A pH-Dependent Model of the ActivationMechanism of the Histamine H2 Receptor

Jesus Giraldo*LABORATORIO DE MEDICINA COMPUTACIONAL, UNIDAD DE BIOESTADıSTICA, FACULTAD DE MEDICINA,

UNIVERSIDAD AUTONOMA DE BARCELONA, 08193 BELLATERRA, BARCELONA, SPAIN

ABSTRACT. A pH-dependent model of agonist action for the histamine H2 receptor was developed by takinginto account the different ionic states of the amino acid residues that constitute the agonist-binding pocket ofthe receptor. The model offers the possibility of examining diverse mechanistic pathways to yield the active formof the receptor according to the molecular structure of the ligand. The rationale is valid for either tautomericor non-tautomeric agonists and provides new insight into the mechanism of receptor activation. The subsequentapplication of the operational model of agonism allows one to derive agonist concentration–effect relationshipsthat may prove useful for both the simulation of agonist profiles under different physiological conditions and theestimation of the pharmacologic parameters of efficacy and potency. General principles involved in theformulation are expected to be valid for other G-protein-coupled receptors. BIOCHEM PHARMACOL 58;2:343–353, 1999. © 1999 Elsevier Science Inc.

KEY WORDS. Histamine H2 receptor; receptor activation mechanism; operational model of agonism; efficacy;potency; pH

There are two general approaches for understanding howpharmacologic receptors translate extracellular data embodiedin the chemical structure of agonists into intracellular infor-mation: selection or induction of receptor-active states [1–4].The first approach, in its simplest form, assumes that receptorsexist in two non-interconvertible states, one inactive (R) andthe other active (R*). Those ligands that are able to discrim-inate between these forms by binding preferentially to theactive state are denoted agonists, whereas those that do notdistinguish between them are designated antagonists. Thesecond approach focuses on the molecular processes bywhich an inactive receptor is transformed into an activeone. In this approach, both agonists and antagonists havethe ability to bind to the inactive receptor (receptorrecognition), but only agonists can promote the generationof the active state by inducing a chemical alteration on thebound receptor (receptor activation).

GPCR† form one of the major cellular mechanisms ofsignal transduction [5–7]. The inherent intricacy of theregulation mechanisms of biological information associated

with GPCR makes it necessary to increase the complexityof pharmacologic models. A ternary complex model wasinitially suggested to explain agonist binding to the b-ad-renergic receptor [1]. This model is composed of two bindingsteps: the binding of the agonist to the receptor (AR),followed by the binding of the G-protein to this binaryagonist–receptor complex to form a ternary complex (ARG).The ternary complex model posits the existence of tworeceptor states, one of low and the other of high affinity, withthe latter involving the binding of the G-protein. Moreover,the possibility exists of receptor binding to G-protein in theabsence of agonist (RG). The ternary complex model hadproved instrumental in reproducing marked GPCR pharma-cological activity until the constitutively active mutant recep-tors appeared [8]. A distinctive feature of constitutively activemutant receptors, i.e. their higher affinity for agonists but notfor antagonists when compared with their native forms,cannot be accommodated within the framework of the ternarycomplex model. Moreover, the observed correlation betweenthe increased affinity of a ligand for a constitutively activemutant receptor relative to the wild-type receptor and theintrinsic efficacy of the ligand cannot be adequately rational-ized by the ternary complex model [8]. However, the explicitinclusion of a receptor isomerization step in an active stateprevious to G-protein coupling (the allosteric ternarycomplex model) [8, 9] has been shown to be an effectivecondition capable of accounting for constitutively activereceptors and the ensuing behavior of inverse agonists [10].

Recently, additional progress in pharmacologic modelinghas been made. Weiss et al. [11] completed the allostericternary complex model by allowing the G-protein to bind

* Corresponding author: Dr. J. Giraldo, Laboratorio de Medicina Com-putacional, Unidad de Bioestadıstica, Facultad de Medicina, UniversidadAutonoma de Barcelona, 08193 Bellaterra, Barcelona, Spain. Tel. (3493)581 23 48; FAX (3493) 581 23 44; E-mail: jgiraldo@servet.uab.es

† Abbreviations: GPCR, G-protein-coupled receptors; HA, histamine;TA, 5-(2-aminoethyl)4-methylthiazole, KL, ligand–receptor binding con-stant; KT, occupancy–response transducer constant; [R0], total receptorconcentration; Em, maximum possible effect; K1, first proton transferreaction constant; K2, second proton transfer reaction constant; KLR,ternary ligand-activated receptor–G-protein complex binding constant;and E/[L], agonist concentration effect.

Received 4 June 1998; accepted 12 January 1999.

Biochemical Pharmacology, Vol. 58, pp. 343–353, 1999. ISSN 0006-2952/99/$–see front matter© 1999 Elsevier Science Inc. All rights reserved. PII S0006-2952(99)00100-8

the inactive receptor (the cubic ternary complex model).Leff et al. [12] derived a three-state receptor model byincluding one inactive and two active receptor states,whereas a complementary model considering m inactiveand one active receptor states was developed by Pardo et al.[13]. A final point worth mentioning in this regard is thatthe foregoing models are all operational inasmuch as nospecific molecular mechanisms are proposed for the pro-cesses of ligand recognition and receptor activation. How-ever, there are situations in which the inclusion of molec-ular structure-related variables in the mathematical model-ing may provide new strategies for a better understanding ofthe mechanisms of drug action. Within this scope, weaimed to explore in this paper different mechanistic routesfor the activation of the histamine H2 receptor with theultimate goal that the general principles involved might beapplicable to a wide variety of other GPCR.

The histamine H2 receptor is one of the best character-ized GPCR both experimentally and theoretically. Struc-ture–activity relationships [14 and references therein], site-directed mutagenesis [15], and theoretical studies [16–27]have made it possible to characterize the molecular deter-minants of the ligands and the receptor associated withagonism and antagonism. On the basis of quantum chem-ical calculations on the HA molecule, the natural agonist,a mechanistic model of action (induction approach), wasproposed [16, 17]. The model assumes that HA comes intothe receptor as the N(3)-H tautomer (teleposition relativeto the side chain) of the monocationic form, the mostabundant species at the physiological pH of 7.4. Theinteraction of the HA cationic side chain with a putativenegative region of the receptor (site I) causes an electroncharge redistribution of the imidazole ring, which shifts thetautomeric stability towards N(1)-H (proximal positionrelative to the side chain). As the authors suggested, a protonacceptor group (site II), matching the imidazole N(3)-Hmoiety, and a proton donor group (site III), matching theimidazole N(1) nitrogen, would allow, in principle, the HAN(3)-H tautomer to be converted into N(1)-H, the energet-ically most stable form in the agonist-binding pocket. Theprocess involves two proton transfers, the first from site IIIto HA N(1) to give the imidazolium cation and the secondfrom N(3)-H to site II to give the N(1)-H tautomer.

The elucidation of the amino acid sequence of the HAH2 receptor [28] permitted the investigation of the residuesresponsible for pharmacologic action. Comparison withother known GPCR and mutational studies [15] identifiedAsp98 in the third transmembrane domain as the counterion for positively charged side chain amines (site I in theaforementioned receptor model). In addition, a non-con-served Asp186 in the fifth helix was found to be related toboth ligand recognition and receptor activation. Mutationsof Asp186 to Ala186 or Asn186 resulted in a complete loss ofbinding of the [methyl-3H]tiotidine antagonist and a de-crease in the HA maximum response to 35% of thatobserved with the wild-type receptor. The authors proposedAsp186 as the residue corresponding to supposed site II [15].

The same authors also suggested Thr190 as the proton donorresidue (site III). Ala190 mutants retained the ability totransduce the HA signal, but the maximum physiologicresponse was 50% of that observed with the wild-typereceptor. Based on receptor sequence comparisons [29] andquantum-chemical calculations, Arg257 in the sixth helixwas recently identified as the putative site III [30].

Concurrently with these findings, a new H2 receptor acti-vation model appeared to justify the agonistic activity of somenon-tautomeric thiazoles [31]. These compounds, which be-have as full agonists, are structurally capable of accepting aproton from a receptor site but not of donating a proton to aproton-accepting site of the receptor. Consequently, the re-quirement of the second proton transfer proposed in theoriginal activation mechanism [16] was questioned [31]. Thisobjection joined some others concerning the necessity ofligand tautomerism to activate the HA H2 receptor [14, 32,33]. Alternatively, the authors suggested a mechanistic modelin which the aromatic ring of the agonist, after anchoring thepositively charged side chain onto receptor site I, is protonatedby a proton transfer from the proton-donating site III of thereceptor. The resulting positive charge, which spreads over thering atoms according to the probability of the differentmesomeric forms, yields a pure electrostatic interaction be-tween a partially positively charged atom of the ligand ringand a negatively charged residue of the receptor (site II). Thiselectrostatic interaction, which is structurally likely for eithertautomeric or non-tautomeric ligands, becomes one of thedeterminants of the receptor activation model [31] and appar-ently renders unnecessary the suggested early proton trans-fer between the protonated ligand and the receptor site IIfor the understanding of the mechanism. More recently, inorder to justify the activity of the histamine H2 receptorafter Thr1903Ala190 mutation, the same authors suggesteda tyrosine residue (Tyr182) as the proton donor site [26, 27].

In the present paper, we aimed to show that the two currentmechanistic models of HA H2 receptor activation [16, 31] arecompatible if the amino acid residues which constitute therecognition center of the receptor (sites I, II, and III) arepresent in different acid–base conjugate forms. This assump-tion leads to a dynamic pharmacologic system comprisingan ensemble of various ligand, receptor, and ligand–recep-tor ionic populations whose relative proportions are gov-erned by a set of equilibrium constants. The rationale of theallosteric ternary complex model [8, 9] admits the inclusionof the aforementioned mechanistic hypothesis for theagonist-induced receptor isomerization step (receptor acti-vation). Quantitative pharmacologic relationships are de-rived by applying the operational model of agonism [34].

MATERIALS AND METHODSThe Operational Model of Agonism

The operational model of agonism was developed to pro-vide an explicit description of agonist action [34]. Thismodel furnishes an agonist concentration–effect, E/[L]equation (Eqn 1) which can be used either to simulate

344 J. Giraldo

theoretical E/[L] curves under different physiological con-ditions or to fit experimental E/[L] curve data with the aimof estimating the pharmacologic parameters associated withagonist affinity and efficacy [35–38].

R 1 LKL

^ L z R · · ·KT

3 Effect(1)

E 5Em z [R0] z KL z KT z [L]

1 1 KL z (1 1 KT z [R0]) z [L]

In Eqn 1, an agonist, L, binds to a receptor molecule, R, toform the agonist–receptor complex, LR. Suspension pointsembody the sequence of biochemical processes linkingreceptor occupation to physiologic effect. By applying thelaw of mass action for receptor conservation and thenecessity of saturation for the transducer function, a theo-retical E/[L] equation is derived. KL is the ligand–receptorbinding constant, KT is a constant modulating the effi-ciency of transduction of receptor occupancy into response,Em is the maximum possible effect in a given system, and[R0] is the total concentration of receptors.

Algebraic exploitation of Eqn 1 leads one to deducemeaningful expressions for the geometric properties whichcharacterize the E/[L] curves, a and [L50] (asymptote andlocation parameters; see Eqn 2).

a 5 lim[L]3`

E 5Em z [R0] z KT

1 1 KT z [R0]5

Em z t

1 1 t, with t 5 [R0] z KT

[L50] 51

KL z (1 1 t)(2)

pD2 5 2log[L50] 5 log(KL z (1 1 t))

We see that t embodies those pharmacologic propertiesthat make it possible to distinguish between full agonists,partial agonists, and antagonists. For t .. 1, the asymptoteof the E/[L] curve, a, approaches Em and the ligand behavesas a full agonist; for t ' 1, a ' Em/2 and the ligand behavesas a partial agonist; and for t ,, 1, a ' 0 and the ligandbehaves as an antagonist. The value of t is dictated by twoterms, one tissue-dependent [R0] and the other ligand andreceptor structure-dependent, KT. Finally, the potency ofan agonist measured by the [L50] value ([L] for E 5 a/2)relies on both the affinity, KL, and the efficacy, t, of theagonist–receptor pair [34].

The operational model of agonism is a suitable method-ology for GPCR. Substitution of suspension points in Eqn 1by the process of formation of a ternary ligand-receptor–G-protein complex provides KT with a chemical meaning: thebinding constant of the G-protein to the ligand–receptorpair [34]. Moreover, this general model incorporates themechanisms of receptor activation by including the corre-sponding chemical processes and associated equilibriumconstants in the basic pharmacologic model depicted inEqn 1. Validation of a putative mechanism or comparisonof the agonist actions of various ligands can be carried outby simulating the derived E/[L] equations or by estimatingthe pharmacologic parameters of interest. Thus, the oper-

ational model is a useful technique for investigating each ofthe pharmacologic profiles resulting from the presumedmechanisms of activation of the HA H2 receptor.

Computation of Structural and Electronic Properties

Quantum-chemical calculations were performed to gain in-sight into the structural features of the two molecular mech-anisms under consideration. All the calculations were carriedout at the restricted Hartree–Fock level with the 6-31G* basisset in the Gaussian 94 [39] suite of programs. 5-Methylimida-zole and 4,5-dimethylthiazole were used as molecular modelsof HA (tautomeric) and TA (non-tautomeric) ligands, respec-tively. Formate anion and formic acid were used as molecularmodels of receptor site II for the interaction with HA andTA, respectively. The molecular structures of both the freeligands and the ligand–receptor complexes were fully opti-mized. Net atomic charges were derived by least-squarefitting of calculated electrostatic potentials to quantummechanically determined electrostatic potentials accordingto the Singh–Kollman procedure [40].

RESULTSThe pH Dependence of the HA H2 Receptor

Recently, various works have stressed the importance ofconsidering the different protonation states of the ionizableresidues of an enzyme to provide a correct description of acatalytic mechanism [41–43]. The arguments made for thecatalytic mechanism of an enzyme are also expected to bevalid for the activation mechanism of a pharmacologic recep-tor. Thus, in the case of the HA H2 receptor, the differentpossible ionic states for the key residues involved in ligandrecognition should be included in the model (see Appendix1). Therefore, if we denote by Z2 the anchoring center (site I)for protonated amine moieties either in agonist or in antago-nist molecules, by Y2 the general base located in site II, and byXH1 the general acid located in site III, then conjugate acidsZH and YH and a conjugate base X should be contemplated aswell. Experimental and theoretical approaches have suggestedan aspartate residue for both the Z2 and Y2 moieties [15] andeither a threonine [15], tyrosine [26], or arginine [30] for XH1.Obviously, if an alcoholic residue is chosen as the putativeproton donor, a neutral XH and a negative X2 should be usedfor the protonated and deprotonated states, respectively.Guanidinium ions and alcohols present similar pKa values and,consequently, are equivalent within the scope of the presentpaper. Simply as a matter of notation, we have assumed thatsite III bears an arginine residue and the XH1 and X symbolsare thus used throughout the text.

Figure 1 depicts the pH profiles of the proportions of theHA H2 receptor ionic states given by Appendix 1. A simula-tion for pKa1R

5 5 (characteristic value for proposed sites I andII) and pKa2R

5 14 (typical value for proposed site III) wasperformed.

The faR(long dashed line) fraction, which corresponds to

a receptor species with all three of the considered residues

pH Modulation of H2 Receptor Activity 345

protonated (see Appendix 1), displays an asymptote towardsone when the pH decreases and an asymptote towards zerowhen the pH increases. fbR

(dotted line), which corresponds toreceptor molecules in which arginine and one of the twoaspartic acid residues are protonated, describes a bell-shapedcurve with a maximum value of ;0.25 at pH 5 5. We see thatat this pH value the faR

, fbR, and fcR

curves cross. Thus, at pH 5pKa1R

, [R 2 ZH 2 YH 2 XH1] 5 [R 2 Z2 2 YH 2 XH1]5 [R 2 ZH 2 Y2 2 XH1] 5 [R 2 Z2 2 Y2 2 XH1] '[R0]/4, and [R 2 Z2 2 Y2 2 X] is negligible. fcR

(solid line)displays a bell-shaped curve with a maximum value ofapproximately 1 broad spanning between 7 and 12 becauseof the great difference between pKa1R

and pKa2Rvalues. fdR

(short dashed line) exhibits an asymptote towards zerowhen the pH decreases and an asymptote towards one whenthe pH increases. Figure 1 makes clear that at the physio-logical pH of 7.4 the receptor is mostly in the R 2 Z2 2 Y2

2 XH1 state of ionization. Nevertheless, the consequencesof the relative proportions of receptor ionic states for theobserved physiologic response will depend on the mecha-nism of receptor activation.

Molecular Structure and Mechanism of Activation

Two pharmacologic paths for two structurally different H2

agonists, namely HA (imidazol-like) and TA (thiazole-

like), are addressed (see Fig. 2). We follow the rationale ofthe allosteric ternary complex model [8, 9] with differentmechanistic proposals for the agonist-induced receptorisomerization step.

MECHANISM A. IMIDAZOLE-LIKE LIGANDS: RECEPTOR ACTI-VATION BY TWO PROTON TRANSFERS. The chemical struc-ture of the imidazole ring (Fig. 2a, Appendix 2.1) causesimidazole-like ligands to bind preferentially to a deproto-nated (negatively charged) site II and to a protonated(positively charged) site III, i.e. R 2 Z2 2 Y2 2 XH1 formof the receptor, in accordance with early activation mech-anism [16]. Thus, fcR

5 [R 2 Z2 2 Y2 2 XH1]/[R0] rendersthe proportion of free receptors in the proper ionic state toproduce the pharmacologic response (see Appendix 1 andFig. 1, solid line) and can be considered, in some sense, thepH-dependent receptor intrinsic activity under this mech-anism. The value of fcR

will depend on the pH and thereceptor dissociation acidic constants Ka1R

and Ka2R. Ago-

nist binding yields the activated form of the receptor (R 2Z2 2 YH 2 X) by two proton transfers, the first from siteIII to nitrogen N(1) of the imidazole ring and the secondfrom N(3)-H of the imidazole ring to site II.

MECHANISM B. THIAZOLE-LIKE LIGANDS: RECEPTOR ACTIVA-TION BY ONE PROTON TRANSFER. The chemical structure ofthe non-tautomeric thiazole ring (Fig. 2b, Appendix 3.1)suggests that thiazole-like ligands could bind preferentiallyto a protonated (neutral) site II and to a protonated (positivelycharged) site III, i.e. R 2 Z2 2 YH 2 XH1 form of thereceptor. This alternative mechanism would result in the sameassumed active form of the receptor (R 2 Z2 2 YH 2 X) asthat resulting from Mechanism a, but by a single protontransfer: from site III to the nitrogen atom of the thiazole ring.Analogously to fcR

in Mechanism a, fbR5 [R 2 Z2 2 YH 2

XH1]/[R0] (Appendix 1 and Fig. 1, dotted line) can beconsidered the pH-dependent receptor intrinsic activityunder Mechanism b.

To test the likeness of the structural proposals for HAand TA receptor binding, potential based atomic chargeson 5-methylimidazole and 4,5-dimethylthiazole (molecularmodels of HA and TA, respectively) were calculated. Inboth systems, a high negative charge over the nitrogenatom acting as the proton acceptor (20.58 for N1 in HAand 20.55 for N3 in TA, see Fig. 2 for atom notation) wasfound. Interestingly, where a positive charge (0.34) appearson the hydrogen N(3)-H of the imidazole ring, a slightlynegative charge (20.07) is observed on the sulphur atom ofthe thiazole ring. Although the charge on the S-atom islow, it will become presumably more negative after bindingbecause of receptor polarization. The opposite sign of thepartial charges on these two ligand moieties is in qualitativeagreement with our hypothesis of two different modes ofbinding. Figure 3 shows the optimized geometries of themolecular models representing the interactions of HA andTA ligands with the two proposed ionic forms of receptorsite II: 2COO2 for HA and 2COOH for TA. The charged

FIG. 1. A simulation of the pH dependence of the proportions ofthe HA H2 receptor ionic states. ZH, YH, and XH1 symbolize theprotonated forms of receptor sites I, II, and III, respectively (seeAppendix 1). faR

5 [R 2 ZH 2 YH 2 XH1]/[R0] (long dashedline), fbR

5 [R 2 Z2 2 YH 2 XH1]/[R0] 5 [R 2 ZH 2 Y2 2XH1]/[R0] (dotted line), fcR

5 [R 2 Z2 2 Y2 2 XH1]/[R0] (solidline), and fdR

5 [R 2 Z2 2 Y2 2 X]/[R0] (short dashed line).pKa values of 5 for both ZH and YH (aspartic acid residues) and14 for XH1 (threonine, tyrosine, or arginine, see introduction)were assumed. Note that in the case of threonine and tyrosine,the proper symbols should be XH and X2 for protonated anddeprotonated alcohol moieties, respectively.

346 J. Giraldo

5-methylimidazole–formate complex is characterized by aplain structure with a linear N2H . . . O hydrogen bond(H . . . O distance is 1.78 Å), whereas the neutral 4,5-dimethylthiazole–formic acid complex is characterized by anon-plain structure with a weaker S . . . H-O hydrogenbond (S . . . H distance is 2.82 Å, about 0.2 Å below thesum of the van der Waals radii).

The pH Dependence of the HA H2 Receptor Agonists

HA and, in general, all H2 agonists have two protonablemoieties, the side chain amine and the aromatic ring imine.If, as is generally accepted, only the monocationic speciesprotonated on the side chain activates the receptor, the pH ofthe milieu and the pKa values of the ligand will determine theproportion of ligand in the active form, fL 5 [L]/[L0] 5 1/(1 1[H1]/Ka1L

1 Ka2L/[H1]). fL/pH is a bell-shaped curve with a

maximum for pH 5 (pKa1L1 pKa2L

)/2. [L] is the concentrationof monocationic ligand protonated on the side chain amineand [L0] is the total ligand concentration. Ka1L

and Ka2Lare

the dissociation acidic constants of the ring imine and theside chain amine, respectively. Thus, fL can be consideredas the pH-dependent intrinsic activity of the ligand.

Figure 4 displays the fL/pH curves for the two agonists we

are analyzing. pKa values of (5.93, 9.32) for HA and (3.23,8.97) for TA were assumed [31]. The maximum for theimidazole compound is located at a pH of 7.6, whereas themaximum for the thiazole compound is at pH value 6.1.However, because of the great difference between the thiazolepKas, the peak of the curve broad spans around the maximum.For the physiological pH of 7.4, fHA is 0.96, whereas fTA is0.97. Thus, no direct differences coming from the ligands arefound. However, by examining Fig. 1, we see that thepH-dependent intrinsic activity of the receptor (fcR

forMechanism a and fbR

for Mechanism b) is more favorablefor HA than for TA at physiological pH. To express thecombined effect of fR and fL properties on the pharmaco-logic parameters, we need to derive E/[L] relationships.

Mechanism of Activation and Physiologic Effect

The aim of the present study is the analysis of different routesfor agonist-induced histamine H2 receptor activation. Forsimplicity, no basal response or precoupling was considered.This simplification is consistent with the likely negligibleconcentration of active receptor ([R 2 Z2 2 YH 2 X]) in theabsence of agonist on the basis of the acid–base properties ofthe proposed residues located on sites I, II, and III. The

FIG. 2. A mechanistic model for HA H2 receptoractivation by either tautomeric or non-tautomericligands. The ligand side chain and the receptoranchoring site I, which remain constant in bothmechanisms, are represented by a methyl group. (a)Mechanism a: imidazole-like (tautomeric) ligands.The imidazole ring binds preferentially to the pos-itively charged site III and negatively charged siteII. A double proton transfer from site III to ringnitrogen N(1) and from ring N(3)-H moiety to siteII activates the receptor. (b) Mechanism b: thia-zole-like (non-tautomeric) ligands. The thiazolering binds preferentially to the positively chargedsite III and neutral site II. A single proton transferfrom site III to the ring nitrogen activates thereceptor. In both mechanisms, the active form ofthe receptor is that with protonated site II anddeprotonated site III.

pH Modulation of H2 Receptor Activity 347

pharmacologic response corresponding to each of the twomechanisms under discussion can be quantified by using theoperational model of agonism [34, 44].

By applying the law of mass action (Appendix 2.2 and3.2), concentration–effect equations are derived (Appen-dix 2.3 and 3.3). These equations express quantitatively themolecular processes by which agonist binding to HA H2

receptor promotes biological response. It can be seen that tmaintains its operational definition of efficacy. The asymp-tote of the E/[L] relationship, a, is i) equal to the maximumresponse of the system, Em, for high values of t (fullagonists); ii) equal to zero when t is also equal to zero

(antagonists); and iii) lower than Em for low values of t(partial agonists). t depends on the total concentration ofreceptors, [R0], the binding constant of the G-protein tothe binary ligand-activated receptor complex, KLR, and theconstant K1 or pair of constants {K1, K2} that regulate(s) theactivation of the receptor. In addition, pD2, a measure ofthe potency of an agonist, is the sum of two terms. The firstterm depends on the pH of the local environment and onthe acid–base properties of both the receptor and theligand, while the second depends on the series of steps thatlead from ligand binding to the formation of the ternarycomplex. Figure 5 displays the pH-dependent term of pD2

for both ligands. The curves cross at pH 5.54. For a pH ,5.54, TA is predicted to be more potent than HA; for apH . 5.54, HA is expected to be more potent than TA.The difference between the pH-dependent terms ofpD2(log(fcR

z fHA) 2 log(fbRz fTA)) is 2.39 at the pH value

of 7.4. Experimentally, the difference is 1.47 and with thesame sign [31]. Thus, the second term of the equations fromAppendix 2.3 and 3.3, which includes the equilibriumconstants for the recognition and activation receptor pro-cesses, predicts a difference of 0.92 units of pD2 favorable toTA. Note that the activity of TA appears to depend on thepH around its maximum more than the activity of HA.

DISCUSSION

The essential corollary of this paper is that even if only oneionic state of the receptor is expected to be the active form,there can exist different mechanistic paths leading to itdepending on the molecular structure of the ligand. Thepharmacologic effects of the hypothesized mechanisms canbe evaluated if it is possible to incorporate the resultingchemical equations into the concentration–effect (E/[L])relationships. Two activation mechanisms for the histamine

FIG. 3. Optimized geometries (6-31G*, see Methods) of themolecular models representing the interaction of HA and TAligands with receptor site II: (a) 5-methylimidazole–formateanion and (b) 4,5-dimethylthiazole–formic acid. The recognitionof both ligands is by the formation of an H-bond: N3-H . . . Ofor HA and S1

. . . H-O for TA.

FIG. 4. A simulation of the pH dependence of the proportions ofthe ionic active forms of HA and TA. fHA 5 [HA]/[HA0] 51/(1 1 [H1]/Ka1HA

1 Ka2HA/[H1]) (solid line) and fTA 5 [TA]/

[TA0] 5 1/(1 1 [H1]/Ka1TA1 Ka2TA

/[H1]) (dotted line); pKa1HA5

5.93, pKa2HA5 9.32, pKa1TA

5 3.23, and pKa2TA5 8.97 [31].

FIG. 5. A simulation of the pH-dependent term of pD2. For HA,log(fcR

z fHA); for TA, log(fbRz fTA). Algebraic expressions and

numeric values can be found in the legends of Figs. 1 and 4.

348 J. Giraldo

H2 receptor for either tautomeric or non-tautomeric ligandshave been considered. These mechanisms have been pharma-cologically characterized by using the operational model ofagonism. The explicit inclusion of chemical reactions in theoperational model of agonism enlarges its classical framework,thereby building a conceptual bridge between molecular struc-ture and physiologic function. In this regard, the presentmodel can shed new light on some results from molecularbiology and experimental pharmacology. The model assumesthat the active form of the receptor is that with a negative siteI, a neutral site II, and a deprotonated site III (i.e. R 2 Z2 2YH 2 X). G-proteins bind to the ligand-activated receptorcomplexes after ligand-mediated neutralization of sites II andIII by either one or two proton transfers. Thus, if site II werepreviously mutated to a non-protonable neutral residue, itwould be reasonable to expect that the mutated receptor couldstill be activated by HA, albeit with one single proton transfer(from site III to imidazole N(1)). This change in the receptor-binding pocket should induce a conformational change that istransmitted through the receptor molecule towards the intra-cellular portion where the G-protein binds with an affinityconstant KLR. If some of the amino acid residues correspond-ing to the receptor active sites are mutated, it is reasonable tosuppose that the resulting conformational change after agonistbinding will be different from the corresponding changeprovided by the native receptor. Consequently, the values ofKLR and t would be different as well. This hypothesis is inqualitative agreement with the observation that mutation ofAsp186 to Ala186 diminishes a for HA to 35% of that observedwith the wild-type receptor [15]. In addition, the potency of an

agonist, [L50], is determined by the aforementioned activationparameters and three additional ones: the proportion ofreceptors in the proper ionic state for activation, fbR

or fcR; the

proportion of ligand in the proper ionic state to activate thereceptor, fL; and the ligand–receptor binding constant, KL.Note that the product fR z fL affects [L50], whose valuedetermines the location of the E/[L] curve, but not a. Thisresult could explain, in part, the different potency values of agiven agonist on different receptor tissues when the totalreceptor concentrations are similar among the tissues. Like-wise, equations from Appendix 2.3 and 3.3 show that apparentaffinity constants, defined as

Kapp 5 lim[R0]30

1[L50]

,

depend on the mechanism and the efficiency of receptoractivation and on the pH of the system.

Finally, we would like to remark that the formulation wehave developed for the histamine H2 receptor should haveapplicability to GPCR upon inclusion of the mechanistichypothesis pertinent to each specific receptor.

APPENDIX1. Protonic Equilibria among the Different Ionic Formsof the HA H2 Receptor

Assuming that the ligand-binding pocket of the receptorconsists of: ZH, aspartic acid (site I); YH, aspartic acid (site II);and XH1, arginine (site III), the following equilibria and relativepopulations of the ionic forms of the receptor are obtained:

R 2 ZH 2 YH 2 XH1Ka1R

^R 2 Z2 2 YH 2 XH1

R 2 ZH 2 Y2 2 XH1

Ka1R

^ R 2 Z2 2 Y2 2 XH1Ka2R

^ R 2 Z2 2 Y2 2 X

Ka1R 5[R 2 Z2 2 YH 2 XH1] z [H1]

[R 2 ZH 2 YH 2 XH1]5

[R 2 ZH 2 Y2 2 XH1] z [H1][R 2 ZH 2 YH 2 XH1]

5[R 2 Z2 2 Y2 2 XH1] z [H1]

[R 2 Z2 2 YH 2 XH1]5

[R 2 Z2 2 Y2 2 XH1] z [H1][R 2 ZH 2 Y2 2 XH1]

;

Ka2R 5[R 2 Z2 2 Y2 2 X] z [H1]

[R 2 Z2 2 Y2 2 XH1];

faR 5[R 2 ZH 2 YH 2 XH1]

[R0]5

1

1 12 z Ka1R

[H1]1

Ka1R

2

[H1]2 1Ka1R

2 z Ka2R

[H1]3

;

fbR 5[R 2 Z2 2 YH 2 XH1]

[R0]5

[R 2 ZH 2 Y2 2 XH1][R0]

51

2 1[H1]Ka1R

1Ka1R

[H1]1

Ka1R z Ka2R

[H1]2

;

fcR 5[R 2 Z2 2 Y2 2 XH1]

[R0]5

1

1 1Ka2R

[H1]1

2 z [H1]Ka1R

1[H1]2

Ka1R

2

;

fdR 5[R 2 Z2 2 Y2 2 X]

[R0]5

1

1 1[H1]Ka2R

12 z [H1]2

Ka1R z Ka2R

1[H1]3

Ka1R

2 z Ka2R

pH Modulation of H2 Receptor Activity 349

The total concentration of receptors, [R0], can bedecomposed into five subpopulations, {R 2 ZH 2 YH 2XH1, R 2 Z2 2 YH 2 XH1, R 2 ZH 2 Y2 2 XH1,R 2 Z2 2 Y2 2 XH1, R 2 Z2 2 Y2 2 X}, whoseproportions are determined by the pKas of ZH, YH, andXH1 acids and the pH of the local environment. Becauseof the expected relative pKa values of the residuesproposed for sites I, II, and III, we have assumed asnegligible those species in which one or two of theaspartic residues are protonated and in which, in thesame molecule, arginine is deprotonated. Thus, [R 2 ZH2 YH 2 X], [R 2 ZH 2 Y2 2 X], and [R 2 Z2 2 YH2 X] have not been included in [R0]. Moreover, we haveassumed that the amino acid residues which constitutethe ligand-binding pocket are independent of each otherand that the ionic state of any one of them does notaffect the ionic states of the others.

2. Activation of the HA H2 Receptor by Imidazol-likeLigands: Two Proton Transfers

2.1. RECEPTOR-LIGAND EQUILIBRIA. The Weinstein acti-vation model [16, 17] is assumed. Side chain protonatedamine of the ligand binds to negatively charged site I (Z2),whereas the neutral imidazole ring locates between depro-tonated site II (Y2) and protonated site III (XH1). Aproton transfer from site III to site II mediated by the ligandactivates the receptor and allows the binding of theG-protein molecule:

The pharmacologic path leading to the observed physi-ologic effect is governed by: i) a ligand–receptor bindingconstant (KL); ii) a reaction constant (K1) for a protontransfer from site III (XH1) to imidazole (L) and areaction constant (K2) for a proton transfer from proton-ated imidazole (LH1) to site II (Y2); and iii) a bindingconstant (KLR) for the formation of the ternary ligand-activated receptor–G-protein complex. Note that inthese equations, L and L9 denote imidazole N(3)-H andN(1)-H tautomers, respectively, both protonated on theside chain amine. LH1 represents the dicationic form ofthe ligand.

2.2. THE LAW OF MASS ACTION. To derive useful concen-tration–effect relationships, we first need to develop properequations for total receptor and G-protein concentrations.By applying the law of mass action for receptor andG-protein conservation, the following equations are ob-tained:

[R0] 5 [R 2 ZH 2 YH 2 XH1]

1 [R 2 Z2 2 YH 2 XH1]

1 [R 2 ZH 2 Y2 2 XH1]

1 [R 2 Z2 2 Y2 2 XH1]

1 [R 2 Z2 2 Y2 2 X]

1 [L z R 2 Z2 2 Y2 2 XH1]

1 [LH1 z R 2 Z2 2 Y2 2 X]

1 [L9 z R 2 Z2 2 YH 2 X]

1 [L9 z R 2 Z2 2 YH 2 X z G]

' [R 2 ZH 2 YH 2 XH1]

1 [R 2 Z2 2 YH 2 XH1]

1 [R 2 ZH 2 Y2 2 XH1]

1 [R 2 Z2 2 Y2 2 XH1]

1 [R 2 Z2 2 Y2 2 X]

1 [L z R 2 Z2 2 Y2 2 XH1]

1 [LH1 z R 2 Z2 2 Y2 2 X]

1 [L9 z R 2 Z2 2 YH 2 X]

and

[G0] 5 [G] 1 [L9 z R 2 Z2 2 YH 2 X z G]

[R0] and [G0] represent the total receptor and G-proteinconcentrations, respectively. (Note that in these equations, wemake the simplifying assumption that [R0] .. [G0] [34]).

R 2 Z2 2 Y2 2 XH1 1 LKL

^ L z R 2 Z2 2 Y2 2 XH1 K1

^ LH1 z R 2 Z2 2 Y2 2 XK2

^ L9 z R 2 Z2 2 YH 2 X

L9 z R 2 Z2 2 YH 2 X 1 GKLR

^ L9 z R 2 Z2 2 YH 2 X z G3 Effect

KL 5[L z R 2 Z2 2 Y2 2 XH1]

[R 2 Z2 2 Y2 2 XH1] z [L]; K1 5

[LH1 z R 2 Z2 2 Y2 2 X][L z R 2 Z2 2 Y2 2 XH1]

;

K2 5[L9 z R 2 Z2 2 YH 2 X]

[LH1 z R 2 Z2 2 Y2 2 X]; KLR 5

[L9 z R 2 Z2 2 YH 2 X z G][L9 z R 2 Z2 2 YH 2 X] z [G]

350 J. Giraldo

2.3. CONCENTRATION– EFFECT (E/[L]) RELATIONSHIPS. As-suming a direct relationship between the effect and theconcentration of ternary complex [34] and applying thelaw of mass action, the following E/[L] relationships arederived:

3. Activation of the HA H2 Receptor by Thiazol-likeLigands: One Proton Transfer

3.1. RECEPTOR-LIGAND EQUILIBRIA. An alternative ionicform of the receptor for the binding of the ligand isproposed. Side chain protonated amine of the ligand bindsto negatively charged site I (Z2), whereas the neutralthiazole ring locates between protonated sites II (YH) andIII (XH1). A proton transfer from site III to thiazolenitrogen activates the receptor and allows the binding ofthe G-protein molecule:

The pharmacologic path leading to the observed physiologiceffect is governed by i) a ligand–receptor binding constant(KL); ii) a reaction constant (K1) for a proton transfer fromsite III (XH1) to thiazole (L); and iii) a binding constant

(KLR) for the formation of the ternary ligand-activatedreceptor–G-protein complex. Note that in these equations,L denotes the monocationic thiazole protonated on the sidechain amine, whereas LH1 represents the dicationic formof the ligand.

3.2. THE LAW OF MASS ACTION. The total receptor andG-protein concentrations can be expressed as:

[R0] 5 [R 2 ZH 2 YH 2 XH1]

1 [R 2 Z2 2 YH 2 XH1]

1 [R 2 ZH 2 Y2 2 XH1]

1 [R 2 Z2 2 Y2 2 XH1]

1 [R 2 Z2 2 Y2 2 X]

1 [L z R 2 Z2 2 YH 2 XH1]

1 [LH1 z R 2 Z2 2 YH 2 X]

1 [LH z R 2 Z2 2 YH 2 X z G]

EEm

5[L9 z R 2 Z2 2 YH 2 X z G]

[G0];

E 5Em z [R0] z fcR z fL z KL z K1 z K2 z KLR z [L0]

1 1 fcR z fL z KL z (1 1 K1 1 K1 z K2 z (1 1 KLR z [R0])) z [L0];

a 5 lim[L0]3`

E 5Em z [R0] z K1 z K2 z KLR

1 1 K1 1 K1 z K2 z (1 1 KLR z [R0])5

Em z t

1 1 t, with t 5

[R0] z K1 z K2 z KLR

1 1 K1 1 K1 z K2;

[L50] 51

fcR z fL z KL z (1 1 K1 1 K1 z K2 z (1 1 KLR z [R0]));

pD2 5 2log[L50] 5 log(fcR z fL) 1 log(KL z (1 1 K1 1 K1 z K2 z (1 1 KLR z [R0])))

R 2 Z2 2 YH 2 XH1 1 LKL

^ L z R 2 Z2 2 YH 2 XH1 K1

^ LH1 z R 2 Z2 2 YH 2 X

LH1 z R 2 Z2 2 YH 2 X 1 GKLR

^ LH1 z R 2 Z2 2 YH 2 X z G3 Effect

KL 5[L z R 2 Z2 2 YH 2 XH1]

[R 2 Z2 2 YH 2 XH1] z [L]; K1 5

[LH1 z R 2 Z2 2 YH 2 X][L z R 2 Z2 2 YH 2 XH1]

;

KLR 5[LH1 z R 2 Z2 2 YH 2 X z G]

[LH1 z R 2 Z2 2 YH 2 X] z [G]

pH Modulation of H2 Receptor Activity 351

' [R 2 ZH 2 YH 2 XH1]

1 [R 2 Z2 2 YH 2 XH1]

1 [R 2 ZH 2 Y2 2 XH1]

1 [R 2 Z2 2 Y2 2 XH1]

1 [R 2 Z2 2 Y2 2 X]

1 [L z R 2 Z2 2 YH 2 XH1]

1 [LH1 z R 2 Z2 2 YH 2 X]

and

[G0] 5 [G] 1 [LH1 z R 2 Z2 2 YH 2 X z G]

(Note that in these equations, we make the simplifyingassumption that [R0] .. [G0] [34]).

3.3. CONCENTRATION– EFFECT (E/[L]) RELATIONSHIPS. As-suming a direct relationship between the effect and theconcentration of ternary complex [34] and applying the lawof mass action, the following relationships are derived:

EEm

5[LH1 z R 2 Z2 2 YH 2 X z G]

[G0];

E 5Em z [R0] z fbR z fL z KL z K1 z KLR z [L0]

1 1 fbR z fL z KL z (1 1 K1 z (1 1 KLR z [R0])) z [L0];

a 5 lim[L0]3`

E 5Em z [R0] z K1 z KLR

1 1 K1 z (1 1 KLR z [R0])5

Em z t

1 1 t,

with t 5[R0] z K1 z KLR

1 1 K1;

[L50] 51

fbR z fL z KL z (1 1 K1 z (1 1 KLR z [R0]));

pD2 5 2log[L50]

5 log(fbR z fL) 1 log(KL z (1 1 K1 z (1 1 KLR z [R0])))

This work was supported in part by grants from the Ministerio deEducacion y Ciencia, Spain (DGICYT:PB95-0624) and Fundacio LaMarato de TV3 (1014/97). Calculations were performed at the Centrede Computacio i Comunicacions de Catalunya.

References

1. De Lean A, Stadel JM and Lefkowitz RJ, A ternary complexmodel explains the agonist-specific binding properties of theadenylate cyclase-coupled b-adrenergic receptor. J Biol Chem255: 7108–7117, 1980.

2. Kenakin TK, Morgan P and Lutz M, On the importance of the“antagonist assumption” to how receptors express themselves.Biochem Pharmacol 50: 17–26, 1995.

3. Bruns RF, Conformational induction versus conformationalselection: Evidence from allosteric enhancers. Trends Pharma-col Sci 17: 189, 1996.

4. Kenakin T, Receptor conformational induction versus selec-tion: All part of the same energy landscape. Trends PharmacolSci 17: 190–191, 1996.

5. Gilman AG, G proteins: Transducers of receptor-generatedsignals. Annu Rev Biochem 56: 615–649, 1987.

6. Strader CD, Fong TM, Graziano MP and Tota MR, Thefamily of G-protein-coupled receptors. FASEB J 9: 745–754,1995.

7. Wess J, G-protein-coupled receptors: Molecular mechanismsinvolved in receptor activation and selectivity of G-proteinrecognition. FASEB J 11: 346–354, 1997.

8. Samama P, Cotecchia S, Costa T and Lefkowitz RJ, Amutation-induced activated state of the b2-adrenergic recep-tor: Extending the ternary complex model. J Biol Chem 268:4625–4636, 1993.

9. Lefkowitz RJ, Cotecchia S, Samama P and Costa T, Consti-tutive activity of receptors coupled to guanine nucleotideregulatory proteins. Trends Pharmacol Sci 14: 303–307, 1993.

10. Samama P, Pei G, Costa T, Cotecchia S and Lefkowitz RJ,Negative antagonists promote an inactive conformation of theb2-adrenergic receptor. Mol Pharmacol 45: 390–394, 1994.

11. Weiss JM, Morgan PH, Lutz MW and Kenakin TP, The cubicternary complex receptor-occupancy model I. Model descrip-tion. J Theor Biol 178: 151–167, 1996.

12. Leff P, Scaramelli C, Law C and McKechnie K, A three-statereceptor model of agonist action. Trends Pharmacol Sci 18:355–362, 1997.

13. Pardo L, Campillo M and Giraldo J, The effect of themolecular mechanism of G protein-coupled receptor activa-tion on the process of signal transduction. Eur J Pharmacol335: 73–87, 1997.

14. Ganellin CR, Chemistry and structure–activity relationshipsof drugs acting at histamine receptors. In: Pharmacology ofHistamine Receptors (Eds. Ganellin CR and Parsons ME), pp.10–102. Wright PSG, Bristol, 1982.

15. Gantz I, Del Valle J, Wang L, Tashiro T, Munzert G, Guo Y,Konda Y and Yamada T, Molecular basis for the interaction ofhistamine with the histamine H2 receptor. J Biol Chem 267:20840–20843, 1992.

16. Weinstein H, Chou D, Johnson CL, Kang S and Green KP,Tautomerism and the receptor action of histamine: A mech-anistic model. Mol Pharmacol 12: 738–745, 1976.

17. Weinstein H, Mazurek AP, Osman R and Topiol S, Theoret-ical studies on the activation mechanism of the histamineH2-receptors: The proton transfer between histamine and areceptor model. Mol Pharmacol 29: 28–33, 1986.

18. Reggio P, Topiol S and Weinstein H, Molecular determinantsfor the agonist activity of 2-methylhistamine and 4-methyl-histamine at H2-receptors. J Med Chem 29: 2412–2415, 1986.

19. Mazurek AP, Osman R and Weinstein H, Molecular deter-minants for recognition of triazole and tetrazole analogs ofhistamine at H2-receptors. Mol Pharmacol 31: 345–350, 1987.

20. Luque FJ, Illas F and Pouplana R, On the mechanism ofhistamine H2 receptor activation. Mol Pharmacol 32: 557–563, 1987.

21. Pardo L, Mazurek AP, Osman R and Weinstein H, Theoret-ical studies of the activation mechanism of histamine H2-receptors: Dimaprit and the receptor model. Int J Quant ChemQuant Biol Symp 16: 281–290, 1989.

22. Haaksma EEJ, Donne-Op den Kelder GM, Timmerman Hand Weinstein H, Theoretical analysis of the activity ofdimaprit derivatives on the H2-receptor. Agents Actions33(Suppl): 315–324, 1991.

23. Haaksma EEJ, Donne-Op den Kelder GM, Vernooijs P andTimmerman H, A theoretical study concerning the mode of

352 J. Giraldo

interaction of the histamine H2-agonist dimaprit. J MolGraphics 10: 79–87, 1992.

24. Pardo L, Giraldo J, Martin M and Campillo M, Theoreticalstudies on the histamine H2 receptor: Construction of areceptor model based on the structural properties of dimapritand Na-guanylhistamine. Mol Pharmacol 40: 980–987, 1991.

25. Giraldo J, Martın M, Campillo M and Pardo L, Theoreticalstudies on the histamine H2 receptor: Molecular mechanismof action of antagonists. Mol Pharmacol 42: 373–381, 1992.

26. Nederkoorn PHJ, van Lenthe JH, van der Goot H, Donne-Opden Kelder GM and Timmerman H, The agonistic bindingsite at the histamine H2 receptor. I. Theoretical investigationsof histamine binding to an oligopeptide mimicking a part ofthe fifth transmembrane a-helix. J Comput Aid Mol Design10: 461–478, 1996.

27. Nederkoorn PHJ, van Gelder EM, Donne-Op den Kelder GMand Timmerman H, The agonistic binding site at the hista-mine H2 receptor. II. Theoretical investigations of histaminebinding to receptor models of the seven a-helical transmem-brane domain. J Comput Aid Mol Design 10: 479–489, 1996.

28. Gantz I, Schaffer M, Del Valle J, Logsdon C, Campbell V,Uhler M and Yamada T, Molecular cloning of a geneencoding the histamine H2-receptor. Proc Natl Acad Sci USA88: 429–433, 1991.

29. Pardo L, Ballesteros JA, Osman R and Weinstein H, On theuse of the transmembranal domain of bacteriorhodopsin as atemplate for modeling the 3-D structure of G-protein-coupledreceptors. Proc Natl Acad Sci USA 89: 4009–4012, 1992.

30. Campillo M, Giraldo J and Pardo L, The structure andactivity of membrane receptors: Computational simulation ofhistamine H2-receptor activation. J Mol Struct (Teochem)371: 279–286, 1996.

31. Eriks JC, Van der Goot H and Timmerman H, New activa-tion model for the histamine H2 receptor, explaining theactivity of the different classes of histamine H2 receptoragonists. Mol Pharmacol 44: 886–894, 1993.

32. Buschauer A, Schunack W, Arrang JM, Garbarg M, SchwartzJC and Young JM, Histamine receptors. In: Receptor Pharma-cology and Function (Eds. Williams M, Glennon RA andTimmermans PMWM), pp. 293–348. Dekker, New York, 1989.

33. Van der Goot H, Bast A and Timmerman H, Structuralrequirements for histamine H2 agonists and H2 antagonists.In: Handbook of Experimental Pharmacology (Ed. Uvnas B) Vol.97, pp. 573–748. Springer-Verlag, Berlin, 1991.

34. Black JW and Leff P, Operational models of pharmacologicalagonism. Proc R Soc London B 220: 141–162, 1983.

35. Black JW, Leff P, Shankley NP and Wood J, An operationalmodel of pharmacological agonism: The effect of E/[A] curveshape on agonist dissociation constant estimation. Br J Phar-macol 84: 561–571, 1985.

36. Leff P, Prentice DJ, Giles H, Martin GR and Wood J,Estimation of agonist affinity and efficacy by direct, opera-tional model-fitting. J Pharmacol Methods 23: 225–237, 1990.

37. Tabernero A, Giraldo J, Vivas NM and Badia A, Endothelialmodulation of a1-adrenoceptor contractile responses in thetail artery of spontaneously hypertensive rats. Br J Pharmacol119: 765–771, 1996.

38. Vivas NM, Giraldo J, Tabernero A, Vila E, Badia A, Use ofthe operational model of agonism and [3H]prazosin binding toassess altered responsiveness of a1-adrenoceptors in the vasdeferens of spontaneously hypertensive rat. Naunyn-Schmiede-berg’s Arch Pharmacol 356: 383–391, 1997.

39. Frisch MJ, Trucks GW, Schlegel HB, Gill PMW, JohnsonBG, Robb MA, Cheeseman JR, Keith TA, Petersson GA,Montgomery JA, Raghavachari K, Al-Laham MA, ZakrzewskiVG, Ortiz JV, Foresman JB, Cioslowski J, Stefanov BB,Nanayakkara A, Challacombe M, Peng CY, Ayala PY, ChenW, Wong MW, Andres JL, Replogle ES, Gomperts R, MartinRL, Fox DJ, Binkley JS, Defrees DJ, Baker J, Stewart JP,Head-Gordon M, Gonzalez C and Pople JA, Gaussian 94.Gaussian, Inc., Pittsburgh PA, 1995.

40. Singh UC and Kollman PA, An approach to computingelectrostatic charges for molecules. J Comput Chem 5: 129–145, 1984.

41. Brocklehurst K, A sound basis for pH-dependent kineticstudies on enzymes. Protein Eng 7: 291–299, 1994.

42. MacKerell AD, Sommer MS and Karplus M, pH dependenceof binding reactions from free energy simulations and macro-scopic continuum electrostatic calculations: Application to29GMP/39GMP binding to ribonuclease T1 and implicationsfor catalysis. J Mol Biol 247: 774–807, 1995.

43. Gordon-Beresford RMH, Van Belle D, Giraldo J and WodakSJ, Electrostatic properties of the barnase–nucleotide com-plex: Effects of substrate binding on the optimal pH ofcatalysis. Proteins: Struct Funct Genet 25: 180–194, 1996.

44. Giraldo J and Pardo L, A thermodynamic model of signaltransduction: From ligand binding to physiological effect. In:QSAR and Molecular Modelling: Concepts, Computational Toolsand Biological Applications (Eds. Sanz F, Giraldo J and ManautF), pp. 537–540. Prous Science, Barcelona, 1995.

pH Modulation of H2 Receptor Activity 353