Mathematical analysis of the sodium sensitivity of the human histamine H3 receptor
© Wittmann et al.; licensee Springer. 2014
Received: 28 February 2014
Accepted: 28 April 2014
Published: 24 May 2014
It was shown by several experimental studies that some G protein coupled receptors (GPCR) are sensitive to sodium ions. Furthermore, mutagenesis studies or the determination of crystal structures of the adenosine A2A or δ-opioid receptor revealed an allosteric Na+ binding pocket near to the highly conserved Asp2.50. Within a previous study, the influence of NaCl concentration onto the steady-state GTPase activity at the human histamine H3 receptor (hH3R) in presence of the endogenous histamine or the inverse agonist thioperamide was analyzed. The purpose of the present study was to examine and quantify the Na+-sensitivity of hH3R on a molecular level.
To achieve this, we developed a set of equations, describing constitutive activity and the different ligand-receptor equilibria in absence or presence of sodium ions. Furthermore, in order to gain a better understanding of the ligand- and Na+-binding to hH3R on molecular level, we performed molecular dynamic (MD) simulations.
The analysis of the previously determined experimental steady-state GTPase data with the set of equations presented within this study, reveals that thioperamide binds into the orthosteric binding pocket of the hH3R in absence or presence of a Na+ in its allosteric binding site. However, the data suggest that thioperamide binds preferentially into the hH3R in absence of a sodium ion in its allosteric site. These experimental results were supported by MD simulations of thioperamide in the binding pocket of the inactive hH3R. Furthermore, the MD simulations revealed two different binding modes for thioperamide in presence or absence of a Na+ in its allosteric site.
The mathematical model presented within this study describes the experimental data regarding the Na+-sensitivity of hH3R in an excellent manner. Although the present study is focused onto the Na+-sensitivity of the hH3R, the resulting equations, describing Na+- and ligand-binding to a GPCR, can be used for all other ion-sensitive GPCRs.
KeywordsHistamine H3 receptor Na+-sensitivity Mathematical model Molecular dynamics
G protein coupled receptors (GPCRs), one of the largest protein families within the human genome, play an important role in several physiological and pathophysiological processes (Wise et al. ; Foord et al. ; Jacoby et al. ). In general, the two-state model of GPCR activation suggests that GPCRs can exist in two different states, the inactive “R” and active “R*” state (Schütz and Freissmuth ; Lefkowitz et al. ; Leff ; Seifert and Wenzel-Seifert ). These two different conformations were confirmed by crystal structures of the inactive and active state of the β2-adrenergic receptor (Cherezov et al. ; Rosenbaum et al. ; Rasmussen et al. ). Ligands, addressing GPCRs, can be classified as inverse agonists, neutral antagonist or agonists (Seifert and Wenzel-Seifert [2002, 2003]). It is assumed that inverse agonists stabilize the inactive, whereas agonists stabilize the active state of GPCRs (Seifert and Wenzel-Seifert [2002, 2003]). The histamine H3 receptor (H3R), identified in the early 1980s, is one of four histamine receptor subtypes and belongs to the aminergic GPCRS (Hill et al. ; Lovenberg et al. ; Leurs et al. ; Parsons and Genellin ). The H3R regulates the release of the endogenous histamine and other neurotransmitters in the nervous system and is involved in important physiological processes, e.g. cognition, eating-behaviour and the sleep-wake cycle (Leurs et al. ). For the hH3R, a large number of ligands is known (Sasse et al. ; Stark et al. ; Schnell and Seifert ; Strasser et al. ; Seifert et al. ). However, thioperamide is a standard inverse agonist at the hH3R (Arrang et al. ; Schnell and Seifert ). Some GPCRs, showing constitutive activity, change its conformation from the inactive into the active state in absence of an agonist (Seifert and Wenzel-Seifert [2002, 2003]). It was shown that the hH3R and the highly related hH4R exhibit constitutive activity (Morisset et al. ; Schneider et al. ; Schnell et al. ). Experimental studies revealed that sodium ions can act as an allosteric modulator and stabilize the inactive conformation of a GPCR (Seifert and Wenzel-Seifert [2002, 2003]). Experimental studies revealed that only distinct GPCRs are sensitive for sodium ions, whereas other GPCRs are insensitive for sodium ions. The neurotensine receptors (Martin et al. ), the D2 (Neve ; Schetz ; Ericksen et al. ) for example, are sodium sensitive. Within the family of the histamine receptors, the hH3R is sodium sensitive (Schnell and Seifert ) whereas the highly related hH4R is sodium insensitive (Schneider and Seifert ). The corresponding allosteric sodium ion binding site is located between TM II, TM III and TM VII near to the highly conserved Asp2.50, as was shown recently with the crystal structure of the human adenosine A2A receptor (hA2AR) (Liu et al. ) or the δ-opioid receptor (Fenalti et al. ). The location of the allosteric sodium binding site was also supported by mutagenesis of the highly conserved Asp2.50 into the neutral alanine (Neve et al. ; Schetz and Sibley ) or asparagine (Ceresa and Limbird ; Schnell and Seifert ). This is supported by experimental results at hH3R, where the Asp2.50Asn mutant was found to partially mimic the effect of high sodium chloride concentrations by suppressing constitutive activity (Schnell and Seifert ). With MD studies the binding pathway of a sodium ion into the allosteric sodium binding site of the D2 receptor (Selent et al. ) and the μ-opioid receptor (Yuan et al. ) were observed.
Therein, R* represents the ligand- and sodium free- active receptor and R the ligand- and Na+- free inactive receptor.
The solution of the equations 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11 with respect to the concentration terms was calculated using the software package MAPLE 11.0 (Maplesoft Waterloo Maple Inc. 1981-2007). Maple is a computer algebra system, allowing users to define mathematical equations in a simple manner, solve these equations with one command line and plot the corresponding results. To elucidate this, the definition of equations (1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11) (see the following command lines e1 to e11) and their solution with the help of the command “solve” (see command line e12) is shown, using the Maple syntax:
> e1:=K0 = RS/R:
> e2:=K1 = AR/(A0*R):
> e3:=K2 = ARS/(A0*RS):
> e4:=K3 = ARR/AR:
> e5:=K4 = BR/(B0*R):
> e6:=K5 = BRS/(B0*RS):
> e7:=K6 = BRR/(B0*ARR):
> e8:=K7 = CR/(C0*R):
> e9:=K8 = CRS/(C0*RS):
> e10:=K9 = CRR/(C0*ARR):
> e11:=R0 = R + RS + AR + ARS + ARR + BR + BRS + BRR + CR + CRS + CRR:
The last command led to the following expressions for the concentration terms (Maple notation in brackets) R (R), R* (RS), A ortho R (AR), A ortho R* (ARS), A allo R (ARR), BR (BR), BR* (BRS), BA allo R (BRR), CR (CR), CR* (CRS) and CA allo R (CRR):
Description of the efficacy
Least-square fit to obtain the constants K x
There, represents each experimentally determined data point i shown in Figure 1, relative to the effect, determined at a histamine concentration of C 0 ref = 10 μM in absence of sodium chloride and thioperamide. represents the calculated relative effect according to equation 25 for a set of constants K x to be determined by searching the minimum of s 2 using the software MAPLE 11.0. However, to solve this problem, every other software package can be used.
Construction of the inactive model of hH3R
For the construction of the homology model of the inactive hH3R, the crystal structure of the inactive hH1R (3RZE) (Shimamura et al. ) was used as a template. The hH3R homology model was designed using SYBYL 7.0 (Tripos; http://www.tripos.com) according to a protocol, described previously (Strasser and Wittmann ; Darras et al. ; Wagner et al. ). Briefly, the artificial lysozyme in 3RZE was deleted and the homology model was generated according to a hH1R-hH3R amino acid alignment already described (Strasser et al. ). The N-terminus, missing in the crystal structure of hH1R, was completed using SYBYL 7.0 (Tripos Inc), as described previously (Darras et al. ; Wagner et al. ). Furthermore, the E2-loop was completed using the “Loop-Search” module of SYBYL 7.0, as described previously for the hH4R (Darras et al. ; Wagner et al. ). Because there is no information about the conformation of the long I3-loop of the hH3R, containing more than 100 amino acids, the amino acids Ala239 to Arg347 were not included into the model. However, to close the resulting gap between TM V and TM VI on the intracellular side, eight alanines were inserted instead. It was shown previously, that internal water molecules play an important role in stabilization or activation of aminergic GPCRs (Angel et al. ; Liu et al. ). Therefore, the internal water molecules, described in literature were included according to the corresponding crystal structures (Angel et al. ; Liu et al. ). In a first model, thioperamide was docked manually into the binding pocket of hH3R, in such manner that the positively charged imidazole moiety interacts electrostatically with the highly conserved Asp3.32, according to the binding mode for analogue compounds, already described in literature (Schnell and Seifert ). The remaining part of thioperamide was embedded in a pocket between TM III, TM V and TM VI, as already described for similar H3 receptor ligands (Schlegel et al. ; Schnell and Seifert ). In a second model, one sodium ion was docked manually into the allosteric binding site of hH3R, according to the crystal structure of the A2A with a Na+ in the allosteric binding site (Liu et al. ). Furthermore, a third model, containing thioperamide in the orthosteric and one sodium ion in the allosteric binding site was constructed, as described above for the thioperamide- and the sodium-ion- model. The resulting complexes were minimized energetically with SYBYL 7.0. Subsequently the minimized hH3R-models containing thioperamide and/or a sodium ion were embedded in a POPC lipid bilayer. Afterwards, intracellular and extracellular water molecules were added. To achieve electroneutrality, an appropriate number of sodium ions and chloride ions were added into the simulation box. Subsequently, MD simulations were performed with GROMACS 4.0.2 (http://www.gromacs.org) as already described (Strasser et al. ; Igel et al. ; Darras et al. ). The parameterization for thioperamide was obtained from the PRODRG server (http://davapc1.bioch.dundee.ac.uk/prodrg/). However, the partial charges were adopted by the Gasteiger-Hückel partial charged, calculated with SYBYL 7.0. The force field parameters for the POPC lipids were obtained from the online source http://moose.bio.ucalgary.ca/index.php?page=Structures_and_Topologies. For equilibration, a 5 ns MD simulation was performed: Within the first 2.5 ns, force constants of 250 kJ/(mol nm2) were put onto the backbone atoms of the TM domains of hH3R, within the second 2.5 ns, these force constants were reduced to 100 kJ/(mol nm2). Subsequently, 10 ns up to 35 ns productive phase of simulations were performed, without using any force constants.
Constants K 0 to K 9 for the hH3R, determined by steady-state GTPase assays
pK x , K x and Δ R G o values, describing the constitutive activity, the binding of sodium ions, of thioperamide and histamine to hH 3 R
pK x ± S.E.M.
K x ± S.E.M.
Δ R G o [kJ/mol]
R ⇌ R*
-0.04 ± 0.01
0.92 ± 0.03
0.21 ± 0.08
A + R ⇌ A ortho R
0.31 ± 0.03
2.08 ± 0.20
-1.76 ± 0.20
A + R* ⇌ A ortho R*
0.06 ± 0.08
1.29 ± 0.22
-0.33 ± 0.47
A ortho R ⇌ A allo R
1.07 ± 0.04
11.98 ± 0.84
-6.10 ± 0.21
B + R ⇌ BR
7.40 ± 0.03
2.56 · 107 ± 1.35 · 106
-42.25 ± 0.15
B + R* ⇌ BR *
7.01 ± 0.03
1.03 · 107 ± 6.15 · 105
-39.98 ± 0.17
B + A allo R ⇌ BA allo R
7.23 ± 0.03
1.71 · 107 ± 9.96 · 105
-41.25 ± 0.15
C + R ⇌ CR
7.48 ± 0.01
3.05 · 107 ± 1.07 · 106
-42.71 ± 0.08
C + R* ⇌ CR *
7.86 ± 0.01
7.20 · 107 ± 1.71 · 106
-44.84 ± 0.06
C + A allo R ⇌ CA allo R
6.98 ± 0.01
9.48 · 106 ± 3.02 · 105
-39.81 ± 0.08
The constant K 0 , describing the constitutive activity has a value of 0.92. Thus, the active hH3R (R*) is decreased in stability of Δ R G o = 0.21 kJ/mol compared to the inactive hH3R (R) (Table 1) according to R ⇌ R*.
The binding of a sodium ion from the aqueous extracellular side into the allosteric binding site can be divided into two steps, according to the equations 2 and 4. The binding of the Na+ into the orthosteric binding site (A ortho R) according to A + R ⇌ A ortho R with an association constant K 1 of 2.08 is energetically favoured (Δ R G o = -1.76 kJ/mol) (Table 1). The subsequent binding of the sodium ion from the orthosteric into the allosteric binding site, with a K 3 of 11.98, according to A ortho R ⇌ A allo R, is energetically favoured with Δ R G o = -6.10 kJ/mol (Table 1). Thus, the consecutive binding process of the sodium ion into its allosteric binding site, according to A + R ⇌ A ortho R, is energetically favoured with Δ R G o = -7.86 kJ/mol. The binding of a sodium ion into the orthosteric binding site of the active hH3R, according to A + R* ⇌ A ortho R*, with Δ R G o = -0.33 kJ/mol does not differ significantly from zero (Table 1).
The binding of thioperamide to the orthosteric binding site of hH3R in absence of a sodium ion in the allosteric binding site is preferred compared to the binding in presence of a sodium ion in the allosteric binding site, as indicated by the corresponding association constants K 4 , according to B + R ⇌ BR, and K 6 , according to B + A allo R ⇌ BA allo R. The association constant K 5 for the binding of thioperamide to the active state hH3R, according to B + R* ⇌ BR * is smaller than K 4 or K 6 (Table 1), which is in good accordance to the experimental findings that thioperamide acts as an inverse agonist at hH3R (Schnell and Seifert ).
The association constant K 8 of the endogenous agonist histamine to the active hH3R, according to C + R* ⇌ CR * , is higher than for the binding to the inactive hH3R in absence (K 7 ) or presence (K 9 ) of a sodium ion in the allosteric binding site (Table 1). This is in good accordance to the experimental findings revealing histamine as an agonist at hH3R (Schnell and Seifert ).
Relative concentration profiles of different receptor complexes in dependence of thioperamide, histamine and NaCl in the steady-state GTPase assay at hH3R
In absence or presence of 100 mM NaCl, the amount of the ligand- and Na+-free receptor states R* and R decreases to zero with increasing concentrations of histamine whereas the amount of CR* increases (Figure 3). However, regardless of the sodium chloride concentration, a small amount of the Na+-free inactive histamine-hH3R-complex (CR) is present. With increasing concentration of sodium chloride, the amount of CA allo R increases. At a concentration of about 285 mM of NaCl, the concentrations of CR* and CA allo R are nearly equal. For all concentrations of sodium chloride less than 285 mM, CR* is higher than CA allo R (Figure 3). Based on these data it has to be suggested that histamine binds also in the inactive state hH3R with or without Na+ bound in its allosteric binding site. However, histamine is defined as a full agonist, because there is no other ligand with higher stimulatory effect than histamine at hH3R. To support these results, analogue calculations, but without including equations 8 and/or 10 and related variables were performed, but were not able to fit the experimental data. However, in presence of 100 mM NaCl, the concentration of CR* is about 3 times higher than that of CA allo R (Figure 3).
Explanation of the steady-state GTPase results for the hH3R
Calculation of the pEC 50 values
These equations show that the pEC 50 value is dependent of the amount of constitutive activity, described by K 0 as well as of the constants K 1 , K 2 and K 3 , describing the three different equilibria between sodium ions and the receptor (equations 2, 3, 4), and the concentration of sodium ion A 0 itself. Furthermore, the ligand specific constants (thioperamide: K 4 , K 5 and K 6 ; histamine: K 7 , K 8 and K 9 ) have an influence onto the pEC 50 . The equations show that the pEC 50 increases with increase of the ligand-receptor specific constants K 4 , K 5 , K 6 (thioperamide) or K 7 , K 8 , K 9 (histamine). Furthermore, the pEC 50 increases with decreasing K 2 . If no sodium chloride is present, the constants K 1 , K 2 , K 3 , K 6 (thioperamide) and K 9 (histamine) are not relevant. Because of the complexity of the equations 31 and 32, the influence of K 0 , K 1 , K 3 and A 0 onto the pEC 50 depends on the values of the other variables in the equations, and thus, no simple rules to describe the influence of each K x onto pEC 50 can be presented.
Using the K x values, obtained by the fit of the experimental data (Table 1), for the GTPase curve of thioperamide in absence of NaCl, a pEC 50 of 7.26 and in presence of 100 mM NaCl, a pEC 50 of 7.21 was obtained. The pEC 50 value in absence of sodium chloride fits well to the experimental data (7.15 ± 0.31 (Schnell and Seifert )). The calculated pEC 50 value in presence of 100 mM NaCl does not differ within the limits of error from the experimental data (7.43 ± 0.28 (Schnell and Seifert )). Using the K x values, obtained by the fit of the experimental data (Table 1), for the GTPase curve of histamine in absence of NaCl, a pEC 50 of 7.70 and in presence of 100 mM NaCl, a pEC 50 of 7.41 was obtained. The pEC 50 value in absence (exp.: 8.01 ± 0.39 (Schnell and Seifert )) and presence (exp.: 7.53 ± 0.18 (Schnell and Seifert )) of sodium chloride fit well to the experimental data.
Molecular dynamics of different thioperamide- and Na+-hH3R-complexes
In order to study the influence of a sodium ion in its allosteric binding site onto the conformation of the ligand-free inactive hH3R, two different MD simulations were performed: On the one hand, one Na+ was placed into its allosteric site, according to the crystal structures of the A2A (Liu et al. ). For purpose of reference, an identical system, except with the Na+ not located in the allosteric binding site of the hH3R, but somewhere in the aqueous extracellular part of the simulation box was built. The MD simulations, performed under comparable conditions, revealed a stabilization of the inactive conformation of the hH3R, with the sodium ion being stable in its allosteric binding site. In contrast for the reference system, without a Na+ in the allosteric pocket of hH3R, after ~ 6 ns of simulation, the hH3R started to undergo a conformational change especially in the intracellular part of the receptor. Here, a slight outward movement of TM VI was observed. Thus, the findings of the MD simulations support the experimental findings that a sodium ion, bound in its allosteric binding site stabilizes the inactive conformation of hH3R.
The results obtained in this study suggest that thioperamide, known as inverse agonist, not only binds into the inactive state hH3R, but also into the active hH3R. However, as suggested by the corresponding association constants, the binding of thioperamide to the inactive hH3R is preferred, compared to the binding to the active hH3R. Furthermore, the present results indicate that histamine, known as an agonist, not only binds to the active state hH3R, but also to the inactive hH3R. But as suggested by the corresponding association constants, the binding of histamine to the active hH3R is preferred, compared to the binding to the inactive hH3R. Thus, this kind of data analysis presented in this study allows to obtain information about association constants of a ligand to the inactive and active state of a GPCR separately.
In literature, the influence of different cations and anions onto the signalling of various GPCRs is discussed (Schetz and Sibley ; Swaminath et al ; Seifert and Wenzel-Seifert ; Schnell and Seifert ). At hH3R, the GTP hydrolysis in presence of 10 μM histamine or 10 μM thioperamide or the basal GTP hydrolysis without presence of a ligand was analyzed in dependence of the concentration of different monovalent salts, like LiCl, LiBr, LiJ, NaCl, NaBr, NaJ, KCl, KBr and KJ (Schnell and Seifert ). These data indicate that not only cations have an influence onto GPCR signalling, but also anions. Within the MD simulations at hH3R, chloride ions were observed more frequently at the intracellular side of the receptor. This is in very good accordance to the fact that, compared to the extracellular side of the hH3R, more positively charged amino acids are located at the intracellular side of the receptor. Although we could not detect a stable binding of the same chloride at the intracellular part of hH3R over several ns, we observed chloride ions binding for about 300 ps to positively charged amino acids of the hH3R, e.g. Arg3.50 (Figure 8), for several times during the whole simulation. This “sporadic” binding of a chloride ion may hinder the G protein to bind onto the active state hH3R, leading to a decreased basal activity with increasing concentration of chloride or other ions. Additionally, an effect of anions directly onto the G protein has to be considered (Higashijima et al. ). Relevant anion binding sites at G proteins can be identified within future studies by crystal structures or MD simulations. However, in order to obtain a deeper insight onto the influence of cations and anions onto GPCR signalling, more experimental studies, combined with modelling studies have to be performed. In this context it may be of interest to study the influence of monovalent salts onto the GPCR signalling of hH4R in more detail. Although it was shown that the hH4R is insensitive to sodium ions (Schneider and Seifert ), it may be useful to compare two different receptors, coupling to one and the same G protein in order to be able to separate between an effect of ions onto the receptor or onto the G protein.
In this study we developed a mathematical model to describe the sensitivity of GPCRs to sodium ions in presence or absence of a ligand. The excellent quality of the new mathematical model, consisting of a couple equilibrium constants, was shown by fitting experimental data obtained with the steady-state GTPase assay at hH3R. On the one hand, the new mathematical model allows a more detailed insight onto the ligand- and Na+ binding processes to a GPCR on a molecular level. On the other hand, the model may be extended to the quantitative description of arbitrary ligand-ion-receptor-binding processes.
G-protein coupled receptor:
Histamine H3 receptor:
Gibbs free energy of binding:
We would like to thank Dr. D. Schnell for performing the steady-state GTPase assays at hH3R.
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