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Metabolism of Steroid and Amino Acid Moieties of Conjugated Bile Acids in Man
GASTROENTEROLOGY 67:887- 897, 1974 Copyright© 1974 by The Williams & Wilkins Co.
Vol. 67, No. 5
Printed in U.S .A.
METABOLISM OF STEROID AND AMINO ACID MOIETIES OF CONJUGATED BILE ACIDS IN MAN. IV. Description and validation of a multicompartment model NEVILLE
E.
HoFFMAN ,
M.B .,
PH .D. , AND ALAN
F.
HoFMANN,
M.D.
Gastroenterology Unit and the Division of Gastroenterology and Internal Medicine, Mayo Clinic and Mayo Foundation, Rochester, Minnesota
A multicompartment model is described for the enterohepatic circulation of conjugated bile acids in man which encompasses bile acid synthesis, amino acid conjugation, bacterial deconjugation, hepatic reconjugation, and bacterial dehydroxylation. When the model was used to predict the fate of administered ring-labeled bile acid, there was good agreement between observed and calculated values. The model was also used to assess the validity of the customary single-compartment analysis of bile acid specific activity decay curves. The errors in estimates of pool size and synthesis rate were found to be small if the Lindstedt procedure was used (tracer administered as free bile acid and specific activity measurements made on combined conjugates of that acid). However, if tracer was given as a conjugated bile acid and the specific activity was determined on only that conjugate, the errors potentially were unacceptably large, especially if cholyltaurine was used. Several novel functions were defined for the enterohepatic circulation of conjugated bile acids, and these were used to derive equations describing biliary bile acid composition for both steroid and amino acid moiety in terms of hepatic and intestinal factors. The model should be of value for quantitative characterization of bile acid metabolism in health and disease. In previous papers in this series, 1" 3 we defined simultaneously the turnover and the metabolic fate of the steroid and amino
acid moieties of the predominant conjugated bile acids in man. These data showed that the steroid and amino acid moieties of a given conjugated bile acid had different turnover rates and suggested that the generally accepted single-compartment model of the bile acid pool proposed by Lindstedt and Norman 4 • 5 was insufficient to describe conjugated bile acid metabolism in man. In this paper, we describe a multicompartment model for the enterohepatic circulation of the conjugated bile acids which provides a comprehensive description encompassing synthesis, conjugation, deconjugation, reconjugation, and dehydroxylation, thus allowing prediction of the fate of any label introduced into the enterohepatic
Received J a nuary 29, 1974. Accepted May 16, 1974. Address requests for reprints to: Dr. Alan F. Hofmann, Mayo Clinic, Rochester, Minnesota 55901. This investigation was supported in part by Research Grants AM-6908 and AM-16770 from the National Institutes of Health, U.S. Public Health Service, an d by grants from the Share Foundation, Mead Johnson & Company, Eli Lilly and Company, and the Quinn Fund. Dr. Neville H offman was a Fulbright-H ays Fellow. His present address is: Department of M edicine, University of Melbourne, Melbourne, Australia. The auth ors acknowledge the helpful advice of Dr. J. B. Bassingthwaighte and Dr. G. W. Beeler, Jr. 887
888
HOFFMAN AND HOFMANN
circulation. Our previous experimental data have been used to validate the model by means of computer simulation, and we have determined the potential error when bile acid kinetics are treated by using the single-compartment analysis. Finally, based on this model, we have defined several novel descriptive functions for the enterohepatic circulation that allow exact specification of it in health and disease. This paper will deal exclusively with the conjugated bile acids that predominate in human bile. The model makes the following assumptions, all of which have been experimentally verified for healthy man: (1) in health, the primary bile acids are solely cholic and chenodeoxycholic acids; (2) the only secondary bile acid in bile in appreciable quantity is deoxycholic acid; and (3) rehydroxylation of deoxycholic acid to cholic acid does not occur to any appreciable extent. The analysis also assumes that the enterohepatic circulation is in a steady state with respect to synthesis and loss of bile acid. 6
Definitions Bile acid pool. This is the mass of bile acid with which a labeled bile acid mixes after parenteral or oral administration. By convention, the sampling site is distal to the liver. Input. (1) For the primary bile acids, cholic and chenodeoxycholic acids, input denotes entrance into the bile acid pool of molecules derived by de novo synthesis from cholesterol. (2) For the secondary bile acid, deoxycholic acid, input denotes entrance into the bile acid pool by absorption from the intestine of molecules formed by bacterial dehydroxylation of cholic acid. Output. This is loss of a moler:.~lar species from the bile acid pool by excre:wn out of the organism, by physical transforrnation that abolishes exchange, or by transformation into another chemical species. Conversion into an insoluble form in the large intestine with loss into feces is the commonest mechanism of output ; however, dehydroxylation represents output of cholic acid from the cholic acid pool. Reconjugation. This refers to hepatic conjugation, with glycine or taurine, of an unconjugated bile acid that is formed by bacterial hydrolysis of a conjugated bile acid in the small intestine.
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The Multicompartment Model A priori, the steroid moiety of any bile acid in the bile acid pool may be considered to exist in four chemically distinct pools-the conjugate with glycine, the conjugate with taurine, the free bile acid produced by bacterial deconjugation in the small intestine, and a precursor pool for conjugation within the hepatocyte. The free bile acid formed by bacterial deconjugation in the small intestine is not sampled and is not essential to the model. The free bile acid that is absorbed then returns to the hepatocyte, where it enters and mixes with the precursor pool. This pool, by definition, has two inputs-de novo synthesis and absorption of free bile acid formed in the intestinal lumen. Also, by definition, every molecule in this pool is equally available for conjugation with glycine or taurine. Figure 1 shows this threepool model for cholic acid. A similar model can be drawn for chenodeoxycholic acid and deoxycholic acid, except that input to the latter is derived from bacterial 7adehydroxylation. The rate constants k 12 and k 13 are for the sum of the processes of intestinal deconjugation, absorption, portal transport, and entry into the precursor pool. The rate constants k 21 and k 31 indicate conjugation with amino acid, and the constants ko2 and k 03 indicate loss from the cholic acid pool. Although loss usually will involve deconjugation and dehydroxylation, these processes occur subsequent to loss from the pool and are not relevant. tk1o 2
k21
cg
k31
c k12
lko2
1
3
ct k13 lko3
FIG. 1. The multicompartment model for cholic acid and its conjugates. Compartment I (termed " precursor pool" in text) is the exchangeable hepatic pool of unconjugated cholic acid available for conjugation with glycine or taurine. For physiological meaning of rate constants, see text. c, cholic acid precursor pool; cg, cholylglycine; ct, cholyltaurine.
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889
MODEL OF CONJUGATED BILE ACID METABOLISM
In figure 2, the model for cholic acid has been combined with that for deoxycholic acid. The arrows from the conjugated cholic acid pools to the deoxycholic acid precursor pool imply that the only entrance to the deoxycholic acid precursor pool is from cholic acid conjugates: that is, by intestinal bacterial deconjugation and dehydroxylation. There is no arrow connecting the cholic acid precursor pool with the deoxycholic acid precursor pool because dehydroxylation does not occur in the liver. The absence of arrows directly connecting the cholic acid conjugates with the deoxycholic acid conjugates indicates that dehydroxylation without deconjugation (for example, the direct conversion of cholylglycine to deoxycholylglycine) is sufficiently uncommon that it may be neglected. 1 • 2 The input of deoxycholic acid is some fraction of the deoxycholic acid that is formed in the intestinal lumen. Because the maximal amount of deoxycholic acid that can be formed is the output (or input) of cholic acid, it is useful to define a term, fdehydrox, that is the deoxycholic acid input divided by the cholic acid input.
Choli c acid
Input k21
2
cg
k3\
3
kt3
ct
k43 ko2
ko3
5
6
dcg
del
kos
kos
FIG. 2. The multicompartment model for cholic acid and deoxycholic acid and their conjugates. For physiological meaning of rate constants, see text. Compartment 4 (termed "precursor pool" in text) is the exchangeable hepatic pool of unconjugated deoxycholic acid available for conjugation with glycine or taurine. de, deoxycholyl precursor pool; dcg, deoxycholylglycine ; dct, deoxycholyltaurine; c, cholic acid precursor pool; cg, cholylglycine; ct, cholyltaurine.
Using ti1ese assigned pool sizes and the overall. rate constant for cholic acid, we could then assign the individual rate constants in . such a way as to maintain mass balance. We set the fractional turnover rate of the cholyl moiety of cholylglycine, k 42 + k 02 , at one-third that of the glycine Validation of Multicompartment Model moiety of cholylglycine, k 42 + k 0 2 + k12· To validate this model, we have used This reduces to: published data from this laboratory for the k., + k 02 = 0.5 X k 12 turnover of the steroid and amino acid moieties of three of the four conjugated bile ·acids in healthy persons •-s together with The utilization of glycine in bile acid accepted values for bile acid pool composi- conjugation, k 2 ., was taken to be 8 times tion to assign relative values to the rate that of taurine in taurine conjugation, kat constants and pools shown in figure 2. The (the reasoning for this assignment is preoverall fractional turnover rate of the cho- sented later). About one-third of the daily loss of cholyl lyl moiety was set at 0.30 day -•. The hepatic precursor bile acid pools ( c and de) moiety, k 42 + k 02 , is reabsorbed as deoxywere set at about 5% of the total cholic acid cholate, k 42 ; therefore: and deoxycholic acid pools, respectively. k 02 = 2 X k., The cholic acid pool was assumed to be twice as large as the deoxycholic acid pool. The glycine-conjugated bile acid pool was Rate constants were assigned for deoxyassumed to be 3 times as large as the cholylglycine by assuming the same relataurine-conjugated bile acid pool. (For fig- tive values. Thus, the rate of conjugation of ures 1, 2, and 3, the actual relative pool the deoxycholic acid precursor pool (de) sizes assigned for the precursor pool, gly- with glycine, k 54 , was taken to be 8 times cine-conjugated pool, and taurine-conju- the rate of conjugation with taurine, k 64 • The rate of loss of the glycine moiety of gated pool were 0.048, 0.714, and 0.238.)
890
HOFFMAN AND HOFMANN 10,000
Vol. 67, No.5
10,000
Days
Days
FIG. 3. Computer-simulated specific activity decay curves, based on model shown in figure 2, with label introduced as ring-labeled cholylglycine (CG) (left) or as ring-labeled cholyltaurine (CT) (right). Rate constants and pool sizes were assigned as described in text. The following values for rate constants were used (arbitrary units): k 2 , 20; k, 2 , 1.00; k 02 , 0.222; k.,, 0.111; k,, 2.222; k,,, 0.333; k 03 , 0.074; k.,, 0.037; k,., 13.333; k ••• 0.667; k 0 ,, 0.222; k 6 ,, 1.481; k, 6 , 0.222; k 06 , 0.074. DCC, deoxycholyglycine; DCT, deoxycholyltaurine.
deoxycholylglycine was assumed to be 3 times that of the deoxycholyl moiety:
With these constants assigned, a computer simulation was performed using the SIMCON program 7 on a CDC 3200 comk., ~ 0.5 X k., puter. (The program uses a fourth-order The rate of loss of the taurine moiety of Runge-Kutta method to integrate numericholyltaurine was assumed to be 3 times cally the differential equations of the model.) In the simulation, label was introthat of the cholyl moiety: duced as either cholyglycine or cholyltauk., + k 0 , = 0.5 X k 13 rine. Figure 3 shows the specific activity Our previously reported interpretation 3 curves as a function of time for all four conthat the taurine and cholyl moieties of jugated bile acids when the label is introcholyltaurine have similar turnover rates duced as cholyglycine or cholyltaurine_ was not justified; the single-compartment From this simulation and the assigned bilianalysis that we used overestimated the ary bile acid composition, it was also possiturnover rate of the cholyl moiety (the ble to calculate the percentage of label in magnitude of this error is discussed more any bile acid class at any given time. fully below). Because of the limitations of In the experiments of Hepner et al., 1 • 8 our previous data and because no data are the isotope-dilution measurements were available on taurine conjugates of deoxy- made independently of the measurements cholic acid, we have thought it best to of class distribution of administered radiomake the model symmetric and assume activity_ In the simulation, we used the that the relative turnover rates of the kinetic data to generate the class distribusteroid and amino acid moieties of cholyl- tion of radioactivity_ There is good agreetaurine and deoxycholyltaurine were simi- ment between the data generated by the lar to those of cholylglycine and deoxy- computer simulation and the experimental cholylglycine, respectively (specifically: observations of Hepner et al. 1• 3 (figs. 4 and 5)_ An important limitation of the data k21/k 12 = k5Jk.5and ks/k 13 = k 6 Jk. 6 ).
November 1974
891
MODEL OF CONJUGATED BILE ACID METABOLISM 100
80
CG
60
40
.....-beG 20
# ; ; ; ... - - - - - - - - - - - - - - - - - : : . : : - -
-----------6CT--
..r"~·-'"'~-c:T ,..... 2
4
6
8
10
Days
100
80
60
oeoxycholy~--~f~~:~----I--------- 1
40
20
J///I---~.~~t~. ···!~~~i-~-~~t~~ ~~ ~~~~i~~ ·I ·1···
1- ..... .
2
3
4
5
6
7
Time, days FIG. 4. Comparison of simulated (top) and experimental (bottom) class distributions of bile acid tracer. The tracer was introduced as ring-labeled cholylglycine (CG). Calculated data are from simulation of figure 3, left, using the assigned bile acid composition. Experimental data are from Hepner eta!.'; ring-labeled cholylglycine tracer was introduced into healthy human subjects. CT, cholytaurine; DCG, deoxycholylglycine; DCT, deoxycholy Ita urine.
used for the simulation is that they were compartment analysis must be tested. We collected from several groups of patients, have done that by model simulation using and no patient provides data for all aspects a three-pool model for cholic acid as shown of the model. Finally, it must be stressed in figure 1. Measurement of bile acid kinetics, as that the simulation generates data applicable to a group mean and that there is first described by Lindstedt and Norman, 4 considerable variation in the data from required that a labeled free bile acid be introduced into the pool and specific activindividual patients. ity be measured in both conjugates of that bile acid in bile. Generally, this is done by Validity of Single-Compartment Model hydrolyzing bile and measuring specific If this multicompartment model is ap- activity in the free steroid moiety thus propriate, then the validity of the single- obtained. Subsequent workers have intro-
892
HOFFMAN AND HOFMANN
values for pool size and daily synthesis rate with those found by simulation. As can be seen in table 1, if the label is introduced as a free acid and specific activity is measured in that acid after hydrolysis, the potential error is small. However, if label is introduced as a conjugated bile acid and measured in that conjugate, without hydrolysis, large errors are possible. The greatest potential for error occurs when the label is introduced and measured in a taurine-conjugated bile acid. Because the one-compartment assumption does not introduce any great error when the radioactivity is introduced and measured in the chemical form of the free bile acid, we think that its simplicity justifies its continued use for the estimation of total pool size and input for a given steroid moiety.
.---- ·-beG
20
2
4
6
8
Vol. 67, No .5
10
Days 100
Cholyl taurine ,I
Dehydroxylation
2
3
4
Time, days FIG. 5. Comparison of simulated (top) and experimental (bottom) class distributions of bile acid tracer. The tracer was introduced as cholyltaurine (CT) (ring-labeled) . Experimental data are from Hepner et al. ' CG, cholylglycine; DCT, deoxycholyltaurine; DCC, deoxycholylglycine.
duced the label as conjugated bile acid and measured specific activity in that conjugate alone. 1- 3 • 8 " 10 Using the relative rate constants described in the previous section, we simulated the three-compartment model and introduced the label as either cholylglycine, cholyltaurine, or free cholic acid. The specific activity data for the last 9 days of the simulation were then analyzed in terms of the one-compartment model (this is essentially the data usually obtained experimentally). The specific activity was measured in the bile acid administered. We were able to compare the expected
Because the one-compartment model of Lindstedt is useful and valid, the model of figure 2 may be simplified to the two-compartment model shown in figure 6. In this figure, the size of compartment 7 is equal to the sum of compartments 1, 2, and 3 in figure 2 and compartment 8 is the sum of compartments 4, 5, and 6. The term fdehydrox was defined as deoxycholic input expressed as a fraction of cholic acid input (or that fraction of the cholic acid output that is conserved as deoxycholic acid). Therefore, in terms of the model shown in figure 6: k •.,.
fdehydrox = - : - - - : - -
kol '
(1)
+ k2 ' I '
or, in terms of Lindstedt kinetics: fdehydro x = .!de · kdc
(2)
P c·kc
in which Pc and Pdc are pool sizes for cholic and deoxycholic acids, respectively, and kc and kdc are the respective fractional turnover rates. In this model, if label is introduced as free cholic acid, the specific activities of cholic acid and deoxycholic acid could be determined in bile at various times up to, for instance, 10 days. The two
November 1974 TABLE
893
MODEL OF CONJUGATED BILE ACID M.t;'TABOLJSM
1. D etermination of bile acid kinetics by single compartment m odel: influence of chemical form of bile acid administered on calculated pool size and synthesis rate• Variable
Bile acid administered
%Deviation from value obtained by three-pool simulation N.,,' = 0.89
Cholic acid
Pool Input Pool Input Pool Input
Cholylglycine Cholylta urine
3.8 0.1 31 18 32 23
N.,, = 0.80 1.9 1.1
32 23 120 217
N.,, = 0.75
2.4 1.5 31 30 182 213
N.,, = 0.50 5.7 0.1 22 65
498 175
"Based on m odel simulation with the following values in the computer program: fractional turnover of cholyl moiety, 0.33 d ay-'; N' ••• (mole fraction of total conjugated bile acids in bile that are conjugated with glycine) , 0.75; this is equivalent to a glycine to taurine ratio of 3. Specific activity was measured in the chemical form administered. Input refers to the pool of the bile acid administered. P ool size and input are overestimated in each instance. •N,,, is defined as mole fraction of glycine in total amino acid used for bile acid conjugation (glycine used for conjugation/glycine and taurine used for b ile acid conjugation); in healthy man, this value averages about 0.90, if our model is correct.
The cholic acid specific activity decay curve would give Pc. Estimation of the 1 2' relative amounts of cholic acid and deoxyc+cg+cl dc+dcg+dct cholic acid in bile would allow calculation of Pdc· Then, the deoxycholic acid specific activity decay curve would give values for ~k01' ko1 · and k2'l -; ko2 ·; and k2 ' 1./(ko1· + k2'1 ' + ~ ko2' k 02 -). Equation 3 would give a second FIG. 6. Two-compartment model for cholic and estimate of k 01 + k21·
J 0
k2'1'
deoxycholic acid s. The size of compartment I ' is equal to the sum of compartments 1, 2, and 3 in fig ures 1 and 2 and the size of compartment 2', to sum of compartments 4, 5, and 6 in figure 2. c, cholic acid precursor pool; cg, cholylglycine; ct, cholyltaurine; de , deoxycholyl precursor pool; dcg , deoxycholylglycine; dct, deoxycholyltaurine.
Biliary Bile Acid Composition The steroid moiety. For any given bile acid, the pool size is the resultant of two processes-input into the pool and loss from it-so that deductions concerning hepatic or intestinal processes are clearly specific activity decay curves could be hazardous when only bile composition is known. The factors determining biliary described by the following equations: bile acid composition may be described in *Q terms of the one-compartment model with (3) SAc. 1 = - - ex p [-(k" . + k,.,.)t] pool sizes and fractional turnover rates Pc obtained from the Lindstedt procedure. *Q k2T Let Nc be the mole fraction of cholic acid SA•c·<= - - · - - - - - - (4) Pdc , k 01 • + k ,"l" - k 02 • in the total biliary bile acids synthesized daily. Then, N cdco the mole fraction of -(exp (-k 02 -t)- exp [- (k 01 · + kn -)t)) chenodeoxycholic acid synthesized daily, is in which * Q is the quantity of tracer equal to 1 - Nc, by definition. Thus: injected and SAc.1 and SAdc .1 are specific Nc =
894
HOFFMAN AND HOFMANN
turnover rates. Let N' c be the mole fraction of cholic acid in biliary bile acids. Thus, by definition:
Vol. 67, No.5
Ntau is similarly defined for taurine, and, by definition, Ntau = 1 - Ng 1y since bile acids are conjugated exclusively with glycine or taurine. N' gty is the mole fraction in bile of a given steroid moiety that is conjugated Rearranging equation 2 gives: with glycine. N'tau is similarly defined for taurine conjugation. Thus, N'tau = 1 - N'gly· and, from equation 5: The familiar glycine to taurine ratio is P,., = P,-k, (1 - N,)/N,k,., (8) simply N'g 1y/(1 - N'g 1y). Clearly, Ng 1y and By substituting equation 7 and equation 8 N' gly must be measured for each bile acid in turn. Limited data suggest that N' giy is in equation 6, it may be shown that: identical for the major bile acids of human 12 13 N', = N,·kcdc"kdc (9) bile, but no data are available for Ngiy· • N, (kcdc · kdc - kdc · k, Expressions for these follow directly + k, . kcdc . fdehydrox) + kdc. k, from the multicompartment model. For Similar equations can be derived for instance, for conjugated cholic acid, N'cac and N'de· N.,y = k.,!(k,. + k") (lOa) ·. These cumbersome expressions show N'.,y = Pc 8 / (Pc 8 + Pc, ) (lOb) · that at least six variables are needed to describe the enterohepatic circulation. in which Peg and Pet are the sizes of the Two of these, Ne and Ncdc. relate to hepatic cholylglycine and cholyltaurine pools, refunction; three, kc, kcac, and kde• to intestispectively. nal function; and one, fdehydrox. to a mixed If the conjugated bile acids are considbacterial-intestinal function. ered as single pools, with respect to the Amino acid moiety. In the model in amino acid moiety, and the fractional turnfigure 2, each conjugated bile acid was over rates obtained by the conventional treated as a single compartment with reLindstedt procedure are used: spect to its amino acid moiety. Obviously, both glycine and taurine exist in multiple (11) chemically defined compartments, of which conjugated bile acids are one, but consideration of these is not germane to in which kg 1y and ktau are fractional turnover rates for the glycine and taurine moiebile acid metabolism. To describe the metabolism of the amino ties of cholylglycine and cholyltaurine, reacid moiety, new terms, analogous to those spectively. In the multicompartment model (fig. 2), used for the steroid moiety, are required . The steady state is again assumed. kgly is the sum, k 02 + k 12 + k, 2 • Similarly, Input for glycine or taurine denotes con- ktau is k 0 3 + k 13 + k 43 • By substituting jugation in the liver with a given bile acid. equation 11 and equation lOb and rearOutput for glycine and taurine denotes ranging: loss from the enterohepatic circulation. Available evidence suggests that, when bile acids are hydrolyzed, the amino acids are This equation is analogous to equation 9 for degraded by bacteria and reincorporation N' e· It again shows that N' g1y, a term for into bile acids cannot be detected, justify- equilibrium bile composition, is the result ing the treatment of the amino acid moiety of two independent forces-hepatic input as a single compartment. 1 • 3 and intestinal conservation. Ng 1y is the glycine input for conjugaUsing data from Hepner et a!., 1• 3 who tion, expressed as mole fraction of the measured Peg and keg in one group of total amino acid input. subjects, and Pet and kct in another, we can
November 1974
895
MODEL OF CONJUGATED BILE ACID METABOLISM
calculate Ng 1y to be 0.89 and N'giy to be 0.75. Thus, the ratio of conjugation with glycine compared to that with taurine is significantly greater than the glycine-taurine ratio of biliary bile acids . The greater conservation of the taurine moiety is attributable to decreased deconjugation of taurine-conjugated bile acids during enterohepatic cycling and allows a relative expansion of the pool of taurine-conjugated bile acids . Discussion We have presented a comprehensive description of the metabolism of the conjugated bile acids. The basic concepts of this model are not original to this description; however, we think that they have been assembled in a novel fashion that provides some insights not previously apparent. In this paper, we have used the mean data collected from three separate groups of healthy subjects to assign relative magnitudes of the rate constants. Because complete data for any given subject are not available, we have neither attempted to refine our estimates of the rate constants to improve the fit of the simulated data to the experimental observations nor attempted to measure the statistical confidence limits of the rate constants. This can only be done when more information is available from individual subjects. First, we have been able to validate the multicompartment model by comparing published data with computer-simulated data. Second, we have been able to compare the potential error of the commonly used techniques for estimating bile acid kinetics and have confirmed the validity of the method of Lindstedt, in which the label is introduced as free bile acid and the specific activity is measured in hydrolyzed bile. Our analysis indicated that a large error in calculated values for bile acid pool size and input may occur if cholyltaurine is used as a tracer and kinetics values are calculated from its specific activity decay curve . Experimental verification of this prediction seems desirable. The model of cholic acid metabolism shown in figure 6 is essentially similar to a
part of the model developed independently by Quarfordt and Greenfield 14 and originally proposed by Lindstedt and Samuelsson. 15 The data shown in figure 7 appear to permit the assumption that the fractional turnover rate of the steroid moiety of deoxycholic acid is the same as that of chenodeoxycholic acid. If so, the metabolism of the steroid moieties in the enterohepatic circulation may in principle be completely described by measuring the decay of labeled cholic acid in the cholic and deoxycholic acid pools. This analysis of the enterohepatic circulation led us to define Nc, the mole fraction of cholic acid in the total bile acid synthesized-a term that describes a primary hepatic function. We have suggested elsewhere 16 that this term may have value in the analysis of metabolic diseases because striking deviations from the normal \...)
0 .5
•/ /
<::)
~-
~
0.4
....
"'"'C)
:::
·~
0.3
/~
~
--..C)
X
-~
tt"'
/
"/
/
f
0 .2
<:::
<:;
/
0 .1
/
/
/
/
0 .1
/
o/x
0.2
0.3
0 .4
0 .5
Fractional turnover rate, CDC
FIG. 7. Comparison of fractional turnover rates of deoxycholic acid (DC) and chenodeoxycholic acid (CDC) in healthy human subjects. Each point represents a single patient, and broken line is line of identity. Data of Hepner et al. (e) were obtained by isotope dilution studies with [2,4-'H]chenodeoxycholylglycine and [2,4-'H]deoxycholylglycine. Subjects were studied with each bile acid tracer on separate occasions, the interval between studies being several months. Data from Quarfordt and Greenfield" ( x ) were obtained by isotope dilution studies with [1-'H]cholesterol in which the time course of radioactivity incorporation into chenodeoxycholic acid and deoxycholic acid was defined; data were then used in a multicompartment model encompassing both cholesterol and bile acid kinetics to calculate values for the fractional turnover rate of each bile acid.
896
HOFFMAN AND HOFMANN
value of 0.6 (cholic acid synthesis ~ 2 x chenodeoxycholic acid synthesis) are observed in several disease conditions. Finally, we have presented the complex equations necessary to describe biliary bile acid composition for the steroid and the
Vol.67,No. 5
amino acid moiety, showing that equilibrium composition is the resultant of hepatic and intestinal events. For the steroid moiety, the chenodeoxycholic pool is similar in size to the cholic acid pool; although the input of chenodeoxycholic acid is less
Cholic acid Input
t ~
2
k21
1
k31
3
cg
k12
c
k13
ct
k42
r-
k43 Deoxycholic acid Input
5
k54
4
ks4
6
dcg
k45
de
k46
del
lko5
Chenodeoxycholic acid ln~ut
8
ks7
cdcg
t
kg?
7
l
kos
9 cdct
cdc
k79
k78
kos
tkog
FIG. 8. Multicompartment model for major primary and secondary bile acids of man. For a complete model, 'six additional compartments would be required: lithocholic acid, lithocholylglycine, lithocholyltaurine, and their respective 3a-sulfated derivatives. cg, cholylglycine ; c, cholic acid precursor pool; ct, cholyltaurine; dcg, deoxycholylglycine; de, deoxycholyl precursor pool; dct, deoxycholyltaurine; cdcg, chenodeoxycholylglycine; cdc, chenodeoxycholyl precursor pool; cdct, chenodeoxycholyltaurine. ·Cholic ac id -i
="=PU=f=:;;:---....
octenol deconjugofton) Free cholic acid
Cholic acid
' - - - - - CHOLIC ACID OUTPUT _ _ _./ (in feces)
Chenic acid
Lifhocholic acid
'---CHENIC ACID OUTPUT___/ (in feces)
FIG. 9. Schematic model for the major primary and secondary bile acids of man. The narrow bands at the bottom of the annuli indicate free bile acid returning to the liver for reconjugation. The model does not show lithocholic acid input, or its subsequent conjugation or sulfation, but, under most circumstances, the lithocholic acid pool is less than 5% of the total bile pool. •· 12 • 13
November 1974
MODEL OF CONJUGATED BILE ACID METABOLISM
than that of cholic acid, the dihydroxy acid has a slower turnover rate. For the amino acid moiety, taurine-conjugated bile acids are deconjugated less during enterohepatic cycling so that the glycine-taurine ratio of hepatic conjugation is at least twice that reflected in the amino acid composition of the biliary bile acids. Thus, for both the steroid and the amino acid moiety, biliary bile acid composition per se gives little information on rates of input. Figure 8 shows the complete multicompartment model using the conventional compartmental analysis format, and figure 9 shows a semianatomic depiction of the model. Obviously, the model can be refined still further by including lithocholic acid together with its conjugates and sulfates, but we have not done this because these compose only a small part of the circulating bile acid pool and virtually no information is available on lithocholic acid kinetics in man. The approach described here is applicable to animals other than man with appropriate modifications. In the rat, for example, deoxycholic acid is rehydroxylated to cholic acid. 15 Application of the multicompartment model to this species would require addition of a rate constant (k 14 ) between compartments 1 and 4 in figure 2. To our knowledge, this model is the first that permits quantitative prediction of all major hepatic and bacterial biotransformations of an endogenous steroid. REFERENCES 1. Hepner GW, Hofmann AF, Thomas PJ : Metabolism of steroid and amino acid moieties of conjugated bile acids in man. I. Cholylglycine. J Clin Invest 51:1889-1897, 1972 2. Hepner GW, Hofmann AF, Thomas PJ : Metabolism of steroid and amino acid moieties of conjugated bile acids in man. II. Glycine-conjugated dihydroxy bile acids. J Clin Invest 51:1898-1905, 1972
897
3. Hepner GW, Sturman JA, Hofmann AF, et a!: Metabolism of steroid and amino acid moieties of conjugated bile acids in man. III. Cholyltaurine (taurocholic acid) . J Clin Invest 52:433-440, 1973 4. Lindstedt S, Norman A: The turnover of bile acids in the rat: bile acids and steroids 39. Acta Physiol Scand 38:121-128, 1956 5. Lindstedt S: The turnover of cholic acid in man: bile acids and steroids 51. Acta Physiol Scand 40:1-9, 1957 6. Bergstrom S, Danielsson H: Formation and metabolism of bile acids. In Handbook of Physiology, sect 6: Alimentary Canal, vol 5. Edited by CF Code, W Heidel. Washington DC, American Physiological Society, 1968, p 2391-2407 7. Anderson DU, Knopp TJ, Bassingthwaighte JB: SIMCON-simulation control to optimize manmachine interaction. Simulation 14:81-86, 1970 8. Garbutt JT, Wilkins RM, Lack L, eta!: Bacterial modification of taurocholate during enterohepatic recirculation in normal man and patients with small intestinal disease. Gastroenterology 59:553-566, 1970 9. Stahl E , Arnesjo B: Taurocholate metabolism in man. Scand J Gastroenterol 7:559- 566, 1972 10. Low-Beer TS, Heaton KW , Pomare EW, et al: The effect of coeliac disease upon bile salts. Gut 14:204-208, 1973 11. Skinner SM, Clark RE, Baker N, eta! : Complete solution of the three-compartment model in steady state after single injection of radioactive tracer. Am J Physiol 196:238-244, 1959 12. Shioda R, Wood PDS, Kinsell LW: Determination of individual conjugated bile acids in human bile. J Lipid Res 10:546-554, 1969 13. Dam H , Kruse I, Prange I, et a!: Studies on human bile. III. Composition of duodenal bile from healthy young volunteers compared with composition of bladder bile from surgical patients with and without uncomplicated gallstone disease . Z Ernaehrungswiss 10:160-177, 1971 14. Quarfordt SH, Greenfield MF: Estimation of cholesterol and bile acid turnover in man by kinetic analysis. J Clin Invest 52:1937-1945, 1973 15. Lindstedt S, Samuelsson B: Bile acids and steroids. LXXXIII. On the interconversion of cholic and deoxycholic acid in the rat. J Bioi Chern 234:2026-2030, 1959 16. Hofmann AF, Hoffman NE : Measurement of bile acid kinetics by isotope dilution in man. Gastroenterology 67:314-323, 1974
Vol. 67, No. 5
Printed in U.S .A.
METABOLISM OF STEROID AND AMINO ACID MOIETIES OF CONJUGATED BILE ACIDS IN MAN. IV. Description and validation of a multicompartment model NEVILLE
E.
HoFFMAN ,
M.B .,
PH .D. , AND ALAN
F.
HoFMANN,
M.D.
Gastroenterology Unit and the Division of Gastroenterology and Internal Medicine, Mayo Clinic and Mayo Foundation, Rochester, Minnesota
A multicompartment model is described for the enterohepatic circulation of conjugated bile acids in man which encompasses bile acid synthesis, amino acid conjugation, bacterial deconjugation, hepatic reconjugation, and bacterial dehydroxylation. When the model was used to predict the fate of administered ring-labeled bile acid, there was good agreement between observed and calculated values. The model was also used to assess the validity of the customary single-compartment analysis of bile acid specific activity decay curves. The errors in estimates of pool size and synthesis rate were found to be small if the Lindstedt procedure was used (tracer administered as free bile acid and specific activity measurements made on combined conjugates of that acid). However, if tracer was given as a conjugated bile acid and the specific activity was determined on only that conjugate, the errors potentially were unacceptably large, especially if cholyltaurine was used. Several novel functions were defined for the enterohepatic circulation of conjugated bile acids, and these were used to derive equations describing biliary bile acid composition for both steroid and amino acid moiety in terms of hepatic and intestinal factors. The model should be of value for quantitative characterization of bile acid metabolism in health and disease. In previous papers in this series, 1" 3 we defined simultaneously the turnover and the metabolic fate of the steroid and amino
acid moieties of the predominant conjugated bile acids in man. These data showed that the steroid and amino acid moieties of a given conjugated bile acid had different turnover rates and suggested that the generally accepted single-compartment model of the bile acid pool proposed by Lindstedt and Norman 4 • 5 was insufficient to describe conjugated bile acid metabolism in man. In this paper, we describe a multicompartment model for the enterohepatic circulation of the conjugated bile acids which provides a comprehensive description encompassing synthesis, conjugation, deconjugation, reconjugation, and dehydroxylation, thus allowing prediction of the fate of any label introduced into the enterohepatic
Received J a nuary 29, 1974. Accepted May 16, 1974. Address requests for reprints to: Dr. Alan F. Hofmann, Mayo Clinic, Rochester, Minnesota 55901. This investigation was supported in part by Research Grants AM-6908 and AM-16770 from the National Institutes of Health, U.S. Public Health Service, an d by grants from the Share Foundation, Mead Johnson & Company, Eli Lilly and Company, and the Quinn Fund. Dr. Neville H offman was a Fulbright-H ays Fellow. His present address is: Department of M edicine, University of Melbourne, Melbourne, Australia. The auth ors acknowledge the helpful advice of Dr. J. B. Bassingthwaighte and Dr. G. W. Beeler, Jr. 887
888
HOFFMAN AND HOFMANN
circulation. Our previous experimental data have been used to validate the model by means of computer simulation, and we have determined the potential error when bile acid kinetics are treated by using the single-compartment analysis. Finally, based on this model, we have defined several novel descriptive functions for the enterohepatic circulation that allow exact specification of it in health and disease. This paper will deal exclusively with the conjugated bile acids that predominate in human bile. The model makes the following assumptions, all of which have been experimentally verified for healthy man: (1) in health, the primary bile acids are solely cholic and chenodeoxycholic acids; (2) the only secondary bile acid in bile in appreciable quantity is deoxycholic acid; and (3) rehydroxylation of deoxycholic acid to cholic acid does not occur to any appreciable extent. The analysis also assumes that the enterohepatic circulation is in a steady state with respect to synthesis and loss of bile acid. 6
Definitions Bile acid pool. This is the mass of bile acid with which a labeled bile acid mixes after parenteral or oral administration. By convention, the sampling site is distal to the liver. Input. (1) For the primary bile acids, cholic and chenodeoxycholic acids, input denotes entrance into the bile acid pool of molecules derived by de novo synthesis from cholesterol. (2) For the secondary bile acid, deoxycholic acid, input denotes entrance into the bile acid pool by absorption from the intestine of molecules formed by bacterial dehydroxylation of cholic acid. Output. This is loss of a moler:.~lar species from the bile acid pool by excre:wn out of the organism, by physical transforrnation that abolishes exchange, or by transformation into another chemical species. Conversion into an insoluble form in the large intestine with loss into feces is the commonest mechanism of output ; however, dehydroxylation represents output of cholic acid from the cholic acid pool. Reconjugation. This refers to hepatic conjugation, with glycine or taurine, of an unconjugated bile acid that is formed by bacterial hydrolysis of a conjugated bile acid in the small intestine.
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The Multicompartment Model A priori, the steroid moiety of any bile acid in the bile acid pool may be considered to exist in four chemically distinct pools-the conjugate with glycine, the conjugate with taurine, the free bile acid produced by bacterial deconjugation in the small intestine, and a precursor pool for conjugation within the hepatocyte. The free bile acid formed by bacterial deconjugation in the small intestine is not sampled and is not essential to the model. The free bile acid that is absorbed then returns to the hepatocyte, where it enters and mixes with the precursor pool. This pool, by definition, has two inputs-de novo synthesis and absorption of free bile acid formed in the intestinal lumen. Also, by definition, every molecule in this pool is equally available for conjugation with glycine or taurine. Figure 1 shows this threepool model for cholic acid. A similar model can be drawn for chenodeoxycholic acid and deoxycholic acid, except that input to the latter is derived from bacterial 7adehydroxylation. The rate constants k 12 and k 13 are for the sum of the processes of intestinal deconjugation, absorption, portal transport, and entry into the precursor pool. The rate constants k 21 and k 31 indicate conjugation with amino acid, and the constants ko2 and k 03 indicate loss from the cholic acid pool. Although loss usually will involve deconjugation and dehydroxylation, these processes occur subsequent to loss from the pool and are not relevant. tk1o 2
k21
cg
k31
c k12
lko2
1
3
ct k13 lko3
FIG. 1. The multicompartment model for cholic acid and its conjugates. Compartment I (termed " precursor pool" in text) is the exchangeable hepatic pool of unconjugated cholic acid available for conjugation with glycine or taurine. For physiological meaning of rate constants, see text. c, cholic acid precursor pool; cg, cholylglycine; ct, cholyltaurine.
November 1974
889
MODEL OF CONJUGATED BILE ACID METABOLISM
In figure 2, the model for cholic acid has been combined with that for deoxycholic acid. The arrows from the conjugated cholic acid pools to the deoxycholic acid precursor pool imply that the only entrance to the deoxycholic acid precursor pool is from cholic acid conjugates: that is, by intestinal bacterial deconjugation and dehydroxylation. There is no arrow connecting the cholic acid precursor pool with the deoxycholic acid precursor pool because dehydroxylation does not occur in the liver. The absence of arrows directly connecting the cholic acid conjugates with the deoxycholic acid conjugates indicates that dehydroxylation without deconjugation (for example, the direct conversion of cholylglycine to deoxycholylglycine) is sufficiently uncommon that it may be neglected. 1 • 2 The input of deoxycholic acid is some fraction of the deoxycholic acid that is formed in the intestinal lumen. Because the maximal amount of deoxycholic acid that can be formed is the output (or input) of cholic acid, it is useful to define a term, fdehydrox, that is the deoxycholic acid input divided by the cholic acid input.
Choli c acid
Input k21
2
cg
k3\
3
kt3
ct
k43 ko2
ko3
5
6
dcg
del
kos
kos
FIG. 2. The multicompartment model for cholic acid and deoxycholic acid and their conjugates. For physiological meaning of rate constants, see text. Compartment 4 (termed "precursor pool" in text) is the exchangeable hepatic pool of unconjugated deoxycholic acid available for conjugation with glycine or taurine. de, deoxycholyl precursor pool; dcg, deoxycholylglycine ; dct, deoxycholyltaurine; c, cholic acid precursor pool; cg, cholylglycine; ct, cholyltaurine.
Using ti1ese assigned pool sizes and the overall. rate constant for cholic acid, we could then assign the individual rate constants in . such a way as to maintain mass balance. We set the fractional turnover rate of the cholyl moiety of cholylglycine, k 42 + k 02 , at one-third that of the glycine Validation of Multicompartment Model moiety of cholylglycine, k 42 + k 0 2 + k12· To validate this model, we have used This reduces to: published data from this laboratory for the k., + k 02 = 0.5 X k 12 turnover of the steroid and amino acid moieties of three of the four conjugated bile ·acids in healthy persons •-s together with The utilization of glycine in bile acid accepted values for bile acid pool composi- conjugation, k 2 ., was taken to be 8 times tion to assign relative values to the rate that of taurine in taurine conjugation, kat constants and pools shown in figure 2. The (the reasoning for this assignment is preoverall fractional turnover rate of the cho- sented later). About one-third of the daily loss of cholyl lyl moiety was set at 0.30 day -•. The hepatic precursor bile acid pools ( c and de) moiety, k 42 + k 02 , is reabsorbed as deoxywere set at about 5% of the total cholic acid cholate, k 42 ; therefore: and deoxycholic acid pools, respectively. k 02 = 2 X k., The cholic acid pool was assumed to be twice as large as the deoxycholic acid pool. The glycine-conjugated bile acid pool was Rate constants were assigned for deoxyassumed to be 3 times as large as the cholylglycine by assuming the same relataurine-conjugated bile acid pool. (For fig- tive values. Thus, the rate of conjugation of ures 1, 2, and 3, the actual relative pool the deoxycholic acid precursor pool (de) sizes assigned for the precursor pool, gly- with glycine, k 54 , was taken to be 8 times cine-conjugated pool, and taurine-conju- the rate of conjugation with taurine, k 64 • The rate of loss of the glycine moiety of gated pool were 0.048, 0.714, and 0.238.)
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HOFFMAN AND HOFMANN 10,000
Vol. 67, No.5
10,000
Days
Days
FIG. 3. Computer-simulated specific activity decay curves, based on model shown in figure 2, with label introduced as ring-labeled cholylglycine (CG) (left) or as ring-labeled cholyltaurine (CT) (right). Rate constants and pool sizes were assigned as described in text. The following values for rate constants were used (arbitrary units): k 2 , 20; k, 2 , 1.00; k 02 , 0.222; k.,, 0.111; k,, 2.222; k,,, 0.333; k 03 , 0.074; k.,, 0.037; k,., 13.333; k ••• 0.667; k 0 ,, 0.222; k 6 ,, 1.481; k, 6 , 0.222; k 06 , 0.074. DCC, deoxycholyglycine; DCT, deoxycholyltaurine.
deoxycholylglycine was assumed to be 3 times that of the deoxycholyl moiety:
With these constants assigned, a computer simulation was performed using the SIMCON program 7 on a CDC 3200 comk., ~ 0.5 X k., puter. (The program uses a fourth-order The rate of loss of the taurine moiety of Runge-Kutta method to integrate numericholyltaurine was assumed to be 3 times cally the differential equations of the model.) In the simulation, label was introthat of the cholyl moiety: duced as either cholyglycine or cholyltauk., + k 0 , = 0.5 X k 13 rine. Figure 3 shows the specific activity Our previously reported interpretation 3 curves as a function of time for all four conthat the taurine and cholyl moieties of jugated bile acids when the label is introcholyltaurine have similar turnover rates duced as cholyglycine or cholyltaurine_ was not justified; the single-compartment From this simulation and the assigned bilianalysis that we used overestimated the ary bile acid composition, it was also possiturnover rate of the cholyl moiety (the ble to calculate the percentage of label in magnitude of this error is discussed more any bile acid class at any given time. fully below). Because of the limitations of In the experiments of Hepner et al., 1 • 8 our previous data and because no data are the isotope-dilution measurements were available on taurine conjugates of deoxy- made independently of the measurements cholic acid, we have thought it best to of class distribution of administered radiomake the model symmetric and assume activity_ In the simulation, we used the that the relative turnover rates of the kinetic data to generate the class distribusteroid and amino acid moieties of cholyl- tion of radioactivity_ There is good agreetaurine and deoxycholyltaurine were simi- ment between the data generated by the lar to those of cholylglycine and deoxy- computer simulation and the experimental cholylglycine, respectively (specifically: observations of Hepner et al. 1• 3 (figs. 4 and 5)_ An important limitation of the data k21/k 12 = k5Jk.5and ks/k 13 = k 6 Jk. 6 ).
November 1974
891
MODEL OF CONJUGATED BILE ACID METABOLISM 100
80
CG
60
40
.....-beG 20
# ; ; ; ... - - - - - - - - - - - - - - - - - : : . : : - -
-----------6CT--
..r"~·-'"'~-c:T ,..... 2
4
6
8
10
Days
100
80
60
oeoxycholy~--~f~~:~----I--------- 1
40
20
J///I---~.~~t~. ···!~~~i-~-~~t~~ ~~ ~~~~i~~ ·I ·1···
1- ..... .
2
3
4
5
6
7
Time, days FIG. 4. Comparison of simulated (top) and experimental (bottom) class distributions of bile acid tracer. The tracer was introduced as ring-labeled cholylglycine (CG). Calculated data are from simulation of figure 3, left, using the assigned bile acid composition. Experimental data are from Hepner eta!.'; ring-labeled cholylglycine tracer was introduced into healthy human subjects. CT, cholytaurine; DCG, deoxycholylglycine; DCT, deoxycholy Ita urine.
used for the simulation is that they were compartment analysis must be tested. We collected from several groups of patients, have done that by model simulation using and no patient provides data for all aspects a three-pool model for cholic acid as shown of the model. Finally, it must be stressed in figure 1. Measurement of bile acid kinetics, as that the simulation generates data applicable to a group mean and that there is first described by Lindstedt and Norman, 4 considerable variation in the data from required that a labeled free bile acid be introduced into the pool and specific activindividual patients. ity be measured in both conjugates of that bile acid in bile. Generally, this is done by Validity of Single-Compartment Model hydrolyzing bile and measuring specific If this multicompartment model is ap- activity in the free steroid moiety thus propriate, then the validity of the single- obtained. Subsequent workers have intro-
892
HOFFMAN AND HOFMANN
values for pool size and daily synthesis rate with those found by simulation. As can be seen in table 1, if the label is introduced as a free acid and specific activity is measured in that acid after hydrolysis, the potential error is small. However, if label is introduced as a conjugated bile acid and measured in that conjugate, without hydrolysis, large errors are possible. The greatest potential for error occurs when the label is introduced and measured in a taurine-conjugated bile acid. Because the one-compartment assumption does not introduce any great error when the radioactivity is introduced and measured in the chemical form of the free bile acid, we think that its simplicity justifies its continued use for the estimation of total pool size and input for a given steroid moiety.
.---- ·-beG
20
2
4
6
8
Vol. 67, No .5
10
Days 100
Cholyl taurine ,I
Dehydroxylation
2
3
4
Time, days FIG. 5. Comparison of simulated (top) and experimental (bottom) class distributions of bile acid tracer. The tracer was introduced as cholyltaurine (CT) (ring-labeled) . Experimental data are from Hepner et al. ' CG, cholylglycine; DCT, deoxycholyltaurine; DCC, deoxycholylglycine.
duced the label as conjugated bile acid and measured specific activity in that conjugate alone. 1- 3 • 8 " 10 Using the relative rate constants described in the previous section, we simulated the three-compartment model and introduced the label as either cholylglycine, cholyltaurine, or free cholic acid. The specific activity data for the last 9 days of the simulation were then analyzed in terms of the one-compartment model (this is essentially the data usually obtained experimentally). The specific activity was measured in the bile acid administered. We were able to compare the expected
Because the one-compartment model of Lindstedt is useful and valid, the model of figure 2 may be simplified to the two-compartment model shown in figure 6. In this figure, the size of compartment 7 is equal to the sum of compartments 1, 2, and 3 in figure 2 and compartment 8 is the sum of compartments 4, 5, and 6. The term fdehydrox was defined as deoxycholic input expressed as a fraction of cholic acid input (or that fraction of the cholic acid output that is conserved as deoxycholic acid). Therefore, in terms of the model shown in figure 6: k •.,.
fdehydrox = - : - - - : - -
kol '
(1)
+ k2 ' I '
or, in terms of Lindstedt kinetics: fdehydro x = .!de · kdc
(2)
P c·kc
in which Pc and Pdc are pool sizes for cholic and deoxycholic acids, respectively, and kc and kdc are the respective fractional turnover rates. In this model, if label is introduced as free cholic acid, the specific activities of cholic acid and deoxycholic acid could be determined in bile at various times up to, for instance, 10 days. The two
November 1974 TABLE
893
MODEL OF CONJUGATED BILE ACID M.t;'TABOLJSM
1. D etermination of bile acid kinetics by single compartment m odel: influence of chemical form of bile acid administered on calculated pool size and synthesis rate• Variable
Bile acid administered
%Deviation from value obtained by three-pool simulation N.,,' = 0.89
Cholic acid
Pool Input Pool Input Pool Input
Cholylglycine Cholylta urine
3.8 0.1 31 18 32 23
N.,, = 0.80 1.9 1.1
32 23 120 217
N.,, = 0.75
2.4 1.5 31 30 182 213
N.,, = 0.50 5.7 0.1 22 65
498 175
"Based on m odel simulation with the following values in the computer program: fractional turnover of cholyl moiety, 0.33 d ay-'; N' ••• (mole fraction of total conjugated bile acids in bile that are conjugated with glycine) , 0.75; this is equivalent to a glycine to taurine ratio of 3. Specific activity was measured in the chemical form administered. Input refers to the pool of the bile acid administered. P ool size and input are overestimated in each instance. •N,,, is defined as mole fraction of glycine in total amino acid used for bile acid conjugation (glycine used for conjugation/glycine and taurine used for b ile acid conjugation); in healthy man, this value averages about 0.90, if our model is correct.
The cholic acid specific activity decay curve would give Pc. Estimation of the 1 2' relative amounts of cholic acid and deoxyc+cg+cl dc+dcg+dct cholic acid in bile would allow calculation of Pdc· Then, the deoxycholic acid specific activity decay curve would give values for ~k01' ko1 · and k2'l -; ko2 ·; and k2 ' 1./(ko1· + k2'1 ' + ~ ko2' k 02 -). Equation 3 would give a second FIG. 6. Two-compartment model for cholic and estimate of k 01 + k21·
J 0
k2'1'
deoxycholic acid s. The size of compartment I ' is equal to the sum of compartments 1, 2, and 3 in fig ures 1 and 2 and the size of compartment 2', to sum of compartments 4, 5, and 6 in figure 2. c, cholic acid precursor pool; cg, cholylglycine; ct, cholyltaurine; de , deoxycholyl precursor pool; dcg , deoxycholylglycine; dct, deoxycholyltaurine.
Biliary Bile Acid Composition The steroid moiety. For any given bile acid, the pool size is the resultant of two processes-input into the pool and loss from it-so that deductions concerning hepatic or intestinal processes are clearly specific activity decay curves could be hazardous when only bile composition is known. The factors determining biliary described by the following equations: bile acid composition may be described in *Q terms of the one-compartment model with (3) SAc. 1 = - - ex p [-(k" . + k,.,.)t] pool sizes and fractional turnover rates Pc obtained from the Lindstedt procedure. *Q k2T Let Nc be the mole fraction of cholic acid SA•c·<= - - · - - - - - - (4) Pdc , k 01 • + k ,"l" - k 02 • in the total biliary bile acids synthesized daily. Then, N cdco the mole fraction of -(exp (-k 02 -t)- exp [- (k 01 · + kn -)t)) chenodeoxycholic acid synthesized daily, is in which * Q is the quantity of tracer equal to 1 - Nc, by definition. Thus: injected and SAc.1 and SAdc .1 are specific Nc =
894
HOFFMAN AND HOFMANN
turnover rates. Let N' c be the mole fraction of cholic acid in biliary bile acids. Thus, by definition:
Vol. 67, No.5
Ntau is similarly defined for taurine, and, by definition, Ntau = 1 - Ng 1y since bile acids are conjugated exclusively with glycine or taurine. N' gty is the mole fraction in bile of a given steroid moiety that is conjugated Rearranging equation 2 gives: with glycine. N'tau is similarly defined for taurine conjugation. Thus, N'tau = 1 - N'gly· and, from equation 5: The familiar glycine to taurine ratio is P,., = P,-k, (1 - N,)/N,k,., (8) simply N'g 1y/(1 - N'g 1y). Clearly, Ng 1y and By substituting equation 7 and equation 8 N' gly must be measured for each bile acid in turn. Limited data suggest that N' giy is in equation 6, it may be shown that: identical for the major bile acids of human 12 13 N', = N,·kcdc"kdc (9) bile, but no data are available for Ngiy· • N, (kcdc · kdc - kdc · k, Expressions for these follow directly + k, . kcdc . fdehydrox) + kdc. k, from the multicompartment model. For Similar equations can be derived for instance, for conjugated cholic acid, N'cac and N'de· N.,y = k.,!(k,. + k") (lOa) ·. These cumbersome expressions show N'.,y = Pc 8 / (Pc 8 + Pc, ) (lOb) · that at least six variables are needed to describe the enterohepatic circulation. in which Peg and Pet are the sizes of the Two of these, Ne and Ncdc. relate to hepatic cholylglycine and cholyltaurine pools, refunction; three, kc, kcac, and kde• to intestispectively. nal function; and one, fdehydrox. to a mixed If the conjugated bile acids are considbacterial-intestinal function. ered as single pools, with respect to the Amino acid moiety. In the model in amino acid moiety, and the fractional turnfigure 2, each conjugated bile acid was over rates obtained by the conventional treated as a single compartment with reLindstedt procedure are used: spect to its amino acid moiety. Obviously, both glycine and taurine exist in multiple (11) chemically defined compartments, of which conjugated bile acids are one, but consideration of these is not germane to in which kg 1y and ktau are fractional turnover rates for the glycine and taurine moiebile acid metabolism. To describe the metabolism of the amino ties of cholylglycine and cholyltaurine, reacid moiety, new terms, analogous to those spectively. In the multicompartment model (fig. 2), used for the steroid moiety, are required . The steady state is again assumed. kgly is the sum, k 02 + k 12 + k, 2 • Similarly, Input for glycine or taurine denotes con- ktau is k 0 3 + k 13 + k 43 • By substituting jugation in the liver with a given bile acid. equation 11 and equation lOb and rearOutput for glycine and taurine denotes ranging: loss from the enterohepatic circulation. Available evidence suggests that, when bile acids are hydrolyzed, the amino acids are This equation is analogous to equation 9 for degraded by bacteria and reincorporation N' e· It again shows that N' g1y, a term for into bile acids cannot be detected, justify- equilibrium bile composition, is the result ing the treatment of the amino acid moiety of two independent forces-hepatic input as a single compartment. 1 • 3 and intestinal conservation. Ng 1y is the glycine input for conjugaUsing data from Hepner et a!., 1• 3 who tion, expressed as mole fraction of the measured Peg and keg in one group of total amino acid input. subjects, and Pet and kct in another, we can
November 1974
895
MODEL OF CONJUGATED BILE ACID METABOLISM
calculate Ng 1y to be 0.89 and N'giy to be 0.75. Thus, the ratio of conjugation with glycine compared to that with taurine is significantly greater than the glycine-taurine ratio of biliary bile acids . The greater conservation of the taurine moiety is attributable to decreased deconjugation of taurine-conjugated bile acids during enterohepatic cycling and allows a relative expansion of the pool of taurine-conjugated bile acids . Discussion We have presented a comprehensive description of the metabolism of the conjugated bile acids. The basic concepts of this model are not original to this description; however, we think that they have been assembled in a novel fashion that provides some insights not previously apparent. In this paper, we have used the mean data collected from three separate groups of healthy subjects to assign relative magnitudes of the rate constants. Because complete data for any given subject are not available, we have neither attempted to refine our estimates of the rate constants to improve the fit of the simulated data to the experimental observations nor attempted to measure the statistical confidence limits of the rate constants. This can only be done when more information is available from individual subjects. First, we have been able to validate the multicompartment model by comparing published data with computer-simulated data. Second, we have been able to compare the potential error of the commonly used techniques for estimating bile acid kinetics and have confirmed the validity of the method of Lindstedt, in which the label is introduced as free bile acid and the specific activity is measured in hydrolyzed bile. Our analysis indicated that a large error in calculated values for bile acid pool size and input may occur if cholyltaurine is used as a tracer and kinetics values are calculated from its specific activity decay curve . Experimental verification of this prediction seems desirable. The model of cholic acid metabolism shown in figure 6 is essentially similar to a
part of the model developed independently by Quarfordt and Greenfield 14 and originally proposed by Lindstedt and Samuelsson. 15 The data shown in figure 7 appear to permit the assumption that the fractional turnover rate of the steroid moiety of deoxycholic acid is the same as that of chenodeoxycholic acid. If so, the metabolism of the steroid moieties in the enterohepatic circulation may in principle be completely described by measuring the decay of labeled cholic acid in the cholic and deoxycholic acid pools. This analysis of the enterohepatic circulation led us to define Nc, the mole fraction of cholic acid in the total bile acid synthesized-a term that describes a primary hepatic function. We have suggested elsewhere 16 that this term may have value in the analysis of metabolic diseases because striking deviations from the normal \...)
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0 .5
Fractional turnover rate, CDC
FIG. 7. Comparison of fractional turnover rates of deoxycholic acid (DC) and chenodeoxycholic acid (CDC) in healthy human subjects. Each point represents a single patient, and broken line is line of identity. Data of Hepner et al. (e) were obtained by isotope dilution studies with [2,4-'H]chenodeoxycholylglycine and [2,4-'H]deoxycholylglycine. Subjects were studied with each bile acid tracer on separate occasions, the interval between studies being several months. Data from Quarfordt and Greenfield" ( x ) were obtained by isotope dilution studies with [1-'H]cholesterol in which the time course of radioactivity incorporation into chenodeoxycholic acid and deoxycholic acid was defined; data were then used in a multicompartment model encompassing both cholesterol and bile acid kinetics to calculate values for the fractional turnover rate of each bile acid.
896
HOFFMAN AND HOFMANN
value of 0.6 (cholic acid synthesis ~ 2 x chenodeoxycholic acid synthesis) are observed in several disease conditions. Finally, we have presented the complex equations necessary to describe biliary bile acid composition for the steroid and the
Vol.67,No. 5
amino acid moiety, showing that equilibrium composition is the resultant of hepatic and intestinal events. For the steroid moiety, the chenodeoxycholic pool is similar in size to the cholic acid pool; although the input of chenodeoxycholic acid is less
Cholic acid Input
t ~
2
k21
1
k31
3
cg
k12
c
k13
ct
k42
r-
k43 Deoxycholic acid Input
5
k54
4
ks4
6
dcg
k45
de
k46
del
lko5
Chenodeoxycholic acid ln~ut
8
ks7
cdcg
t
kg?
7
l
kos
9 cdct
cdc
k79
k78
kos
tkog
FIG. 8. Multicompartment model for major primary and secondary bile acids of man. For a complete model, 'six additional compartments would be required: lithocholic acid, lithocholylglycine, lithocholyltaurine, and their respective 3a-sulfated derivatives. cg, cholylglycine ; c, cholic acid precursor pool; ct, cholyltaurine; dcg, deoxycholylglycine; de, deoxycholyl precursor pool; dct, deoxycholyltaurine; cdcg, chenodeoxycholylglycine; cdc, chenodeoxycholyl precursor pool; cdct, chenodeoxycholyltaurine. ·Cholic ac id -i
="=PU=f=:;;:---....
octenol deconjugofton) Free cholic acid
Cholic acid
' - - - - - CHOLIC ACID OUTPUT _ _ _./ (in feces)
Chenic acid
Lifhocholic acid
'---CHENIC ACID OUTPUT___/ (in feces)
FIG. 9. Schematic model for the major primary and secondary bile acids of man. The narrow bands at the bottom of the annuli indicate free bile acid returning to the liver for reconjugation. The model does not show lithocholic acid input, or its subsequent conjugation or sulfation, but, under most circumstances, the lithocholic acid pool is less than 5% of the total bile pool. •· 12 • 13
November 1974
MODEL OF CONJUGATED BILE ACID METABOLISM
than that of cholic acid, the dihydroxy acid has a slower turnover rate. For the amino acid moiety, taurine-conjugated bile acids are deconjugated less during enterohepatic cycling so that the glycine-taurine ratio of hepatic conjugation is at least twice that reflected in the amino acid composition of the biliary bile acids. Thus, for both the steroid and the amino acid moiety, biliary bile acid composition per se gives little information on rates of input. Figure 8 shows the complete multicompartment model using the conventional compartmental analysis format, and figure 9 shows a semianatomic depiction of the model. Obviously, the model can be refined still further by including lithocholic acid together with its conjugates and sulfates, but we have not done this because these compose only a small part of the circulating bile acid pool and virtually no information is available on lithocholic acid kinetics in man. The approach described here is applicable to animals other than man with appropriate modifications. In the rat, for example, deoxycholic acid is rehydroxylated to cholic acid. 15 Application of the multicompartment model to this species would require addition of a rate constant (k 14 ) between compartments 1 and 4 in figure 2. To our knowledge, this model is the first that permits quantitative prediction of all major hepatic and bacterial biotransformations of an endogenous steroid. REFERENCES 1. Hepner GW, Hofmann AF, Thomas PJ : Metabolism of steroid and amino acid moieties of conjugated bile acids in man. I. Cholylglycine. J Clin Invest 51:1889-1897, 1972 2. Hepner GW, Hofmann AF, Thomas PJ : Metabolism of steroid and amino acid moieties of conjugated bile acids in man. II. Glycine-conjugated dihydroxy bile acids. J Clin Invest 51:1898-1905, 1972
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3. Hepner GW, Sturman JA, Hofmann AF, et a!: Metabolism of steroid and amino acid moieties of conjugated bile acids in man. III. Cholyltaurine (taurocholic acid) . J Clin Invest 52:433-440, 1973 4. Lindstedt S, Norman A: The turnover of bile acids in the rat: bile acids and steroids 39. Acta Physiol Scand 38:121-128, 1956 5. Lindstedt S: The turnover of cholic acid in man: bile acids and steroids 51. Acta Physiol Scand 40:1-9, 1957 6. Bergstrom S, Danielsson H: Formation and metabolism of bile acids. In Handbook of Physiology, sect 6: Alimentary Canal, vol 5. Edited by CF Code, W Heidel. Washington DC, American Physiological Society, 1968, p 2391-2407 7. Anderson DU, Knopp TJ, Bassingthwaighte JB: SIMCON-simulation control to optimize manmachine interaction. Simulation 14:81-86, 1970 8. Garbutt JT, Wilkins RM, Lack L, eta!: Bacterial modification of taurocholate during enterohepatic recirculation in normal man and patients with small intestinal disease. Gastroenterology 59:553-566, 1970 9. Stahl E , Arnesjo B: Taurocholate metabolism in man. Scand J Gastroenterol 7:559- 566, 1972 10. Low-Beer TS, Heaton KW , Pomare EW, et al: The effect of coeliac disease upon bile salts. Gut 14:204-208, 1973 11. Skinner SM, Clark RE, Baker N, eta! : Complete solution of the three-compartment model in steady state after single injection of radioactive tracer. Am J Physiol 196:238-244, 1959 12. Shioda R, Wood PDS, Kinsell LW: Determination of individual conjugated bile acids in human bile. J Lipid Res 10:546-554, 1969 13. Dam H , Kruse I, Prange I, et a!: Studies on human bile. III. Composition of duodenal bile from healthy young volunteers compared with composition of bladder bile from surgical patients with and without uncomplicated gallstone disease . Z Ernaehrungswiss 10:160-177, 1971 14. Quarfordt SH, Greenfield MF: Estimation of cholesterol and bile acid turnover in man by kinetic analysis. J Clin Invest 52:1937-1945, 1973 15. Lindstedt S, Samuelsson B: Bile acids and steroids. LXXXIII. On the interconversion of cholic and deoxycholic acid in the rat. J Bioi Chern 234:2026-2030, 1959 16. Hofmann AF, Hoffman NE : Measurement of bile acid kinetics by isotope dilution in man. Gastroenterology 67:314-323, 1974