graphical method using Matthews' curve-peeling procedure. 6 B j e -~l' + B z e -~2t
(ill > f12)
2. Estimate the area under the fast component of the VLDL apoB decay curve. This will correspond to the fraction of the VLDL apoB flux which serves as precursor for IDL apoB. Let this area be denoted as Av =
Bl/fll. 3. Approximate the IDL apoB SA curve to a sum of exponential terms. In general, at least three exponential terms will be required to describe the decay curve during the first 48 hr. Cle-~'lt + C2e-r2t - C3e-r3t
4. Estimate the a r e a AI under the IDL apoB SA curve, AI = C1/yl + C2/y2 - C3/y3 2 M, Berman, M. Hall, 111, R. 1. Levy, S. Eisenberg, D. W. Bilheimer, R. D. Phair, and R. H. Goebel, J. Lipid Res. 19, 38 (1978). s M. Berman, Prog, Biomed. Pharmacol. 15, 67 (1979). 4 N.-A. Le, H. N. Ginsberg, and W. V. Brown, in "Lipoprotein Kinetics and Modeling" (M. Berman, S. M. Grundy, and B. Howard, eds.), p. 121. Academic Press, New York, 1982. N.-A. Le, H. N. Ginsberg, R. Ramakrishnan, R. B. Dell, and W. V. Brown, Submitted (1985). 6 C. M. E. Matthews, Phys. Med. Biol. 2, 36 (1957).
390
METABOLISM OF PLASMA LIPOPROTEINS
[23]
Depending on the relationship between the two areas estimated from the precursor and product SA curves, three cases could be considered: C a s e I. If Av > AI, there is direct input or unlabeled apoB into IDL independent of plasma VLDL. This extent of independent apoB influx may be estimated from the ratio under the apoB SA curves: U2/R22 = 1 -
(At/Av)
where/-/2 is the direct influx and R22 is the total apoB flux through IDL. C a s e II. If Av = AI, there is a simple precursor-product between VLDL and IDL apoB and all of the flux in IDL is derived from VLDL. Note again that this does not necessarily imply that all of the VLDL apoB flux is converted to IDL. C a s e I l L If Av < AI, there is a theoretical contradiction in the analysis. Under the present assumption of simple precursor-product between VLDL and IDL apoB, it is impossible for the IDL fraction to have an area under the SA curve which is greater than the area under the VLDL apoB SA curve. In most apoB turnover studies completed by our group to date, however, it appears that the a r e a AI is significantly greater than the area Av with a ratio of the areas ranging from 1 to 4.5. 5,7 Even greater ratios of the areas have been reported by Reardon et al.,7 who used both exponential components of the VLDL apoB decay curve in the computation of the area of the precursor. Two possible explanations may be proposed: 1. The larger area under the IDL apoB SA curve is due to contamination of the injected radiolabeled VLDL preparation, which results in a portion of the injected dose appearing instantaneously in the IDL density range. In this situation we would expect the difference in the areas be proportional to the dose injected as IDL, i.e., to the initial apoB SA observed in IDL. Available data would suggest that at most, only 5-10% of the injected radioactivity is recovered in the IDL density fraction 5 min after the bolus injection. Most of this radioactivity, however, is associated with apolipoproteins other than apoB. Thus the measured apoB SA in IDL at 5 rain is usually low and not sufficient to account for the large difference in the areas observed. 2. The larger area under the IDL apoB SA curve may be indicative of kinetic heterogeneity of apoB within the VLDL density range. The simplest type of heterogeneity would be the situation in which plasma VLDL exist as distinct subpopulations of particles. These subpopulations are metabolically distinct in that one subpopulation can be converted to IDL in a single step while another subpopulation must undergo several transformations within the VLDL density range before becoming IDL. Since 7 M. Reardon, N. H. Fidge, and P. J. Nestel, J. Clin. Invest. 61, 850 (1978).
[231
ANALYSIS USING SPECIFIC RADIOACTIVITY
391
all of the subpopulations in the density less than 1.006 g/ml would be initially isolated and radiolabeled, there will be direct injection of radiolabeled V L D L apoB into each of the subpopulations. In such a system, the radioactivity in the IDL density fraction will represent the cumulative contribution of apoB radioactivity injected into each and every VLDL subpopulation. The SA for apoB in each VLDL subpopulation, on the other hand, will reflect only the radioactivity directly injected into it and that derived from the preceding subpopulations. Thus it can be shown that when VLDL is characterized by a series of pools connected in a cascade process, 2,3 The IDL apoB SA curve will have an area which is greater than that for the entire VLDL apoB cascade process. 5 The theoretical basis of the larger area for the IDL apoB SA curve when the VLDL apoB is represented by a cascade process is discussed in detail elsewhere .5 Stepwise Conversion o f ApoB from VLDL to IDL The conversion of apoB from VLDL to IDL has been analyzed using any of a number of approaches, including (1) deconvolution method using total apoB radioactivity data, 8 (2) difference method using a portion of the VLDL and IDL apoB SA curves, 7 (3) a simple two-pool model for VLDL with an extravascular delay pool between VLDL and IDL, 4 and (4) a fourpool cascade model for VLDL apoB.2.3 Except for the method by difference which does not actually fit the experimental curves, the other three approaches can produce theoretical curves which closely approximate the VLDL and IDL apoB TR decay curves. With respect to the areas under the apoB SA curves, however, none of these analyses can satisfy the experimental data. From the analysis of SA data, the two-pool model for VLDL apoB 4 would result in equality of the areas under the apoB SA curves for V L D L and IDL. The 4-pool cascade model, z,3 on the other hand, would predict an area for IDL apoB SA which will be exactly 1.6 times the area of the apoB SA curve corresponding to the VLDL cascade process. The simplest modification of the four-pool VLDL cascade process which can account for a wide range of ratios between the areas for VLDL and IDL apoB SA curves is to allow for a variable distribution of the total VLDL apoB mass among the four VLDL subpopulations. The basic assumption of this system is that newly secreted VLDL particles are associated with subpopulation 1 which will require, on the average, four metabolic steps to be converted to an IDL particle. The percentage of the total VLDL apoB mass which is associated with this subpopulation of newly 8 A. H. Kissebah, S. Alfarsi, P, W. Adams, and V. Wynn,
Diabetologia 12, 501 (1976).
392
METABOLISM OF PLASMA LIPOPROTEINS
[23]
secreted VLDL will depend directly on the relationship between the areas under the SA curves obtained experimentally for VLDL and IDL. Based on our own experimental SA data in normolipidemic and hypertriglyceridemic subjects, from 5 to as much as 45% of the VLDL apoB mass may be associated with the subpopulation of newly secreted VLDL particles. This distribution scheme for the VLDL apoB mass is a theoretical concept and further investigation would be needed to determine the physicochemical characteristics of these VLDL subpopulations. Although experimental data at this time is not available to further define the subpopulations proposed in our model for the conversion of VLDL apoB to IDL, several statements concerning the apoB flux from VLDL to IDL can be made, including the following: Direct Loss from Each Subpopulation. With influx of newly secreted VLDL only into the first subpopulation, direct loss of apoB flux from each subpopulation within the VLDL cascade will increase the ratio of the areas, i.e., the area under the IDL apoB SA curve will be greater. Direct Secretion into Each Subpopulation. With efflux of VLDL apoB only out of the last subpopulation, any direct input of newly synthesized apoB into the various subpopulations within the cascade will decrease the ratio of the areas. In some situations, the area under the IDL apoB SA curve could be less than that for the VLDL apoB cascade. Direct Conversion of Each VLDL Subpopulation to IDL. Direct conversion of apoB from any of the VLDL subpopulations to IDL will not affect the area under the IDL apoB SA curve to any significant degree. This is an important concept which illustrates the difference between the traditional analysis based on total radioactivity data and analysis using SA data. The area under the SA curve for a product is a weighted average of the areas of all contributing precursors. In this cascade process, since the last subpopulation reflects the apoB radioactivities injected into all of the subpopulations, it will have the largest area. Thus, while direct conversion of VLDL apoB from the first subpopulation to IDL is expected to increase the apoB radioactivity in IDL during the early time points, the larger area under the IDL apoB SA curve must still be explained by the large area generated in the last subpopulation by the cascades process. In fact, it can be shown that, if all of the subpopulations within the VLDL cascade can be directly converted to IDL, the ratio of the areas under the SA curves will be exactly 1. Relationship in Equilibrating Systems: Metabolism of ApoC-III Another class of metabolic systems in which specific radioactivity data can provide additional insight into the underlying kinetics is systems
[23]
ANALYSIS USING SPECIFIC RADIOACTIVITY
393
in which there is rapid equilibration among metabolically distinct pools. An example of such exchange systems is the dynamic equilibration of apoC among different VLDL particles as well as with lipoprotein particles of other density classes. This exchange of apoC radioactivity was first described by Bilheimer and co-workers. 9,1° Combining in vitro observations with in oivo data in animals, these investigators concluded that the equilibration of the C-apolipoproteins was instantaneous. They had no data, however, to demonstrate that this equilibration was complete. If the equilibration of apoC is supposed to be complete, the bolus injection of a dose D as apoC radioactivity should result in a uniform SA for plasma apoC, which depend only on the dose injected and the apoC pool size in plasma. In other words, the same initial SA will be obtained for apoC in VLDL, IDL, LDL, and HDL. Divergence in the SA curves after the initial time would reflect differences in the metabolism of apoC associated with the various lipoprotein classes. We recently described an immunoaffinity method for the direct determination of the SA of apoC-III in radiolabeled lipoproteins.l~,12 Following the injection of radiolabeled VLDL in a group of subjects we have noted the significant difference in the apoC-III SA in VLDL and HDL. Over a 75-hr period the two SA curves for VLDL and HDL apoC-III were parallel, as demonstrated elsewhere in this volume. ~2Thus, if the experimental SA data for the two curves were multiplied by the appropriate apoC-III pool sizes and expressed as a percentage of the injected dose, then the decay curves for VLDL and HDL apo C-Ill would be indistinguishable. However, by considering the specific activity data it must be concluded that the variability in the SA between VLDL and HDL apoC-III among subjects is indicative of the lack of complete equilibration of apoC-III in plasma. Experimental protocols can then be designed to specifically characterize the nature of this equilibration processes) 2'j3 These studies have demonstrated that portions of the apoC-III pools in both VLDL and HDL did not participate in the equilibration process in vitro. The lack of complete equilibration of apoC-III between VLDL and HDL can also be used to define a relationship between the exchangeable pools of apoC-III in VLDL and HDL. In particular, from the injection of 9 D. W. Bilheimer, S. Eisenberg, and R. 1. Levy, Biochim. Biophys. Acta 260, 361 (1972). l0 S. Eisenberg, D. W. Bilheimer, and R. I. Levy, Biochim. Biophys. Acta 326, 361 (1973). 11 p. R. Bukberg, N.-A. Le, J. C. Gibson, L. Goldman, H. N. Ginsberg, and W. V. Brown, J. Lipid Res. 24, 1251 (1983). 12 N.-A. Le, P. R. Bukberg, H. N. Ginsberg, J. C. Gibson, and W. V. Brown, This volume [27]. 13 p. R. Bukberg, N.-A. Le, H. N. Ginsberg, J. C. Gibson, and W. V. Brown, J. Lipid Res. 26, 1047 (1985).
394
METABOLISM OF PLASMALIPOPROTEINS
[23]
radiolabeled VLDL, it is expected that the SA of apoC-III in the whole VLDL fraction will be the same as the SA in the equilibrating and nonequilibrating components of VLDL apoC-III prior to equilibration, that is, Sv= Sve=Svn where Sv, Sw, and Sv. correspond to the apoC-III SA in whole, equilibrating, and nonequilibrating pools of VLDL apoC-III, respectively. Prior to equilibration, no apoC-III radioactivity is expected in HDL, or, S H = SHe = SHn ~--- 0
with SH, SHe, and SHn denoting the apoC-III SA in whole HDL, the equilibrating, and nonequilibrating pools in HDL, respectively. After the instantaneous equilibration, the SA in the nonequilibrating pools of VLDL and HDL should not be affected by the in vitro incubation. The SA for apoC-III in the exchangeable pools of VLDL and HDL will reach a new equilibrium value which reflects fPv, the fraction of the exchangeable mass of apoC-III which is associated with VLDL, i.e., SHe = Sve = fpvSve
The overall apoC-III SA in each lipoprotein class is a weighted average of the SA in the equilibrating and nonequilibrating pool. Sv = Svefv + SVn(1 - - f v )
SH = Saefn
where fv =
mass of equilibrating VLDL apoC-III total mass of apoC-III in VLDL
wherefH =
mass of equilibrating HDL apoC-III total mass of apoC-III in HDL
The ratio R of the apoC-III SA between VLDL and HDL as obtained from the decay curves is defined as R = Sv/S H
which is the ratio of the SA of VLDL apoC-III to that of HDL apoC-III observed in vivo following the tracer injection of radioiodinated VLDL. R = (Svefv + Svn(l - f v ) )
7,,v-- Ve or, (1 - fpv~
1
f n = - \ Rfpv / f v + R]pv
[24]
METABOLISM OF A p o B - C O N T A I N I N G LIPOPROTEINS
395
In other words, for a given ratio of the apoC-III specific activity between VLDL and HDL observed in vivo following the injection of radioiodinated VLDL, the fraction of apoC-III in VLDL which can participate in the equilibration process is negatively correlated to the fraction of equilibrating apoC-III in HDL. Any kinetic system proposed to explain the metabolism of apoC-III in man must address this relationship. Acknowledgments This w o r k w a s initiated u n d e r a postdoctoral training program from N H L B I (HL-07343). Dr. Le is currently s u p p o r t e d by a N e w Investigator A w a r d from N H L B I (HL-27170).
[24] M e t a b o l i s m o f t h e A p o l i p o p r o t e i n B - C o n t a i n i n g Lipoproteins By GEORGE STEINER, MARY E. POAPST, STEVEN L. DAVID M. F O S T E R
SHUMAK,
and
Introduction This chapter will describe, in general terms, the approaches that can be taken to study the kinetics of apoB-containing lipoproteins in vivo. These lipoproteins fall into the classes generally called chylomicrons, VLDL, IDL, and LDL. Unlike glucose, a lipoprotein is not a single molecule in solution in the plasma. Therefore, when describing its metabolism one must consider its various components. One focus here will be on apoB itself, as this is the key apolipoprotein in this family of lipoproteins, and as it appears to stay constant in amount with the particle during its lifetime in the circulation. The other focus will be on the triglyceride of these iipoproteins. This will be of particular importance because it is now recognized that, although the metabolism of the lipoprotein's protein and lipid moieties are related, they may still be independent of each other, t-3 For example, triglyceride in the VLDL particle is hydrolyzed by the repetitive interactions with lipoprotein lipase (LPL). The result is a succession of VLDL particles of increasing density. Furthermore, triglyci j. Melish, N. A. Le, H. Ginsberg, D. Steinberg, and W. V. Brown, Am. J. Physiol. 239, E354 (1980). -' G. Steiner and M. F. Reardon, in " L i p o p r o t e i n Kinetics and Modeling" (M. B e r m a n , S. M. G r u n d y and B. V. H o w a r d , eds.), p. 237. Academic Press, N e w York, 1982. 3 G. Steiner and M. F. Reardon, Metabolism 32, 342 (1983).
METHODS IN ENZYMOLOGY, VOL. 129
Copyright © 1986by AcademicPress, lnc. All rights of reproduction in any form reserved.