DIFFICULTIES IN DETERMINING VALID RATE CONSTANTS FOR TRANSPORT AND METABOLIC PROCESSES

Transcription

1 GASTROENTl!;ROLOGY Copyright 1970 by The Williams & Wilkins Co. Vol. 58, No.6 I' rinted in U.S.A. SPECIAL ARTICLE Special articles of general interest, although not reports of original or clinical research, are occasionally published a t the discretion of the Edi tor. DIFFICULTIES IN DETERMINING VALID RATE CONSTANTS FOR TRANSPORT AND METABOLIC PROCESSES JOHN M. DIETSCHY, M.D. Gastrointestinal-Liver Unit, Department of Internal Medicine, University of Texas (Southwestern) Medical School at Dallas, Texas Each year many conclusions are published concerning various transport and enzymatic processes based upon a comparison of rate constants determined under a variety of experimental conditions. For example, relative rates of absorption or cell uptake frequently are determined for various test substances. Data commonly are presented that are meant to show that a particular substance, e.g., a sugar, amino acid, purine, fatty acid, etc., is transported more efficiently by one area of the small intestine than by another area. Alternatively, rates of transport of several closely related compounds are compared at one particular level of the intestine and such data then are used to speculate on the sterospecific nature of the absorptive mechanism. In a second, common type of study, the rates of a given enzymatic process are compared under different experimental conditions. The level of disaccharidase activity at various levels of the small bowel or in different individuals, Received January 6, Address requests for reprints to: Dr. John M. Dietschy, Department of Internal Medicine, Southwestern Medical School, 5323 Harry Hines Boulevard, Dallas, Texas This work was supported by Research Grant He and Training Grant T1-AM-5490, from the United States Public Health Service, and by a grant from the John and Mary Markle Foundation. 863 the rate of hepatic cholesterogenesis in intact animals and in animals with biliary diversion, and the relative rates of fatty acid esterification at different levels of the small intestine or at the same level of the intestine after the administration of a particular drug are only a few of the many examples of this kind of study that could be cited. In many of these investigations the rates of transport or the rates of a given enzymatic process have been determined under precisely defined and theoretically acceptable conditions, so that a valid comparison is possible. Often, however, the reasons why particular conditions were chosen for assay of a rate constant are not stated explicitly. Not uncommonly it appears that the time interval over which the assay was made, the initial concentration of substrate utilized, etc., were chosen arbitrarily. Data obtained under these experimental circumstances may yield rate constants which, at the very least, are inaccurate and which, under the worst circumstances, may be entirely erroneous. Many studies in gastroenterology involve the determination of rates, and yet the conditions under which these measurements should be made rarely are explained. The purpose, therefore, of these comments is (1) to point out some of the technical problems encountered in the de-

2 864 SPECIAL ARTICLE Vol. 58, No.6 termination of rate constants and (2) to outline the conditions under which valid, comparable rate constants may be measured. It is hoped that these remarks will be particularly useful to less experienced investigators who may be interested in studying transport and metabolic phenomena. Determination of Rate Constants for Transport Processes The first feature of an assay system that must be defined is the relationship between substrate utilization and time under the conditions of the assay procedure. For example, if one is measuring the transport of substance S across the intestine over a 2-hr period, as shown in figure la, the amount of S absorbed should be linear with respect to time throughout the experimental period. The slope of this line, i.e., the amount of S transported per unit surface area divided by time, will give a valid measure of the rate of transport, i.e., the amount of S transported per unit surface area per unit time. However, two other situations encountered in some assay systems are illustrated in figure 1, B and C. As shown in figure IB, the amount of S transported is linear with respect to time for the 1st hour of the incubation; thereafter, the rate of transport begins to decline. This relationship may be seen in in vitro systems where the tissue preparation begins to degenerate after prolonged incubation. It is apparent that, if this situation obtains, valid rate constants can be measured only during the 1st hour of the incubation so all experimental observations should be made within this time period. In contrast to these first two examples, an experimental situation is shown in figure lc in which the amount of S transported is never linear with respect to time; consequently, the rate of transport is declining constantly throughout the entire period of observation. This situation is encountered when the absolute amount of S transported out of the incubation media is large relative to the mass of S present in the solution; hence, the concentration of S rapidly diminishes and the rate of transport declines correspondingly throughout the incubation period. If this situation obtains, it usually can be readily corrected by increasing the volume of the incubation media (and hence the mass of S) so that the amount of S transported out of the incubation fluid is small relative to the amount of S available for absorption. Under these conditions, the concentration of S will remain essentially constant throughout the L1 Slope equols rote, Le., amount of S tronsported I unit surface area/unit time 2 HOURS 2 0 HOURS 2 HOURS FIG. 1. The relationship between the amount of a test substance transported (or, in the case of a metabolic process, the amount of substrate utilized) and time during incubation of an assay system. B and C, respectively, illustrate the situations where the tissue preparation begins to degenerate during the 2nd hour of the incubation and where depletion of test substance from the incubation media has occurred.

3 June 1970 SPECIAL ARTICLE 865 ~ 60 Vl V!50 u. 0_ 0> ~. 40 0, "- 0 VlO> ~ ~ 30 Q::Ul... u.:: 20 o BOO CONCENTRATION SUBSTRATE,[S] FIG. 2. The relationship between the rate of transport and the concentration of test substance for a passive transport process. The passive permeation constant, P, equals the slope of the line defining this relationship, which is first order throughout. The numbers have no absolute meaning and are for illustrative purposes only. of incubation and the amount of S transported will become, for practical purposes, linear with respect to time. It is apparent that if these latter two situations are not recognized the measured rate constants may be significantly in error. For example, if, in the three experimental situations shown in figure 1, the rate of transport of S is determined by making a single observation arbitrarily at 2 hr, then three grossly different. rates of transport would be obtained (A > B > C). As illustrated, however, the initial rates in all three situations are equal and the apparent lower rates in Band C clearly are artifacts of the arrangement of the respective assay systems. From these considerations, it is apparent that the volume of the media containing the test substance S and the time interval over which the rate of transport is to be measured must be adjusted so that the amount of S transported is linear with respect to time during the interval when the experimental measurements are being obtained. If a comparison is to be made of the rates of transport of different substrates at the same anatomical location or of the same substrate at different anatomical locations, then these conditions must be shown to obtain for each specific substrate at each specific anatomical location. Once the conditions for valid determination of the rate of absorption have been established, it is next necessary to define the relationship between the rate of absorption of S and the concentration of S in the solution from which absorption is taking place. In the case of a passive absorptive process, as illustrated in figure 2, this relationship is straightforward, since the rate of absorption usually is related linearly to the concentration of S in the mucosal test solution; as the concentration of S is increased, the rate of absorption increases proportionately. The slope of the line defining this relationship, i.e., rate of transport of S divided by the concentration of S at which that rate is measured, equals the permeation constant, P; this constant defines the amount of S transported per unit area per unit time per unit concentration of S. Thus, for a passive transport process, it usually is irrelevant what concentration of S is used to determine the rate of absorption, since the value of P that defines the passive permeability of the membrane for S is the same at all concentrations of S. Similarly, if a comparison is to be made of the passive transport of S at different anatomical locations or if the passive transport of different substrates at the same anatomical location is to be measured, the concentration of test substances will not be critical. The situation is somewhat more complicated with respect to an active transport system in which the substrate competes for a carrier within the membrane. Generally speaking, such transport systems conform closely to a Michaelis-Menten kinetics described by the equation: Rate (or velocity) of transport of S (1) = Vrnax [Ka ~ \ S ] ] in which Vmax represents the apparent maximal rate of transport achievable at infinitely high concentrations of substrate, [S]; Ka (the apparent Michaelis constant) equals the concentration of substrate at which one-half of this maximal rate of transport is achieved.

4 866 SPECIAL ARTICLE Vol. 58, No.6 {" Limiting Velocity,V mox Ul ,.. ~./ ~ ~ v I- E.75 Q::;: Ul", Z <[0 0:... I-Ul en ~ ~.25 ::I U J ~ I- <[ 0: / 2Ko 4Ko 6K o CONCENTRATION SUBSTRATE, [5] '0", ~ V m o x , ~ ~ Y M ~ Ko ---- [5] o 10K o 100Ka --- [5] FIG. 3. The relationship between the rate of transport and the concentration of test substance for an active transport process. This kinetic relationship also applies to many metabolic processes. In B the lower end of the concentration scale for [S1 has been expanded, while in C the higher concentration range has been compressed. Several features of this well known relationship, plotted graphically in figure 3A, require emphasis. When the concentration of S equals KG, the rate of transport is equal to 50% of the maximal or limiting rate of transport, V rnax At very low substrate concentrations, shown in figure 3B, the rate of transport of S essentially becomes linear with respect to the concentration of S. For example, at values of [S] which vary from 0.1 KG down to 0.01 K G, the rate of transport varies from 91 to 99%, respectively, of achieving a first order kinetic relationship with [S]. Hence, if one is measuring transport rates at substrate concentrations well below the apparent Ka for that process, then first order kinetics indistinguishable from those described above for passive transport will be obtained. At the other extreme of values of [S], as shown in figure 3C, the rate of transport of S approaches the maximal transport rate, V rnax At concentrations of S equal to 2, 4, and 10 K a, the rate of transport is equal to 66, 80, and 91 %, respectively, of the values of V rnax At concentrations of S equal to 100 K a, the transport rate varies < 1 % from the value of the maximal transport rate. If one is attempting to make a

5 June 1970 SPECIAL ARTICLE 867 comparison between the maximal rates of active transport of different substances at one level of the intestine or between the rates of active transport of a single substance at different anatomical locations, then it is essential that these rates be measured utilizing concentrations of 8 at which V max essentially is achieved. As is apparent from figures 3A, at concentrations of 8 greater than 4 K a, zero order kinetics are, for practical purposes, achieved; the rate of transport becomes essentially constant and independent of further increases in [8); finally, the measured transport rates are within 20% or less of the desired values of V max. From these considerations, it is apparent that the concentration of 8 used in a given assay system must be sufficiently high (usually > 4 Ka) in order that the measured rates of transport essentially equal those of V max for the particular substrate and membrane system being studied. Transport rates 6 RATE OF TRANSPORT OF TEST SUBSTANCE 4 ( ~ m oicm. l. 2 1 s hour) 8 2 {,{, 4Ee,. e,.., e, 4 er 'Ileum measured under experimental conditions in which the relationship of the concentration of 8 to the value of Ka for the transport carrier is unknown are of no value for comparative purposes. An example illustrating the importance of the factors discussed thus far is shown in figure 4. Assume that one is interested in comparing the rates of transport of a test substance across the jejunum, ileum, and colon. The rates of transport obtained at these levels of the bowel by measuring the uptake of the test substance at the end of a 1-hr period from a mucosal solution containing the test molecule at an arbitrary concentration of 100 mg per 100 ml are illustrated in figure 4. The interpretation that these data demonstrate more rapid transport of the test material by the jejunum than by the ileum, which, in turn, has a higher transport rate than colon, is not necessarily correct. For example, it is possible that an analysis of the B a w m 11:6 0 '" m <t ",4... z ;5 2 ::i; <t JEJUNUM ILEUM COLON HOURS 2 e'.. 2 T"'-Cofon e,. o 0 ~ too too [S ],. m~ g... [ S ].. ~ m g CONCENTRATION CONCENTRATION OF S USED OF S USED v[ too [S]. mg'y.... CONCENTRATION OF S USED FIG. 4. Several examples illustrating the possible relationship between the rate of active transport of a test substance and the concentration of that substance in the incubation media. A shows the hypothetical results obtained with transport of a test substance across the jejunum, ileum, and colon; B to E illustrate the various situations which could account for these data.

6 868 SPECIAL ARTICLE Vol. 58, No.6 uptake of the test substance, S, with respect to time during the 1-hr experimental period would have revealed the results shown in figure 4B. It is apparent that the uptake of S by the ileum and colon is not linear during the period of observation and the differences in the apparent rates of transport are, therefore, an artifact of the assay system and do not reflect true differences in the rates of transport of S at these different levels of the bowel. If, on the other hand, such an analysis did reveal that the uptake of S was nearly linear at all three anatomical locations, the data still require further clarification with regard to the relationship between the values of Ka for the transport process at each anatomical location and the concentration of S used in this assay system. Three of the various possibilities are shown in the lower portion of figure 4. In figure 4C, the situation is illustrated where the values of Ka for the three transport mechanisms are the same and where the concentration of S, arbitrarily chosen at 100 mg per 100 ml, is several-fold greater than the Ka values. If these conditions obtain, then the rates shown in figure 4A reflect in a valid manner the relative values of V max for the transport systems in these three tissues. In contrast, another possibility is shown in figure 4D where V max for the three transport systems is the same, but where the values of Ka vary in each tissue (colon > ileum > jejunum). If these conditions prevail, then the data in figure 4A reflect primarily the differences in the values of Ka for the transport process in each tissue and, therefore, these rates do not represent a valid measure of the maximal transport capacity of the three areas of the intestine. Finally, figure 4E illustrates the situation where the values of both V max and Ka are different for each transport system at each anatomical location. Here again, if as shown in this diagram a concentration of S equal to 100 mg per 100 ml is used in the assay system, valid quantification of the values of V max would be obtained. However, the point to be emphasized in this example is that entirely different data would have resulted if one arbitrarily had chosen concentrations of S less than 100 mg per 100 ml for measurement of the rate constants. For example, at a concentration of S of 50 mg per 100 ml the apparent rates of transport in the ileum and jejunum would be nearly equal, but both would be greater than the rate in the colon. At a value of 6 mg per 100 ml for [S] the relative rates of transport would be reversed from that shown in figure 4A (colon > ileum > jejunum). These various illustrations, then, all serve to emphasize that measurement of valid transport rates can be undertaken only when one has precise knowledge of the relationship of the concentration of S used in the assay system to the value of Ka for the transport process. In summary, relative rates of active transport have meaning only if (1) the rate of uptake of the substrate is linear with respect to time during the experimental period when the rates are measured, (2) the rates are determined using concentrations of test substance in the perfusing solution which exceed the value of Ka for that transport mechanism by at least 4-fold, and, finally, (3) both of these conditions have been shown to obtain for each different test substance at each different anatomical location at which transport rates are to be measured and compared. Determination of Rate Constants for Metabolic Processes Under many circumstances, determination of valid rate constants for metabolic processes is more difficult than determination of such constants for transport processes. Most such measurements are made under in vitro conditions using one of several tissue preparations. The most commonly used system is to measure the rate of metabolism of a radiolabeled substance by whole cells in the form of tissue slices, cell suspensions or, in the case of man, biopsy specimens. A second commonly used preparation is to measure the me-

7 June 1970 SPECIAL ARTICLE 869 tabolism of a substrate in homogenates or in subcellular preparations such as mitochondria or microsomes. Finally, rarely it may be possible to isolate in crystalline form the rate-limiting enzyme of a given metabolic pathway and assay its activity directly. Problems inherent in the determination of rate constants in such preparations are illustrated in figure 5. In the first example, figure 5A, assume that one is interested in measuring the rates at which radiolabeled substrate S* is metabolized to product X* by whole cell preparations obtained from different anatomical areas or obtained from the same tissue in animals subjected to various experimental manipulations, the experimental problem being to determine whether the rate of metabolism of S* to product X* varies in different tissues or, alternatively, whether certain experimental manipulations (drug administration, dietary change, etc.) alter the rate of metabolism of S* to product X* in a given tissue. In order to be incorporated in.to product X *, the substrate S* must penetrate the cell membrane, mix with the tissue pool of unlabeled S, pass through a number of enzymatic steps and pools of intermediate compounds including the rate-limiting step (RLE) in the pathway, and, finally, be converted to radiolabeled product X* which then mixes with the pre-existing unlabeled cellular pool of product X. It should be emphasized that the over-all rate of incorporation of S* into product X* is a valid measure of the effective rate of this metabolic pathway only if the conditions of the assay have been chosen so that this rate accurately reflects the maximal functional capacity, i.e., V max, of the single rate-limiting step in the pathwayin this example, the enzyme designated RLE which converts intermediate compound B to compound C. However, there are a number of factors which affect the over-all rate of incorporation of S* to product X* besides the absolute enzymatic activity of RLE; these factors must be evaluated and eliminated as significantly altering the apparent rate of metabolism of S* before any tissue assay system can be assumed to measure the velocity of the rate-limiting enzyme. The specific factors that may lead to spurious incorporation rates may be outlined as follows. A. WHOLE CELL / ' ' ' ' ; : ' ~ 5 " '. ~ O POOL S OF PREEXIS..... T IN. G.... p..... o O..... L (.. D.. UC.T... X * CD i ABC I. * J. S e : : ; O; ; WO ~ P R~ O DX U C T... PRODUCT PRODUCT v* w* B. CELL HOMOGENATE OR SUBCELLULAR PREPARATION ~c : : >O PRODUCT C:>O RLE' Ot=) PRODUCT ;: ABC /'\.. PRODUCT v* w* FIG. 5. The possible sources of error in determination of rate constants for metabolic processes in whole cell (A) and broken cell (B) tissue preparations. RLE, rate-limiting enzyme.

8 870 SPECIAL ARTICLE Vol. 58, No The initial event is penetration of the cell membrane by S*. Obviously if the rate of movement of S* into the cell is less than the capacity of RLE to metabolize intermediate compound B, then the overall rate of incorporation of S* to product X * will reflect the rate of cell membrane transport of S* and not the inherent capacity of the metabolic pathway to synthesize product X. 2. Following its entrance into the cell, S* will mix with the intracellular, unlabeled pool of S. If this intracellular pool is large relative to the amount of S* entering the cell, then significant alteration in the specific activity of the intracellular pool of S* occurs and may lead to erroneous rate constants. For example, suppose that the pool of S is relatively large and, further, that after some experimental manipulation the tissue pool of S doubles in size. If under the influence of this experimental procedure the rate of S* entry into the cell and the rate of enzymatic activity of RLE both remain constant, then the measured rate of conversion of S* to product X* will be significantly decreased, suggesting that the experimental manipulation altered the rate of metabolism of S along the metabolic pathway. In point of fact, this conclusion would be erroneous, for the decreased rate of conversion of S* to product X* in this case reflects the decrease in the specific activity of the intracellular precursor pool of S*. In practice, this difficulty usually can be overcome by using a sufficiently high concentration of S* in the incubation media so that the mass of S* entering the cell is very large relative to the intracellular pool of S. Under this circumstance, dilution of the specific activity of S* by intracellular S is insignificant and, although changes in the intracellular pool of S may occur following different experimental manipulations, these changes will not, for practical purposes, alter the specific activity of the intracellular precursor pool of S*. Furthermore, it is possible to test directly whether a change in the rate of S* incorporation into product X* is due to this artifact. As shown in figure 5A, in many tissue preparations it is possible to measure simultaneously the rates of incorporation of S* into other end products, in this case products y* and W*, as well as into product X*. If products X*, Y*, and W* all arise from the same common intracellular pool of S* and if the rates of incorporation of S* into products y* and W* remain constant in the face of an experimental manipulation which has significantly altered the rate of incorporation of S* into product X*, then such a rate change cannot be the artifactual consequence of a change in the specific activity of the intracellular pool of S*. In addition, such results also would indicate that the rate of cell penetration of S* (step 1) is not rate-limiting under the conditions of this particular experiment. 3. Having gained access to the intracellular pool, S* next must pass through a series of intermediate compounds before reaching product X*. The third condition of the assay system that must be met is that the incubation time be sufficiently long so that all intermediate compounds reach isotopic equilibrium. If this condition is not met, spurious values for the incorporation of S* into product X* again may be encountered. For example, consider the situation in which under control conditions the pool size of compound B is very small but under the influence of some experimental treatment this pool is greatly expanded. Assume further that the maximal activity of RLE is constant in both situations. If, under these circumstances, the over-all rate of incorporation of S* into product X* was measured over a fairly short time interval before the pool of intermediate compound B had attained isotopic equilibrium in both the control and experimental tissues, then the experimental tissue would manifest an apparent lower rate of S* incorporation into product X*. This low incorporation rate would not reflect lower enzymatic activity of RLE, but, rather, it would be due to trapping and dilution of the specific activity of the labeled precursor in the expanded pool of intermediate compound B. One method of detecting this situation is to

9 June 1970 SPECIAL ARTICLE 871 determine the specific activity of each of the intermediate compounds in the biochemical sequence. However, this not only is technically difficult to do but, more importantly, may actually lead to confusing results, for only a small portion of the pool of an intermediate compound need necessarily be on the mainstream metabolic pathway. The remainder of the compound may be sequestered in a metabolically inert pool; determination of the specific activity of this intermediate compound would, therefore, lead to the erroneous conclusion that it is not in isotopic equibrium. A more practical method is to analyze the relationship of the amount of S* incorporated into product X* to time throughout the period of incubation. During the initial part of the incubation, the amount of S* incorporated into product X* will be found to increase with each successive time interval; however, a point will be reached at which the amount of S* utilized per unit time will become constant. At this point when the amount of S* incorporation into product X* becomes linear with respect to time, i.e., the rate of incorporation of S* into product X* becomes constant, all functionally significant pools of intermediate compounds must have attained isotopic equilibrium. It is imperative that the total duration of the assay procedure be adjusted so that the time interval required to reach this equilibrium state equals only a fraction of the total duration of the incubation period. Rate constants measured during the period of disequilibrium obviously may reflect primarily the interplay of the labeled precursor in the intermediate pools and not the inherent activity of RLE. 4. It again should be stressed that the purpose of most experiments in which assay of a rate constant for a particular metabolic pathway is undertaken is to measure the maximal enzymatic activity, i.e., V max, for the enzyme which mediates the rate-limiting step in the over-all metabolic pathway. In the example shown in figure 5A, the purpose of determining the overall rate of incorporation of S* into product X* is to obtain a quantitative idea of the magnitude of V max for RLE. If, as outlined above, cell membrane penetration and intracellular pool size phenomena can be excluded as significantly affecting the rate of S* incorporation into product X*, then the over-all kinetics of this reaction should reflect the kinetics of the rate-limiting enzyme. Often the kinetic relationship between the concentration of substrate and the over-all rate of conversion of S* to product X* is similar to that discussed above for active transport and shown in figure 3. It should be apparent, then, that the same principles discussed in regard to the measurement of V max for an active transport process must be applied to the assay for enzymatic activity. First, after the initial equilibrium period the amount of S* incorporated into product X* should be linear with respect to time and should not decline as shown in figure 1, Band C. Such a finding may indicate either that the tissue is degenerating during the incubation or that nearly all of the substrate is being utilized from the incubation media. Second, the concentration of S* should be sufficiently high that zero order kinetics are achieved, i.e., that the over-all rate of incorporation of S* into product X* is essentially constant and independent of any further increases in the concentration of S* in the incubation media. 5. Finally, the results of such enzyme assays commonly are expressed as the amount of S* incorporated into product X* per unit of tissue; alternatively, the results may be expressed in terms of the specific activity of product X*, i.e., the amount of radioactivity (from S*) found in product X* per unit mass of product X at the end of the incubation period. If this latter measurement is used, it should be recognized that yet another variable is introduced into the assay system. For example, the absolute activity of RLE may be constant under the influence of an experimental manipulation that does alter the size of the intracellular pool of product X. Thus, although the amount of S* converted to product X* is constant, the specific activity of product X* may be increased or decreased depending upon the manner in

10 872 SPECIAL ARTICLE Vol. 58, No.6 which the experimental procedure has altered the size of the pre-existing intracellular pool of product X. In this situation, the specific activity of product X* would not reflect the activity of RLE. As illustrated in figure 5B, the use of a broken cell preparation avoids some of these difficulties. For example, the overall rate of incorporation of S* into product X* may be assayed in the appropriate cell homogenate system. Such a system has the advantage of eliminating the problems associated with cell membrane penetration (step 1, fig. 5A) and, indeed, homogenates must be used to assay metabolic systems in which it has been determined that penetration of the cell membrane is the ratelimiting step in the over-all incorporation of S* into product X* by a whole cell preparation. Aside from this advantage, however, the problems of dilution of substrate specific activity, of variations in the pool size of intermediate compounds, of establishment of conditions which allow proper evaluation of the kinetics of RLE, and of independent alteration in the pool size of unlabeled product X, all of which have been outlined above for the whole cell preparation, still remain as potential sources of error and must be dealt with in proper experimental fashion. t [ ~ t ~ l Limit of Solubility of S Limit of Solubility of S FIG. 6. The relationship of the values of K, for transport or metabolic processes to the rate of utilization of the test substance. A illustrates the situation where the values of K, for two substrates are the same and B shows the situation where these values are different. Finally, it occasionally is possible to isolate in more or less pure form the single rate-limiting enzyme in the biochemical sequence. Thus, as also shown in figure 5B, it would be possible to assay directly activity of RLE by measuring the conversion of compound B to compound C. Isolation and purification of specific enzymes seldom has been accomplished, however, in many metabolic pathways of interest to the gastroenterologist so that this method frequently is not avialable. In summary, in order to obtain valid rate constants for metabolic pathways in tissue preparations it should be demonstrated that, after an initial equilibration period, the incorporations of S* into product X* is linear with respect to time, that the initial equilibration period is short with respect to the total duration of time over which the rate constant is measured, and, that a sufficient concentration of S* is utilized to achieve zero order kinetics for the ratelimiting enzyme. Finally, if possible, the rates of incorporation of S* into several products other than the desired product 'also should be measured simultaneously. These conditions must obtain for each specific substrate in each specific tissue under each specific experimental condition if the rates obtained are to be comparable. In concluding this section, one other point should be emphasized. It has been stressed in regard to measuring rate constants both for active transport processes and for metabolic processes that a sufficiently high substrate concentration be utilized in order to achieve zero order kinetics during the assay. Occasionally, however, because of limited solubility or toxicity of the substrate, it is impossible to obtain concentrations of S in the incubation media that are significantly above the Ka value of the transport system or ratelimiting enzyme. In one special circumstance, as illustrated in figure 6, it is nevertheless possible to obtain rate constant data from which valid comparisons can be made. This is the situation in which one is dealing with the transport or metabolism of substrates in an assay system in which it can be determined that the Ka values for

11 June 1970 SPECIAL ARTICLE 873 would be very much greater than that for substrate Y. B. C. ph RELATED DISTRIBUTION FIG. 7. The transport processes which affect the value of the final serosal to mucosal ratios in the everted gut sac preparation. A - and AH represent the ionized and unionized forms of a weak acid; Band BH' represent the corresponding forms of a weak base. utilization of the substrates are the same in all experimental situations. If this condition obtains, then, as shown in figure 6A, the rate constants determined at any concentration of S accurately reflect the relative differences in substrate utilization (but not the absolute values of V max ) by this system; thus, at any concentration of S the rate of utilization of X is always greater than Y. This is true, it should again be emphasized, only when the values of Ka are essentially identical for the transport or metabolism of the various substrates being studied. In contrast, however, if one has no knowledge of the Ka values for the utilization of these substrates or if the values are grossly different, as shown in the example in figure 6B, then determination of rate constants at low concentrations of substrate may yield very misleading results. In this case, for example, determination of rate constants at low substrate concentrations would suggest that the rate of utilization of substrate Y is greater than utilization of substrate X, and yet it is apparent that if Vmax for these two processes could be measured that the value for substrate X Use of the Everted Gut Sac to Determine Relative Transport Rates One final preparation that deserves comment is the everted gut sac which often is used to determine, indirectly, rate constants for the transport of various substances. The concentration of the test substance is usually the same in the serosal and mucosal compartments at the beginning of the incubation and results commonly are expressed as the ratio of the final concentration of the test substance in the serosal fluid to that in the mucosal fluid found at the end of the incubation period. It should be understood, however, that this ratio is the result, as shown diagrammatically in figure 7, of a number of opposing fluxes and so only very indirectly reflects the magnitude of the maximal transport rate of the test substance across the intestinal membrane. A number of situations may be encountered using such a system in which differences in the serosal to mucosal ratios do not reflect valid differences in the active transport of various substances across the membrane. 1. The magnitude of the active flux (figure 7 A) will depend upon the concentration of substrate present in the mucosal solution relative to the apparent value of Ka for the active transport process. Thus, if the movement of a given substance is measured in everted sacs made from different levels of the bowel or if the transport of different substances is measured in sacs prepared from the same level of intestine, greatly varying values for the final serosal to mucosal ratios may be found without these differences necessarily indicating any valid variation in the maximal rate of transport of the test substance(s) under these experimental conditions. If the ratios were measured, for example, using a single arbitrary concentration of test substance, these differences simply may reflect the variations in the Ka values for the transport processes. 2. The value of the serosal to mucosal

12 874 SPECIAL ARTICLE Vol. 58, No.6 ratio may depend in a significant way upon the magnitude of the passive back flux of the test substance from the serosal to mucosal compartment (fig. 7B). Thus, if the passive permeation constant, P, is greater for one test substance than for another, a higher serosal to mucosal ratio may be achieved with the second substance than with the first, although in this example the magnitude of the active flux is identical for both test substances. 3. During the course of the incubation of everted gut sacs, the serosal fluid usually becomes slightly acid; this establishes a ph gradient across the intestinal wall which also can result in major artifacts in the determined values of the serosal to mucosal ratios if one is dealing with the movement of substances which are either weak acids or weak bases. This point is illustrated in figure 7C. In the case of the weak acid, the concentration of protonated acid (All) will be higher in the serosal solution than in the mucosal solution; since the passive permeation constant is usually much greater for the unionized species (All) than for the ionized species (A - ), this will result in a marked increase in the net passive flux of the acid from the serosal to the mucosal solution. The opposite will be true for a weak base where the ph gradient between the mucosal and serosal compartments will result in a net passive flux of the test substance into the serosal fluid. Thus, it is apparent that the values of the serosal to mucosal ratios achieved with weak acids or bases may reflect this passive distribution in the existing ph gradient as much as the active transport flux; the value of the ratio will be spuriously low in the case of a weak acid and high in the case of a weak base. Thus, the validity of using serosal to mucosal ratios obtained in everted gut sacs preparations as a basis for comparison of the magnitude of the active transport flux should be viewed with considerable skepticism. Under many circumstances, the value of these ratios is altered in a significant way by passive transport phenomena which bear no relationship to the active transport component. Only when it has been established that the concentration of the test substance in the mucosal solution is sufficiently high so that the maximal transport rate is achieved, when the active flux is linear with respect to time throughout the assay period, and when the passive permeability constants, P, for each test substance are either low relative to the value of V max for the active transport process or else that the values of P are essentially equal for each test substance can the serosal to mucosal ratios be used for comparative purposes to approximate the relative values of the maximal transport rates of various test substances. Furthermore, if one is dealing with test substances which have acidic or basic groups with pka or pkb values near neutrality, ph-related distribution across the gut sac probably will so alter the values of the serosal to mucosal ratios that these data will be of little use for valid comparison with other test substances. In conclusion, it should be stressed that these remarks deliberately have been kept as brief as possible and, therefore, a number of other difficulties as well as exceptions to these guidelines have not been discussed in detail. The problems, for example, of SQlvent drag, of passive permeability coefficients that are not independent of [S], etc. have not been dealt with. Nevertheless, by stressing the major specific points where artifacts may enter into the determinations of rate constants for transport and metabolic processes and by outlining the minimal criteria which should be met in most assay systems, it is hoped that these remarks will be of value in promoting a more critical appraisal of rate data presented in the medical literature dealing with research of interest to gastroenterologists.