Genetic Determination of Kinetic Parameters in 8-Glucuronidase Induction by Androgen*

A regulatory locus, Gus-r, determines the rate and extent of androgen inducibility of /3-glucuronidase in mouse kidney epithelial cells. The kinetics of induction are strikingly similar when enyzme concentration, rates of enzyme synthesis, and /&glucuronidase mRNA are measured. After an initial lag period the accumulation of mRNA activity obeys simple turnover kinetics defined by k, a zero order rate constant for acquisition of mRNA activity, and Rb, a first order rate constant for loss of activity. The induced state is approached with a half-life of 8-9 days in the presence of testosterone and decays rapidly in the absence of testosterone. The half- life of both &glucuronidase and its mRNA appear to be much shorter, approximately 1-2 days, in both the presence and absence of testosterone. We conclude that the material accumulating in response to androgen is probably a transcriptionally activated state of P-glu-curonidase chromatin. Comparison of the a and b alleles of Gus-r, and a newly described h allele, shows that Gus-r determines k, and the duration of the lag period, but not Rh which was genetically invariant. The changes in R, and the duration of the lag are inversely related, suggesting that they reflect a common step during induction. These results are most simply for by as- suming that &glucuronidase regions in chromatin react with many molecules of androgen receptor pro- tein-testosterone complex and that the rate of transcription is a function of the of molecules The lag period, then, reflects a requirement that a is linear in RNA concentration above a threshold corresponding to 10 microunits of P-glucuronidase formed/oocyte, which corresponds to 0.36 microunit/ng of RNA injected under the standard assay conditions used here. Apparent mouse P-glucuronidase mRNA activities are corrected for this threshold.

duration of the lag are inversely related, suggesting that they reflect a common step during induction.
These results are most simply accounted for by assuming that &glucuronidase regions in chromatin react with many molecules of androgen receptor protein-testosterone complex and that the rate of transcription is a function of the number of molecules bound. The lag period, then, reflects a requirement that a minimum number of sites must be occupied before transcription begins to increase. We suggest that the Gus-r locus determines the accessibility or affinity of androgen receptor complexes to chromatin. Because of this Gus-r determines both k, and the duration of the lag and the two parameters are inversely related t o each other.
The p-glucuronidase gene complex, [Gus], located near the end of chromosome 5 of the mouse, contains the structural gene for p-glucuronidase, Gus-s, together with much associated regulatory information. One of these closely linked loci, Gus-r, acts cis to control the rate and extent of p-glucuronidase induction by androgen in mouse kidney epithelial cells (1,2). During induction there is a hundred-fold or more increase in the rate of /?-glucuronidase synthesis, and Gus-r This work was supported in part by Grant GM 19521 from the National Institutes of Health. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked "aduertkement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. specifically determines the extent of this increase; genetic variation at Gus-r has no effect on the basal rate of enzyme synthesis, the induction of other enzymes in the same cells, or the rate of P-glucuronidase synthesis in other cell types (1,2). Assays of p-glucuronidase mRNA have shown that induction of enzyme synthesis reflects a corresponding increase in pglucuronidase mRNA activity and that Gus-r acts by controlling the magnitude of this response (3).
Induction requires the participation of androgen receptor protein since no induction is seen in a mutant lacking this protein (4-9) and also requires the participation of pituitary hormones in some unknown manner (1,2,10). Induction is cell type specific in the sense that other androgen-responsive cells do not induce p-glucuronidase and each type of responsive cell induces a different spectrum of proteins.
The availability of a sensitive and quantitative catalytic assay for P-glucuronidase mRNA (11) has allowed us to examine the androgen-stimulated accumulation of p-glucuronidase mRNA in detail. This accumulation appears to follow a time c o m e described by a simple rate equation that is defined by three kinetic parameters. These are a lag period, a zero order rate constant, k,, that describes the accumulation of pglucuronidase mRNA activity, and a fist order rate constant, kb, for the loss of mRNA activity. Because P-glucuronidase mRNA appears to turn over much more rapidly than it accumulates, we suggest that the two rate constants, k, and k b , determine the formation and breakdown of an activated state of P-glucuronidase chromatin which is rate-limiting in p-glucuronidase mRNA synthesis.
The ability to describe induction in this way also offers the possibility of identifying the steps in the induction process that are determined by the Gus-r regulatory locus. For this purpose, we have compared the kinetic parameters of induction in mice carrying different alleles of the Gus-r regulatory locus. We find that the stability of the induced state, k b , is not affected by variation at Gus-r; instead, Gus-r determines the duration of the lag period and k,, the subsequent rate at which P-glucuronidase mRNA-synthesizing capacity is acquired. Remarkably, the duration of the lag is inversely related to k,.
To account for these results we suggest that Gus-r determines the affinity or accessibility of [Gus] chromatin to androgen receptor protein, that [Gus] chromatin can potentially bind many molecules of receptor protein, and that the rate of transcription is a function of the number of molecules of receptor protein bound.

EXPERIMENTAL PROCEDURES
Jackson Laboratory. Inbred strains A/J, C57BL/M and C3H/HeJ

Mice"
mice were mature females and were obtained from The (referred to as A, B/6, and C3H) were used. Mice were induced by subcutaneous implantation of a testosterone pellet (30 mg) at the nape of the neck and were deinduced by surgically removing the remaining intact portion of the pellet. Following removal of the 3005 testosterone pellet, dissolved testosterone is rapidly cleared from the animal's system.' P-Glucuronidase Determinations-P-Glucuronidase activity was determined by a fluorometric assay employing 4-methylumbelliferylfi-D-glucuronide as the substrate (12).
Relative rates of synthesis of P-glucuronidase were determined by isolation of pulse-labeled enzyme using antibody columns after partial enzyme purification. In some earlier experiments direct antibody precipitation was used instead of columns. Mice that were induced for less than 3 days beyond the end of the lag period were injected intraperitoneally with 200 or 300 pCi of [3H]leucine (60 Ci/rnmol), and the kidneys from 2-3 animals were pooled in one homogenate. Mice induced for longer periods of time were injected with 100 pCi of r3H]leucine, and the kidneys from separate mice were not pooled. All mice were killed 1 h after injection with label and the kidneys were homogenized with a Polytron (Kinematica GMBH Lucerne) in 0.15 M NaCl, 0.1 M Tris-HC1 (pH 7.5) to make 10% (w/v) homogenates. Incorporation of labeled leucine into total protein was determined by trichloroacetic acid precipitation of small aliquots of homogenate on filter paper circles as previously described (13).
For the antibody column method, Triton X-100 was added to homogenates to a final concentration of I%, and the pH was adjusted to 4.6 with 1 M acetic acid. Acidified homogenates were treated 15 min at 56"C, adjusted to pH 7.5 with 1 M Tris-HC1 (pH 8.0), and centrifuged 30 min at 100,OOO X g. The supernatant fraction was loaded on a small affinity column (170-4 bed volume) consisting of anti-P-glucuronidase (immunoglobulin G fraction) bound to Sepharose 4-B (Pharmacia) using the cyanogen bromide method of Cuatrecasas (14). The enzyme was washed into the column with 0.4 ml of homogenization buffer plus 1% Triton X-100. Virtually all of the Pglucuronidase activity was bound to the column a t this stage. The column was then washed in sequence with the following, all of which contained 1% Triton and 0. Since P-glucuronidase retains catalytic activity under these conditions, the recovery of enzyme was easily determined. Generally 40-60% of the original activity was recovered in purified form. Label incorporated into P-glucuronidase was counted at this point for all samples induced 3 or more days beyond the end of the lag. Periodic checking of these samples by sodium dodecyl sulfate-gel electrophoresis (15) consistently showed that at least 95% of the counts co-migrated with the subunit of P-glucuronidase. For samples at earlier time points, however, the ratio of P-glucuronidase to other proteins is much lower, and as much as 50% of the label in a gel was not associated with the 8-glucuronidase subunit. Therefore, all samples from mice induced less than 3 days beyond the lag were routinely subjected to sodium dodecyl sulfate-gel electrophoresis, and only the radioactivity contained within the P-glucuronidase subunit band was ascribed to P-glucuronidase. All samples, both column eluates and gel slices, were digested in NCS (Amersham) before adding scintillant and counting. The relative rate of P-glucuronidase synthesis was calculated as the ratio of label incorporated into purified P-glucuronidase (corrected for recovery of enzyme activity) to label incorporated into total protein.
When rates of synthesis were determined using antibody precipitation of P-glucuronidase, the same procedures were followed for labeling mice and measuring total protein synthesis. P-Glucuronidase was then purified by deoxycholate extraction, heat treatment, ammonium sulfate precipitation, and immunoprecipitation of P-glucuronidase as described elsewhere (16). The relative rate of P-glucuronidase synthesis was calculated as radioactivity in the immunoprecipitate divided by the radioactivity incorporated into total protein.
mRNA Actiuity-Total kidney RNA was extracted by the guanidine-HC1 method of Cox (17). P-Glucuronidase mRNA activity was determined by injecting Xenopus laevis oocytes with total RNA and measuring the catalytically active mouse @-glucuronidase synthesized (3,11). Routinely, 28 nl/oocyte of RNA extract containing 1 to 3 mg/ ml of total RNA were injected into batches of 30 oocytes. Injected oocytes were transferred to microtiter plates containing 10 p1 of BARTH medium (18)/well. Each oocyte was thus incubated individually for 24 h at room temperature. ' L. P. Bullock, personal communication.
Individual oocytes were then heated in 0.1 M acetate (pH 4.6), 0.1% Triton x-100 at 65OC for 1 h to destroy endogenous frog P-glucuronidase. The remaining mouse enzyme, which is completely stable under these conditions, was assayed with 4-methylumbeUiery1 glucuronide as substrate for 20 h at 37°C. Inactive oocytes were discarded. The enzyme yield from individual active oocytes, expressed as microunits/ oocyte, was averaged. One microunit represents the formation of 1 pmol of 4-methylumbelliferone/h at 37OC. This assay is linear in RNA concentration above a threshold corresponding to 10 microunits of P-glucuronidase formed/oocyte, which corresponds to 0.36 microunit/ng of RNA injected under the standard assay conditions used here. Apparent mouse P-glucuronidase mRNA activities are corrected for this threshold.

RESULTS
Time Course of Induction-The induction of /3-glucuronidase in mouse kidney by androgen occurs over a period of weeks. The course of induction can be followed by measuring (a) the accumulation of &glucuronidase enzymatic activity, ( b ) changes in the rate of P-glucuronidase synthesis relative to totaI protein synthesis, and (c) the activity level of /3glucuronidase mRNA (Fig. 1). The assays for P-glucuronidase enzymatic activity and the relative rate of P-glucuronidase synthesis are sufficiently sensitive to measure the entire induction curve, but the assay for &glucuronidase mRNA is not sensitive enough to measure messenger changes during the earliest phase. Following the administration of androgen to strain A mice, there is a lag period of 1 day during which there is no measurable increase in either enzyme concentration or the rate of enzyme synthesis. This is followed by a slow rise in mRNA activity, the rate of enzyme synthesis, and enzyme concentration to a new steady state level that is reached after 20-30 days. These data are in accord with the earlier data of I I I I 1 one was administered continuously to female mice from strain A from day zero until animals were killed or until 39 days. After 39 days testosterone pellets were removed (indicated by arrows) and deinduction was allowed to proceed for an additional 24 or 48 h. The parameters measured were: a, P-glucuronidase activity as units/g of kidney (x lo-*); b, the relative rate of P-glucuronidase synthesis (x IO3); and c, P-glucuronidase mRNA activity (microunits of Pglucuronidase/oocyte/day/ng of RNA).

-
Swank et al. (1) on enzyme concentration. The general shapes of the induction curves defined by all three parameters are strikingly similar. The major quantitative exception to this similarity is the observation that the extent of induction expressed as an increase in the rate of enzyme synthesis (about 220-fold) is appreciably greater than the extent of induction detected by the increase in /?-glucuronidase enzymatic activity (about 40fold). This difference derives from the fact that kidney lysosomal enzymes are actively secreted from epithelial cells and appear in urine. This process is enhanced following testosterone administration (19-21). As a result, the fractional loss of enzyme per day from kidney in fully induced animals is considerably greater than it was before induction (20,21), and kidney enzyme activity does not increase to the same extent as the rate of enzyme synthesis. Genes determining rates of enzyme loss affect the final levels of induced enzyme without altering rates of enzyme synthesis (13).
The combination of intracellular turnover and enzyme excretion results in a half-life for newly synthesized enzyme of about 1 day. T h i s is much shorter than the time span of induction, which is the reason that enzyme concentration changes follow changes in the rate of enzyme synthesis so closely.
Basic Rate Equation-The induction curve of /?-glucuronidase has three distinct phases; a lag, a rise, and a plateau.
The rate of /?-glucuronidase synthesis is currently the most useful parameter for defining the induction kinetics of each phase. The presence of a lower limit of sensitivity restricts use of the mRNA assay (noninduced mRNA levels are below the threshold for the assay), and the complications of changing excretion rates during induction affect the use of enzyme activity.
In strain A mice, the lag period is about 24 h. The subsequent long rise in the rate of enzyme synthesis approaches its plateau asymptotically. This accumulation of enzyme-synthesizing capacity follows simple turnover kinetics and can be described by two rate constants, a zero order constant, k,, for the accumulation of synthesizing capacity, and a f i s t order constant, kt,, for the loss of synthesizing capacity. Using these constants the change in the rate of synthesis with time after the lag period is described by the following equation: where R is the rate of enzyme synthesis. The initial slope of the induction curve, dR/dt, provides an estimate of k , when R is small and the productkb R is negligible. For strain A k, has a value of 3.7 X day" when R is expressed as the rate of /?-glucuronidase synthesis relative to the rate of total protein synthesis.
The procedure for evaluating kb also provides the experimental evidence that induction actually follows a time course defined by Equation 1. Integrating Equation 1 gives Solving this equation for t = rn provides the relationship k,/kb = R,. Substituting in Equation 2 yields and rearranging yields This mathematical treatment is formally identical with that originally developed for protein turnover by Schimke et al.  Fig. 2 A ) , confirming that the data fit a time course described by Equation 1. Fig. 2, B and H , tests the experimental fit to Equation 4 in two other mouse strains carrying different Gus-r alleles as discussed below. (In general, it should be noted that the later time points in plots of the integrated equation contain a large experimental error since they represent a small difference between two large numbers, one of which, R,, is subject to appreciable experimental error.) Using the earlier part of the induction curve the slope of the line fitted by linear regression in Fig. 2A gives a value for kh of 0.084 day", corresponding to a half-life of 8.3 days for the turnover of enzyme-synthesizing capacity.
A check on the constancy and values of k, and kt, derives from a consideration of Equation 1. Using the relationship R , = k,/kt, and the calculated values of k, and kt,, the predicted value for R , at the new steady state is 4.4 X This is in good agreement with the observed value of 4.6 X Since the predicted value of R, is derived primarily from measurements made early during induction (see Fig. 2 A ) and since the observed value is derived from measurements made much later at the plateau, this result suggests that both k, and kt, are true constants in the sense that they do not change significantly during induction.
From these experiments we conclude that the time course of induction follows turnover kinetics in which the relevant constants describe the rates of formation and breakdown of some substance that is ultimately rate-limiting in P-glucuronidase synthesis.
/?-Glucuronidase mRNA Turnover-The half-life of /?-glucuronidase mRNA appears to be much shorter than the halflife of 8.3 days for induction. When fully induced animals were deinduced by removing testosterone, P-glucuronidase mRNA activity, the rate of enzyme synthesis, and enzyme activity, all dropped rapidly with half-lives of 1-2 days (Fig. 1).
This estimate of the half-life of the messenger was made after removal of testosterone. We have also tested whether the presence of testosterone might affect the apparent half-life of /3-glucuronidase mRNA. For this purpose mRNA s pthesis in fully induced animals was blocked by administration of a-amanitin. The subsequent decay of messenger activity and enzyme-synthesizing capacity was then examined in both animals deprived of exogenous testosterone and those continuing to receive it (Table I); the decay of messenger activity was equally rapid in both groups of animals. This supports the observation that P-glucuronidase mRNA has a half-life of approximately 1 day and provides evidence that testosterone administration does not directly stabilize glucuronidase mRNA activity. Interpretation of these results is, of course, subject to the usual reservations attending general inhibitor studies in whole animals.
Because both P-glucuronidase synthesis and total protein synthesis decline equally following a-amanitin treatment, the relative rate of P-glucuronidase synthesis remains unchanged after the administration of a-amanitin. This implies that Pglucuronidase mRNA turns over at essentially the same rate as the average of all kidney mRNA (assuming that total mRNA l i t s the rate of total protein synthesis).
Thus, direct estimates of the stability of the glucuronidase messenger indicate that it has a half-life of 1-2 days in both the presence and absence of testosterone. This value is comparable to measurements of other mammalian mRNA halflives and is considerably shorter than the 8-9-day half-life observed for the accumulation of mRNA activity. From this we conclude that k , and k b do not describe the synthesis and turnover of P-glucuronidase mRNA itself but, rather, the formation and breakdown of some material that is rate-limiting in the synthesis or activation of this messenger.
Strain Genotypes-Variant forms, or haplotypes, of the Pglucuronidase gene complex are found in mouse strains A, B/ 6, and C3H. (The use of a haplotype nomenclature follows the recent recommendations of the Committee on Standardized Genetic Nomenclature for Mice. The application of this nomenclature to the /I-glucuronidase gene complex has been described by Paigen (23).) The [GuslA haplotype found in strain A includes the Gus-r" and Gus-sa alleles of the inducibility regulator and structural gene, the [GuslB haplotype found in strain B/6 includes the Gus&' and Gus-sb alleles of these loci, and the [GUS]" haplotype found in strain C3H

TABLE I Stability of P-glucuronidase mRNA activity in the presence and
absence of testosterone Twenty-four animals were induced with testosterone for 32 days. One-third of the animals were deinduced by removing the testosterone pellets. These, plus another third of the animals, were injected intraperitoneally with a-amanitin ( includes the Gus-rh and Gus-sh alleles. The regulatory and structural properties of the A and B haplotypes have been described (1,24,25). In the case of the [GusIH haplotype the properties of the Gus-sh structural allele have been reported (26, 2% but the properties of the Gus-rh allele of the inducibility regulator have not been reported previously and are described here for the first time. More extended descriptions are available of the genetics and biochemistry of the /?-glucuronidase gene complex in general (23,28) and P-glucuronidase induction in particular (2). Genetic Determination of mRNA Activity-During induction of strain A mice rates of P-glucuronidase synthesis and levels of P-glucuronidase mRNA activity are proportional to each other (Fig. 1). A difference in mRNA activity between fully induced Gus-r" and Gus-rb animals has also been previously described (3). Comparing the /?-glucuronidase mRNA activity levels from fully induced animals of strains A and B/ 6 ( Fig. 3) confirms that the rate of synthesis differences attributed to the a and b alleles of Gus-r reflect similar differences in P-glucuronidase mRNA activity. Unfortunately, P-glucuronidase mRNA levels from Gus-sh animals cannot be accurately determined with our existing oocyte assay. This is because Gus-sh codes for a heat-labile enzyme variant that is partially denatured under the conditions required to destroy frog /?-glucuronidase activity in the course of the messenger assay.

pg/animal). This was a lethal dose of a-amanitin that would have N e d the animals in 40-45 h. The animals in the last group (control) did not receive a-amanitin and continued to be fully induced since they retained their testosterone pellets. All animals were injected with C3H)1eucine 29 h after the time of a-amanitin injection. One h after injection
Kinetic Parameters of Gus-r Alleles-The kinetics of /?glucuronidase induction were compared in strains A, B/6, and C3H by assaying both enzyme activity and the relative rate of /?-glucuronidase synthesis. For comparative purposes measurements of the relative rate of enzyme synthesis are preferable to mRNA assays because the increased thermolability of enzyme coded by the Gus-sh structural allele present in C3H mice makes assay of their /?-glucuronidase mRNA different and because measurements of enzyme synthesis allow us to describe the earliest phases of enzyme induction. As Fig. 1 shows the relative rate of enzyme synthesis and the tissue content of /?-glucuronidase mRNA activity are directly related.
The data (Fig. 4 ) show that measurements of enzyme activity and enzyme synthesis gave similar, but not identical, curves. Enzyme activity did not accumulate to the same extent that enzyme synthesis increased for the reason already mentioned that testosterone also induces an increased rate of , L?glucuronidase excretion (19)(20)(21).
Comparing the rates of enzyme synthesis in the three strains (Fig. 4b) it is clear that the strains differed in 1) the length of the lag following testosterone administration, 2) the rate at which the rate of synthesis increased, and 3) the plateau level which the rate of synthesis eventually reached. A more detailed analysis of the lag for strains A and B/6 is shown in Fig.   5. The lag periods for strains A, B/6 and C3H were approxi-  mately-l,2, and 4 days, respectively.
After the lag period the kinetics of induction for all three strains are described by the basic equation for turnover kinetics (Equation 1). The plots of ( R , -R t ) / ( R , -Ro) for all three are shown in Fig. 2. The slopes of the lines fit by linear regression estimate kb; these are quite similar (Table 11). For each strain k, was estimated from the initial slope of each induction curve in Fig. 4b. The values of k, (Table 11) differ significantly for the three strains. Interestingly, the values for k, are inversely proportional to the length of the lag.
As already discussed, the eventual value of R can be predicted by utilizing the relationship R , = k,/kb and the estimates of k, and k b which are derived from measurements of the early part of the induction curve. The good agreement between the predicted and observed values for R, (Table 11) further c o n f i s the conclusion that k, and kb are true constants and do not change significantly throughout the induction period.
Because of their ready availability, it was most convenient to work with the original mouse strains in which the various [Gus] haplotypes were f i s t identified. p-Glucuronidase induction has also been studied in congenic mouse strains where the three [Gus] haplotypes have been transferred into a common genetic background. These experiments will be reported in detail elsewhere as part of a more extended study of congenic lines. They show that the kinetics of p-glucuronidase induction, as defied by changes in the rate of enzyme synthesis, are determined by the [Gus] complex itself and not by extraneous genetic differences between strains.
Thus, the Gus-r locus appears to determine the duration of the lag period and k,, but not kb. The differences between strains in the rate and extent of induction can be wholly attributed to the differences in k,. Furthermore, the duration of the lag appears to be inversely related to k,, suggesting that both parameters reflect the rate of a common process during induction.

DISCUSSION
Our results confirm previous findings (1) that induction of glucuronidase activity reflects the synthesis of new enzyme molecules rather than a change in the stability or activation of pre-existing enzyme molecules. They also confirm that the control of induction occurs primarily prior to translation and affects the amount of active glucuronidase mRNA available (3).
In these respects the androgen-mediated induction of pglucuronidase in mouse kidney epithelial cells is similar to other steroid mediated inductions (for list, see Ref. 29). What distinguishes p-glucuronidase induction from other systems is the surprisingly slow rate at which induction proceeds. There is a conspicuous lag period between the time hormone is administered and the time at which the rate of enzyme synthesis begins to increase, and once this increase begins induction does not reach a maximum for several weeks.
Lag Period-Our present results show that the long lag, which was previously noted in terms of accumulation of enzyme activity (l), is actually a delay in the onset of increased p-glucuronidase synthesis and is not simply a post-translational phenomenon. The lag lasts from 1-4 days, depending upon the Gus-r allele present, and ends rather abruptly. This

TABLE I1
Kinetic parameters of P-glucuronidase induction is much longer than the time required for entry of androgen into the nucleus since this has already reached its maximum at 30 min (30). It is also much longer than the lag for other androgen-inducible proteins in the same tissue (1). These facts suggest that the lag reflects some property of the P-glucuronidase gene itself. Enzyme Induction-In strain A the rate of enzyme synthesis increases 220-fold over the time course of induction; lesser increases are seen in the other strains. This is probably an underestimate of the true magnitude of induction since there is considerable cellular hypertrophy during this time and our estimates are all based on the relative rate of enzyme synthesis. /?-Glucuronidase protein accumulates to a lesser extent because an excretion mechanism for P-glucuronidase is also induced by androgen (19)(20)(21).
The combination of intracellular enzyme degradation and enzyme excretion results in an enzyme half-life of 1-2 days in induced cells. Because the capacity to synthesize P-glucuronidase accumulates slowly, the concentration of enzyme changes in concert with increases in the rate of enzyme synthesis and messenger activity. There is no significant damping of the enzyme response as there is in systems where the induced protein turns over slowly relative to the speed of induction.
Following the lag, the proportional increases in P-glucuronidase mRNA activity and the in vivo rate of enzyme synthesis during induction indicate that within the cell the availability of /?-glucuronidase mRNA is the rate-limiting factor in enzyme synthesis. The proportionality of these two measures, one estimated in vitro with extracted RNA and the other in vivo with intact mice, supports the validity of both sets of measurements. It also suggests that there is probably a lag before mRNA activity starts to rise that is comparable to the lag measured for P-glucuronidase synthesis. This has not been tested directly, however, because the basal level of mRNA activity is below the threshold for the assay.
Transcriptional Control-In principle, the increased p-glucuronidase activity present after induction could result from either increased transcription of the P-glucuronidase gene or to an increase in the fraction of primary transcripts that are correctly processed into functional mRNA. However, for induction to represent an increase in the probability of correct versus incorrect processing of primary transcripts to mature mRNA several factors must apply. First, the probability of correct maturation would have to be less than 0.005 in the basal state to &ow for a 200-fold or greater induction of Pglucuronidase synthesis. Second, androgen must induce a set of new and more efficient processing factors that are specific for induced transcripts. These would have a half-life of 8-9 days and would increase in activity during induction. Third, the function of these factors would require androgen since withdrawing testosterone immediately reduces the production of mature mRNA. And fourth, Gus-r, which is a cis-acting regulator, must determine the structure of ,@glucuronidase transcripts in a manner that influences the probability of correct versus incorrect processing for the induced processing enzymes but not the basal processing enzymes. It is unlikely that all of these are true. Additionally, these assumptions are difficult to reconcile with the fact that Gus-r also determines the duration of the lag period and that the duration of the lag is inversely related to k,. It is likely, therefore, that induction of p-glucuronidase represents an increase in the primary rate of transcription as it does in other steroid-inducible systems (29,31,32). The final test of this conclusion will be to measure rates of /?-glucuronidase gene transcription directly; unfortunately, this is technically not yet feasible in this system.
Induction of mRNA Synthesis Capacity-The accumula-tion of P-glucuronidase mRNA and enzyme synthesizing capacity follows simple turnover kinetics defined by k,, a zero order rate of acquisition, and kb, a first order rate of loss. The half-time for induction described by k b is rather long, being 8-9 days. This is much longer than the half-lives of either Pglucuronidase protein or its mRNA, both of which appear to be approximately 1-2 days and independent of the presence or absence of the inducer testosterone.
In a transition from one steady state to another the kinetics observed describe the properties of the most slowly turning over species in the chain of events. In essence, all of the parameters measured, mRNA activity, the rate of enzyme synthesis, and enzyme concentration, follow similar induction kinetics because the first component in the chain of processes turns over slowly and the subsequent components, mRNA and enzyme, turn over much faster. Because P-glucuronidase mRNA has a short half-life, changes in its concentration rapidly reflect changes in its rate of synthesis in the same manner that changes in /?-glucuronidase concentration rapidly reflect changes in the relative rate of enzyme synthesis. We are therefore left with the result that the time course of androgen induction of P-glucuronidase follows simple mass action kinetics and that measurements of enzyme induction kinetics made on intact mice appear to describe the formation and decay of something that is rate-limiting for /3-glucuronidase mRNA formation.
An important feature of the measurements on /?-glucuronidase induction is the fact that the half-lives of induction and deinduction are quite different. The 8-9-day half-life of the induced state, during the induction phase when testosterone is present, is much longer than the I-%day half-life of the induced state during the deinduction phase after testosterone removal. This means that the same process cannot be ratelimiting in both cases, or more exactly, that the material with a long half-life that accumulates following testosterone administration must decay with a very short half-life when testosterone is removed. Thus, an important function of testosterone in /?-glucuronidase induction is to stabilize and prevent the decay of a substance or complex that is rate-limiting in Pglucuronidase messenger synthesis.
Progressive Activation of Chromatin-A progressively increasing capacity to make p-glucuronidase mRNA could represent the continued entry of new cells into the inducing population or it could represent an increase in the synthetic capacity/cell in a f i e d population of responding cells. In separate experiments' the number of induced cells at various times during induction have been counted by dissociating the cells and then staining for P-glucuronidase activity. No change was found in the number of induced cells from the earliest times through to the plateau period, although the amount of enzyme/cell, judged from staining intensities, progressively increased. Since P-glucuronidase enzyme activity is closely correlated with mRNA activity, induction apparently represents an increasing level of P-glucuronidase mRNA activity/ cell and, by extension, per chromosome. It has also been shown that in kidney there is no increase in tot& cellular levels of androgen receptor protein during ind~ction.~ This indicates that the progressive induction of P-glucuronidase cannot be accounted for by an accumulation of androgen receptor protein such as might be expected if the synthesis or turnover of receptor protein were itself controlled by testosterone. Taken together these facts imply that, if induction is controlled at the level of transcription, the P-glucuronidase structural gene is not simply switched from a low activity ' A. Jakubowski and K. Paigen, unpublished data. .' K. Paigen and J. Peterson, unpublished data. state to a high activity state but is activated through progressively increasing rates of transcription.
Function of the Gus-r Locus-The Gus-r regulatory locus acts cis to control the rate and extent of induction of the adjacent P-glucuronidase structural gene (1,2). Regulation by Gus-r alleles is limited to induced P-glucuronidase synthesis and is expressed by controlling the extent to which /?-glucuronidase mRNA production from the same chromosome can be stimulated by androgen. It now appears that Gus-r acts by determining the duration of the lag period and k,, the apparent rate of chromatin activation; however, Gus-r does not determine k b (Table 11) nor does it significantly affect the rate of deinduction (data not shown). The genetic differences in lag period and k , are related, the duration of the lag period being inversely proportional to k,. From examination, this also appears to be true when k , is altered metabolically by using a different inducing steroid (33).
Variation in the lag and k, entirely account for the phenotypic effects of mutation at Gus-r. Additionally, the similar expression of Gus-r alleles in their strains of origin and after transfer into the C57BL/6 genetic background suggests that there are no other significant genetic differences between these strains that affect induction of /?-glucuronidase synthesis.
Molecular Basis of Gus-r Function-Present concepts of steroid hormone action suggest binding of the steroid to a cytoplasmic receptor, translocation of the complex into the nucleus, and stoichiometric binding of receptor at specific chromatin sites to activate genetic transcription. However, as stated, these ideas are not sufficient to account for our present results without making some additional assumptions. Similar difficulties with other systems have been pointed out by Yamamoto and Alberts (34). We would like to point out that these issues would be resolved if a specific region of chromatin is capable of reacting with many molecules of receptor protein according to the following rules.
1. The chromatin surrounding the /?-glucuronidase gene can react with or sequester many molecules of androgen receptor protein.
2. The kinetics of induction describe the progressive attachment and release of androgen receptor protein molecules with /?-glucuronidase chromatin.
3. A minimum number of androgen receptor protein molecules must be associated with P-glucuronidase chromatin before the rate of transcription increases. The time required for this to come about is the lag period.
4. The subsequent rate of /?-glucuronidase gene transcription is a linear function of the number of additional molecules of androgen receptor protein bound. 5. The Gus-r locus determines either the spatial accessibility or chemical affinity of androgen receptor complex to its binding sites. As a consequence, Gus-r determines both k , and the duration of the lag period, and the two parameters are inversely related.
In the absence of any evidence to the contrary we have assumed that the genetic activator molecule is the anhogen receptor protein itself. The argument would be little changed if some other molecule performed the same function.
These assumptions provide a relatively simple and coherent explanation of our observations. However, they do include two novel assumptions. One is that a gene can react with many molecules of androgen receptor protein, and the second is that gene activation is progressive. That is, a locus can react with many molecules of a regulatory protein to reach increasingly higher rates of activity.
At this time these ideas are purely speculative, but they do provide an explanation for the very large number of nuclear binding sites for steroid receptors that are characteristically observed, and they may prove useful in suggesting interesting lines of experimentation.