Thermodynamics of the Interaction of Insulin with Its Receptor*

Insulin binding to its cellular receptors is markedly dependent on the temperature. The thermodynamic parameters for the reaction of insulin with the high affinity state of its receptor have been evaluated with equilibrium studies at multiple temperatures between 5 degrees and 37 degrees C. The thermodynamics of the insulin-receptor interaction is not classical. The van't Hoff plot is not linear. Both the enthalpy and entropy changes, due to the formation of the hormone . receptor complex, decrease markedly with temperature, corresponding to a large heat capacity change of -766 cal/(mol deg) at 25 degrees C. The reaction is endothermic and entropically driven at low temperature and exothermic and enthalpically driven at higher temperature. This thermodynamic behavior is suggestive of a hydrophobic reaction and supports Blundell's concept that the loss of non-polar surface residues in the formation of the hormone . receptor complex is an important driving force of the reaction. Alternatively, this nonclassical behavior may indicate that the reaction of insulin with its receptor involves more than one step.


Insulin
binding to its cellular receptors is markedly dependent on the temperature. The thermodynamic parameters for the reaction of insulin with the high affinity state of its receptor have been evaluated from equilibrium studies at multiple temperatures between 5" and 37°C. The thermodynamics of the insulin-receptor interaction is not classical. The van't Hoff plot is not linear. Both the enthalpy and entropy changes, due to the formation of the hormone*receptor complex, decrease markedly with temperature, corresponding to a large heat capacity change of -766 cal/(mol deg) at 25°C. The reaction is endothermic and entropically driven at low temperature and exothermic and enthalpically driven at higher temperature. This thermodynamic behavior is suggestive of a hydrophobic reaction and supports Blundell's concept that the loss of nonpolar surface residues in the formation of the hormoneareceptor complex is an important driving force of the reaction.
Alternatively, this nonclassical behavior may indicate that the reaction of insulin with its receptor involves more than one step.
An increasing body of information has been gathered over the last few years on the nature of the reaction of insulin with its receptors in the membrane of target cells (l-5).
In particular, parallel studies of x-ray diffraction, circular dichroi'sm, biological potency, and receptor binding of a variety of native and chemically modified insulins have allowed the mapping of the presumed receptor-binding region on the surface of the insulin monomer (6)(7)(8)(9)(10)(11)(12) that is responsible for inducing the biological activity of the hormone ("bioactive site"), as well as a discrete surface region responsible for inducing the negatively cooperative interactions among the receptor sites (13,14). Blundell and coworkers have suggested (12,15) that the so-called "hydrophobic reaction" (16) plays an important role in the reaction with its receptor of insulin and other polypeptide hormones like glucagon.
Indeed, the insulin monomer appears to be folded around an inside core of buried hydrophobic residues, but there are also two patches of clustered hydrophobic residues on the surface of the monomer. The first hydrophobic domain is part of the putative receptor-binding region, constitutes most of In the present work, we have attempted such a thermodynamic analysis for the reaction of insulin with its receptor on cultured human lymphocytes.
Such a detailed analysis has not previously been performed for the reaction of a polypeptide with its receptor.

MATERIALS AND METHODS
Insulin-Crystalline porcine insulin was purchased from Elanco. Carrier-free Na'*"I was bought from Amersham. Insulin was iodinated with "'1 at a specific activity of 200 to 250 &!i/pg by a modification of the chloramine-T method as previously described (20,21 12"I-Insulin (6.7 x 10-l' M) was incubated with human cultured lymphocytes (IM 9) at a concentration of 5 x lo7 cells/ml for 30 min at 15°C and pH 7.6 in a total volume of 15 ml. The cells were then sedimented at 4°C. The supernatant was discarded and replaced by an equal aliquot of chilled (4'C) fresh medium, the cells were resuspended, an aliquot (100 ~1) was removed for measurement of bound radioactive hormone ("time zero"), and aliquots were transferred to ten series of tubes that contained 10 ml of medium at 15°C (IOO-fold dilution) to initiate dissociation.
One of the series of tubes contained medium only, a second series 1.7 x 10m7 M unlabeled insulin. In the eight other series of tubes, the addition of unlabeled insulin was delayed, respectively, by 1 to 8 h from the time of initiation of dissociation.
At intervals, a tube of each set was centrifuged, and the radioactivity in the cell pellet was counted. The radioactivity on the cells, expressed as a percentage of the radioactivity present at time zero, is plotted as a function of the time elapsed after the dilution of the system. zero. This was true for all the concentrations of unlabeled insulin used to define the "standard curve" submitted to equilibrium analysis. Second, we studied the dissociation kinetics of the insulin.receptor complex under two conditions: (a) in an "infinite dilution" (lO@fold) of the complex in buffer, a condition in which the tracer dissociates slowly, reflecting the kinetics of the high affinity state of the receptor, and (b) in a IOO-fold dilution of the complex in buffer containing an excess of unlabeled insulin, a condition in which the tracer dissociates much faster, reflecting the kinetics of the insulin-induced low affinity state of the receptor (3,4). We demonstrated that the addition of unlabeled insulin to the dissociating buffer could be delayed up to 8 h after the initiation of dissociation without loss of the fast reversal induced by insulin (Fig. 3).
In these conditions, we feel entitled to apply thermodynamic analysis to this ligand-receptor interaction with a reasonable chance of being close to a thermodynamic equilibrium. With the Temperature-The binding of insulin depends markedly on the pH, with a sharp optimum. Thus, to interpret the effects of the temperature on binding in terms of hydrophobic contributions, we should take into account the effect of temperature on the pH dependence of the binding, since the groups involved may also have significant enthalpies of ionization. This factor has often been neglected in thermodynamic analyses. We found indeed that the pH optimum of insulin binding varies markedly with the temperature.
We thus measured the binding at the pH optimum corresponding to each temperature (pH 8.2 at 5"C, 8.1 at lO"C, 8.0 at 15"C, 7.9 at 2O"C, 7.8 at 25"C, 7.7 at 3O"C, 7.6 at 37°C) and corrected the data to take into account the ionization constants. The method used for this correction is detailed in another paper' describing a theoretical analysis of the pH dependence of the insulin receptor and only briefly summarized here. We assumed, adapting the generalized pH theory of Reiner (26) to receptor binding, that binding is optimal when certain groups of the insulin and the receptor are protonated, whereas other groups must be deprotonated.
If one assumes that only the moieties in the correct ionization state can bind, one can derive an equation giving the "true" affinity constant (a,,.) of the insulin. receptor complex as a function of the pH, the number, and pKs of the groups whose state of ionization matters.
By computer curve fitting, one can derive the number of groups involved, their pK values, and the enthalpies of ionization of the groups involved.
In the case of insulin, only one group was found to be involved on each side of the pH optimum, and the equation simplifies to (Equation  1): 1% t,,, where Z?e is the apparent t measured at a given pH, &tme is the affinity of the insulin.receptor complex when both the insulin and the receptor are in the correct ionic state, pK1 is the pK (= -log Kionimation) of the group which must be deprotonated for binding, and pK2 is the pK of the group which must be protonated for binding.

Equilibrium
Constant and Free Energy Change--The equilibrium constant for the association reaction in the high affinity state, &., varies markedly with temperature.
A van't Hoff plot of the data (Fig. 4) is curvilinear with a maximum around 20°C for the corrected data. The standard free energy change is AGO = -RT In I?e (Equation 2) where R is the gas constant and T the absolute temperature.
A plot of AGO against the temperature (Fig. 5) also shows a marked curvilinearity with a maximum at 37°C. The enthalpy change, AH', is usually determined from the slope of the van't Hoff plot at various temperatures, but this procedure would give inexact values in this case because of the curvature of the plot. Therefore, we used the same procedure as Osborne et al. (18) and performed a regression analysis of the free energy change by using Equation 3: The best fit analysis of the experimental data is represented by the solid line in Fig where AS0 is the entropy change of the reaction. ACp", the heat capacity change, can also be derived ACp" = 6AH0/6T = -2.57 T As shown in Fig. 6, the changes in both enthalpy and entropy for the insulin-receptor association decrease continuously and within the limits studied vary quasi-linearly with temperature.
The thermodynamic stability of the complex (MG'/GT = -AS0 = 0) is maximum at 37°C. The change in heat capacity, that is the slope of the AH0 curve, is negative, indicating that the heat capacity for the separated insulin and receptor molecules is greater than in the hormone.receptor complex. Although the plot of AH0 against temperature appears linear within the experimental errors and the range of temperatures studied, it is represented by a second degree equation (Equation 5), and its first derivative, ACp', also varies with temperature (Fig. 3). The absolute value of the variation is, however, a second derivative of the initial data plot and thus relatively imprecise.
The value of ACp' is traditionally expressed at 25°C and is in this case -766 cal/(mol deg). Fig. 7 presents a complete analysis of the driving forces in the formation of the insulin. receptor complex in the case where the effect of temperature on ionization is "eliminated" by appropriate correction.

DISCUSSION
The characteristics of the thermodynamic parameters of the association of insulin to its receptor are strikingly similar to those of other types of interactions determined by so-called hydrophobic effects (17)(18)(19). Our results are remarkably comparable to those obtained by Osborne et al. in a thermodynamic study of the self association of the reduced and carboxymethylated form of apoA-II protein from the human high density lipoprotein complex (18). That reaction showed a similar shape in the temperature dependence of the free energy change, with a maximum near 28°C (37'C in the case of insulin), the same inverse relationship between AH0 or AS0 and the temperature, and a quite comparable change in heat capacity between the unassociated and associated molecules -1250 cal/(mol deg) uersus -766 in our case.
Similarly, analysis of the free energy change of association of glutamic dehydrogenase between 10 and 40°C showed a linear dependence of the enthalpy on temperature with posi-tive values below 28'C and negative values above 28°C and a heat capacity change of -600 cal/(mol deg). Many similar findings are listed in Ref. 17. This type of behavior is typical of the interactions with water on the nonpolar moieties of a variety of compounds such as acids, bases, alcohols, amino acids, and surfactants and contrasts with the interactions of polar moieties with water (17). This "hydrophobic effect" and its consequences on the thermodynamics of various model systems has been lucidly analyzed by Edelhoch et al. (17) and understanding its basis may prove crucial in many hormone-receptor interactions.
The most useful thermodynamic parameter that expresses the interaction of various groups with water is the heat capacity change (17)(18)(19). From the large negative heat capacity change observed in our study, it appears that the insulinreceptor interaction is critically dependent on the properties of water. Since ionic and polar groups interact strongly with water, a large part of the driving force in the insulin-receptor interaction is probably contributed by the removal of water from the less polar moieties (probably surface residues of both proteins) and the resultant changes in the cooperative organization of the hydrogen binding between water molecules.
Using Tanford's estimates for the heat capacity associated with the exposure of various nonpolar groups (27), we have calculated the theoretical contribution of the nonpolar residues in the putative receptor-binding regions of insulin (12), assuming that they change from totally exposed in the medium to completely buried in the hormone-receptor complex (AN Tyr, IL Phe, I%:, Phe, BZG Tyr, BH Val, 3316 Tyr).
It amounts to -460 cal/(mol deg). Thus, insulin may contribute more than half of the heat capacity change of the reaction as determined in our study, (-766 cal/(mol deg)), and burying hydrophobic residues from the receptor or membrane site must contribute the other half. However, more precise calculations must be done, taking in account the accessibility of each group and the hydrophobic contribution from polar groups. This quantification will need further studies.
These data strongly support Blundell's concept that hydrophobic forces play an important role in the interaction of polypeptide hormones with their receptors. They are also in line with the general principles of protein-protein recognition proposed by Chothia and Janin (28), whereby hydrophobicity is the major factor which stabilizes protein-protein association while van der Waals and polar interactions determine which proteins may recognize each other since the proper formation of hydrogen bonds and of van der Waals contacts requires complementarity of the surfaces involved. Similar data were recently reported in the interaction of steroids with their cytoplasmic receptors (29).
This interpretation of our data must, however, be taken with caution since it is based on the critical assumption that the reaction of insulin with the initial state of its receptor is a simple, one-step reaction, H + Re + HRe, with a simple high affinity equilibrium constant = if,. An alternative explanation of our data would be that the reaction involves more than one step, for example H + Re + HRe = HR'e, or that there is another coupled reaction. Even if the thermodynamics of each step was classical (i.e. linear van't Hoff plot), the resulting steady state may yield curvilinear van't Hoff plots even in the absence of hydrophobic effects. The fact that the kinetics of dissociation of many receptors is not fist order could certainly suggest that such an explanation is plausible. This restriction is not unique to our case but could be valid also in other systems, like protein denaturation