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Modulation of the cAMP Response by G\(\alpha _i\) and G\(\beta \gamma \): A Computational Study of G Protein Signaling in Immune Cells

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Abstract

Cyclic AMP is important for the resolution of inflammation, as it promotes anti-inflammatory signaling in several immune cell lines. In this paper, we present an immune cell specific model of the cAMP signaling cascade, paying close attention to the specific isoforms of adenylyl cyclase (AC) and phosphodiesterase that control cAMP production and degradation, respectively, in these cells. The model describes the role that G protein subunits, including G\(\alpha _s\), G\(\alpha _i\), and G\(\beta \gamma \), have in regulating cAMP production. Previously, G\(\alpha _i\) activation has been shown to increase the level of cAMP in certain immune cell types. This increase in cAMP is thought to be mediated by \(\beta \gamma \) subunits which are released upon G\(\alpha \) activation and can directly stimulate specific isoforms of AC. We conduct numerical experiments in order to explore the mechanisms through which G\(\alpha _i\) activation can increase cAMP production. An important conclusion of our analysis is that the relative abundance of different G protein subunits is an essential determinant of the cAMP profile in immune cells. In particular, our model predicts that limited availability of \(\beta \gamma \) subunits may both \((i)\) enable immune cells to link inflammatory G\(\alpha _i\) signaling to anti-inflammatory cAMP production thereby creating a balanced immune response to stimulation with low concentrations of PGE2, and \((ii)\) prohibit robust anti-inflammatory cAMP signaling in response to stimulation with high concentrations of PGE2.

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  • 13 June 2020

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Acknowledgments

The work of Avner Friedman was supported by the Mathematical Biosciences Institute. The work of Rachel Leander was supported by the National Science Foundation under agreement No. 0931642.

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Appendix

Appendix

1.1 EP Receptors and PGE2

Prostaglandin E2 (PGE2) is an important regulator of the immune response which has been implicated in the immuno-pathogenesis of chronic infections, cancer, and allergies (Sreermkumar et al. 2011; Kalinski 2012). In both macrophages and T cells, the immunosuppressive effects of PGE2 are mediated primarily through cAMP signaling downstream from the \(G\alpha _s\)-coupled EP2 and EP4 receptors (Ikegami et al. 2001; Sreermkumar et al. 2011).

We assume that, like rhodopsin (Epsa et al. 2011) and the \(\beta _2\)-adrenergic receptor (Rasmussen et al. 2011), ligand binding promotes the association of the EP receptor with G protein. In particular, we assume that EP receptor association with PGE2 necessarily precedes EP receptor association with G protein. In addition, we assume that ligand binding and EP receptor activation is rapid so that the concentration of ligand-bound EP receptors is determined by the concentration and dissociation constant for PGE2:

$$\begin{aligned} \left[ E\!P\right] ^*&= \frac{[P\!G\!E2\!]E\!P\!^\mathrm{tot}}{[P\!G\!E2\!]+K\!_5}, \end{aligned}$$
(15)

where \([EP]\) represents the total concentration of EP2 receptors in the cell. The value of \(K_5\) depends on the identity of the EP receptor as the dissociation constant for EP4 is less than that of EP2 (Kalinski 2012). In addition, we assume that only ligand-bound receptors bind to and activate G proteins.

For simplicity, we model EP2 as the primary prostaglandin receptor. The dissociation constant for PGE2 and EP2, \(K_5\), was measured in Sugimoto et al. (2003). The cellular concentration of EP2 receptors was approximated as the concentration of EP receptors in T cells (Katanaev and Chornomorets 2007).

1.2 C5a Receptors

C5a is a powerful inflammatory peptide that serves as a chemoattractant for neutrophils, monocytes, and macrophages, an enhancer of phagocytosis and a modulator of cytokine production (Guo and Ward 2005). Elevated levels of C5a are associated with sepsis, asthma, and cancer (Guo and Ward 2005; Ostrand-Rosenberg and Sinha 2009).

The C5a Receptor (C5aR) is abundantly expressed by a variety of immune cells (Klos et al. 2009). C5aR signals primarily thorough the pertussis toxin sensitive G\(\alpha _{i2}\) protein (Klos et al. 2009). In the absence of C5a, C5aR is precoupled to G proteins, and the association of C5aR with G protein appears to be required for C5a binding (Klos et al. 2009). We assume that G\(\alpha \) association and C5a binding are fast so that the concentrations of G\(\alpha \)-associated receptors (\(\left[ C5aR-\alpha _i\beta \gamma \right] \)) and C5a-bound receptors (\(\left[ C5aR^*\right] \)) are given by \((16)\) and \((17)\).

$$\begin{aligned} \left[ C5aR-\alpha _i\beta \gamma \right]&= C5aR^\mathrm{tot}\frac{[\alpha _i\beta \gamma ]}{[\alpha _i\beta \gamma ]+K_1}\end{aligned}$$
(16)
$$\begin{aligned} \left[ C5aR^*\right]&= [C5aR-\alpha _i\beta \gamma ]\frac{[C5a]}{[C5a]+K_{2}}. \end{aligned}$$
(17)

We were unable to find estimates of \(K_1\), the dissociation constant between C5aR and G\(\alpha _i\), so we take \(K_1\) equal to the dissociation constant between the \(\beta \)-adrenoreceptor and G\(\alpha _s\) (Friedman and Johnson 1995).

1.3 Trimeric G Proteins

Trimeric G proteins are composed of \(\alpha \), \(\beta \), and \(\gamma \) subunits. G\(\alpha \) is a guanine nucleotide-binding protein that hydrolyses GTP to GDP. The activity of the G\(\alpha \) is determined by the identity of the nucleotide to which it is bound, with G\(\alpha \)-GTP being active and G\(\alpha \)-GDP being inactive. In the absence of stimulation, G\(\alpha \) is usually bound to GDP due to the slow rate of nucleotide dissociation. In response to stimulation, GPCRs activate G\(\alpha \) by accelerating the rate of GDP dissociation (Cabrera-Vera et al. 2003; Wettschureck and Offermanns 2005). The \(\beta \gamma \) subunits are essential for G\(\alpha \) activation, as association with \(\beta \gamma \) is a prerequisite for receptor-stimulated G\(\alpha \) activation (Cabrera-Vera et al. 2003). \(\beta \gamma \) subunits transmit signals independently from G\(\alpha \) and in the canonical model of G protein signaling, \(\beta \gamma \) subunits are released through G\(\alpha \) activation (Cabrera-Vera et al. 2003; Wettschureck and Offermanns 2005). This point has become somewhat controversial, and there is some evidence that, at least in some models, \(\beta \gamma \) subunits may not dissociate but undergo a conformational rearrangement in response to G\(\alpha \) activation (Levitzki and Klein 2002; Bünemann et al. 2003; Chisari et al. 2009). Since, however, \(\beta \gamma \) signaling is inhibited by the addition of excess \(\beta \gamma \) sequestering agents, including the \(\beta \gamma \)-binding domain of GRK, inactive G\(\alpha \) subunits, fragments of AC, and the cytosolic protein phosducin, it seems certain that G\(\alpha \)-GTP has reduced affinity for \(\beta \gamma \) (Olianas et al. 1998; Casey et al. 2010; Uezono et al. 2004; Blüml et al. 1997). For simplicity, we assume that the affinity of \(\beta \gamma \) for G\(\alpha \)-GTP is negligible compared to that of \(\beta \gamma \) for G\(\alpha \)-GDP so that G\(\alpha \)-GTP does not bind \(\beta \gamma \). Depending on the relative abundance of G\(\alpha \) and \(\beta \gamma \) subunits, resting cells may contain significant amounts of free G\(\alpha \)-GDP or \(\beta \gamma \). Our model of G protein activation tracks the concentration of active G\(\alpha \)-GTP, G\(\alpha \)-GDP, G\(\alpha \)-GDP-\(\beta \gamma \), and \(\beta \gamma \), similar to the model proposed in Katanaev and Chornomorets (2007). Our model of G protein activation differs from previous models in that we do not assume that the concentration of \(\beta \gamma \) subunits is equal to the concentration of G\(\alpha \) subunits. As mentioned previously, we assume that G protein binding to GPCR is rapid so that the fraction of receptors bound to G protein is determined by the concentration of and dissociation constant of G\(\alpha \)-GDP-\(\beta \gamma \). We assume that binding of GTP is rapid compared to receptor-catalyzed GDP dissociation so that receptors catalyze the transition from G\(\alpha \)-GDP-\(\beta \gamma \) to G\(\alpha \)-GTP in a single step. Deactivation of G\(\alpha \)-GTP occurs through hydrolysis which yields G\(\alpha \)-GDP. G\(\alpha \)-GDP binds \(\beta \gamma \) to yield G\(\alpha \)-GDP-\(\beta \gamma \) and the cycle resumes. The associated equations are as follows:

$$\begin{aligned} \frac{d[\alpha ^*_s]}{dt}&= k_1[EP^*]\frac{[\alpha _s\beta \gamma ]}{[\alpha _s\beta \gamma ]+K_{5}}-{k_{2}}[\alpha ^*_s]\end{aligned}$$
(18)
$$\begin{aligned} \frac{d[\alpha _s\beta \gamma ]}{dt}&= -k_1[EP^*]\frac{[\alpha _s\beta \gamma ]}{[\alpha _s\beta \gamma ]+K_{5}}+k_{3}[\beta \gamma ][\alpha _s]-k_{4}[\alpha _s\beta \gamma ]\end{aligned}$$
(19)
$$\begin{aligned} \frac{d[\alpha ^*_i]}{dt}&= k_5[C5aR^*]-k_{6}[\alpha ^*_i]\end{aligned}$$
(20)
$$\begin{aligned} \frac{d[\alpha _i\beta \gamma ]}{dt}&= -k_5[C5aR^*]+k_{7}[\beta \gamma ][\alpha _i]-k_8[\alpha _i\beta \gamma ]\end{aligned}$$
(21)
$$\begin{aligned} \frac{d[\beta \gamma ]}{dt}&= k_5[C5aR^*]+k_1[EP^*]\frac{[\alpha _s\beta \gamma ]}{[\alpha _s\beta \gamma ]+K_{5}}\end{aligned}$$
(22)
$$\begin{aligned}&+\,k_8[\alpha _i\beta \gamma ]+k_4[\alpha _s\beta \gamma ]-[\beta \gamma ](k_{3}[\alpha _s]+k_{7}[\alpha _i]). \end{aligned}$$
(23)

G\(\alpha _i\) subunits are abundantly expressed in neutrophils and macrophages (Gary and Bokoch 1988; Lattin et al. 2007). G\(\alpha _i\) and \(\beta \gamma \) expression (pmol/mg membrane protein) in neutrophils have been quantified previously (Gary and Bokoch 1988). Under the assumption that membrane proteins account for 5 % of total cellular protein mass, we estimate that neutrophils contain approximately \(1.8\,\mu \mathrm{M}\) \(\beta \gamma \) and \(8\,\mu \mathrm{M}\) G\(\alpha _i\). We were unable to determine the expression of G\(\alpha _s\) subunits in neutrophils, macrophages, or other immune cells, but in general, the level of G\(\alpha _s\) is thought to be significantly less than that of G\(\alpha _i\) (Smrcka 2008; Wettschureck and Offermanns 2005; Ostrom et al. 2000). We take the concentration of G\(\alpha _s\) in the model to be equal to that of rat cardio myocytes (\(2.3\,\mu \mathrm{M}\)), as measured in Post et al. (1995).

The affinity of G\(\alpha _i\) and \(G\alpha _s\) for \(\beta \gamma \) subunits was measured in Sarvazyan et al. (2002) (approximately .2 and 27 nM, respectively). The association rate of G\(\alpha _i\) and \(\beta \gamma \) (\(k_{7}\)) was taken equal to the association rate of fluorescence labeled G\(\alpha _i\) (Sarvazyan and Remmers 1998). The dissociation rate (\(k_{8}\)) was calculated accordingly. Measurements of the association and dissociation rates of the G\(\alpha _s\)\(\beta \gamma \) complex were unavailable. In numerical simulations, we set the association rate of G\(\alpha _s\) equal to that of G\(\alpha _i\) and calculated the dissociation rate (\(k_4\)) accordingly.

G\(\alpha _i\) and G\(\alpha _s\) are deactivated through hydrolysis, with intrinsic rates of \(.03\,\mathrm{s}^{-1}\) and \(.04-.07\,\mathrm{s}^{-1}\), respectively (Lan et al. 2000; Ross and Wilkie 2000; Graziano et al. 1989). The rate of G\(\alpha _i\) hydrolysis may be accelerated up to 90-fold by Regulator of G protein Signaling (RGS) molecules (Lan et al. 2000; Kimple et al. 2011), and there is evidence that RGS proteins may be important regulators of GPCR signaling (Kehrl 1998). In vivo RGS molecules lower agonist sensitivity and accelerate both the onset and recovery of GPCR responses (Kimple et al. 2011). Although the catalytic efficiency of RGS4 for G\(\alpha _i\) has been reported (Lan et al. 2000), we were unable to find quantitative estimates of the RGS protein concentration in immune cells. In addition, RGS activity and expression can be modulated by GPCR signaling (Hollinger and Helper 2002). Since the mechanisms through which RGS proteins are regulated during the immune response are complex and incompletely defined, we vary the rate of G\(\alpha _i\) hydrolysis in performing numerical experiments and sensitivity analysis.

We were unable to find the EP and C5a receptor-mediated G\(\alpha _s\) and G\(\alpha _i\) activation rates (\(k_1\) and \(k_5\)). In their place, we have used the \(\beta \)-adrenergic receptor-mediated G\(\alpha _s\) activation rate and the \(\alpha _{2a}\) adrenoceptor-mediated G\(\alpha _i\) activation rate (Katanaev and Chornomorets 2007). The dissociation constant of the EP receptor–G\(\alpha _s\) complex is taken equal to that of \(\beta \)-adrenergic receptor–G\(\alpha _s\) complex (Friedman and Johnson 1995).

1.4 cAMP

Adenylyl cyclases (ACs) and phosphodiesterases (PDEs) catalyze the synthesis and degradation of cAMP. The basal activity of both these enzymes is regulated through G protein signaling. The mechanism and character of G protein-mediated regulation, however, is context dependent. Indeed, AC isoforms are differentially regulated by G\(\alpha _i\), G\(\beta \gamma \), and calcium, while PDE activity is differentially regulated through both PKA and ERK, which signal downstream of G\(\alpha _s\) and G\(\alpha _i\), respectively. Because cAMP signaling in highly contextual, it is important to identify the isoforms of AC and PDE that are responsible for cAMP production and degradation in response to inflammatory signaling in immune cells.

In the canonical cAMP pathway, AC is activated by G\(\alpha _s\) subunits and is inhibited by G\(\alpha _i\) subunits. In immune cells, however, G\(\alpha _i\) and \(\beta \gamma \) signaling have emerged as an important promoter of cAMP production, and stimulation of G\(\alpha _i\)-coupled receptors can increase cAMP levels independently or in synergy with G\(\alpha _s\)-coupled receptors (Duan et al. 2010; Mahadeo et al. 2007; Wang et al. 2010). For example, in macrophages, AC VII, which belongs to a class of AC that is not inhibited by G\(\alpha _i\) but is stimulated by G \(\beta \gamma \), controls cytokine production in response to LPS (Duan et al. 2010); and cAMP production by AC VII is linked to signaling through receptors that couple to G\(\alpha \) subunits aside from G\(\alpha _s\) (Duan et al. 2010). It was also found that T cells and B cells deficient in AC VII exhibit a severely limited capacity to produce cAMP in response to combinations of ligands that stimulate multiple G proteins including G\(\alpha _s\) (Duan et al. 2010). As a result of these studies, our model assumes that the AC isoforms which mediate cAMP production in immune cells share many similarities with AC VII; that is, they are activated by \(G\alpha _s\) subunits, further stimulated by \(\beta \gamma \) subunits, and not inhibited by G\(\alpha _i\) subunits.

We assume that a fraction of adenylyl cyclase is bound to G\(\alpha _s\), and hence activated. In addition, some fractions of the activated AC may be bound to \(\beta \gamma \), and hence super activated. The concentrations of activated and super activated AC are given as follows:

$$\begin{aligned} \left[ AC^*\right]&= \frac{AC^\mathrm{tot}\alpha ^*_s}{\alpha ^*_s+K_4}\end{aligned}$$
(24)
$$\begin{aligned} \left[ AC^*-\beta \gamma \right]&= [AC^*]\frac{[\beta \gamma ]}{K_6+[\beta \gamma ]}. \end{aligned}$$
(25)

PDE4B isoforms have been identified as important regulators of cAMP production in diverse immune cells including monocytes, neutrophils, and macrophages (Wang et al. 1999; Catherine et al. 2005). In particular, the short PDE4B2 variant is the predominant PDE subtype in neutrophils, monocytes, and macrophage-like cells (Wang et al. 1999; Shepard et al. 2004). As a result, we consider PDE4B2 to be the principle enzyme responsible for cAMP degradation.

Although PDE4B2 is an important determinant of the cAMP response to stimuli, its low affinity for cAMP makes it ineffective at controlling basal cAMP levels. For this reason, we include another PDE isoform, PDE3, in our model. Along with PDE4B2, PDE3 is an important regulator of cAMP signaling in immune cell lines (Schudt et al. 1995; Shepard et al. 2004).

The production and degradation of cAMP is described by the following equation:

$$\begin{aligned} \frac{d[cAMP]}{dt}&= k_{9}\frac{[AC^*]}{K_6+[\beta \gamma ]}(K_6+C_1[\beta \gamma ])+k_{10}[AC]\nonumber \\&-\,k_{11}P\!D\!E4^\mathrm{tot}\frac{[cAMP]}{[c\!A\!M\!P]+K_{7}}\!-\!k_{12}P\!D\!E3^\mathrm{tot}\frac{[c\!A\!M\!P]}{[c\!A\!M\!P]\!+\!K_{8}}.\quad \quad \end{aligned}$$
(26)

Although ERK-mediated phosphorylation was shown to stimulate the activity of PDE4B2 by 132 % (Baillie et al. 2000), and PDE3 is subject to PKA-mediated stimulation (Schudt et al. 1995), an explicit description of these processes is beyond the scope of this model.

Our model of cAMP production is similar to other models that also employ a Hill coefficient of 1 (Saucerman et al. 2003; Xin et al. 2008). Another model of cAMP production (Iancu et al. 2007) which considers the activation of multiple AC isoforms by Gs uses Hill coefficients of \(.9787\) and \(1.0043\).

The dissociation constant \(K_{7}\) for PDE4B2 and cAMP was measured in (Huston et al. 1997). The rate of cAMP degradation by an unspecified variant of PDE4B was measured in Wang et al. (1997). Under the assumption that the PDE4B variant of (Wang et al. 1997) was PDE4B1, (an assumption that was based on the variant’s molecular weight), we calculated \(k_{11}\) from using the Vmax of PDE4B2 relative to PDE4B1, which was reported in Huston et al. (1997).

A range of values for \(K_{8}\) was reported in (Matthiesen and Nielsen 2011). For numerical simulations, we took \(K_{8}=.15\). The rate of PDE3-mediated cAMP degradation, \(k_{12}\) reported in Grant and Colman (1984), was converted to the appropriate units using the molecular weight reported in Dong et al. (2010).

Using the parameter values outlined above, the total concentration of PDE3 and PDE4 in the cell was calculated from the rates of PDE3- and PDE4-mediated cAMP hydrolysis which was reported in Schudt et al. (1995) (in so doing, we assume that human macrophage has a volume of \(5\times {10^3}\,\mu \mathrm{M}^3\) (Krombach et al. 1997).

We take the basal rate of cAMP production by ACII, the G\(\alpha _s\)-stimulated rate of cAMP production by ACII, and the fold increase in the rate of G\(\alpha _s\)-stimulated cAMP production by ACII after \(\beta \gamma \) binding (\(k_{10}\), \(k_{9}\), and \(C_1\), respectively) from Diel et al. (2006). The values reported in Diel et al. (2006) were converted to the appropriate units under the assumption that ACII has a molecular weight of 106kDa (Taussig et al. 1993), and that, similar to ACI, ACII constitutes .1 % of transfected S49 membranes (Tang et al. 1991). \(K_4\), the dissociation constant between G\(\alpha _s\) and adenylyl cyclase, was taken from Graziano et al. (1989). \(K_6\), the dissociation constant between ACII and \(\beta \gamma \), was taken from Dessauer and Gilman (1996).

In general, the dissociation constant between adenylyl cyclase and cAMP appears to be well below the cellular concentration of ATP (Litvin et al. 2003; Gribble et al. 2000). Hence, we use mass action kinetics to describe the production of cAMP by AC.

We were unable to find estimates of the concentration of adenylyl cyclase in immune cells. We take the cellular concentration of AC equal to that of rat ventricular myocytes, which was reported in Post et al. (1995).

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Leander, R., Friedman, A. Modulation of the cAMP Response by G\(\alpha _i\) and G\(\beta \gamma \): A Computational Study of G Protein Signaling in Immune Cells. Bull Math Biol 76, 1352–1375 (2014). https://doi.org/10.1007/s11538-014-9964-4

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