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MBW:Determining Metabolic Constants from Gas Uptake Data

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Article review by Tyler Janes, March 2013.

Article: Gargas ML, Andersen ME, Clewell HJ 3rd. A physiologically based simulation approach for determining metabolic constants from gas uptake data. Toxicol Appl Pharmacol. 1986 Dec;86(3):341-52. PubMed PMID: 3787629.

Executive Summary

The authors sought to develop an approach for determining metabolic constants from gas uptake data using a physiologically-based pharmocokinetic model. They collected uptake curves for chemicals at various initial concentrations by using closed-chamber gas-uptake systems. The five chemicals used were 1,1-dichloroethylene (1,1-DCE), diethyl ether (DE), bromochloromethane (BCM), methyl chloroform (MC), and carbon tetrachloride. Since the general shapes of these curves were functions of both tissue partition coefficients and other metabolic characteristics and constants, the authors first experimentally determined the tissue:air partition coefficients. From there, they incorporated these now unknown coefficients into a physiological kinetic model which was then used to simulate the uptake and metabolic process. The next step was then to find the last set of unknown parameters, the biochemical constants for metabolism. The authors did this by adjusting the biochemical constants until they produced an optimal fit of the family of uptake curves for each chemical. This process was done visually instead of numerically due to the fact that both procedures provided similar results in previous experiments. Moreover, the authors distinguished between single and multiple metabolic pathways for each chemical and provided kinetic constants that can be used to predict the kinetics of metabolism and toxicokinetic models for describing various routes of exposure.

Context/Biological Phenomena

The details involving metabolism of various chemicals in the atmosphere has been an ongoing area of study for several decades now. The reasoning behind their study is that the health-effects that arise as a result of inhalation of chemicals is often very dependent on the metabolic process that ensues. Thus, being able to predict metabolism via toxicokinetic models for inhalation exposures is a key element of risk-assessment. Metabolism is a key element in providing explanations for how toxicity works. BCM, for example, is a volatile solvent that has been previously used in fire extinguishers, but is now banned for use in them. BCM, however, is still a common biproduct of water chlorination, and is rapidly absorbed via inhalation due to its volatility. Moreover, prolonged exposure to BCM has been linked to hepato- and nephro-toxicity. How toxic BCM is, though, is dependent on which metabolism route it would lead to. As such, a simulation approach has been developed to estimate metabolic kinetic constants from gas uptake studies.

History

Starting in the late 70's, gas uptake studies have been used to attempt to establish reasonable estimates for kinetic constants for the in vivo metabolism of inhaled chemicals ([1]). In these experiments, a set number of rats were placed in closed-chamber systems for gas uptake exposures, and various concentrations of a certain chemical were injected. Then, the concentration of chemical in the chamber was monitored over time and plotted as uptake curves. In some early models, the rat was considered to be a single compartment itself, and nothing more was done[2]. In other papers, the approach was to determine the metabolic rates of the linear portions of the uptake curves and analyzed the data via the Michaelis-Menten equation. In more present studies, the authors simulated the data by developing a physiologically-based pharmacokinetic model which broke the rat up into several compartments (adipose tissue, muscles, kidney, liver, etc.), each of which had certain partition coefficients and metabolic constants. Then, the chamber concentration was simulated by mass balance differential equations which took into account tissue volumes, blood flows, and now metabolic-loss equations that were modeled by Michaelis-Menten behaviors or linear pathways. From this, one can manipulate the shape and values of the uptake curves by altering the metabolic constants until finding the constants that give the most optimal graphs. By optimal we mean the graphs that most accurately match the observed change in chamber concentration, which is obtained by placing several rats in a chamber, injecting in various levels of concentration of a chemical, and then measuring the change using a gas chromatograph. Pictured below is an example of a PBPK model.

Pbpk.jpg

A. Description of the Model

The model is a system of five mass balance differential equations which represent the change in concentration of each compartment (chamber, liver, viscera, muscle/skin, and fat). The mass balance equations were determined by incorporating tissue volumes, blood flows, and partition coefficients that correspond to the specific male Fischer-344 rats used. However, the chamber of most interest was the chamber compartment, as it is what we can compare to the observed data from gas chromatography:

{\frac  {dC_{{CH}}}{dt}}=N*{\frac  {Q_{P}}{V_{{CH}}}}*({\frac  {C_{{art}}}{Pb}}-C_{{CH}})-k_{L}C_{{CH}}

where

C_{{CH}} (mg/liter) is the concentration of the chemical in the atmosphere of the chamber,

Q_{p} (liters/hr) is the alveolar ventilation,

N is the number of rats used,

V_{{CH}} (L) is the volume of the empty chamber minus volume occupied by the rats (assuming 1 liter/kg of rat),

k_{L} (1/hr) is the first-order loss rate of chemical from an empty chamber,

{\frac  {C_{{art}}}{Pb}} is the exhaled-end-alveolar air,

C_{{art}} (mg/liter) is the arterial blood concentration (calculated)

P_{b} is the blood:air partition coefficient (experimentally determined)


The other important equation is the mass balance equation for the liver, since it involves the metabolism term:


{\frac  {dAMT_{L}}{dt}}=Q_{L}C_{A}-{\frac  {Q_{L}C_{L}}{P_{L}}}-MM-linear

where

C_{L} (mg/liter) is the chemical concentration in the liver

P_{L} is the liver:air partition coefficient (experimentally determined)

MM={\frac  {V_{{max}}{\frac  {C_{L}}{P_{L}}}}{K_{m}+{\frac  {C_{L}}{P_{L}}}}} is the Michaelis-Menten equation for metabolism (single saturable process); V_{{max}} (mg/hr) is the metabolic rate; K_{m} (mg/liter) is the Michaelis constant.

linear=k_{f}V_{L}{\frac  {C_{L}}{P_{L}}} is the first-order process for metabolism; k_{f} (1/hr) is the first-order constant.


Note: the physiological values used were similar to those used in previous studies, with ventilatoin and cardiac output increased, such that Q_{p} = total alveolar ventilation = 4.6 liters/hour, Q_{c} = caridac output = 4.9 liters/hr. This was needed to scale down to a 225-g rat.

Blood flows to the liver, viscera, muscle/skin, and fat tissue groups were 25, 51, 15, and 9% respectively, of cardiac output. Volumes for liver, viscera, muscle/skin and fat tissue groups were 4, 5, 75, and 7% respectively, of total body weight. The remaining 9% was considered to be skeletal and structural components.

B. Assumptions

(1) Concentration of chemical in the blood that was leaving the lung was assumed to be in equilibrium with the concentration in the alveolar air (which is determined by the blood:air partition coefficient).

(2) The chemical freely perfused to all tissues and was completely eliminated via exhalation and hepatic metabolism.

(3) The remaining 9% of body weight that is assumed to be skeletal has negligible blood perfusion.

(4) The biggest assumption was that adjusting the metabolic constants via a trial and error technique was a sufficient method. However, even though no rigorous numerical optimization took place, each of the kinetic parameters affected the behavior of the simulations differently, and using this guess-and-check method allowed the authors to determine the best value for each constant independently.

Results

Partition Coefficients

The first step in this whole process was to experimentally determine the blood:air and tissue:blood partition coefficients, which describe the measure of the differential solubility of a chemical as the chemical passes between two different phases. They are unitless fractions which account for the amount of a chemical absorbed by compartmental tissue as it passes into the bloodstream or from the blood into the air. Moreover, determining these values by careful measurement is critical in reducing the number of unknowns which must be estimated by the simulation, thereby increasing the accuracy of the values we truly care about: the metabolic constants. It's important to note that the tissue:blood partition coefficients required were determined by dividing the appropriate tissue:air coefficient by the blood:air coefficient, that is

P_{{organ}}=tissue:blood={\frac  {tissue:air}{blood:air}}. This is done for each organ/compartartment included. Saline, olive oil, blood, liver, muscle and fat substrate:air partition coefficients were estimated and their results are seen in Table 1. Saline-air partition coefficients, which relate the partition coefficients of saline homogenates to the actual tissue:air partition coefficients were required. Note: olive oil was compared to the fat tissue, and for each of the five chemicals, their values seemed to be in agreement.



                          Gargastable1.jpg



Gas-Uptake Studies: Single Saturable Pathways

Only a few of the chemicals' uptake kinetics could be accurately described by a model with a single saturable metabolic pathway. In particular, the uptake kinetics of 1,1-DCE and tetrachloride could be adequately explained by the Michaelis-Menten equation mentioned previously. One other important aspect that the authors examined was the introduction of pyrazole, an inhibitor of saturable pathways that blocks oxidative microsomal metabolism. The addition of pyrazole was extremely effective in stopping metabolism for most of the chemicals. The figure below demonstrates both the basic shape for an uptake curve, and moreover the effect of pyrazole pretreatment:

Figure2gar.jpg

The introduction had a similar effect on the uptake curve for tetrachloride, but in general the uptake curves for 1,1-DCE and tetrachloride looked significantly different. This was not only due to the fact that their respective solubilities in fatty tissue were vastly different (see Table 1), but more importantly 1,1-DCE had a massive V_{{max}} (27.2) compared to the V_{{max}} of tetrachloride (.92).

Gas-Uptake Studies: Single first-order pathway

Not all of the chemicals could be adequately described using only Michaelis-Menten for metabolism, however. The chemical MC, for example, exhibited uptake behavior that corresponded to a first-order uptake process for each of the concentrations tested. As expected, a pretreatment of pyrazole did decrease the uptake of MC, but not as significantly as for the previous chemicals discussed.

Figure4gar.jpg

Gas-Uptake Studies: Combined staurable, first-order uptake

BCM and DE were chemicals that did not fit in either the saturable classificaition or the first-order classification, but instead, both chemicals exhibited signs of complex uptake behavior that showed contributions from both processes. The interesting result that came out of the uptake curves for these chemicals was that pyrazole pretreatment had a significant effect on the saturable portion of the process, but little-to-no effect on the linear portion. This is demonstrated in the right-half column of the figure below:

Figure5gar.jpg

Overall, the uptake curves for naive rats (those without pyrazole treatment) for the two chemicals were strikingly similar, which is likely due to their similar V_{{max}} values (19.9 vs. 26.1). However, the uptake curves for BCM and DE in pyrazole-pretreated rats in which metabolism is inhibited led to significantly different uptake curves. In fact, with BCM, there was a large initial drop in concentration in the chamber in the first two hours due to its much greater blood:air and tissue:air partition coefficients.

Pyrazole Treatment: Effects

The overall effect of introducing pyrazole into the rat's system was to slow down the saturable (which the authors assume are also oxidative) metabolic pathways. DCE, BCM, DE, and tetrachloride all showed signs of this idea. In terms of the model and the metabolic constants, this corresponded to an increase in K_{m}. In fact, the K_{m} increased by as much as 250 times the K_{m} for native rats. Though theoretically increasing V_{{max}} would lead us to the same result, attempts at modeling the data by increasing V_{{max}} did not fit the data sets well.

Kinetic Constants

The table below displays the metabolic constants for both naive and pyrazole-treated rats.



            Table2gar.jpg

Discussion

Physiological Simulation

The simulation-based approach to analysis of closed-chamber gas uptake data is in some ways more straightforward than previous methods, but at the same time more complex. It feels more realistic and natural to break down a rat's body into its compartments (organs) and see what is going on in each of them and how they all are connected. Simulation requires more extensive data on various physiological parameters and tissue solubilities, which adds an extra layer of complexity but more importantly an extra layer of accuracy. It's important to keep in mind that these models are not perfect, however, and deviation from the expectation is common. Discrepancies in uptake curves could be possibly explained by some sort of saturable metabolism in the tissue, but it's more likely that they differ because of upper airway clearance of the water-soluble vapors early on in exposure.

Though the tissue partition coeffecients used are easily measured for volatiles with a vial equilibrium method, one main difficulty is finding tissues that physiologically resemble the muscle/skin and fat tissue groups. This is just another problem modelers run into when using this approach.

Yet, once the parameters are determined, the only step left is to find the metabolic constants. This involves discovering whether the uptake of a certain chemical can be adequately described by a particular form (saturable, first-order, etc.) and then determining the constants for that particular equation. In general, the more complex the metabolic equation, the more work is required in determining the metabolic constants we wish to analyze.

Uptake Behaviors

Four of our five chemicals could be sufficiently described by one of the metabolic forms described earlier. 1,1-DCE and tetrachloride both exhibited saturable metabolism, even though their uptake curves were vastly different. Both of the chemicals had uptake curves with slopes that decreased steadily with increased concentration, indicative of saturable metabolism.

Although the uptake curves for tetrachloride and MC were very similar, MC did not exhibit signs of saturable metabolism. Instead, MC was best modeled as a first-order process. Closer inspection revealed some signs of discrepancy, but the differences in behavior for MC and tetrachloride were in general not very noticeable.

BCM was the only the chemical that required contributions from both saturable and first-order components to adequately explain its behavior. This was because at high concentrations (> 1000 ppm), metabolic saturation could not sufficiently describe metabolism, and required the addition of a linear term to fit the data well. Increasing the V_{{max}} term was an alternative idea but it led to uptake curves that still did not fit the data well. Gargas has argued that the linear process is most likely due to a glutoathione conjugation of BCM whereas the saturable process is oxidation to carbon monoxide and other products.

DE was the only chemical that could not be sufficiently described by any of our metabolic behaviors. DE was highly metabolized at low concentrations which contradicts literature stating it is practically metabolically inert. Metabolism of DE is highly dose-dependent and at low concentrations oxidation appears to be the primary (but not the only) source of metabolism.

Comparisons to Other Studies

In general, the results that came from this paper agree with other studies more often than not. Previous work by Gargas led to slightly higher values for V_{{max}} which is likely due to a lack of complexity. Specifically, previous work did not take into account the nonmetabolic contribution from continued partitioning into tissues, which would lead to an inflated V_{{max}}.

Conclusion

Though more complex in nature, the process of simulating metabolism via physiologically-based pharmacokinetic models leads to more accurate results. The uptake curves are dependent on metabolic characteristics of the chemical, partition coefficients, blood flow values, volumes, etc. Simulations based on the model which incorporates all of these values are then fit to experimental data by adjusting the metabolic constants until we reach an optimal fit. These constants can then be used to predict the metabolic process and possibly make risk-assessment claims.

References

  1. Andersen ME, Gargas ML, Jones RA, Jenkins LJ Jr. The use of inhalation techniques to assess the kinetic constants of 1,1-dichloroethylene metabolism. Toxicol Appl Pharmacol. 1979 Feb;47(2):395-409. PubMed PMID: 452031.
  2. Filser, J.G. and Bolt, H.M. (1979). Pharmacokinetics of halogenated ethylenes in rats. Arch. Toxicol. 42, 123-136.