A calorimetric investigation of the interaction of the lac repressor with inducer.

A calorimetric study has been made of the interaction between the lac repressor and isopropyl-1-thio-beta-D-galactopyranoside (IPTG). The buffer-corrected enthalpy of reaction at 25 degrees C was found to be -15.6, -24.7, -4.6 kJ/mol of bound IPTG at pH 7.0, pH 8.1, and pH 9.0, respectively. This large range of enthalpy values is in contrast to a maximum difference in the free energy of the reaction of only 1.5 kJ/mol of bound IPTG between these pH values. The reaction was found by calorimetric measurements in different buffers to be accompanied by an uptake of 0.29 mol of protons/mol of bound IPTG at pH 8.1. The pH dependency of the reaction enthalpy suggests differences in the extent of protonation of the binding site and the involvement of H bonding with IPTG. The lack of strong hydrophobic contributions in the IPTG binding process is revealed by the absence of any determinable heat capacity change for the reaction at pH 7.0. The presence of phosphate buffer significantly alters the enthalpy of IPTG binding at higher pH values, but has little effect upon the binding constant. This implies that highly negative phosphate species change the nature of the IPTG binding site without any displacement of phosphate upon IPTG binding.

The Escherichia coli lactose operon is under negative control of the lac repressor protein which binds specifically to the operator portion of the E. coli genome. In vivo, the interaction between the repressor protein and the operator is modulated by an inducer, allolactose . A number of kinetic and equilibrium physical chemical methods has been applied in vitro to determine the binding constants for the interaction of various synthetic inducers with the repressor protein as well as the number of binding sites for these inducers on the repressor which is a tetrameric protein (for recent reviews, see Barkley andBourgeois, 1978, andvon Hippel, 1979). The effect of temperature, pH, ionic strength, operator DNA, and DNA free of operator on these parameters have also been studied. The interaction of the most extensively used synthetic inducer, IPTG', with the repressor protein is characterized by a dissociation constant in the order of M, the exact value being somewhat dependent on pH, ionic strength, and temperature.
* This work was supported by Grant 5 R01 GM25889-03 from the National Institute 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 "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact. The abbreviation used is: IPTG, isopropyl-I-thio-P-D-galactopyranoside.
The action of the inducer was imagined to cause an increase in the population of the conformation of the repressor protein which does not bind to the operator region. This allosteric mechanism in its simplest form has a necessary consequence of cooperative inducer binding, yet no such cooperativity had been clearly observed in IPTG binding studies of the repressor in the absence of operator.
This situation has been clarified by O'Gorman et al. (1980) who found signs of positive cooperativity for the binding of IPTG to the repressor protein in the presence of a 29-base pair operator DNA fragment using fluorescence spectroscopy to determine the extent of IPTG binding at pH 7.5. Assuming that the repressor tetramer has two binding sites for the operator and four for IPTG, they could fit their data to the Monod-Wyman-Changeux model (Monod et aL, 1965). However, in the absence of the operator fragment, no cooperativity is observed. The presence of the operator is required to cause a shift in the repressor population to the T form which has a lower affinity for IPTG. The presence of IPTG with its higher affinity to the R form gives rise to an increase in the amount of R form repressor and gives rise to the observation of positive cooperativity.
In view of the general importance of this regulatory protein, we were interested in gaining further thermodynamic information to aid in the interpretation of the nature of the interaction between IPTG and the repressor protein. The free energy of IPTG binding is obtainable from the binding studies mentioned above. By measuring the heat of reaction, the change of the entropy of the IPTG binding reaction can be assessed, and the relative importance of enthalpy and entropy contributions to the free energy can then be delineated. Extending the heats of reaction studies to various temperatures, the heat capacity change can be evaluated. These thermodynamic parameters might reflect any unusual energetic or hydrophobic features of the IPTG binding to the repressor protein. Heat of reaction determined under different pH conditions could also reveal the importance of protons in the binding process. Although reasonable quantities of repressor can be obtained for selected calorimetric studies, sufficient amounts of operator fragments are not yet available for our purposes. Consequently, our initial efforts have been limited to IPTG binding to repressor in the absence of operator. We have made use of a recently developed titrating calorimeter designed for the use of nanomolar amounts of reactants (Spokane and Gill, 1981) which are compatible with the quantity of repressor that is available with reasonable purification efforts. Further minaturization of calorimetric techniques along with enhanced production of operator fragments should allow extension of the present investigations.

MATERIALS AND METHODS
Chemicals-Diisopropyl fluorophosphate, IPTG, and tetracycline hydrochloride were bought from Sigma. "C-labeled IPTG was ob-  (Hare and Sadler, 1978) was used as the repressor source (the gift of these cells from Drs. J. L. Bets and J. R. Sadler is gratefully acknowledged).
The cells were grown in SLBH broth as described by Betz and Sadler (1976) with tetracycline at a concentration of 10 mg/liter until the A525 = 10. The cells were then harvested and stored at -70 "C until the repressor was to be extracted. We employed the method of Rosenberg et al. (1977) for the extraction and purification of the Zuc repressor from these cells. These cumulative heats are designated by QO and once determined may be subtracted from QM to isolate the heat of reaction.
A simple graphical estimate of the stoichiometry of the reaction can be obtained by extrapolating the ends of a plot ( Fig. 2) of the cumulative Q.+r as a function of the ratio between the concentration of IPTG and repressor subunits after each injection (see below). For the experiments described in this paper, the stoichiometry determined graphically was found to be 1 mol of IPTG/mol of repressor subunit. In order to determine the enthalpy change/m01 of reaction, AH", and the dissociation constant, Ks, for the binding of IPTG to the lac repressor, a nonlinear least square fit using the Marquardt algorithm (Marquardt, 1963) was employed. As outlined above, QM=QE+QD (3) and QR is a function of KD and AH" (see below), so the KD, AH", and Qb that give the best fit to the experimental Q.+, values are looked for. Since Qn is dominated by factors other than the true dilution heat, it is assumed to have the same value during a given series of injections. The heat of reaction after the ith injection, QRi, is QRi = (8, -e,-,)n&i!z" (4) where 4 is the fraction of repressor binding sites occupied by IPTG after the ith injection and ni is the total amount of repressor binding sites after the ith injection. 0, depends on FIG Table I presents the results of this data fitting procedure as applied to heat values from experiments conducted at different pH values and in the presence of different buffer ions. The standard error of the difference between the measured injection heat values and those derived from the use of the best fit parameters is in all cases within a factor of two of the standard error of the calorimetric base-line fluctuations. Thus, the simple identical site model is found to be consistent with the precision of our data.
Two things are noteworthy in Table I. First, at pH 7.0 and 9.0, the AH" for the reaction is insensitive to the presence of either Tris or bis-tris. That means that neither of these two buffer ions interact with the repressor or, if they do, there is no change in the interaction when IPTG is bound. It also suggests that there is no change in protonation upon IPTG binding as is also implied by the lack of pH dependence of KD   a This value was taken from the bis-tris experiment at the same pH and fiied in the fitting procedure described under "Results and Discussion" so as to get the best fit. at these pH values from the results of O'Gorman et al. (1980). At the intermediate pH 8.1, however, there is a difference between the A H o values of 5.6 kJ/mol when Tris or bis-tris is used. Since the heat of proton dissociation of bis-tris is 28.2 kJ/mol (Paabo and Bates, 1970) and of Tris is 47.6 kJ/mol (Christensen et al., 1968) at 25 "C, this difference can be explained by an uptake of 0.29 mol of protons/mol of bound IPTG. This gives a buffer corrected AH" = -24.7 kJ/mol of bound IPTG at pH 8.1. Butler et al. (1977) found at pH 7.6 that AH" = -25.9 kJ/mol, a value derived from a van't Hoff plot using the AGO values at 4 and 25 "C. The expected value should be the sum of the heat of protonation of basic groups in the repressor and an intrinsic IPTG binding heat value of -10 kJ/mol (the average AH" values for the binding of IPTG in the presence of bis-tris and Tris at pH 7.0 and 9.0, where linked protonation is absent). Thus, the heat of IPTG-linked protonation of basic groups in the repressor would be approximately -15 kJ/mol of IPTG bound, i e . -45 kJ/mol of protons. This value agrees with heats of protonation of the side chains of free lysine and arginine (Christensen et al., 1976).
In order to examine the importance of contributing thermodynamic factors into the energetics of IPTG binding, we utilized the enthalpy of reaction values in conjunction with the equilibrium constant determinations. From the average of values of KD for the T r i s and bis-tris experiments, the free energy change, AGO, for the binding of IPTG to the repressor binding sites is -30.8 kJ/mol at pH 7.0 and -29.3 kJ/mol at pH 9.0 with a standard state of 1 M. The associated change in entropy, AS", using AS" = ( A H " -AG")/T, is 51.0 J/K.mol at pH 7.0 and 82.9 J/K. mol at pH 9.0. If AS" is based on mole fractions instead of moles/liter, the sign changes so that the value becomes -2.76 kJ/K at pH 7.0 and -0.72 kJ/K at pH 9.0. These results suggest that the binding of IPTG at these pH values involves little hydrophobic interaction. This is confirmed more directly by the lack of significant AC," from measurements of AH" = -14.1 kJ/mol at 14.95 "C in Tris at pH 7.0.
The deceitful lack of major difference between AGO for the binding of IPTG at pH 7.0 and 9.0 agrees well with values found in the earlier literature (Barkley and Bourgeois, 1978).
It is contrasted by the strikingly large differences found for AH" values at these pH values. Thus, despite the similar AGO values, the intrinsic binding site for IPTG on the repressor must be quite different at pH 7.0 and 9.0, most likely due to differences in the extent of protonation of the binding site at the two pH values. Presumably at the low pH value (7.0), the protonated site interacts with H bond formation to IPTG to give a significantly more exothermic reaction.
The calorimetric results obtained in the presence of phosphate buffer (Table I) indicate that a complex role is played by this buffer in its effect upon IPTG binding. Curiously, no significant effect was found upon the binding constant at all pH values studied. Even at 0.5 M potassium phosphate (pH 7.0), no noticeable effect was observed on KD. However, at pH 8.1 where AH" = -16.1 kJ/mol of IPTG in phosphate buffer, compared to buffer-corrected heat (Tris and bis-tris) of -25 kJ/mol of IPTG, the presence of phosphate contributes nearly +9 kJ to the IPTG binding process. Moreover, at pH 9.0 where a surprising value of -32 kJ/mol of IPTG in the presence of phosphate was found in comparison with -5 kJ/ mol of IPTG in Tris and bis-tris buffers, the presence of phosphate contributes nearly -27 kJ to the binding enthalpy, when compared to tris buffer. These facts suggest that the phosphate significantly alters the IPTG binding site in SO far as the enthalpy and entropy change of the reaction are concerned but leaves the free energy change of IPTG binding unaffected. Furthermore, the bound phosphate must not be displaced upon IPTG binding under the solution conditions employed since the phosphate effect on KD is negligible. The large enthalpy effects at high pH suggests that highly negatively charged phosphate species are involved in modifying the nature of the IPTG binding site.
Overall, these results show that IPTG binding to repressor in the absence of operator is characterized by a reaction to identical equivalent sites without any implication of allosteric transition involved in the process. The energetics of the binding process suggests the absence of hydrophobic interactions and the likely presence of nonionic hydrogen bonding effects.