Compartmental modeling, 3-caroten

MATHEMATICAL MODELING IN NUTRITION CONSTRUCTING A PHYSIOLOGIC COMPARTMENTAL MODEL OF THE DYNAMICS OF jS-CAROTENE METABOLISM... 

Plasma was separated by centrifugation and the concentrations of total (deuterated and protonated) /3-carotene and total retinol in all plasma specimens (after saponification) were measured by high-performance liquid chromatography (HPLC) the fractional standard deviation (FSD) of the analytical method was <0.04. Ratios of /3-carotene-dg//3-carotene in all plasma specimens were determined by HPLC the FSD of this analytical method was 0.0325. Ratios of retinol-dVretinol in all plasma specimens were determined by gas chromatography mass spectrometry the FSD of this method was 0.045. Details of these laboratory analytical procedures are previously described (Handelman etal., 1993 Dueker etaL, 1993,1994). The physiologic compartmental model of the dynamics of /3-carotene metabolism based on these data is also previously described (Novotny et al.,... 

To allow plotting of the concentration-time data for the tracer, the ratio of -carotene-dg/)3-carotene in each plasma specimen was multiplied by the concentration of total /S-carotene in that specimen to obtain the concentration of 0-carotene-dg in each specimen. The concentration of retinol-d4 in each plasma specimen was calculated as the ratio of retinol-dVretinol times the concentration of total retinol. So that compartmental modeling could be performed using units of analyte mass in the plasma compartment (for example), the concentrations of total /3-carotene and total retinol in plasma were multiplied by the subject s estimated plasma volume to give the total mass of /3-carotene and retinol in the plasma compartment. The 94-kg test subject was assumed to have 45 ml plasma/kg body wt (Snyder et al, 1975), and the estimated plasma volume therefore was 4.23 liters. 

The stoichiometry of conversion of /3-carotene to retinol is still an unsettled issue. Central cleavage of /3-carotene theoretically yields 2 mol retinol per mole /3-carotene (Goodman and Huang, 1%5 Olson and Hayaishi, 1965 Olson, 1989) and eccentric cleavage of /3-carotene yields 1 mol retinol per mole /3-carotene (Olson, 1989, Krinsky et al., 1994). Brubacher and Weiser (1985) determined the retinol equivalent of /3-carotene in vivo using rats and chicks and found that 1 mol of absorbed /3-carotene yielded 1 mol retinol. Because the body reserves of retinol in these animals were low, the yield of retinol from /3-carotene was probably maximal. Based on these in vivo results, a ratio of 1 mol retinol per mole /3-carotene (after absorption) was used in constructing the present compartmental model of the dynamics of /3-carotene metabolism. 

We began modeling under the assumption that the introduction of the tracer (mass) into the system did not affect the mechanisms present for metabolism of the tracee. The compartmental model was compatible with the assumption that non-steady-state mechanisms for metabolism of /3-carotene were not induced by the tracer because the model prediction of the tracer state, the tracee state, and the steady state could be achieved using the same set of fractional transfer coefficients (FTCs). The appropriateness of this assumption is discussed again under Statistical Considerations. FTC is the fraction of analyte in a donor compartment that is transferred to a recipient compartment per unit of time, in this case per day. 

The first step in constructing a compartmental model is to examine the experimental observations for clues concerning the functionality of the system. This is especially true if the experimental observations are available prior to modeling because it helps direct the construction of the model. The experimental observations were available when construction of the compartmental model of the dynamics of /3-carotene metabolism started. 

Construction of the physiologic compartmental model began with a simple conceptual model based on existing knowledge of/3-carotene and retinol metabolism. The simplest version of a relevant compartmental model is depicted in Fig. 2. 

FIG. 2. Conceptual physiologic compartmental model of /3-carotene metaboliroi in humans. Each circle represents a kinetically distinct form of /3-carotene or retinoid. The arrows indicate flows between compartments. Reprinted with permission from Novotny et al. (1995). 

If conversion of /3-carotene to retinyl ester in the enterocyte were small, it might be a rate-limiting step that could be augmented by hepatic conversion, since the liver also contains the carotenoid-lS,lS -dioxygenase enzyme that catalyzes this process. To test if the compartmental model could predict such system behavior accurately if the liver were the only site for conversion, model parameters were altered so that only intact /3-carotene-ds was absorbed and conversion to retinyl-d4 ester in the enterocyte did not occur. Under these conditions, the compartmental model could not predict the experimental observations because fitting the first /3-carotene-dg peak limited the amount of /3-carotene-dg and retinoid-d4 which was introduced into the system, and thus underestimated either the second /3-carotene-dg peak or the retinoid-d4 peak. It was concluded therefore, that the enterocyte is an important site of conversion of /3-carotene to retinoid. Considerable evidence already exists for conversion of /3-carotene to retinoid in the intestine (Dimitrov et al, 1988 Olson, 1989 Wang et al., 1992 Sdta et aL, 1993). 

Once the model provides a good fit of experimental observations, the statistical certainties of the model parameters are inspected. If parameters are highly correlated, it is often possible to alter one parameter and compensate for the alteration with another parameter without compromising the fit of model. For example, in the compartmental model of the dynamics of )3-carotene metabolism, /3-carotene absorption was highly (positively) correlated with the irreversible loss of /3-carotene from the EHT compartment. Therefore, the absorption of /3-carotene and its irreversible loss from the EHT could be increased simultaneously, along with minor adjustments to a few other FTCs, without materially altering the compartmental model s prediction of the experimental observations. 

It must be realized, however, that the data used to build a particular compartmental model may not always provide sufficient statistical certainty of a given parameter s value. Because retinol-d4 and retinyl-d4 ester were not measured individually in the plasma after the subject ingested the /3-carotene-dg, we were unable to determine with statistical certainty the FTCs specifically for retinyl ester. Movement of retinyl ester from the enterocyte into the plasma was highly correlated with its removal from the plasma into the liver via chylomicron remnant. Therefore, the FTCs describing movement of retinyl ester from the enterocyte to the plasma and from the plasma to the liver could be increased simultaneously without compromising the model s prediction of the experimental observations. 

The resulting physiologic compartmental model of the dynamics of fi-carotene metabolism in a human volunteer is shown in Fig. 3. The numbers in the compartments represent the model-predicted steady-state masses in /imol/compartment, and the numbers beside each arrow represent the flow rates in jumol/day (in the direction of the arrow) of analyte from donor to recipient compartments. Flow rate equals FTC from donor to recipient compartment multiplied by the mass of analyte in the donor compartment. 

Figure 4 shows the compartmental model prediction of plasma /3-carotene-dg and retinol-d4 as a function of time after ingesting the /3-carotene-dg (fitted lines) along with the experimentally observed data (filled circles) in the left panels. The right panels show the compartmental model prediction of plasma total j8-carotene and total retinol as a function of time after ingesting the jS-carotene-dg (fitted lines) along with the experimentally observed data (filled circles). The compartmental model s prediction of all four measurements was quite accurate (Fig. 4). 

The residence time for /8-carotene in the test subject was predicted by the compartmental model to be 51 days. The residence time of 51 days is in excellent agreement with the 56-day mean sojourn time (MST = residence time) that can be calculated from the rate of decrease in plasma /3-carotene concentration of women fed a diet of natural foods very low in carotene (Dixon et at., 1994). 

At the same time, the 51-day residence time for /3-carotene is substantially longer than the 13-day MST predicted from the empirical polyexponenti description of the experimental observations in our system under investigation (presented in Section IX of this paper). While the reason for this discrepancy between the MSTs predicted by the compartmental model and the empirical description calculated from the same experimental observa-... 

The compartmental model of /8-carotene metabolism presented here is compatible with previously developed compartmental models of retinol metabolism (Green et aL, 1985 Lewis et aL, 1990). For example, the compartmental model of the dynamics of /S-carotene metabolism features two kinetically distinct pools of retinol in the liver, recycling of plasma retinol by liver, and irreversible loss of retinol from the plasma. These aspects of retinol metabolism (predicted by the compaitmental model) are compatible with already described aspects of retinol metabolism. 

In addition to the information presented in Table n, the physiologic compartmental model of the dynamics of /3-carotene metabolism was constructed and used to also provide values for critical parameters so that... 

FIG. 6. Compartmental model predicted masses and concentrations of jS-carotene in plasma, liver, and extrahepatic tissue of a healthy adult who ingested a angle 73-/imol dose of JS-carotene-dg orally. Panels labeled Past turnover liver total -carotene, Slow turnover liver total /3-carotene, and Extrahepatic total /3-carotene each include protio and deuterated... 

The compartmental model was also able to predict the efficiency of conversion of /3-carotene to vitamin A in our subject. The model predicted that 1 (ig dietary /3-carotene yielded 0.054 /ug retinol (the same as 0.101 /unol retinol/pimol /3-carotene). The 0.054-/i4g value is considerably lower than the 0.167 fig retinol//ug /3-carotene which is widely accepted. However, the 0.167-/iig value was established in growing rats with low reserves of retinol who were adapted to maximizing the retinol yield (Brubacher and Weiser, 1985). If our subject had been in marginal or deficient vitamin A status, the predicted yield would probably have exceeded 0.054 fig retinol//ig /3-carotene. Further studies are needed to determine the influence of vitamin A status on conversion of /3-carotene to vitamin A and the ability of dietary carotene to maintain tissue retinoid. 

To allow the information from the compartmental model of the dynamics of /8-carotene metabolism to be compared with that from an empirical description of the same experimental observations, polyexponential fits (empirical descriptions) of our experimental observations were also made. 

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