Mathematical Model of Contraction in Vascular Smooth Muscle

*Muscle Cell and Tissue - Novel Molecular Targets and Current Advances*

[51] Bozkurt MC, Tağil SM, Ozçakar L, Ersoy M, Tekdemir I. Anatomical variations as potential risk factors for ulnar tunnel syndrome: A cadaveric study. Clinical Anatomy. 2005;**18**:274-280. DOI: 10.1002/ca.20107

[52] Gross MS, Gelberman RH. The anatomy of the distal ulnar tunnel. Clinical Orthopaedics and Related Research. 1985;**196**:238-247

[53] Zeiss J, Guilliam-Haidet L. MR demonstration of anomalous muscles about the volar aspect of the wrist and forearm. Clinical Imaging. 1996;**20**:219-221. DOI: 10.1016/0899-7071(95)00013-5

**84**

**Chapter 6**

*Aleš Fajmut*

channels (ClCa), Na<sup>+</sup>

mathematical model, ionic fluxes

,50

/K<sup>+</sup>

**1. Introduction**

**87**

Cyclic guanosine 3<sup>0</sup>

and Na+

**Abstract**

Molecular Mechanisms and

Targets of Cyclic Guanosine

Monophosphate (cGMP) in

Molecular mechanisms and targets of cyclic guanosine monophosphate (cGMP) accounting for vascular smooth muscles (VSM) contractility are reviewed. Mathematical models of five published mechanisms are presented, and four novel mechanisms are proposed. cGMP, which is primarily produced by the nitric oxide (NO) dependent soluble guanylate cyclase (sGC), activates cGMP-dependent protein kinase (PKG). The NO/cGMP/PKG signaling pathway targets are the mechanisms that regulate cytosolic calcium ([Ca2+]i) signaling and those implicated in the Ca2+ desensitization of the contractile apparatus. In addition to previous mathematical models of cGMP-mediated molecular mechanisms targeting [Ca2+]i regulation, such as large-conductance Ca2+-activated K+ channels (BKCa), Ca2+-dependent Cl�

/K<sup>+</sup>



on the existing but perhaps overlooked experimental results. These are the effects of cGMP on the sarco�/endo- plasmic reticulum Ca2+-ATPase (SERCA), the plasma membrane Ca2+-ATPase (PMCA), the inositol 1,4,5-trisphosphate (IP3) receptor channels type 1 (IP3R1), and on the myosin light chain phosphatase (MLCP), which is implicated in the Ca2+-desensitization. Different modeling approaches are

**Keywords:** vascular smooth muscle, contraction, relaxation, nitric oxide, cyclic guanosine monophosphate, protein kinase G, Ca2+ signaling, desensitization,

messenger that mediates a broad spectrum of physiologic processes in multiple cell types within the cardiovascular, gastrointestinal, urinary, reproductive, nervous, endocrine, and immune systems. In particular, cGMP signaling plays a vital role in the endothelium, vascular smooth muscle cells (VSMC), and cardiac myocytes. cGMP was first synthesized in 1960, and soon after, its endogenous production was detected in rats. In the late 70s, two separate experiments confirmed that the gas nitric oxide (NO) stimulated cGMP production by activating soluble guanylate

/Cl� cotransport (NKCC),

/Ca2+ exchanger (NCX), Na<sup>+</sup>

presented and discussed, and novel model descriptions are proposed.

Vascular Smooth Muscles

#### **Chapter 6**

## Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular Smooth Muscles

*Aleš Fajmut*

### **Abstract**

Molecular mechanisms and targets of cyclic guanosine monophosphate (cGMP) accounting for vascular smooth muscles (VSM) contractility are reviewed. Mathematical models of five published mechanisms are presented, and four novel mechanisms are proposed. cGMP, which is primarily produced by the nitric oxide (NO) dependent soluble guanylate cyclase (sGC), activates cGMP-dependent protein kinase (PKG). The NO/cGMP/PKG signaling pathway targets are the mechanisms that regulate cytosolic calcium ([Ca2+]i) signaling and those implicated in the Ca2+ desensitization of the contractile apparatus. In addition to previous mathematical models of cGMP-mediated molecular mechanisms targeting [Ca2+]i regulation, such as large-conductance Ca2+-activated K+ channels (BKCa), Ca2+-dependent Cl� channels (ClCa), Na<sup>+</sup> /Ca2+ exchanger (NCX), Na<sup>+</sup> /K<sup>+</sup> /Cl� cotransport (NKCC), and Na+ /K<sup>+</sup> -ATPase (NKA), other four novel mechanisms are proposed here based on the existing but perhaps overlooked experimental results. These are the effects of cGMP on the sarco�/endo- plasmic reticulum Ca2+-ATPase (SERCA), the plasma membrane Ca2+-ATPase (PMCA), the inositol 1,4,5-trisphosphate (IP3) receptor channels type 1 (IP3R1), and on the myosin light chain phosphatase (MLCP), which is implicated in the Ca2+-desensitization. Different modeling approaches are presented and discussed, and novel model descriptions are proposed.

**Keywords:** vascular smooth muscle, contraction, relaxation, nitric oxide, cyclic guanosine monophosphate, protein kinase G, Ca2+ signaling, desensitization, mathematical model, ionic fluxes

#### **1. Introduction**

Cyclic guanosine 3<sup>0</sup> ,50 -monophosphate (cGMP) is an intracellular secondmessenger that mediates a broad spectrum of physiologic processes in multiple cell types within the cardiovascular, gastrointestinal, urinary, reproductive, nervous, endocrine, and immune systems. In particular, cGMP signaling plays a vital role in the endothelium, vascular smooth muscle cells (VSMC), and cardiac myocytes. cGMP was first synthesized in 1960, and soon after, its endogenous production was detected in rats. In the late 70s, two separate experiments confirmed that the gas nitric oxide (NO) stimulated cGMP production by activating soluble guanylate

cyclase (sGC). In 1980, it was reported that a diffusible substance causing vasodilatation is released from the endothelium. The so-called endothelium-derived relaxing factor (EDRF) was identified seven years later as NO. See [1] for review.

ANP, respectively). Natriuretic peptides (NPs) activate pGC, while NO diffuses into the cytosol, binds to, and activates sGC. cGMP exerts its action predominantly through binding and activating its target, cGMP-dependent protein kinase (PKG) [3]. There are two other types of cGMP-target effector molecules. The first type is phosphodiesterases (PDEs), which also degrade other cyclic nucleotides. The second type is nonselective cation channels, which are present in the visual and olfactory systems. PDEs degrade cGMP and, hence shape its spatiotemporal levels. CGMP also cross-regulates cyclic adenosine monophosphate levels (cAMP) since other PDEs (e.g. PDE2) that degrade both cAMP and cGMP are stimulated by cGMP [10]. In addition to PDE5, which selectively degrades cGMP, several other PDE isoforms can hydrolyze both, cGMP and cAMP. These are PDE1, PDE2, and PDE3. The strategy of inhibiting PDEs to enhance cGMP and related signaling has already been successfully used with the PDE5 inhibitors, especially sildenafil, to treat erectile dysfunction, pulmonary hypertension, and chronic heart failure [10]. Other cGMP-elevating drugs, such as nitrovasodilators that donate NO, and various NP analogs, have also been successfully used in humans to treat cardiovascular diseases. NO-generating drugs such as glyceryl trinitrate or sodium nitroprusside have been used to treat angina pectoris in humans for more than 100 years [11].

*DOI: http://dx.doi.org/10.5772/intechopen.97708*

*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular…*

**3. Calcium-contraction coupling in vascular smooth muscle cells**

The contractile state of VSMCs is regulated dynamically by hormones and neurotransmitters via the increase of the cytosolic calcium concentration ([Ca2+]i). Ca2+ is mostly released from its intracellular store sarcoplasmic reticulum (SR) via IP3 sensitive or ryanodine receptor channels (IP3R and RyR, respectively). In part, Ca2+ entry to the cytosol could be ascribed to the fluxes across the plasma membrane via the Ca2+- selective voltage-dependent channels. The rise in [Ca2+]i initiates binding of Ca2+ to CaM and the consequent interactions of myosin light chain kinase (MLCK) with Ca2+/CaM complexes. Active MLCK is the one that is bound with the Ca4CaM complex. Active MLCK phosphorylates the regulatory myosin light chain (MLC), enabling the attachment of myosin heads to the actin filaments and crossbridge cycling [12]. The smooth muscle cell's contractile state is determined by the extent of MLC phosphorylation regulated by the balance of MLCK and MLC phosphatase (MLCP) activities. The latter dephosphorylates MLC. High vascular tone is maintained as long as the phosphorylation rate is higher than that of dephosphorylation. Relaxation occurs when [Ca2+]i decreases, which results in the dissociation of Ca2+ from CaM and inactivation of MLCK. In that case, the activity of MLCP predominates the activity of MLCK, and the active actin-myosin cross-bridge cycling is not established. However, a passive latch state is possible [13]. The level of smooth muscle contractility can also be modulated at constant [Ca2+]i. The protein kinase C (PKC) and Rho kinase (ROCK) pathways play an essential role in regulating MLCP activity. They may cause diminished activity of MLCP and result in increased levels of phosphorylated MLC and a higher tension at a given [Ca2+]i. This increased contractility is called Ca2+ sensitization [12]. In reality, the process is much more complex since it is composed of many cross-interacting pathways with different feedbacks, nonlinear behavior of the interactions, dynamical changes of many variables – especially [Ca2+]i [14]. In this complex system of interactions [Ca2+]i signaling still represents a bottleneck according to its bow-tie structure of encoding and decoding [15]. cGMP/PKG signaling occurs on both – the encoding and the decoding sides and represents a predominant mechanism in regulating vasoactivity, particularly vasorelaxation. More than ten substrates being

**(VSMC)**

**89**

The molecular mechanisms of cardiovascular NO signaling are not entirely understood. Still, it is currently accepted that many effects are mediated, at least in part, via cGMP-dependent pathways. Within the cardiovascular system, these signaling pathways play a vital role in vasodilatation as well as in proliferation, migration, differentiation, and inflammation of VSMC and endothelial cells (ECs), in the modulation of myocyte contractility as well as of cardiac remodeling and thrombosis [2–4]. Impaired functioning at any signaling step from the synthesis through the effector activation and the degradation process of either NO or cGMP accounts for numerous cardiovascular diseases, such as hypertension, atherosclerosis, cardiac hypertrophy, and heart failure [3, 4]. Hence, these signaling pathways represent the potential targets for pharmacological treatment.

#### **2. Nitric oxide (NO) and cyclic guanosine monophosphate (cGMP) production and degradation**

Various stimuli can trigger relaxation responses of VSMC via the production and signaling of NO in the vascular endothelium. These are endogenous neurotransmitters (e.g., substance P and acetylcholine), humoral substances (e.g., bradykinin), and mechanical stimuli (e.g., the increase in hemodynamic shear stress or intraluminal pressure). They all trigger a complex cascade of biochemical reactions, accounting for either the mobilization, activation, or increase in the catalytic activity of NOS to produce NO or for upregulation of its gene expression. In the cardiovascular system, most of NO is produced in the endothelium by the endothelial NOS (eNOS). eNOS is also detected in cardiac myocytes, platelets, certain neurons, and kidney tubular epithelial cells. The other two isoforms are neuronal- and inducible- NOS (nNOS and iNOS, respectively). The former is mainly located in the nervous system, and the latter, which is induced by cytokines, is predominantly found in the immune system. They all catalyze the oxidation of the amino acid Larginine into L-citrulline, where the by-product is NO [5].

Sensing of shear stress is still under intensive research since it is mediated by rapid and almost simultaneous activation of various membrane molecules and microdomains, including ion channels, tyrosine kinase receptors, G-proteincoupled receptors, caveolae, adhesion proteins, cytoskeleton, glycocalyx, primary cilia, and filaments [6]. Though the underlying biochemical signaling processes are not entirely understood, three main mechanisms of mechanotransduction were proposed. The first one involves the mechanisms which account for the entry of Ca2+ across the EC plasma membrane either via capacitive Ca2+ entry (CCE) [7] or via activation of mechanosensing ion channels (MSICs) [8]. Both processes lead to further increases in [Ca2+]i, its consequent interaction with calmodulin (CaM), and finally to NOS activation. The other two mechanisms cross-correlate many signaling pathways mediated by G protein-coupled receptors (GPCR) and integrins involving protein kinases A, B, C, and G (PKA, Akt, PKC, and PKG, respectively), as well as phosphatidylinositide 3-kinase (PI3K). These signaling pathways regulate the activation of different nuclear factors affecting NOS gene expression [9], the recruitment of NOS from caveolae, the phosphorylation of NOS, and the cytosolic [Ca2+]i concentration and signaling [6].

Downstream the NO production cGMP is produced either by the soluble or the membrane-bound particulate guanylate cyclases, sGC and pGC, respectively, in response to either elevated NO or brain and atrial natriuretic peptides (BNP and

*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular… DOI: http://dx.doi.org/10.5772/intechopen.97708*

ANP, respectively). Natriuretic peptides (NPs) activate pGC, while NO diffuses into the cytosol, binds to, and activates sGC. cGMP exerts its action predominantly through binding and activating its target, cGMP-dependent protein kinase (PKG) [3]. There are two other types of cGMP-target effector molecules. The first type is phosphodiesterases (PDEs), which also degrade other cyclic nucleotides. The second type is nonselective cation channels, which are present in the visual and olfactory systems. PDEs degrade cGMP and, hence shape its spatiotemporal levels. CGMP also cross-regulates cyclic adenosine monophosphate levels (cAMP) since other PDEs (e.g. PDE2) that degrade both cAMP and cGMP are stimulated by cGMP [10]. In addition to PDE5, which selectively degrades cGMP, several other PDE isoforms can hydrolyze both, cGMP and cAMP. These are PDE1, PDE2, and PDE3. The strategy of inhibiting PDEs to enhance cGMP and related signaling has already been successfully used with the PDE5 inhibitors, especially sildenafil, to treat erectile dysfunction, pulmonary hypertension, and chronic heart failure [10]. Other cGMP-elevating drugs, such as nitrovasodilators that donate NO, and various NP analogs, have also been successfully used in humans to treat cardiovascular diseases. NO-generating drugs such as glyceryl trinitrate or sodium nitroprusside have been used to treat angina pectoris in humans for more than 100 years [11].

#### **3. Calcium-contraction coupling in vascular smooth muscle cells (VSMC)**

The contractile state of VSMCs is regulated dynamically by hormones and neurotransmitters via the increase of the cytosolic calcium concentration ([Ca2+]i). Ca2+ is mostly released from its intracellular store sarcoplasmic reticulum (SR) via IP3 sensitive or ryanodine receptor channels (IP3R and RyR, respectively). In part, Ca2+ entry to the cytosol could be ascribed to the fluxes across the plasma membrane via the Ca2+- selective voltage-dependent channels. The rise in [Ca2+]i initiates binding of Ca2+ to CaM and the consequent interactions of myosin light chain kinase (MLCK) with Ca2+/CaM complexes. Active MLCK is the one that is bound with the Ca4CaM complex. Active MLCK phosphorylates the regulatory myosin light chain (MLC), enabling the attachment of myosin heads to the actin filaments and crossbridge cycling [12]. The smooth muscle cell's contractile state is determined by the extent of MLC phosphorylation regulated by the balance of MLCK and MLC phosphatase (MLCP) activities. The latter dephosphorylates MLC. High vascular tone is maintained as long as the phosphorylation rate is higher than that of dephosphorylation. Relaxation occurs when [Ca2+]i decreases, which results in the dissociation of Ca2+ from CaM and inactivation of MLCK. In that case, the activity of MLCP predominates the activity of MLCK, and the active actin-myosin cross-bridge cycling is not established. However, a passive latch state is possible [13]. The level of smooth muscle contractility can also be modulated at constant [Ca2+]i. The protein kinase C (PKC) and Rho kinase (ROCK) pathways play an essential role in regulating MLCP activity. They may cause diminished activity of MLCP and result in increased levels of phosphorylated MLC and a higher tension at a given [Ca2+]i. This increased contractility is called Ca2+ sensitization [12]. In reality, the process is much more complex since it is composed of many cross-interacting pathways with different feedbacks, nonlinear behavior of the interactions, dynamical changes of many variables – especially [Ca2+]i [14]. In this complex system of interactions [Ca2+]i signaling still represents a bottleneck according to its bow-tie structure of encoding and decoding [15]. cGMP/PKG signaling occurs on both – the encoding and the decoding sides and represents a predominant mechanism in regulating vasoactivity, particularly vasorelaxation. More than ten substrates being

cyclase (sGC). In 1980, it was reported that a diffusible substance causing vasodilatation is released from the endothelium. The so-called endothelium-derived relaxing factor (EDRF) was identified seven years later as NO. See [1] for review. The molecular mechanisms of cardiovascular NO signaling are not entirely understood. Still, it is currently accepted that many effects are mediated, at least in part, via cGMP-dependent pathways. Within the cardiovascular system, these signaling pathways play a vital role in vasodilatation as well as in proliferation, migration, differentiation, and inflammation of VSMC and endothelial cells (ECs), in the modulation of myocyte contractility as well as of cardiac remodeling and thrombosis [2–4]. Impaired functioning at any signaling step from the synthesis through the effector activation and the degradation process of either NO or cGMP accounts for numerous cardiovascular diseases, such as hypertension, atherosclerosis, cardiac hypertrophy, and heart failure [3, 4]. Hence, these signaling pathways represent the potential targets for pharmacological treatment.

*Muscle Cell and Tissue - Novel Molecular Targets and Current Advances*

**2. Nitric oxide (NO) and cyclic guanosine monophosphate (cGMP)**

Various stimuli can trigger relaxation responses of VSMC via the production and signaling of NO in the vascular endothelium. These are endogenous neurotransmitters (e.g., substance P and acetylcholine), humoral substances (e.g., bradykinin), and mechanical stimuli (e.g., the increase in hemodynamic shear stress or

intraluminal pressure). They all trigger a complex cascade of biochemical reactions, accounting for either the mobilization, activation, or increase in the catalytic activity of NOS to produce NO or for upregulation of its gene expression. In the cardiovascular system, most of NO is produced in the endothelium by the endothelial NOS (eNOS). eNOS is also detected in cardiac myocytes, platelets, certain neurons, and kidney tubular epithelial cells. The other two isoforms are neuronal- and inducible- NOS (nNOS and iNOS, respectively). The former is mainly located in the nervous system, and the latter, which is induced by cytokines, is predominantly found in the immune system. They all catalyze the oxidation of the amino acid L-

Sensing of shear stress is still under intensive research since it is mediated by rapid and almost simultaneous activation of various membrane molecules and microdomains, including ion channels, tyrosine kinase receptors, G-proteincoupled receptors, caveolae, adhesion proteins, cytoskeleton, glycocalyx, primary cilia, and filaments [6]. Though the underlying biochemical signaling processes are not entirely understood, three main mechanisms of mechanotransduction were proposed. The first one involves the mechanisms which account for the entry of Ca2+ across the EC plasma membrane either via capacitive Ca2+ entry (CCE) [7] or via activation of mechanosensing ion channels (MSICs) [8]. Both processes lead to further increases in [Ca2+]i, its consequent interaction with calmodulin (CaM), and finally to NOS activation. The other two mechanisms cross-correlate many signaling pathways mediated by G protein-coupled receptors (GPCR) and integrins involving protein kinases A, B, C, and G (PKA, Akt, PKC, and PKG, respectively), as well as phosphatidylinositide 3-kinase (PI3K). These signaling pathways regulate the activation of different nuclear factors affecting NOS gene expression [9], the recruitment of NOS from caveolae, the phosphorylation of NOS, and the cytosolic [Ca2+]i

Downstream the NO production cGMP is produced either by the soluble or the membrane-bound particulate guanylate cyclases, sGC and pGC, respectively, in response to either elevated NO or brain and atrial natriuretic peptides (BNP and

arginine into L-citrulline, where the by-product is NO [5].

**production and degradation**

concentration and signaling [6].

**88**

phosphorylated *in vivo* by PKG were identified, and many of them take part in the [Ca2+]i encoding and decoding processes [3, 16].

the signal transduction of the contractile agonists mediated by the Gq-coupled receptors and terminates thereby the activity of PLC [25]. It was also proposed that PKG-Iα/RGS2 pathway might inhibit hormone receptor-triggered Ca2+ release and vasoconstriction *in vivo* [27]. It has also been shown that PKG can directly phosphorylate PLC-β *in vitro* in cultured COS-7 cells and *in vivo* in aortic VSMC, which blocked the activation of the enzymes correlated with the G-protein subunits and

*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular…*

influx across the plasma membrane through the voltage-operated Ca2+ channels (VOCC). cGMP/PKG has the opposite effect as cAMP/PKA on this type of channel. The former inhibited and the latter enhanced L-type Ca2+ channel (LTCC) activity in rabbit portal vein myocytes [28]. On the other hand, in rat cerebral arterial VSMC, which express T-type Ca2+ channels (TTCC) PKA [29] and PKG [30] both had a suppressing effect on their conductance. In both cases, a rightward shift of the voltage-response curve was observed. A similar effect was observed for the nonselective transient receptor potential cationic 1/3 channels (TRPC1/3) [31]. On the other hand, the experiments on the macroscopic and single-channel Ca2+ currents from guinea-pig basilar artery showed that the addition of 10 μM cGMP did not affect single-channel properties, such as conductance, voltage dependence, the number of open states, and different time constants, but significantly reduced the channel

There is also evidence that PKG may cause vasodilatation by suppressing the Ca2+

cGMP/PKG is supposed to enhance the activities of all three major Ca2+-removal systems in VSMCs. The Primary [Ca2+]i-off mechanism is refilling the Ca2+ stores via sarco/endo- plasmic reticulum Ca2+-ATPase (SERCA). The increase in SERCA activity in response to cGMP was first identified in isolated SR vesicles from cardiac and smooth muscles [33]. Later it was demonstrated that NO-induced relaxation of cultured VSMC from the aorta was associated with increased PKG-dependent phospholamban (PLB) phosphorylation [34]. Using a solid-state nuclear magnetic resonance (NMR) spectroscopy, it was found that PLB binds to SERCA allosterically [35]. Moreover, the phosphorylation at Ser16 of PLB, which gradually lowers PLB interaction with SERCA, was found to increase SERCA activity [35]. In gastric SMC, cGMP-mediated Ca2+ uptake via SERCA was observed *in vitro* in a concentration-

Experiments on cultured aortic VSMC provided evidence that cGMP also accel-

Another cGMP/PKG-mediated [Ca2+]i-off mechanism is the plasma membrane Ca2+ ATP-ase (PMCA). The evidence was first obtained with experiments on isolated proteins [38] and experiments performed on cultured VSMC [39]. All results suggested that the phosphorylation of the PMCA by PKG was responsible for stimulating the Ca2+-pumping activity, which was 2.4-fold higher after adding 500 μM of membrane-permeable cGMP analog. The leftward shift in the pumping activity vs. [Ca2+]i dependence was also observed [39]. Experiment on isolated and purified PMCA from porcine aorta [40] confirmed the previous two results at much

Na<sup>+</sup> concentrations [37]. cGMP increased both forward and reversed Na<sup>+</sup>

exchange modes by approximately 50% after adding 500 μM of membranepermeable cGMP analog. The [Ca2+]i pumping activity gradually increased with cGMP concentration. Phosphorylation by PKG was proposed as the underlying

/ Ca2+ exchangers (NCX) at different

/ Ca2+

attenuated agonist-induced IP3 production and Ca2+ release [26].

*DOI: http://dx.doi.org/10.5772/intechopen.97708*

**3.3 "[Ca2+]i-off" mechanisms as targets of cGMP/PKG signaling**

availability [32].

dependent manner [36].

mechanism for this effect [37].

smaller cGMP concentrations.

**91**

erates [Ca2+]i extrusion by stimulating the Na<sup>+</sup>

#### **3.1 cGMP-dependent protein kinase (PKG)**

The enzyme PKG belongs to the family of serine/threonine (Ser/Thr) kinases. In mammals, PKG-I and PKG-II are encoded by different genes, prkg1 and prkg2, respectively. PKG-I exists in two isoforms PKG-Iα and PKG-Iβ. PKG-I is present at high concentrations in all smooth muscles, including the uterus, vessels, intestine, and trachea. PKG-II is expressed in several brain nuclei, intestinal mucosa, kidney, adrenal cortex, chondrocytes, and lung. Only PKG-Iα and PKG-Iβ are expressed in the vascular system. See [3] for a review. All types of PKG are homodimers. Each monomer contains a regulatory and a catalytic domain. Each of the PKG regulatory domains binds two cGMP molecules allosterically with high cooperativity. The affinities of the two binding sites on each of the subunits of PKG-Iα differ by approximately tenfold. Binding sites occupied by cGMP induce significant conformation changes in the molecular structure. By that, autoinhibition of the catalytic center is released, and the basal activity is increased. Hence, the phosphorylation of serine/ threonine residues of the target proteins as well as of the autophosphorylation site is possible. All four binding sites have to be occupied with cGMP for the fully active holoenzyme PKG [17]. PKG-I mediates both receptortriggered and depolarization-induced vasorelaxation by several mechanisms. Many of them are not entirely understood, and some of them are still unknown. In general, PKG-mediated relaxation is induced either by attenuation of [Ca2+]i and/or desensitization of the contractile apparatus. The first effect is achieved by negatively affecting the "[Ca2+] i-on" mechanisms and by positively affecting the "[Ca2+]i-off" mechanisms. On the [Ca2+]i-decoding part, PKG's effect is concentrated mainly on the activation of the MLCP, which desensitizes the contractile apparatus to [Ca2+]i [18].

### **3.2 "[Ca2+]i-on" mechanisms as targets of cGMP/PKG signaling**

One of the primary targets of cGMP/PKG signaling to elevate [Ca2+]i is the IP3 receptor channel type 1 (IP3R1) and its correlated cGMP-associated kinase substrate protein (IRAG). If IRAG is colocalized with IP3R1 and PKG-Iβ in the presence of cGMP, it inhibits Ca2+ release through IP3R1 via its phosphorylation [19]. It was shown that PKG-Iβ exclusively phosphorylated only the type 1 but not the type 2 and 3 IP3R *in vivo* and that both, PKG and PKA, phosphorylated IP3R1 *in vitro* in gastric smooth muscles*,* which resulted in diminished IP3 and Ca2+-induced Ca2+ release (ICICR) from the SR [20]. *In vivo* experiments on mice with mutated IRAG, which did not interact with IP3R, showed that PKG/IRAG/ IP3R interactions indeed decrease the receptor-triggered [Ca2+]i and hence contraction [21]. In the *in vitro* experiments, it was also shown that PKG-Iβ phosphorylated IRAG but not IP3R [22]. The same was confirmed with COS-7 transfected cells where the phosphorylation of IRAG resulted in the reduced Ca2+ release during concurrent activation of PKA and PKG. The effect was observed for all three IP3R sub-types [23]. It is supposed that IRAG signaling does not modulate basal tone but might be important for blood pressure regulation under pathophysiological conditions [24].

PKG-Iα may also attenuate receptor-activated contraction via inhibition of IP3 production mediated by GPCR signaling [25] and interfering with phospholipase C-β (PLC-β) [26]. It has been shown that the isoform PKG-Iα binds, phosphorylates, and activates the regulator of G protein signaling 2 (RGS2), which terminates *Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular… DOI: http://dx.doi.org/10.5772/intechopen.97708*

the signal transduction of the contractile agonists mediated by the Gq-coupled receptors and terminates thereby the activity of PLC [25]. It was also proposed that PKG-Iα/RGS2 pathway might inhibit hormone receptor-triggered Ca2+ release and vasoconstriction *in vivo* [27]. It has also been shown that PKG can directly phosphorylate PLC-β *in vitro* in cultured COS-7 cells and *in vivo* in aortic VSMC, which blocked the activation of the enzymes correlated with the G-protein subunits and attenuated agonist-induced IP3 production and Ca2+ release [26].

There is also evidence that PKG may cause vasodilatation by suppressing the Ca2+ influx across the plasma membrane through the voltage-operated Ca2+ channels (VOCC). cGMP/PKG has the opposite effect as cAMP/PKA on this type of channel. The former inhibited and the latter enhanced L-type Ca2+ channel (LTCC) activity in rabbit portal vein myocytes [28]. On the other hand, in rat cerebral arterial VSMC, which express T-type Ca2+ channels (TTCC) PKA [29] and PKG [30] both had a suppressing effect on their conductance. In both cases, a rightward shift of the voltage-response curve was observed. A similar effect was observed for the nonselective transient receptor potential cationic 1/3 channels (TRPC1/3) [31]. On the other hand, the experiments on the macroscopic and single-channel Ca2+ currents from guinea-pig basilar artery showed that the addition of 10 μM cGMP did not affect single-channel properties, such as conductance, voltage dependence, the number of open states, and different time constants, but significantly reduced the channel availability [32].

### **3.3 "[Ca2+]i-off" mechanisms as targets of cGMP/PKG signaling**

cGMP/PKG is supposed to enhance the activities of all three major Ca2+-removal systems in VSMCs. The Primary [Ca2+]i-off mechanism is refilling the Ca2+ stores via sarco/endo- plasmic reticulum Ca2+-ATPase (SERCA). The increase in SERCA activity in response to cGMP was first identified in isolated SR vesicles from cardiac and smooth muscles [33]. Later it was demonstrated that NO-induced relaxation of cultured VSMC from the aorta was associated with increased PKG-dependent phospholamban (PLB) phosphorylation [34]. Using a solid-state nuclear magnetic resonance (NMR) spectroscopy, it was found that PLB binds to SERCA allosterically [35]. Moreover, the phosphorylation at Ser16 of PLB, which gradually lowers PLB interaction with SERCA, was found to increase SERCA activity [35]. In gastric SMC, cGMP-mediated Ca2+ uptake via SERCA was observed *in vitro* in a concentrationdependent manner [36].

Experiments on cultured aortic VSMC provided evidence that cGMP also accelerates [Ca2+]i extrusion by stimulating the Na<sup>+</sup> / Ca2+ exchangers (NCX) at different Na<sup>+</sup> concentrations [37]. cGMP increased both forward and reversed Na<sup>+</sup> / Ca2+ exchange modes by approximately 50% after adding 500 μM of membranepermeable cGMP analog. The [Ca2+]i pumping activity gradually increased with cGMP concentration. Phosphorylation by PKG was proposed as the underlying mechanism for this effect [37].

Another cGMP/PKG-mediated [Ca2+]i-off mechanism is the plasma membrane Ca2+ ATP-ase (PMCA). The evidence was first obtained with experiments on isolated proteins [38] and experiments performed on cultured VSMC [39]. All results suggested that the phosphorylation of the PMCA by PKG was responsible for stimulating the Ca2+-pumping activity, which was 2.4-fold higher after adding 500 μM of membrane-permeable cGMP analog. The leftward shift in the pumping activity vs. [Ca2+]i dependence was also observed [39]. Experiment on isolated and purified PMCA from porcine aorta [40] confirmed the previous two results at much smaller cGMP concentrations.

phosphorylated *in vivo* by PKG were identified, and many of them take part in the

The enzyme PKG belongs to the family of serine/threonine (Ser/Thr) kinases. In

mammals, PKG-I and PKG-II are encoded by different genes, prkg1 and prkg2, respectively. PKG-I exists in two isoforms PKG-Iα and PKG-Iβ. PKG-I is present at high concentrations in all smooth muscles, including the uterus, vessels, intestine, and trachea. PKG-II is expressed in several brain nuclei, intestinal mucosa, kidney, adrenal cortex, chondrocytes, and lung. Only PKG-Iα and PKG-Iβ are expressed in the vascular system. See [3] for a review. All types of PKG are homodimers. Each monomer contains a regulatory and a catalytic domain. Each of the PKG regulatory domains binds two cGMP molecules allosterically with high cooperativity. The affinities of the two binding sites on each of the subunits of PKG-Iα differ by approximately tenfold. Binding sites occupied by cGMP induce significant conformation changes in the molecular structure. By that, autoinhibition of the catalytic center is released, and the basal activity is increased. Hence, the phosphorylation of

autophosphorylation site is possible. All four binding sites have to be occupied with cGMP for the fully active holoenzyme PKG [17]. PKG-I mediates both receptortriggered and depolarization-induced vasorelaxation by several mechanisms. Many of them are not entirely understood, and some of them are still unknown. In general, PKG-mediated relaxation is induced either by attenuation of [Ca2+]i and/or desensitization of the contractile apparatus. The first effect is achieved by negatively affecting the "[Ca2+] i-on" mechanisms and by positively affecting the "[Ca2+]i-off" mechanisms. On the [Ca2+]i-decoding part, PKG's effect is concentrated mainly on the activation of the MLCP, which desensitizes the contractile

One of the primary targets of cGMP/PKG signaling to elevate [Ca2+]i is the IP3 receptor channel type 1 (IP3R1) and its correlated cGMP-associated kinase substrate protein (IRAG). If IRAG is colocalized with IP3R1 and PKG-Iβ in the presence of cGMP, it inhibits Ca2+ release through IP3R1 via its phosphorylation [19]. It was shown that PKG-Iβ exclusively phosphorylated only the type 1 but not the type 2 and 3 IP3R *in vivo* and that both, PKG and PKA, phosphorylated IP3R1 *in vitro* in gastric smooth muscles*,* which resulted in diminished IP3 and Ca2+-induced Ca2+ release (ICICR) from the SR [20]. *In vivo* experiments on mice with mutated IRAG, which did not interact with IP3R, showed that PKG/IRAG/ IP3R interactions indeed decrease the receptor-triggered [Ca2+]i and hence contraction [21]. In the *in vitro* experiments, it was also shown that PKG-Iβ phosphorylated IRAG but not IP3R [22]. The same was confirmed with COS-7 transfected cells where the phosphorylation of IRAG resulted in the reduced Ca2+ release during concurrent activation of PKA and PKG. The effect was observed for all three IP3R sub-types [23]. It is supposed that IRAG signaling does not modulate basal tone but might be important

serine/ threonine residues of the target proteins as well as of the

**3.2 "[Ca2+]i-on" mechanisms as targets of cGMP/PKG signaling**

for blood pressure regulation under pathophysiological conditions [24].

PKG-Iα may also attenuate receptor-activated contraction via inhibition of IP3 production mediated by GPCR signaling [25] and interfering with phospholipase C-β (PLC-β) [26]. It has been shown that the isoform PKG-Iα binds, phosphorylates, and activates the regulator of G protein signaling 2 (RGS2), which terminates

[Ca2+]i encoding and decoding processes [3, 16].

*Muscle Cell and Tissue - Novel Molecular Targets and Current Advances*

**3.1 cGMP-dependent protein kinase (PKG)**

apparatus to [Ca2+]i [18].

**90**

### **3.4 cGMP/PKG-dependent mechanisms that indirectly affect [Ca2+]i**

The mechanisms by which cGMP/PKG signaling interferes with [Ca2+]i are primarily linked with cell-membrane depolarization/hyperpolarization. Although depolarization-induced contraction remains mostly unresolved, these mechanisms are intensively studied [41]. One of the established targets of cGMP/PKG signaling is the large-conductance Ca2+-activated K+ channel (BKCa). The modulation of BKCa by different protein kinases in different smooth muscle tissues as well as the sites and mechanisms of their action remain unresolved [42]. The activation BKCa presumably hyperpolarises the cell membrane, thereby influences the gating of voltage-operated Ca2+ channels and lowers [Ca2+]i. PKG-I is known to activate BKCa either directly by phosphorylation [43] or indirectly via protein phosphatase regulation [44]. Activation of BKCa in the presence of NO/cGMP in isolated rat afferent arterioles attenuated extracellular Ca2+ influx upon KCl stimulation [45]. The role and importance of BKCa in vasorelaxation were highlighted with the experiments performed on BKCa-deficient mice. Their deletion led to a relatively mild increase in blood pressure. However, it increased vascular tone in small arteries due to a complete lack of spontaneous K+ efflux and, therefore, depolarised state of the membrane, and reduced suppression of Ca2+ transients in response to cGMP [46].

PKG [54]. The residues Ser695 and Thr696 as well as Ser852 and Thr853, are close within the MYPT1 sequence, and thus phosphorylation of one site prevents the phosphorylation of the neighboring site. It was proposed and also demonstrated that PKA or PKG-dependent phosphorylation of Ser695 and Ser852 prevents the

*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular…*

The current hypothesis is that the phosphorylation of Thr696 and Thr853 induces such structural changes in MYPT1 that these phosphorylated sites interact with the MLCP catalytic subunit PP1c [56] and is supported by the fact that MYPT1 is quite flexible at this part of the structure. Moreover, the sequences around Thr696 or Thr853 are similar to that of Ser19, where MLC is phosphorylated [57]. It is hypothesized that P-Thr696 and P-Thr853 may represent either substrate analogs to P-Ser19 of MLC or a potent autoinhibitory site docking to the PP1c catalytic subunit of MLCP [56]. In all these scenarios, the MLCP-dependent rate of MLC dephosphorylation is decreased. On the other hand, if MYPT is phosphorylated at Ser695 and Ser852 beforehand, Thr696 and Thr853 phosphorylation is blocked

Phosphorylation of Thr853 is a less potent inhibitor of MLCP than Thr696 [56]. It was also reported that PKA could phosphorylate all four sites, Ser695, Thr696, Ser852, Thr853, simultaneously. However, such a form of MYPT1 did not inhibit PP1c [58]. Another possibility of MLCP activity inhibition is binding the phosphorylated form of PKC-potentiated phosphatase inhibitor protein of 17 kDa (CPI-17) to the catalytic subunit PP1c. The phosphorylation increases the affinity of CPI-17 for PP1c by approximately 1000-fold, resulting in suppressed MLCP activity [59]. CPI-17 is expressed predominantly in tonic smooth muscles with slow and sustained contraction, especially in VSMC from the aorta and femoral arteries. The enzymes linked with the phosphorylation of CPI-17 are PKC, ROCK, zipper-interacting protein kinase (ZIPK), integrin-linked kinase (ILK). However, PKC and ROCK are most commonly mentioned [60]. ROCK signaling interferes with PKG and PKA signaling since PKA and PKG phosphorylate RhoA, the ROCK activator. Increased level of RhoA phosphorylation attenuates ROCK activity. In this way, PKG mediates vasorelaxation via reduced activity of ROCK and the correlated reduced inhibition

of MLCP. That leads to faster MLC dephosphorylation and relaxation [61].

Thr696 and Thr853 phosphorylation [62].

**93**

The role of PKC and ROCK in the stimulation-contraction coupling is still not well understood [62]. It is also possible that their role and importance in different smooth muscles is different. However, it is believed that CPI-17 phosphorylation and the corresponding inhibition of MLCP is the predominant process of the early phase of contraction. It was reported that PKC is believed to be primarily responsible for fast CPI-17 phosphorylation during the early phase of vasoconstriction, and ROCK was found responsible for slow, sustained CPI-17 phosphorylation during the sustained phase of contraction [63]. On the other hand, in the rat airways, ROCK activation and the consequent MLCP inhibition contributed to the early phase of the smooth muscles' contractile response. Whatever the agonist in that system was, the ROCK inhibitor Y27632 did not modify the basal tension. Still, it decreased the amplitude of the short duration response without altering the superimposed delayed contraction [64]. That indicates that in rat airway SMC, ROCK plays a major role in CPI-17 phosphorylation and that other kinases are responsible for

Moreover, PKG may affect MLCP activity also by the phosphorylation of telokin, which is a smooth muscle-specific protein whose sequence is identical to that of the noncatalytic terminus of MLCK. Telokin does not increase MLCP activity *per se* but acts synergistically with PKA and PKG [65]. By binding to either phosphorylated MYPT1 and/or phosphorylated MLC, telokin is supposed to facilitate the

interaction between the enzyme and its substrate and de-inhibits the auto-

phosphorylation of Thr696 and Thr853 and vice versa [12, 54, 55].

*DOI: http://dx.doi.org/10.5772/intechopen.97708*

[54, 56].

Another mechanism by which cGMP/PKG signaling may affect [Ca2+]i influx is via Ca2+-activated Cl channels [47]. These type of channels was observed in VSMC of mesenteric resistance arteries. Since their activation required phosphorylation, was sensitive to PKG inhibitors, and was evoked by adding PKG, it is believed that the effect of cGMP on the Cl current is mediated through PKG [47]. The physiological role of Ca2+-activated Cl channels is ambiguous since their excessive activation would promote an inward Cl current leading to cell depolarization, activation of VOCC, increase in [Ca2+]i, and, hence, vasoconstriction.

Information on the effect of cGMP/PKG on Na<sup>+</sup> /K<sup>+</sup> ATPase (NKA) [48] and cotransport of Na<sup>+</sup> /K+ /Cl (NKCC) [49] in terms of VSMC physiology is very limited and vague. However, these mechanisms have been implicated in the mathematical models [50, 51]. It was reported that cGMP might increase the activity of NKCC in vascular SMC of rat thoracic aorta by up to 3.5-fold [49]. In the canine pulmonary artery SMC, nitroprusside/cGMP-mediated relaxation was accompanied by increase NKA activity [48].

#### **3.5 cGMP/PKG signaling targeting the Ca2+-desensitization mechanisms**

PKG may also cause vasodilatation by desensitizing the contractile apparatus in response to elevated [Ca2+]i, resulting from either MLCP activation or MLCK deactivation. Both effects lead to MLC dephosphorylation, myosin cross-bridge detachment, and relaxation even at high [Ca2+]i. The enzyme MLCP plays a major role in the Ca2+-desensitization since it is not directly Ca2+-dependent, and it embodies various possibilities for regulating its activity [52]. These different options arise from its complex structure and widespread distribution in different tissues. MLCP holoenzyme is composed of three subunits – catalytic (PP1c), regulatory (MYPT1), and a small subunit (M20/M21). It is a Ser/Thr phosphatase that belongs to the protein phosphatase type 1 (PP1) family. Active PP1c is required for its catalytic activity, while MYPT1 targets the enzyme to its substrates and also autoregulates the catalytic activity of PP1c. This autoregulation emerges because MYPT1 contains different, for its structure and activity important, phosphorylation sites. In human sequence, these phosphorylation sites are Thr696 and Thr853, which are phosphorylated by ROCK [53] and other agonist-induced kinases. There are also Ser695 and Ser852 phosphorylation sites on MYPT1, which are phosphorylated by PKA and

#### *Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular… DOI: http://dx.doi.org/10.5772/intechopen.97708*

PKG [54]. The residues Ser695 and Thr696 as well as Ser852 and Thr853, are close within the MYPT1 sequence, and thus phosphorylation of one site prevents the phosphorylation of the neighboring site. It was proposed and also demonstrated that PKA or PKG-dependent phosphorylation of Ser695 and Ser852 prevents the phosphorylation of Thr696 and Thr853 and vice versa [12, 54, 55].

The current hypothesis is that the phosphorylation of Thr696 and Thr853 induces such structural changes in MYPT1 that these phosphorylated sites interact with the MLCP catalytic subunit PP1c [56] and is supported by the fact that MYPT1 is quite flexible at this part of the structure. Moreover, the sequences around Thr696 or Thr853 are similar to that of Ser19, where MLC is phosphorylated [57]. It is hypothesized that P-Thr696 and P-Thr853 may represent either substrate analogs to P-Ser19 of MLC or a potent autoinhibitory site docking to the PP1c catalytic subunit of MLCP [56]. In all these scenarios, the MLCP-dependent rate of MLC dephosphorylation is decreased. On the other hand, if MYPT is phosphorylated at Ser695 and Ser852 beforehand, Thr696 and Thr853 phosphorylation is blocked [54, 56].

Phosphorylation of Thr853 is a less potent inhibitor of MLCP than Thr696 [56]. It was also reported that PKA could phosphorylate all four sites, Ser695, Thr696, Ser852, Thr853, simultaneously. However, such a form of MYPT1 did not inhibit PP1c [58]. Another possibility of MLCP activity inhibition is binding the phosphorylated form of PKC-potentiated phosphatase inhibitor protein of 17 kDa (CPI-17) to the catalytic subunit PP1c. The phosphorylation increases the affinity of CPI-17 for PP1c by approximately 1000-fold, resulting in suppressed MLCP activity [59]. CPI-17 is expressed predominantly in tonic smooth muscles with slow and sustained contraction, especially in VSMC from the aorta and femoral arteries. The enzymes linked with the phosphorylation of CPI-17 are PKC, ROCK, zipper-interacting protein kinase (ZIPK), integrin-linked kinase (ILK). However, PKC and ROCK are most commonly mentioned [60]. ROCK signaling interferes with PKG and PKA signaling since PKA and PKG phosphorylate RhoA, the ROCK activator. Increased level of RhoA phosphorylation attenuates ROCK activity. In this way, PKG mediates vasorelaxation via reduced activity of ROCK and the correlated reduced inhibition of MLCP. That leads to faster MLC dephosphorylation and relaxation [61].

The role of PKC and ROCK in the stimulation-contraction coupling is still not well understood [62]. It is also possible that their role and importance in different smooth muscles is different. However, it is believed that CPI-17 phosphorylation and the corresponding inhibition of MLCP is the predominant process of the early phase of contraction. It was reported that PKC is believed to be primarily responsible for fast CPI-17 phosphorylation during the early phase of vasoconstriction, and ROCK was found responsible for slow, sustained CPI-17 phosphorylation during the sustained phase of contraction [63]. On the other hand, in the rat airways, ROCK activation and the consequent MLCP inhibition contributed to the early phase of the smooth muscles' contractile response. Whatever the agonist in that system was, the ROCK inhibitor Y27632 did not modify the basal tension. Still, it decreased the amplitude of the short duration response without altering the superimposed delayed contraction [64]. That indicates that in rat airway SMC, ROCK plays a major role in CPI-17 phosphorylation and that other kinases are responsible for Thr696 and Thr853 phosphorylation [62].

Moreover, PKG may affect MLCP activity also by the phosphorylation of telokin, which is a smooth muscle-specific protein whose sequence is identical to that of the noncatalytic terminus of MLCK. Telokin does not increase MLCP activity *per se* but acts synergistically with PKA and PKG [65]. By binding to either phosphorylated MYPT1 and/or phosphorylated MLC, telokin is supposed to facilitate the interaction between the enzyme and its substrate and de-inhibits the auto-

**3.4 cGMP/PKG-dependent mechanisms that indirectly affect [Ca2+]i**

*Muscle Cell and Tissue - Novel Molecular Targets and Current Advances*

The mechanisms by which cGMP/PKG signaling interferes with [Ca2+]i are primarily linked with cell-membrane depolarization/hyperpolarization. Although depolarization-induced contraction remains mostly unresolved, these mechanisms are intensively studied [41]. One of the established targets of cGMP/PKG signaling is the large-conductance Ca2+-activated K+ channel (BKCa). The modulation of BKCa by different protein kinases in different smooth muscle tissues as well as the sites and mechanisms of their action remain unresolved [42]. The activation BKCa presumably hyperpolarises the cell membrane, thereby influences the gating of voltage-operated Ca2+ channels and lowers [Ca2+]i. PKG-I is known to activate BKCa either directly by phosphorylation [43] or indirectly via protein phosphatase regulation [44]. Activation of BKCa in the presence of NO/cGMP in isolated rat afferent arterioles attenuated extracellular Ca2+ influx upon KCl stimulation [45]. The role and

importance of BKCa in vasorelaxation were highlighted with the experiments performed on BKCa-deficient mice. Their deletion led to a relatively mild increase in blood pressure. However, it increased vascular tone in small arteries due to a complete lack of spontaneous K+ efflux and, therefore, depolarised state of the membrane, and reduced suppression of Ca2+ transients in response to cGMP [46].

Information on the effect of cGMP/PKG on Na<sup>+</sup>

/K+

by increase NKA activity [48].

cotransport of Na<sup>+</sup>

**92**

Another mechanism by which cGMP/PKG signaling may affect [Ca2+]i influx is via Ca2+-activated Cl channels [47]. These type of channels was observed in VSMC of mesenteric resistance arteries. Since their activation required phosphorylation, was sensitive to PKG inhibitors, and was evoked by adding PKG, it is believed that the effect of cGMP on the Cl current is mediated through PKG [47]. The physiological role of Ca2+-activated Cl channels is ambiguous since their excessive activation would promote an inward Cl current leading to cell depolarization, activation of VOCC, increase in [Ca2+]i, and, hence, vasoconstriction.

limited and vague. However, these mechanisms have been implicated in the mathematical models [50, 51]. It was reported that cGMP might increase the activity of NKCC in vascular SMC of rat thoracic aorta by up to 3.5-fold [49]. In the canine pulmonary artery SMC, nitroprusside/cGMP-mediated relaxation was accompanied

PKG may also cause vasodilatation by desensitizing the contractile apparatus in response to elevated [Ca2+]i, resulting from either MLCP activation or MLCK deactivation. Both effects lead to MLC dephosphorylation, myosin cross-bridge detachment, and relaxation even at high [Ca2+]i. The enzyme MLCP plays a major role in the Ca2+-desensitization since it is not directly Ca2+-dependent, and it embodies various possibilities for regulating its activity [52]. These different options arise from its complex structure and widespread distribution in different tissues. MLCP holoenzyme is composed of three subunits – catalytic (PP1c), regulatory (MYPT1), and a small subunit (M20/M21). It is a Ser/Thr phosphatase that belongs to the protein phosphatase type 1 (PP1) family. Active PP1c is required for its catalytic activity, while MYPT1 targets the enzyme to its substrates and also autoregulates the catalytic activity of PP1c. This autoregulation emerges because MYPT1 contains different, for its structure and activity important, phosphorylation sites. In human sequence, these phosphorylation sites are Thr696 and Thr853, which are phosphorylated by ROCK [53] and other agonist-induced kinases. There are also Ser695 and Ser852 phosphorylation sites on MYPT1, which are phosphorylated by PKA and

**3.5 cGMP/PKG signaling targeting the Ca2+-desensitization mechanisms**

/Cl (NKCC) [49] in terms of VSMC physiology is very

/K<sup>+</sup> ATPase (NKA) [48] and

[Ca2+]i, Ca2+-desensitization of the contractile apparatus, and the reduction in force. In terms of cGMP-mediated target-regulation, they considered the effects on the BKCa and the contractile mechanism. Model simulations reproduced major NO/cGMP-induced VSMC relaxation effects. Additionally, cGMP was also considered in sGC desensitization, limiting cGMP production well below maximum [67]. The activating effect of NO/cGMP on BKCa was assumed as cGMP-dependent and

*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular…*

In 2007 and 2008, another two whole-cell-like models for VSMC were presented [50, 51]. However, both focused only on [Ca2+]i signaling and did not consider the processes of the contractile apparatus. Jacobsen et al. [50] focused primarily on the role of Ca2+-dependent Cl� channels that may cause the transitions between different types of [Ca2+]i signals in rat mesenteric small arteries upon α-adrenoreceptor stimulation. Instead of cGMP's influence on BKCa, they considered the cGMPdependent mechanisms of Ca2+-dependent Cl� channels and NKA. Kapela et al. [51] focused primarily on the plasma membrane electrophysiological properties and considered eleven ionic currents across the plasma membrane. Four of them considered cGMP-dependent mechanisms, i.e. Ca2+-dependent Cl� channels, BKCa, NCX, and NKCC. The model's purpose was to provide a working database of the rat mesenteric SMC physiological data. It was considered as the building block of the

**4.1 The model of cGMP-mediated current through the large-conductance**

BKCa is the most frequently modeled cGMP-dependent mechanism accounting for [Ca2+]i signaling. The first model of Yang et al. [67] was based on the experimental studies of Zhou et al. [69], who suggested that PKG stimulates the activity of two isoforms of BKCa either by phosphorylation of the channel or its regulatory proteins. The resultant effect on the potassium electric current (*IK*) was modeled with a left-shift of the voltage dependency of equilibrium open probability (*PK*,*<sup>o</sup>*) towards more negative potentials [67]. The complete mathematical description of [68] follows the Hodgkin-Huxley formalism. The general expression for*IK*is:

where *gK*is a channel conductance, *PK*,*<sup>o</sup>* is open probability or gating of the channel and ð Þ *Vm* � *VK* is the driving force of the current, where *Vm* is a membrane potential, and the *VK* is the Nernst equilibrium potential. Eq. (1) is analogous to Ohm's law. The overall gating factor *PK*,*<sup>o</sup>* consists of two parts – a fast gating term

where *f <sup>K</sup>* is a fraction of fast channels, and *sK* is a fraction of slow channels. Fast and slow gating terms are described with a first-order ordinary differential equation

> <sup>d</sup>*<sup>t</sup>* <sup>¼</sup> *PK*,*<sup>o</sup>* � *PK*,*<sup>f</sup> τ<sup>K</sup>*,*<sup>f</sup>*

> <sup>d</sup>*<sup>t</sup>* <sup>¼</sup> *PK*,*<sup>o</sup>* � *PK*,*<sup>s</sup> τ<sup>K</sup>*,*<sup>s</sup>*

d*PK*,*<sup>f</sup>*

d*PK*,*<sup>s</sup>*

*IK* ¼ *gKPK*,*<sup>o</sup>*ð Þ *Vm* � *VK* , (1)

*PK*,*<sup>o</sup>* ¼ *f <sup>K</sup>PK*,*<sup>f</sup>* þ *sKPK*,*<sup>s</sup>*, (2)

, (3)

, (4)

partially NO-dependent.

*DOI: http://dx.doi.org/10.5772/intechopen.97708*

future multi-cellular models of the vascular wall [51].

**Ca2+-activated K+ channels (BKCa)**

(*PK*,*<sup>f</sup>* ) and a slow gating term (*PK*,*<sup>s</sup>*):

for a biphasic (open-close) transition:

**95**

#### **Figure 1.**

*Molecular mechanisms and targets of cyclic guanosine monophosphate (cGMP)/protein kinase G (PKG) signaling in vascular smooth muscle cells (VSMCs) described in chapters 4.1 to 4.9 (full dark red lines denoted with Ch. 4.1 to 4.9) and others described in the text (dashed dark red lines). For explanation see text. Abbreviations used: GPCR (G protein-coupled receptor), RGS2 (regulator of Gq protein signaling 2), Gq (G protein), PLC (phospholipase C), PKC (protein kinase C), IP3 (inositol 1,4,5-trisphosphate), NO (nitric oxide), NPR (natriuretic peptide receptor), NP (natriuretic peptide), GTP (guanosine 5*<sup>0</sup> *-triphosphate), cGMP (cyclic guanosine monophosphate), 5'-GMP (guanosine 5*<sup>0</sup> *-monophosphate), pGC (particulate guanylate cyclase), sGC (soluble guanylate cyclase), PDE5 (phosphodiesterase 5), BKCa (large-conductance Ca2+-activated K+ channels), ClCa (Ca2+-dependent Cl*� *channels), VOCC (voltage-operated Ca2+ channel), NCX (Na<sup>+</sup> /Ca2+ exchanger), NKA (Na<sup>+</sup> /K<sup>+</sup> -ATPase), NKCC (Na<sup>+</sup> /K+ /Cl*� *cotransport), PMCA (plasma membrane Ca2+-ATPase), RhoA (ROCK activator), ROCK (rho kinase), CPI-17 (PKC-potentiated phosphatase inhibitor protein of 17 kDa), PP1c (MLCP catalytic subunit), MYPT1 (MLCP regulatory subunit), M20 (MLCP small subunit), MLCP (myosin light chain phosphatase),T696/ T853 (threonine 696/ 853 of the MYPT1), S695/S852 (serine 696/853 of the MYPT1), MLCK (myosin light chain kinase), MLC-20 (20 kDa myosin light chain), Ca4CaM (calmodulin with bound 4 Ca2+), Ca2+-CaM (Ca2+-calmodulin complexes), SR (sarcoplasmic reticulum), SERCA (sarco*�*/endo- plasmic reticulum Ca2+-ATPase), PLB (phospholamban), [Ca2+]i (cytosolic Ca2+ concentration), IRAG (IP3R1-correlated cGMP-associated kinase substrate protein), IP3R1 (1,4,5-trisphosphate receptor channel type 1), P (phosphorylated form of protein).*

suppressed MLCP activity emerging from Thr696 and Thr853 phosphorylation. This mechanism results in an increased rate of MLC dephosphorylation [66]. The majority of the described mechanisms and targets of cGMP/PKG signaling are summarized in **Figure 1**. 11 targets are depicted, from which 9 of them are described by mathematical models presented in the following chapter.

#### **4. Mathematical modeling of cGMP/PKG-mediated ionic fluxes and Ca2+-desensitization of the contractile apparatus**

The first attempt to build a whole-cell-like model of VSMC, also considering the NO/sGC/cGMP signaling cascade, was performed by Yang et al. [67]. They upgraded their existing models for rat cerebrovascular arteries [68]. The model [67] predicted the NO-induced cGMP production and the corresponding attenuation of

*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular… DOI: http://dx.doi.org/10.5772/intechopen.97708*

[Ca2+]i, Ca2+-desensitization of the contractile apparatus, and the reduction in force. In terms of cGMP-mediated target-regulation, they considered the effects on the BKCa and the contractile mechanism. Model simulations reproduced major NO/cGMP-induced VSMC relaxation effects. Additionally, cGMP was also considered in sGC desensitization, limiting cGMP production well below maximum [67]. The activating effect of NO/cGMP on BKCa was assumed as cGMP-dependent and partially NO-dependent.

In 2007 and 2008, another two whole-cell-like models for VSMC were presented [50, 51]. However, both focused only on [Ca2+]i signaling and did not consider the processes of the contractile apparatus. Jacobsen et al. [50] focused primarily on the role of Ca2+-dependent Cl� channels that may cause the transitions between different types of [Ca2+]i signals in rat mesenteric small arteries upon α-adrenoreceptor stimulation. Instead of cGMP's influence on BKCa, they considered the cGMPdependent mechanisms of Ca2+-dependent Cl� channels and NKA. Kapela et al. [51] focused primarily on the plasma membrane electrophysiological properties and considered eleven ionic currents across the plasma membrane. Four of them considered cGMP-dependent mechanisms, i.e. Ca2+-dependent Cl� channels, BKCa, NCX, and NKCC. The model's purpose was to provide a working database of the rat mesenteric SMC physiological data. It was considered as the building block of the future multi-cellular models of the vascular wall [51].

#### **4.1 The model of cGMP-mediated current through the large-conductance Ca2+-activated K+ channels (BKCa)**

BKCa is the most frequently modeled cGMP-dependent mechanism accounting for [Ca2+]i signaling. The first model of Yang et al. [67] was based on the experimental studies of Zhou et al. [69], who suggested that PKG stimulates the activity of two isoforms of BKCa either by phosphorylation of the channel or its regulatory proteins. The resultant effect on the potassium electric current (*IK*) was modeled with a left-shift of the voltage dependency of equilibrium open probability (*PK*,*<sup>o</sup>*) towards more negative potentials [67]. The complete mathematical description of [68] follows the Hodgkin-Huxley formalism. The general expression for*IK*is:

$$I\_K = \mathbb{g}\_K P\_{K, \rho} (V\_m - V\_K), \tag{1}$$

where *gK*is a channel conductance, *PK*,*<sup>o</sup>* is open probability or gating of the channel and ð Þ *Vm* � *VK* is the driving force of the current, where *Vm* is a membrane potential, and the *VK* is the Nernst equilibrium potential. Eq. (1) is analogous to Ohm's law. The overall gating factor *PK*,*<sup>o</sup>* consists of two parts – a fast gating term (*PK*,*<sup>f</sup>* ) and a slow gating term (*PK*,*<sup>s</sup>*):

$$P\_{K, \rho} = f\_K P\_{K, \f} + s\_K P\_{K, \mathfrak{s}},\tag{2}$$

where *f <sup>K</sup>* is a fraction of fast channels, and *sK* is a fraction of slow channels. Fast and slow gating terms are described with a first-order ordinary differential equation for a biphasic (open-close) transition:

$$\frac{\mathrm{d}P\_{Kf}}{\mathrm{d}t} = \frac{\overline{P}\_{K,\rho} - P\_{Kf}}{\tau\_{Kf}},\tag{3}$$

$$\frac{\mathrm{d}P\_{K,\mathrm{s}}}{\mathrm{d}t} = \frac{P\_{K,\mathrm{o}} - P\_{K,\mathrm{s}}}{\tau\_{K,\mathrm{s}}},\tag{4}$$

suppressed MLCP activity emerging from Thr696 and Thr853 phosphorylation. This mechanism results in an increased rate of MLC dephosphorylation [66]. The majority of the described mechanisms and targets of cGMP/PKG signaling are summarized in **Figure 1**. 11 targets are depicted, from which 9 of them are described by mathematical models presented in the following chapter.

*Molecular mechanisms and targets of cyclic guanosine monophosphate (cGMP)/protein kinase G (PKG) signaling in vascular smooth muscle cells (VSMCs) described in chapters 4.1 to 4.9 (full dark red lines denoted with Ch. 4.1 to 4.9) and others described in the text (dashed dark red lines). For explanation see text. Abbreviations used: GPCR (G protein-coupled receptor), RGS2 (regulator of Gq protein signaling 2), Gq (G protein), PLC (phospholipase C), PKC (protein kinase C), IP3 (inositol 1,4,5-trisphosphate), NO (nitric*

*guanylate cyclase), sGC (soluble guanylate cyclase), PDE5 (phosphodiesterase 5), BKCa (large-conductance Ca2+-activated K+ channels), ClCa (Ca2+-dependent Cl*� *channels), VOCC (voltage-operated Ca2+ channel),*

*membrane Ca2+-ATPase), RhoA (ROCK activator), ROCK (rho kinase), CPI-17 (PKC-potentiated phosphatase inhibitor protein of 17 kDa), PP1c (MLCP catalytic subunit), MYPT1 (MLCP regulatory subunit), M20 (MLCP small subunit), MLCP (myosin light chain phosphatase),T696/ T853 (threonine 696/ 853 of the MYPT1), S695/S852 (serine 696/853 of the MYPT1), MLCK (myosin light chain kinase), MLC-20 (20 kDa myosin light chain), Ca4CaM (calmodulin with bound 4 Ca2+), Ca2+-CaM (Ca2+-calmodulin complexes), SR (sarcoplasmic reticulum), SERCA (sarco*�*/endo- plasmic reticulum Ca2+-ATPase), PLB (phospholamban), [Ca2+]i (cytosolic Ca2+ concentration), IRAG (IP3R1-correlated cGMP-associated kinase substrate protein), IP3R1 (1,4,5-trisphosphate receptor channel type 1), P (phosphorylated form of protein).*

*-ATPase), NKCC (Na<sup>+</sup>*

*/K+*

*-triphosphate),*

*-monophosphate), pGC (particulate*

*/Cl*� *cotransport), PMCA (plasma*

*oxide), NPR (natriuretic peptide receptor), NP (natriuretic peptide), GTP (guanosine 5*<sup>0</sup>

*Muscle Cell and Tissue - Novel Molecular Targets and Current Advances*

*/K<sup>+</sup>*

*cGMP (cyclic guanosine monophosphate), 5'-GMP (guanosine 5*<sup>0</sup>

*/Ca2+ exchanger), NKA (Na<sup>+</sup>*

**4. Mathematical modeling of cGMP/PKG-mediated ionic fluxes and**

NO/sGC/cGMP signaling cascade, was performed by Yang et al. [67]. They

The first attempt to build a whole-cell-like model of VSMC, also considering the

upgraded their existing models for rat cerebrovascular arteries [68]. The model [67] predicted the NO-induced cGMP production and the corresponding attenuation of

**Ca2+-desensitization of the contractile apparatus**

**Figure 1.**

*NCX (Na<sup>+</sup>*

**94**

where *τK*,*<sup>f</sup>* and *τK*,*<sup>s</sup>* are the characteristic opening times and *PK*,*o*is an equilibrium open probability, which is a sigmoidal function of the membrane potential (*Vm*):

$$\overline{P}\_{K,\rho} = \frac{1}{\mathbf{1} + \mathbf{e}^{-\left(V\_m - V\_{K,1/2}\right)/S\_{K,0}}} \,. \tag{5}$$

The parameter's value *S*0,*<sup>K</sup>* represents the slope of the sigmoidal function, and its sign defines the orientation (declining/ increasing). Typically, *V*1*=*2,*<sup>K</sup>* is a parameter and represents the membrane potential, at which half-maximal value *PK*,*<sup>o</sup>* is achieved; however, here, it is a function of [Ca2+]i, [*cGMP*], and [*NO*]:

$$\mathbf{V}\_{K,1/2} = -\mathbf{V}\_{K,\mathbf{C}a} \log\left( \left[ \mathbf{C} a^{2+} \right]\_i \right) - \mathbf{V}\_{K,0} - \mathbf{V}\_{K,\mathbf{c}\mathbf{GMP}} \mathbf{R}\_{K,\mathbf{GMP}} - \mathbf{V}\_{K,\mathbf{NO}} \mathbf{R}\_{K,\mathbf{NO}},\tag{6}$$

where *VK*,0 is a basal value of *V*1/2, and *VK*,*NO*, *VK*,*cGMP* and *VK*,*Ca* are maximal induced shifts of *V*1/2 towards lower values, and, *RK*,*cGMP* and *RK*,*NO* are the regulatory Hill functions:

$$R\_{K, \text{cGMP}} = \frac{[\text{cGMP}]^{n\_{\text{cGMP},K}}}{[\text{cGMP}]^{n\_{\text{cGMP},K}} + K\_{\text{cGMP},K}^{n\_{\text{cGMP},K}}} \,, \tag{7}$$

$$R\_{K,NO} = \frac{[NO]^{n\_{NO,K}}}{[NO]^{n\_{NO,K}} + K\_{NO,K}^{n\_{NO,K}}},\tag{8}$$

The Cl� electric current (*ICl*) across the plasma membrane is defined as that for

**Parameter Description Value [67] Value [51]** *gK* Overall maximal conductance of the BKCa 0.5 nS / *fK* Fraction of fast channels 0.65 0.17 *sK* Fraction of slow channels 0.35 0.83 *τ<sup>K</sup>*,*<sup>f</sup>* The characteristic time of fast-channel activation 0.5 ms 0.84 ms *τ<sup>K</sup>*,*<sup>s</sup>* The characteristic time of slow-channel activation 11.5 ms 35.9 ms *SK*,0 The slope of the *Po*vs. *Vm* function 30.8 mV 18.25 mV *VK*,*Ca* Maximal Ca2+-induced V1/2 shift 53.7 mV 41.7 mV *VK*,0 Basal V1/2value 283.7 mV 128.2 mV *VK*,*cGMP* Maximal cGMP-induced V1/2 shift 66.9 mV 76 mV *VK*,*NO* Maximal NO-induced V1/2 shift 100 mV 46.3 mV *ncGMP*,*<sup>K</sup>* Hill coefficient 2 2 *nNO*,*<sup>K</sup>* Hill coefficient 1 1

*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular…*

<sup>d</sup>*<sup>t</sup>* <sup>¼</sup> *PCl*,*<sup>o</sup>* � *PCl*,*<sup>o</sup> τCl*

> *Ca*<sup>2</sup><sup>þ</sup> *nCa*,*Cl i*

½ � *cGMP ncGMP*,*Cl* <sup>þ</sup> *<sup>K</sup>ncGMP*,*Cl*

where *nCa*,*Cl*, *KCa*,*cGMP*,*Cl* and ρ are parameters, and *RcGMP*,*Cl* is cGMP-dependent:

but the equilibrium open probability *PCl*,*<sup>o</sup>* is not defined according to the Hodgkin-Huxley formalism but rather with an adapted Hill-type function:

*RcGMP*,*Cl* <sup>¼</sup> ½ � *cGMP ncGMP*,*Cl*

For *ICl*, Kapela et al. [51] used a similar approach as Jacobsen et al. [50]. However, the former authors applied slight modifications. The general description of the Cl� current is the same as in [50] (Eq. (10)), only the expression *PCl*,*<sup>o</sup>* is different. Kapela et al. [51] considered that a fraction of Ca2+-dependent Cl� channels is cGMP dependent, and a fraction is cGMP-independent. That is evident

The expression for *PCl*,*<sup>o</sup>* is analogous to Eq. (3):

*KcGMP*,*<sup>K</sup>* Half saturation constant in the regulatory cGMP-

*DOI: http://dx.doi.org/10.5772/intechopen.97708*

*KNO*,*<sup>K</sup>* Half saturation constant in the regulatory NO-

*Parameter values for the cGMP-dependent Ca2+-activated K+ (BKCa) current.*

dependent Hill function

dependent Hill function

*Ca*<sup>2</sup><sup>þ</sup> *nCa*,*Cl*

from the two terms within the expression for *PCl*,*<sup>o</sup>*:

d*PCl*,*<sup>o</sup>*

*ICl* ¼ *gClPCl*,*<sup>o</sup>*ð Þ *Vm* � *VCl* , (10)

*<sup>i</sup>* <sup>þ</sup> ð Þ *KCa*,*cGMP*,*Cl*ð Þ <sup>1</sup> � *<sup>ρ</sup>RcGMP*,*Cl nCa*,*Cl* , (12)

*cGMP*,*Cl*

, (11)

0.55 μM 1.5 μM

0.2 μM 0.2 μM

*:* (13)

potassium in Eq. (1):

**Table 1.**

**97**

*PCl*,*<sup>o</sup>* ¼ *RcGMP*,*Cl*

where *ncGMP*,*<sup>K</sup>* and *nNO*,*<sup>K</sup>* are the Hill coefficients and, *KcGMP*,*<sup>K</sup>* and *KNO*,*<sup>K</sup>* are the half-saturation constants. The same notation for Hill function parameters is used elsewhere in the text. The descriptions of all parameters are given in tables.

Authors Kapela et al. [51] used almost the same approach as Yang et al. [67]. In the former cas the authors used the Goldman-Hodgkin-Katz model to describe the potassium flux *IK*:

$$I\_K = A\_m N\_{BK\text{Ca}} P\_{K,o} P\_{BK\text{Ca}} V\_m \frac{F^2}{RT} \frac{[K]\_o - [K]\_i e^{\frac{F}{RT}Vm}}{1 - e^{\frac{F}{RT}Vm}},\tag{9}$$

where *Am* is a cell-membrane surface area, *NBKCa* is a channel density, *PBKCa* is a single channel permeability, *Vm* is a membrane potential, [*K*]o and [*K*]i are the external and internal potassium concentrations, respectively, *F* is a Faraday constant, *R* is the universal gas constant, and *T* is the absolute temperature. These cell-specific and general parameter values could be found in [51]. cGMP-dependent gating *PK*,*<sup>o</sup>* is defined the same as above in Eqs. (2)–(8).

The comparison of parameter values presented in **Table 1** reveals similarities but also differences. The model of Kapela et al. [51] was written more specifically for the rat mesenteric arteriole, whereby the parameters for the BKCa were such that they fitted experimental data of [70]. In contrast, the model of Yang et al. [67] was compared with the experimental data for rabbit femoral arteries [71], and the parameters for BKca accounted for [72].

#### **4.2 The model of cGMP-mediated current through the Ca2+ activated Cl**� **channels (ClCa)**

The model was first proposed by Jacobsen et al. [50] and was based on the measurements performed on the rat mesenteric resistance arteries [47]. *Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular… DOI: http://dx.doi.org/10.5772/intechopen.97708*


#### **Table 1.**

where *τK*,*<sup>f</sup>* and *τK*,*<sup>s</sup>* are the characteristic opening times and *PK*,*o*is an equilibrium open probability, which is a sigmoidal function of the membrane potential (*Vm*):

The parameter's value *S*0,*<sup>K</sup>* represents the slope of the sigmoidal function, and its sign defines the orientation (declining/ increasing). Typically, *V*1*=*2,*<sup>K</sup>* is a parameter

where *VK*,0 is a basal value of *V*1/2, and *VK*,*NO*, *VK*,*cGMP* and *VK*,*Ca* are maximal

½ � *cGMP ncGMP*,*<sup>K</sup>* <sup>þ</sup> *<sup>K</sup>ncGMP*,*<sup>K</sup>*

½ � *NO nNO*,*<sup>K</sup>* <sup>þ</sup> *<sup>K</sup>nNO*,*<sup>K</sup>*

�ð Þ *Vm*�*VK*,1*=*<sup>2</sup> *<sup>=</sup>SK*,0

� *VK*,0 � *VK*,*cGMPRK*,*cGMP* � *VK*,*NORK*,*NO*, (6)

*cGMP*,*K*

*NO*,*K*

*:* (5)

, (7)

, (8)

*RTVm* , (9)

*PK*,*<sup>o</sup>* <sup>¼</sup> <sup>1</sup> 1 þ *e*

and represents the membrane potential, at which half-maximal value *PK*,*<sup>o</sup>* is achieved; however, here, it is a function of [Ca2+]i, [*cGMP*], and [*NO*]:

induced shifts of *V*1/2 towards lower values, and, *RK*,*cGMP* and *RK*,*NO* are the

*RK*,*cGMP* <sup>¼</sup> ½ � *cGMP ncGMP*,*<sup>K</sup>*

*RK*,*NO* <sup>¼</sup> ½ � *NO nNO*,*<sup>K</sup>*

where *ncGMP*,*<sup>K</sup>* and *nNO*,*<sup>K</sup>* are the Hill coefficients and, *KcGMP*,*<sup>K</sup>* and *KNO*,*<sup>K</sup>*

parameters is used elsewhere in the text. The descriptions of all parameters are

Authors Kapela et al. [51] used almost the same approach as Yang et al. [67]. In the former cas the authors used the Goldman-Hodgkin-Katz model to describe the

where *Am* is a cell-membrane surface area, *NBKCa* is a channel density, *PBKCa* is a

The comparison of parameter values presented in **Table 1** reveals similarities but also differences. The model of Kapela et al. [51] was written more specifically for the rat mesenteric arteriole, whereby the parameters for the BKCa were such that they fitted experimental data of [70]. In contrast, the model of Yang et al. [67] was compared with the experimental data for rabbit femoral arteries [71], and the

single channel permeability, *Vm* is a membrane potential, [*K*]o and [*K*]i are the external and internal potassium concentrations, respectively, *F* is a Faraday constant, *R* is the universal gas constant, and *T* is the absolute temperature. These cell-specific and general parameter values could be found in [51]. cGMP-dependent

**4.2 The model of cGMP-mediated current through the Ca2+ activated**

The model was first proposed by Jacobsen et al. [50] and was based on the measurements performed on the rat mesenteric resistance arteries [47].

*F*2 *RT*

½ � *K <sup>o</sup>* � ½ � *K <sup>i</sup>*

1 � *e F* *e F RTVm*

are the half-saturation constants. The same notation for Hill function

*IK* ¼ *AmNBKCaPK*,*oPBKCaVm*

gating *PK*,*<sup>o</sup>* is defined the same as above in Eqs. (2)–(8).

parameters for BKca accounted for [72].

**Cl**� **channels (ClCa)**

**96**

i

*Muscle Cell and Tissue - Novel Molecular Targets and Current Advances*

*VK*,1*=*<sup>2</sup> ¼ �*VK*,*Ca* log *Ca*2<sup>þ</sup>

regulatory Hill functions:

given in tables.

potassium flux *IK*:

*Parameter values for the cGMP-dependent Ca2+-activated K+ (BKCa) current.*

The Cl� electric current (*ICl*) across the plasma membrane is defined as that for potassium in Eq. (1):

$$I\_{\mathcal{CI}} = \mathbf{g}\_{\mathcal{CI}} P\_{\mathcal{CI}\rho} (V\_m - V\_{\mathcal{CI}}),\tag{10}$$

The expression for *PCl*,*<sup>o</sup>* is analogous to Eq. (3):

$$\frac{\mathrm{d}P\_{\mathrm{Cl},\rho}}{\mathrm{d}t} = \frac{\overline{P}\_{\mathrm{Cl},\rho} - P\_{\mathrm{Cl},\rho}}{\tau\_{\mathrm{Cl}}},\tag{11}$$

but the equilibrium open probability *PCl*,*<sup>o</sup>* is not defined according to the Hodgkin-Huxley formalism but rather with an adapted Hill-type function:

$$\overline{P}\_{\text{Cl},\rho} = R\_{\text{cGMP},\text{Cl}} \frac{\left[\text{Ca}^{2+}\right]\_i^{\text{n}\_{\text{Ca},\text{Cl}}}}{\left[\text{Ca}^{2+}\right]\_i^{\text{n}\_{\text{Ca},\text{Cl}}} + \left(K\_{\text{Ca},\text{cGMP},\text{Cl}}(\mathbf{1}-\rho R\_{\text{cGMP},\text{Cl}})\right)^{\text{n}\_{\text{Ca},\text{Cl}}}},\tag{12}$$

where *nCa*,*Cl*, *KCa*,*cGMP*,*Cl* and ρ are parameters, and *RcGMP*,*Cl* is cGMP-dependent:

$$R\_{c\text{GMP},\text{Cl}} = \frac{[c\text{GMP}]^{n\_{c\text{GMP},\text{Cl}}}}{[c\text{GMP}]^{n\_{c\text{GMP},\text{Cl}}} + K\_{c\text{GMP},\text{Cl}}^{n\_{c\text{GMP},\text{Cl}}}} \,. \tag{13}$$

For *ICl*, Kapela et al. [51] used a similar approach as Jacobsen et al. [50]. However, the former authors applied slight modifications. The general description of the Cl� current is the same as in [50] (Eq. (10)), only the expression *PCl*,*<sup>o</sup>* is different. Kapela et al. [51] considered that a fraction of Ca2+-dependent Cl� channels is cGMP dependent, and a fraction is cGMP-independent. That is evident from the two terms within the expression for *PCl*,*<sup>o</sup>*:

$$\begin{split} P\_{\text{Cl},\rho} &= R\_{I,\text{Cl}} \frac{\left[\text{Ca}^{2+}\right]\_{i}^{\text{nCa},\text{Cl}}}{\left[\text{Ca}^{2+}\right]\_{i}^{\text{nCa},\text{Cl}} + \text{K}\_{\text{Ca},\text{Cl}}} \\ &+ R\_{\text{cGMP,\text{Cl}}} \frac{\left[\text{Ca}^{2+}\right]\_{i}^{\text{nCa},\text{Cl}}}{\left[\text{Ca}^{2+}\right]\_{i}^{\text{nCa},\text{Cl}} + \left(\text{K}\_{\text{Ca},\text{cGMP,\text{Cl}}} (1 - \rho R\_{\text{cGMP,\text{Cl}}})\right)^{n\_{\text{Ca},\text{Cl}}}},\end{split} \tag{14}$$

where *INCX*,*<sup>s</sup>* is a scaling factor for *INCX*, *dNCX* is the denominator constant, *γ* is voltage-dependence parameter, and *RNCX*,*cGMP* is a cGMP-dependent regulatory

*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular…*

where *f NCX*,*cGMP* is an additional fold-increase in NCX current due to cGMP and *KcGMP*,*NCX* is a half-saturation constant. Parameter values are presented in

In experiments [37], [Ca2+]i pumping activity gradually increased with cGMP

adding a large, probably unphysiological concentration (500 μM) of membranepermeable cGMP analog. Hence, the effects of low cGMP concentrations on the overall [Ca2+]i and contractile response are expected to be small. That is also evident from a large half-saturation constant (*KcGMP*,*NCX*) in the cGMP-dependent function *RNCX*,*cGMP*. However, the overall effect should be tested by integrating all mecha-

½ � *cGMP* ½ �þ *cGMP KcGMP*,*NCX*

, (16)

**-ATPase (NKA)**

. Jacobsen

, (17)

:2 K<sup>+</sup>

/ Ca2+ exchange was observed after

**/K<sup>+</sup>**

*Vm* þ Δ*V*<sup>1</sup> *Vm* þ Δ*V*<sup>2</sup>

*RNCX*,*cGMP* ¼ 1 þ *f NCX*,*cGMP*

**4.4 The model of cGMP-mediated current through the Na<sup>+</sup>**

*K*<sup>þ</sup> ½ �*<sup>i</sup> K*<sup>þ</sup> ½ �*<sup>i</sup>* þ *KK*,*NaK*

The NKA pumps Na<sup>+</sup> out and K<sup>+</sup> in and has stoichiometry 3 Na<sup>+</sup>

et al. [50] modeled the whole-cell electric current through NKA (*INaK*) as in [68]:

whereby the maximal current (*INaK*, *max* ) is considered as linearly cGMP-

All parameter descriptions and their values are presented in **Table 4**. In terms of membrane potential, increased NKA activity hyperpolarizes the membrane and enhances the Ca2+ influx through VOCC, which is similar to the effect of cGMP on BKCa. The effect of cGMP/PKG on NKA has not been studied often. The mathematical model is built on a single measurement on purified pig renal NKA at one single concentration of cGMP, which in addition to PKG increased the activity 1.6-fold. cGMP alone did not change the activity, and PKG alone increased it 1.2-fold [76]. Due to the lack of credible measurements, the reliability of

**Parameter Description Values [51]** *INCX*,*<sup>s</sup>* Current scaling factor 0.0487–0.487 pA *dNCX* Denominator constant <sup>3</sup> � <sup>10</sup>�<sup>4</sup> *γ* Voltage-dependence parameter 0.45 *f NCX*,*cGMP* Additional fold increase in electric current due to cGMP 0.55 *KcGMP*,*NCX* Half saturation constant in cGMP-dependent term 45 μM

*Na*<sup>þ</sup> ½ �*nNaK*,*Na*

*Na*<sup>þ</sup> ½ �*nNaK*,*Na i*

*<sup>i</sup>* <sup>þ</sup> *<sup>K</sup>nNaK*,*Na*

*INaK*, *max* ¼ *k*1,*NaK*,*cGMP*½ �� *cGMP k*2,*NaK*,*cGMP:* (18)

*/ Ca2+ exchange (NCX) current.*

*Na*,*NaK*

concentration. However, a 50% increase in Na<sup>+</sup>

*DOI: http://dx.doi.org/10.5772/intechopen.97708*

nisms in a whole-cell-like VSMC model.

*INaK* ¼ *INaK*, *max*

dependent:

this model is limited.

*Parameter values for the cGMP-dependent Na<sup>+</sup>*

**Table 3.**

**99**

function:

**Table 3**.

where *RI*,*Cl* is a cGMP-independent component and *RcGMP*,*Cl* is defined the same as in Eq. (13). Parameter values and their descriptions are presented in **Table 2**.

The comparison of parameter values presented in **Table 2** shows remarkable similarity. However, there are two significant differences in the modeling approach. Jacobsen et al. [50], who first proposed the cGMP-dependent model for *ICl*, defined *PCl*,*<sup>o</sup>* as a time-dependent function, whereas Kapela et al. [51] proposed an equilibrium model and omitted differential Eq. (11). On the other hand, they added a cGMPindependent term (compare Eq. (12) and Eq. (14)). In both cases, the same reference with experimental data for rat mesenteric arteries was used to determine the parameter values [47], except for the half-saturation constant in the cGMP-independent term (*KCa*,*Cl*) of [51], which was determined for the rat portal vein SMC [73].

It is suggested that the effect of cGMP on Ca2+-activated Cl� current is not likely to be essential for the tonic receptor-activated contractile response but rather for the synchronization among VSMCs as between VSMCs and ECs [47, 50, 74].

#### **4.3 The model of cGMP-mediated current through the Na<sup>+</sup> /Ca2+ exchanger (NCX)**

The framework for the mathematical description of the plasma membrane Na<sup>+</sup> /Ca2+ exchange (NCX) (*INCX*) in Kapela et al. was taken from the model of Di Francesco and Noble 1985 [75], which was developed for the atrial myocytes. Kapela et al. [51] adjusted the maximal exchanger conductivity, which is much lower in SMC than in atrial myocytes, and added the effect of cGMP according to the measured results of [37]:

$$I\_{\rm NCX} = I\_{\rm NCX, \beta} R\_{\rm NCX, \rm cGMP} \frac{[\rm Na^{+}]\_{i}^{3} [\rm Ca^{2+}]\_{o} e^{\frac{\rm N'\_{\rm mF}}{RT}} - [\rm Na^{+}]\_{o}^{3} [\rm Ca^{2+}]\_{i} e^{\frac{(r-1)V\_{\rm mF}}{RT}}}{1 + d\_{\rm NCX} \left( [\rm Na^{+}]\_{o}^{3} [\rm Ca^{2+}]\_{i} - [\rm Na^{+}]\_{i}^{3} [\rm Ca^{2+}]\_{o} \right)},\tag{15}$$


**Table 2.**

*Parameter values for the cGMP-dependent Ca2+-activated Cl*� *current.*

*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular… DOI: http://dx.doi.org/10.5772/intechopen.97708*

where *INCX*,*<sup>s</sup>* is a scaling factor for *INCX*, *dNCX* is the denominator constant, *γ* is voltage-dependence parameter, and *RNCX*,*cGMP* is a cGMP-dependent regulatory function:

$$R\_{\rm NCX,cGMP} = \mathbf{1} + f\_{\rm NCX,cGMP} \frac{[c\,\text{GMP}]}{[c\,\text{GMP}] + K\_{c\,\text{GMP},\text{NCX}}},\tag{16}$$

where *f NCX*,*cGMP* is an additional fold-increase in NCX current due to cGMP and *KcGMP*,*NCX* is a half-saturation constant. Parameter values are presented in **Table 3**.

In experiments [37], [Ca2+]i pumping activity gradually increased with cGMP concentration. However, a 50% increase in Na<sup>+</sup> / Ca2+ exchange was observed after adding a large, probably unphysiological concentration (500 μM) of membranepermeable cGMP analog. Hence, the effects of low cGMP concentrations on the overall [Ca2+]i and contractile response are expected to be small. That is also evident from a large half-saturation constant (*KcGMP*,*NCX*) in the cGMP-dependent function *RNCX*,*cGMP*. However, the overall effect should be tested by integrating all mechanisms in a whole-cell-like VSMC model.

#### **4.4 The model of cGMP-mediated current through the Na<sup>+</sup> /K<sup>+</sup> -ATPase (NKA)**

The NKA pumps Na<sup>+</sup> out and K<sup>+</sup> in and has stoichiometry 3 Na<sup>+</sup> :2 K<sup>+</sup> . Jacobsen et al. [50] modeled the whole-cell electric current through NKA (*INaK*) as in [68]:

$$I\_{NaK} = I\_{NaK,max} \frac{[K^+]\_i}{[K^+]\_i + K\_{K,NaK}} \frac{[Na^+]\_i^{\text{NaKNa}}}{[Na^+]\_i^{\text{NaKNa}} + K\_{Na,NaK}^{\text{mKNa}}} \frac{V\_m + \Delta V\_1}{V\_m + \Delta V\_2},\tag{17}$$

whereby the maximal current (*INaK*, *max* ) is considered as linearly cGMPdependent:

$$I\_{\rm NaK,max} = k\_{1,\rm NaK,c\rm GMP}[c\rm GMP] - k\_{2,\rm NaK,c\rm GMP}.\tag{18}$$

All parameter descriptions and their values are presented in **Table 4**.

In terms of membrane potential, increased NKA activity hyperpolarizes the membrane and enhances the Ca2+ influx through VOCC, which is similar to the effect of cGMP on BKCa. The effect of cGMP/PKG on NKA has not been studied often. The mathematical model is built on a single measurement on purified pig renal NKA at one single concentration of cGMP, which in addition to PKG increased the activity 1.6-fold. cGMP alone did not change the activity, and PKG alone increased it 1.2-fold [76]. Due to the lack of credible measurements, the reliability of this model is limited.


**Table 3.** *Parameter values for the cGMP-dependent Na<sup>+</sup> / Ca2+ exchange (NCX) current.*

*PCl*,*<sup>o</sup>* ¼ *RI*,*Cl*

**(NCX)**

the measured results of [37]:

*INCX* ¼ *INCX*,*sRNCX*,*cGMP*

Na<sup>+</sup>

**Table 2.**

**98**

*Ca*2<sup>þ</sup> *nCa*,*Cl i*

*<sup>i</sup>* <sup>þ</sup> *<sup>K</sup>nCa*,*Cl Ca*,*Cl*

*Muscle Cell and Tissue - Novel Molecular Targets and Current Advances*

**4.3 The model of cGMP-mediated current through the Na<sup>+</sup>**

*Na*<sup>þ</sup> ½ �<sup>3</sup>

ρ The determinant of cGMP influence on the half-

*KcGMP*,*Cl* Half saturation constant in the regulatory cGMP-

*Parameter values for the cGMP-dependent Ca2+-activated Cl*� *current.*

*Ca*2<sup>þ</sup> *nCa*,*Cl*

*Ca*2<sup>þ</sup> *nCa*,*Cl i*

where *RI*,*Cl* is a cGMP-independent component and *RcGMP*,*Cl* is defined the same as in Eq. (13). Parameter values and their descriptions are presented in **Table 2**. The comparison of parameter values presented in **Table 2** shows remarkable similarity. However, there are two significant differences in the modeling approach. Jacobsen et al. [50], who first proposed the cGMP-dependent model for *ICl*, defined *PCl*,*<sup>o</sup>* as a time-dependent function, whereas Kapela et al. [51] proposed an equilibrium model and omitted differential Eq. (11). On the other hand, they added a cGMPindependent term (compare Eq. (12) and Eq. (14)). In both cases, the same reference with experimental data for rat mesenteric arteries was used to determine the parameter values [47], except for the half-saturation constant in the cGMP-independent term (*KCa*,*Cl*) of [51], which was determined for the rat portal vein SMC [73].

It is suggested that the effect of cGMP on Ca2+-activated Cl� current is not likely to be essential for the tonic receptor-activated contractile response but rather for the synchronization among VSMCs as between VSMCs and ECs [47, 50, 74].

The framework for the mathematical description of the plasma membrane

Francesco and Noble 1985 [75], which was developed for the atrial myocytes. Kapela et al. [51] adjusted the maximal exchanger conductivity, which is much lower in SMC than in atrial myocytes, and added the effect of cGMP according to

> *<sup>i</sup> Ca*<sup>2</sup><sup>þ</sup> *o e γVmF*

**Parameter Description Values [50] Values [51]** *gCl* Overall maximal conductance 3.8 nS 5.75 nS *τCl* The characteristic time constant of channel activation 50 ms / *nCa*,*Cl* Hill coefficient 3 2 *KCa*,*cGMP*,*Cl* Half saturation constant in cGMP-dependent factor 0.4 μM 0.4 μM

<sup>1</sup> <sup>þ</sup> *dNCX Na*<sup>þ</sup> ½ �<sup>3</sup>

saturation constant

dependent Hill function

*ncGMP*,*Cl* Hill coefficient 3.3 3.3

*KCa*,*Cl* Half saturation constant in cGMP-independent term / 0.365 μM *RI*,*Cl* Weight of the cGMP-independent term / 0.0132

/Ca2+ exchange (NCX) (*INCX*) in Kapela et al. was taken from the model of Di

*RT* � *Na*<sup>þ</sup> ½ �<sup>3</sup>

*<sup>o</sup> Ca*<sup>2</sup><sup>þ</sup>

*<sup>o</sup> Ca*<sup>2</sup><sup>þ</sup> *i e* ð Þ *γ*�1 *VmF RT*

, (15)

*<sup>i</sup> Ca*<sup>2</sup><sup>þ</sup> *o*

0.9 0.9

6.4 μM 6.4 μM

*<sup>i</sup>* � *Na*<sup>þ</sup> ½ �<sup>3</sup>

*<sup>i</sup>* <sup>þ</sup> ð Þ *KCa*,*cGMP*,*Cl*ð Þ <sup>1</sup> � *<sup>ρ</sup>RcGMP*,*Cl nCa*,*Cl* , (14)

**/Ca2+ exchanger**

*Ca*2<sup>þ</sup> *nCa*,*Cl*

þ *RcGMP*,*Cl*


#### **Table 4.**

*Parameter values for the cGMP-dependent current trough Na<sup>+</sup> /K<sup>+</sup> -ATPase (NKA).*

#### **4.5 The model of cGMP-mediated current through the Na<sup>+</sup> /K<sup>+</sup> /Cl**� **cotransporter (NKCC)**

Instead of cGMP-dependent NKA, Kapela et al. [51] modeled the cGMP influence on the Na<sup>+</sup> /K<sup>+</sup> /Cl� cotransport (NKCC) having the 1:1:2 stoichiometry. The expression describing the electric current for a particular ion (*I i NaKCl*, where *i* is either Na, K, or Cl) was taken from [77] and upgraded with a cGMP dependency. According to [77], electric currents of individual ions are defined according to the valence (*Z*) and the stoichiometry:

$$I\_{NaKCl}^{Na} = I\_{NaKCl}^{K} = -\frac{1}{2} I\_{NaKCl}^{Cl}.\tag{19}$$

determining the reliable parameter values. The knowledge of the overall impact of NKCC on VSMC contraction is lacking. Hence, their inclusion in the cGMP-

*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular…*

**4.6 The model of cGMP-mediated Ca2+ flux through the sarco**�**/endo-plasmic**

Here we present a novel model of cGMP-dependent activation of the SERCA pump based on the solid-state NMR spectroscopy measurements [35] and the measurements performed on the isolated gastric SMC [36]. The former experiment [35] revealed the physical interactions between the SERCA and the PLB in either a phosphorylated or dephosphorylated state, and the latter experiment [36] offered the results on the increase in Ca2+ uptake as a function of cGMP. The experiments

dependent SERCA activity regulation is allosteric and that SERCA activity depends on the transient conformational equilibrium states of PLB [35]. It was found that phosphorylation at Ser16 of PLB shifts the conformation of PLB towards a more extended and SERCA-bound state, which is non-inhibitory [35]. Phosphorylation of PLB was induced by β-adrenergic stimulation, and it was supposed that the phosphorylation was cAMP/PKA dependent [35]. However, the cGMP/PKG-I dependent phosphorylation of PLB at Ser16 in contact with SERCA was previously shown *in vitro* [33]. Gustavsson et al. [35] proposed that PLB does not function as a simple on/off switch of SERCA. Still, its different conformational equilibrium states exert a gradual control on SERCA activity. PLB phosphorylation does not cause complete dissociation of PLB from SERCA, but it influences the conformational equilibrium of PLB's regulatory domain and shifts its populations towards the non-inhibitory state. That relieves the inhibition of SERCA [35]. According to [35], different PLB/ SERCA states exhibit functioning that follows Michaelis–Menten kinetics with the same Hill coefficient (*n*) and same (*Vmax*) but different half-saturation constant (*Km*), which is lower for higher relaxation-agonist level. Since the effect of cGMP solely on the half-saturation constant could not explain the increase in Ca2+ uptake as a function of high cGMP concentration that was observed *in vitro* in gastric SMC [36], we upgraded the model also by adding a cGMP-dependent regulatory factor into the parameter Vmax of the standard Michaelis–Menten kinetics, which for

> *Ca*<sup>2</sup><sup>þ</sup> *nSERCA*,*Ca i*

½ � *cGMP nSERCA*,*cGMP*,*<sup>V</sup>* ½ � *cGMP nSERCA*,*cGMP*,*<sup>V</sup>* <sup>þ</sup> *<sup>K</sup>nSERCA*,*cGMP*,*<sup>V</sup>*

½ � *cGMP nSERCA*,*cGMP*,*<sup>K</sup>* ½ � *cGMP nSERCA*,*cGMP*,*<sup>K</sup>* <sup>þ</sup> *<sup>K</sup>nSERCA*,*cGMP*,*<sup>K</sup>*

*Ca*,*cGMPKnSERCA*,*Ca*

*Ca*,*SERCA*, *max*

*cGMP*,*SERCA*,*V*

*cGMP*,*SERCA*,*K*

, (22)

*:* (23)

*:* (24)

*<sup>i</sup>* <sup>þ</sup> *<sup>R</sup>nSERCA*,*Ca*

*Ca*<sup>2</sup><sup>þ</sup> *nSERCA*,*Ca*

where *RSERCA*,*cGMP* is a cGMP-dependent pumping rate regulatory factor, which is according to [36] an increasing Hill function superimposed on the basal pumping rate *VSERCA*, *min* . The Hill function represents the best fit to the measured data of

*RCa*,*cGMP* is a cGMP-dependent half-saturation constant regulatory factor in the Eq. (22), which is according to the measurements [35] a decaying Hill function:

performed on isolated lipid bilayer-bound proteins revealed that the PLB-

dependent mechanisms seems speculative.

*DOI: http://dx.doi.org/10.5772/intechopen.97708*

**reticulum Ca2+-ATPase (SERCA)**

SERCA reads:

**101**

*JSERCA* ¼ *VSERCA*, *min RSERCA*,*cGMP*

cGMP dependent increase in Ca2+ uptake [36]:

*RSERCA*,*cGMP* ¼ 1 þ *f SERCA*,*cGMP*

*RCa*,*cGMP* ¼ 1 � *f Ca*,*cGMP*

Here only the electric current for Cl� (*I Cl NaKCl*) is written:

$$I\_{\rm NaKCl}^{\rm Cl} = -I\_{\rm NaKCl} \mathbf{Z}\_{\rm Cl} \mathbf{R}\_{\rm NaKCl,cGMP} \ln\left(\frac{[\rm Na^{+}]\_{o}}{[\rm Na^{+}]\_{i}} \frac{[\rm K^{+}]\_{o}}{[\rm K^{+}]\_{i}} \left(\frac{[\rm Cl^{-}]\_{o}}{[\rm Cl^{-}]\_{i}}\right)^{2}\right),\tag{20}$$

where *ZCl* is the valence of Cl�, *INaKCl* is a cotransport current coefficient, and *Na*<sup>þ</sup> ½ �, *K*<sup>þ</sup> ½ � and *Cl*� ½ � are the corresponding concentrations outside and inside (subscripts *o* and *i*, respectively) of the cell. *RNaKCl*,*cGMP* represents the cGMPdependent regulation factor that is defined as:

$$R\_{\rm NaKCl,cGMP} = \mathbf{1} + f\_{\rm NaKCl,cGMP} \frac{[c\rm GMP]}{[c\rm GMP] + K\_{cGMP,NaKCl}},\tag{21}$$

where *f NaKCl*,*cGMP* is a fold-increase in cotransport current due to cGMP. All parameters and their values are presented in **Table 5**.

Very little is known about the effect of cGMP on the NKCC. The model is more or less built on one single reference [49], which also offers limited information for


**Table 5.**

*Parameter values for the cGMP-dependent Na<sup>+</sup> /K<sup>+</sup> /Cl*� *cotransport (NKCC) current.* *Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular… DOI: http://dx.doi.org/10.5772/intechopen.97708*

determining the reliable parameter values. The knowledge of the overall impact of NKCC on VSMC contraction is lacking. Hence, their inclusion in the cGMPdependent mechanisms seems speculative.

#### **4.6 The model of cGMP-mediated Ca2+ flux through the sarco**�**/endo-plasmic reticulum Ca2+-ATPase (SERCA)**

Here we present a novel model of cGMP-dependent activation of the SERCA pump based on the solid-state NMR spectroscopy measurements [35] and the measurements performed on the isolated gastric SMC [36]. The former experiment [35] revealed the physical interactions between the SERCA and the PLB in either a phosphorylated or dephosphorylated state, and the latter experiment [36] offered the results on the increase in Ca2+ uptake as a function of cGMP. The experiments performed on isolated lipid bilayer-bound proteins revealed that the PLBdependent SERCA activity regulation is allosteric and that SERCA activity depends on the transient conformational equilibrium states of PLB [35]. It was found that phosphorylation at Ser16 of PLB shifts the conformation of PLB towards a more extended and SERCA-bound state, which is non-inhibitory [35]. Phosphorylation of PLB was induced by β-adrenergic stimulation, and it was supposed that the phosphorylation was cAMP/PKA dependent [35]. However, the cGMP/PKG-I dependent phosphorylation of PLB at Ser16 in contact with SERCA was previously shown *in vitro* [33]. Gustavsson et al. [35] proposed that PLB does not function as a simple on/off switch of SERCA. Still, its different conformational equilibrium states exert a gradual control on SERCA activity. PLB phosphorylation does not cause complete dissociation of PLB from SERCA, but it influences the conformational equilibrium of PLB's regulatory domain and shifts its populations towards the non-inhibitory state. That relieves the inhibition of SERCA [35]. According to [35], different PLB/ SERCA states exhibit functioning that follows Michaelis–Menten kinetics with the same Hill coefficient (*n*) and same (*Vmax*) but different half-saturation constant (*Km*), which is lower for higher relaxation-agonist level. Since the effect of cGMP solely on the half-saturation constant could not explain the increase in Ca2+ uptake as a function of high cGMP concentration that was observed *in vitro* in gastric SMC [36], we upgraded the model also by adding a cGMP-dependent regulatory factor into the parameter Vmax of the standard Michaelis–Menten kinetics, which for SERCA reads:

$$J\_{\rm SERCA} = V\_{\rm SERCA,min} R\_{\rm SERCA,c\rmGMP} \frac{[\rm Ca^{2+}]\_i^{\rm n\rm SERCA,ca}\_i}{[\rm Ca^{2+}]\_i^{\rm n\rm SERCA,Cr}\_i + R\_{\rm Ca,c\rm GMP}^{\rm n\rm SERCA,Ca} R\_{\rm Ca,SERCA,max}}},\tag{22}$$

where *RSERCA*,*cGMP* is a cGMP-dependent pumping rate regulatory factor, which is according to [36] an increasing Hill function superimposed on the basal pumping rate *VSERCA*, *min* . The Hill function represents the best fit to the measured data of cGMP dependent increase in Ca2+ uptake [36]:

$$R\_{\text{SERCA},\text{GMP}} = \mathbf{1} + f\_{\text{SERCA},\text{GMP}} \frac{[\text{cGMP}]^{\text{gSERCA},\text{cM}\text{P},V}}{[\text{cGMP}]^{\text{gSERCA},\text{cM}\text{P},V} + K\_{\text{cGMP},\text{SERCA},V}^{\text{gSERCA},\text{cM}\text{P},V}} \tag{23}$$

*RCa*,*cGMP* is a cGMP-dependent half-saturation constant regulatory factor in the Eq. (22), which is according to the measurements [35] a decaying Hill function:

$$R\_{\text{Ca},\text{cGP}} = 1 - f\_{\text{Ca},\text{cGP}} \frac{[\text{cGMP}]^{\text{nSERA},\text{cGP},\text{X}}}{[\text{cGMP}]^{\text{nSERA},\text{cGMP},\text{X}} + K\_{\text{cGMP},\text{SERCA},\text{X}}^{\text{nSERA},\text{cGP},\text{X}}} . \tag{24}$$

**4.5 The model of cGMP-mediated current through the Na<sup>+</sup>**

*Muscle Cell and Tissue - Novel Molecular Targets and Current Advances*

*Parameter values for the cGMP-dependent current trough Na<sup>+</sup>*

expression describing the electric current for a particular ion (*I*

*I Na NaKCl* ¼ *I*

*NaKCl* ¼ �*INaKClZClRNaKCl*,*cGMP* ln *Na*<sup>þ</sup> ½ �*<sup>o</sup>*

*RNaKCl*,*cGMP* ¼ 1 þ *f NaKCl*,*cGMP*

parameters and their values are presented in **Table 5**.

Here only the electric current for Cl� (*I*

dependent regulation factor that is defined as:

*Parameter values for the cGMP-dependent Na<sup>+</sup>*

Instead of cGMP-dependent NKA, Kapela et al. [51] modeled the cGMP influ-

**Parameter Description Values [50]** *KK*,*NaK* Half-saturation constant 1 mM *KNa*,*NaK* Half-saturation constant 11 mM *nNaK*,*Na* Hill coefficient 1.5 Δ*V*<sup>1</sup> Electric potential shift 150 mV Δ*V*<sup>2</sup> Electric potential shift 200 mV *k*1,*NaK*,*cGMP* cGMP-concentration weighted electric current 30 pA/μM *k*2,*NaK*,*cGMP* Electric current constant 30 pA

either Na, K, or Cl) was taken from [77] and upgraded with a cGMP dependency. According to [77], electric currents of individual ions are defined according to the

*NaKCl* ¼ � <sup>1</sup>

*Cl*

where *ZCl* is the valence of Cl�, *INaKCl* is a cotransport current coefficient, and

where *f NaKCl*,*cGMP* is a fold-increase in cotransport current due to cGMP. All

Very little is known about the effect of cGMP on the NKCC. The model is more or less built on one single reference [49], which also offers limited information for

**Parameter Description Values [51]** *INaKCl* Cotransport current coefficient 0.106 pA *f NaKCl*,*cGMP* Additional fold-increase in electric current due to cGMP 3.5 *KcGMP*,*NaKCl* Half-saturation constant in cGMP-dependent factor 6.4 μM

*/K<sup>+</sup>*

*Na*<sup>þ</sup> ½ �, *K*<sup>þ</sup> ½ � and *Cl*� ½ � are the corresponding concentrations outside and inside (subscripts *o* and *i*, respectively) of the cell. *RNaKCl*,*cGMP* represents the cGMP-

*Na*<sup>þ</sup> ½ �*<sup>i</sup>*

2 *I Cl*

*NaKCl*) is written:

*K*<sup>þ</sup> ½ �*<sup>o</sup> K*<sup>þ</sup> ½ �*<sup>i</sup>*

� �2 !

½ � *cGMP* ½ �þ *cGMP KcGMP*,*NaKCl*

*/Cl*� *cotransport (NKCC) current.*

*Cl*� ½ �*<sup>o</sup> Cl*� ½ �*<sup>i</sup>*

*K*

/Cl� cotransport (NKCC) having the 1:1:2 stoichiometry. The

*/K<sup>+</sup>*

**cotransporter (NKCC)**

/K<sup>+</sup>

valence (*Z*) and the stoichiometry:

ence on the Na<sup>+</sup>

**Table 4.**

*I Cl*

**Table 5.**

**100**

**/K<sup>+</sup> /Cl**�

*-ATPase (NKA).*

*i*

*NaKCl:* (19)

*NaKCl*, where *i* is

, (20)

, (21)


#### **Table 6.**

*Parameter values for the cGMP-dependent Ca2+ efflux via SERCA.*

All parameter values and their descriptions are presented in **Table 6**.

It has to be noted that the parameter values for Eq. (25) were determined by the best fit to only three measured values from [35], and that *KSERCA*,*Ca*, *max* is considered the same as in the existing model for VSMC [50]. In the case of *VSERCA*, *min* , the best fit was done to five measured points [36].

where *IPMCA*, *min* is a minimal pumping rate translated into electric current, which is, according to [40], a function of PKG. Yoshida et al. [40] conducted all their experiments at variable PKG concentrations and 5 to 20 times higher cGMP concentration. Since all our functions were written as cGMP-dependent, we translate PKG concentrations into cGMP by considering the active PKG:cGMP molar ratio 1:4. The Hill function fitted to measured data [40] is superimposed on the basal pumping current *IPMCA*, *min* and is here represented as a cGMP-dependent

*nPMCA*,*cGMP* Hill coefficient 1.7 Recalculated by fitting from [40]

**Parameter Description Value References**

*IPMCA*, *min* Minimal Ca2+ pumping current 0.90 pA [50]

*k<sup>β</sup>* PMCA voltage sensitivity constant �100 mV [50] *k<sup>α</sup>* PMCA voltage sensitivity constant 250 mV [50]

*nPMCA*,*Ca* Hill coefficient 0.6 Recalculated by fitting from [40]

*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular…*

Parameter values and their descriptions are presented in **Table 7**.

might impact the [Ca2+]i, which the whole-cell-like model could demonstrate.

The proposed model for cGMP-mediated IP3R1 deactivation is also presented here for the first time. The framework of the proposed mechanism is the model of

**4.8 The model of cGMP-mediated Ca2+ flux through the inositol 1,4,5-trisphosphate (IP3) receptor channels type 1 (IP3R1)**

In Eq. (25), *KCa*,*PMCA* is a half-saturation constant. The value was determined by fitting the Hill function to two sets of measured data [40], the control case, and the PKG-dependent case, with 0.2 μM PKG and 1 μM cGMP. For the former case, the value is 0.22 μM, and for the latter case, it is 0.14 μM. Since the change is rather small and there are only two measured values available, we do not assume cGMP dependency in this case. That decision is also supported by the results of [39] where the left-shift in that value was only by 27% at supramaximal membrane-permeable cGMP analog concentration (500 μM). We propose here the average value. Elsewhere the value is similar (0.2 μM) [50, 79] and 0.17 μM [51]. *nPMCA*,*Ca* is also determined by fitting to the same set of measured data [40]. The values were 0.7 and 0.5 for the control and the PKG-dependent case, respectively. We propose here an average. Value 1 was used elsewhere [50, 51, 79]. Fold-increase in electric current due to cGMP is quite large and

½ � *cGMP nPMCA*,*cGMP* ½ � *cGMP nPMCA*,*cGMP* <sup>þ</sup> *<sup>K</sup>nPMCA*,*cGMP*

*cGMP*,*PMCA*

0.18 μM Recalculated by fitting from [40]

3 Recalculated by fitting from [40]

0.50 μM Recalculated by fitting from [40]

*:* (26)

regulatory factor:

**Table 7.**

*4.8.1 Variant A*

**103**

*RPMCA*,*cGMP* ¼ 1 þ *f PMCA*,*cGMP*

*KCa*,*PMCA* Half-saturation constant in Ca<sup>2</sup> +

*DOI: http://dx.doi.org/10.5772/intechopen.97708*

*f PMCA*,*cGMP* Additional fold-increase in electric

*KcGMP*,*PMCA* Half-saturation constant in the


current due to cGMP

cGMP-dependent regulatory Hill function

*Parameter values for the cGMP-dependent Ca2+ current via PMCA.*

The significance of the cGMP effect on SERCA is still debated, and it is challenging to consider it independently of other [Ca2+]i-off mechanisms. It is suggested [78] that cGMP-dependent SERCA activity can play a significant role in modulating smooth muscle [Ca2+]i, but its role in the cGMP-mediated relaxation is minor. Therefore, it would be worth testing the significance of that mechanism on the whole-cell-like VSMC model.

#### **4.7 The model of cGMP-mediated current through the plasma membrane Ca2+-ATPase (PMCA)**

Yoshida et al. [40] demonstrated that PKG phosphorylated and stimulated PMCA in a concentration-dependent manner. The experiment was conducted on isolated and purified PMCA from the porcine aorta. Much smaller - physiological cGMP concentration, 1 μM, than in previous experiments (500 μM) [38, 39], was added to 10 μg/mL (roughly 0.2 μM) PKG at different free Ca2+ concentrations. That increased PMCA activity by approximately 3-fold over the whole range of Ca2+ concentrations and slightly shifted the pumping activity towards the left. cGMP alone did not affect the pump activity [40]. In modeling these effects, we use a similar approach as for SERCA, which obeys Michaelis–Menten kinetics. However, previous studies [50, 79] also included weak membrane-potential-dependence, which we also consider here:

$$I\_{\rm PMCA} = I\_{\rm PMCA,min} R\_{\rm PMCA,c\rm GMP} \frac{\left[\text{Ca}^{2+}\right]\_i^{\rm PNMA,Ca}}{\left[\text{Ca}^{2+}\right]\_i^{\rm PNMA,Ca} + K\_{\rm Ca,PMCA}^{\rm n\_{\rm PMCA},Ca}} \left(1 + \frac{V\_m - k\_\beta}{k\_a}\right), \tag{25}$$

*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular… DOI: http://dx.doi.org/10.5772/intechopen.97708*


#### **Table 7.**

All parameter values and their descriptions are presented in **Table 6**.

**Parameter Description Value References** *nSERCA*,*Ca* Hill coefficient 2.5 [50] *VSERCA*, *min* Minimal Ca2+ pumping rate 1.88 � <sup>10</sup><sup>3</sup> <sup>μ</sup>M/s [50]

*nSERCA*,*cGMP*,*<sup>V</sup>* Hill coefficient 0.092 Recalculated by

*nSERCA*,*cGMP*,*<sup>K</sup>* Hill coefficient 1.2 Recalculated by

best fit was done to five measured points [36].

*f SERCA*,*cGMP* Additional fold increase in SERCA activity due

*KcGMP*,*SERCA*,*<sup>V</sup>* Half-saturation constant in the cGMP-

*KCa*,*SERCA*, *max* Maximal value of SERCA half-saturation

*f Ca*,*cGMP* Additional fold decrease in SERCA activity

*KcGMP*,*SERCA*,*<sup>K</sup>* Half saturation constant in the cGMP-

*Parameter values for the cGMP-dependent Ca2+ efflux via SERCA.*

to cGMP

*Muscle Cell and Tissue - Novel Molecular Targets and Current Advances*

dependent regulatory Hill function

constant

due to cGMP

dependent regulatory Hill function

whole-cell-like VSMC model.

**Table 6.**

**Ca2+-ATPase (PMCA)**

which we also consider here:

**102**

*IPMCA* ¼ *IPMCA*, *min RPMCA*,*cGMP*

It has to be noted that the parameter values for Eq. (25) were determined by the best fit to only three measured values from [35], and that *KSERCA*,*Ca*, *max* is considered the same as in the existing model for VSMC [50]. In the case of *VSERCA*, *min* , the

The significance of the cGMP effect on SERCA is still debated, and it is challenging to consider it independently of other [Ca2+]i-off mechanisms. It is suggested [78] that cGMP-dependent SERCA activity can play a significant role in modulating smooth muscle [Ca2+]i, but its role in the cGMP-mediated relaxation is minor. Therefore, it would be worth testing the significance of that mechanism on the

**4.7 The model of cGMP-mediated current through the plasma membrane**

Yoshida et al. [40] demonstrated that PKG phosphorylated and stimulated PMCA in a concentration-dependent manner. The experiment was conducted on isolated and purified PMCA from the porcine aorta. Much smaller - physiological cGMP concentration, 1 μM, than in previous experiments (500 μM) [38, 39], was added to 10 μg/mL (roughly 0.2 μM) PKG at different free Ca2+ concentrations. That increased PMCA activity by approximately 3-fold over the whole range of Ca2+ concentrations and slightly shifted the pumping activity towards the left. cGMP alone did not affect the pump activity [40]. In modeling these effects, we use a similar approach as for SERCA, which obeys Michaelis–Menten kinetics. However, previous studies [50, 79] also included weak membrane-potential-dependence,

> *Ca*<sup>2</sup><sup>þ</sup> *nPMCA*,*Ca i*

*<sup>i</sup>* <sup>þ</sup> *<sup>K</sup>nPMCA*,*Ca*

*Ca*,*PMCA*

1 þ

*Vm* � *k<sup>β</sup> kα* 

1.44 Recalculated by

1.44 � <sup>10</sup><sup>2</sup> <sup>μ</sup>M Recalculated by

0.07 μM [50]

70 Recalculated by

0.1 μM Recalculated by

fitting from [36]

fitting from [36]

fitting from [36]

fitting from [36]

fitting from [35]

fitting from [35]

, (25)

*Ca*<sup>2</sup><sup>þ</sup> *nPMCA*,*Ca*

*Parameter values for the cGMP-dependent Ca2+ current via PMCA.*

where *IPMCA*, *min* is a minimal pumping rate translated into electric current, which is, according to [40], a function of PKG. Yoshida et al. [40] conducted all their experiments at variable PKG concentrations and 5 to 20 times higher cGMP concentration. Since all our functions were written as cGMP-dependent, we translate PKG concentrations into cGMP by considering the active PKG:cGMP molar ratio 1:4. The Hill function fitted to measured data [40] is superimposed on the basal pumping current *IPMCA*, *min* and is here represented as a cGMP-dependent regulatory factor:

$$R\_{\rm PMCA,c\rm GMP} = 1 + f\_{\rm PMCA,c\rm GMP} \frac{[c\rm GMP]^{\rm np\rm pCA,c\rm GMP}}{[c\rm GMP]^{\rm np\rm pCA,c\rm GMP} + K\_{c\rm GMP,p\rm MCA}^{\rm np\rm pCA,c\rm GMP}} \,\tag{26}$$

Parameter values and their descriptions are presented in **Table 7**.

In Eq. (25), *KCa*,*PMCA* is a half-saturation constant. The value was determined by fitting the Hill function to two sets of measured data [40], the control case, and the PKG-dependent case, with 0.2 μM PKG and 1 μM cGMP. For the former case, the value is 0.22 μM, and for the latter case, it is 0.14 μM. Since the change is rather small and there are only two measured values available, we do not assume cGMP dependency in this case. That decision is also supported by the results of [39] where the left-shift in that value was only by 27% at supramaximal membrane-permeable cGMP analog concentration (500 μM). We propose here the average value. Elsewhere the value is similar (0.2 μM) [50, 79] and 0.17 μM [51]. *nPMCA*,*Ca* is also determined by fitting to the same set of measured data [40]. The values were 0.7 and 0.5 for the control and the PKG-dependent case, respectively. We propose here an average. Value 1 was used elsewhere [50, 51, 79]. Fold-increase in electric current due to cGMP is quite large and might impact the [Ca2+]i, which the whole-cell-like model could demonstrate.

#### **4.8 The model of cGMP-mediated Ca2+ flux through the inositol 1,4,5-trisphosphate (IP3) receptor channels type 1 (IP3R1)**

#### *4.8.1 Variant A*

The proposed model for cGMP-mediated IP3R1 deactivation is also presented here for the first time. The framework of the proposed mechanism is the model of the Ca2+ efflux via IP3R1 as proposed by [50]. That model is upgraded here according to the experimental data of [36], with an additional regulatory factor *RIR*1,*cGMP*, which accounts for the drop in Ca2+ release after IP3 stimulation with increasing cGMP levels [36]. General description of the Ca2+ flux across the SR membrane through the IP3R1 channels (*JIR*1) follows [50]:

$$J\_{IR1} = \mathbf{g}\_{IR1} \mathbf{P}\_{IR1} \left( \left[ \mathbf{Ca}^{2+} \right]\_{\text{SR}} - \left[ \mathbf{Ca}^{2+} \right]\_i \right), \tag{27}$$

where *gIR*1is an overall maximal rate of the channel permeability and *PIR*1is the channel open probability, which is a biphasic bell-shaped function of [Ca2+]i, and is also dependent on the cytosolic IP3 and sarcoplasmic Ca2+ concentrations ([*IP3*] and [*Ca2+*]*SR*, respectively). It is modeled as in [50, 80]:

$$P\_{IR1} = f\_{IR1,A} \left(\mathbf{1} - f\_{IR1,J}\right) R\_{IR1,c\text{GMP}} \frac{[IP\_3]^{n\text{p}\text{s}}}{[IP\_3]^{n\text{p}\text{s}} + K\_{IP3}^{n\text{p}\text{s}}} \frac{[\text{Ca}^{2+}]\_{SR}^{\text{nS\text{R}}}}{[\text{Ca}^{2+}]\_{SR}^{\text{nS\text{R}}} + K\_{Ca,SR}^{n\text{s}}}.\tag{28}$$

The regulatory factor *RIR*1,*cGMP* is a decaying Hill function that depends on the cGMP concentration and is an upgrade from the previous model [50]. The proposed function is the best fit to the measured decay of IP3-induced Ca2+ release as a function of cGMP concentration in isolated gastric SMC [36]:

$$R\_{IR1,c\text{GMP}} = 1 - f\_{IR1,c\text{GMP}} \frac{[c\text{GMP}]^{n\_{IR1,c\text{GMP}}}}{[c\text{GMP}]^{n\_{IR1,c\text{GMP}}} + K\_{c\text{GMP},IR1}^{n\_{IR1,c\text{GMP}}}},\tag{29}$$

where *f IR*1,*cGMP* is an additional fold decrease in the channel open probability due to cGMP. *f IR*1,*<sup>A</sup>*, and *f IR*1,*<sup>I</sup>* in Eq. (29) are the fractions of the channel population occupied by [Ca2+]i at the activation sites and inactivation sites, respectively. In this way, the bell-shaped dependency on [Ca2+]i is achieved. Since activation is a fast process, it is considered to be in the equilibrium:

$$f\_{IR1,A} = \frac{\left[\text{Ca}^{2+}\right]\_i^{n\_A}}{\left[\text{Ca}^{2+}\right]\_i^{n\_A} + K\_{\text{Ca},A}^{n\_A}},\tag{30}$$

cGMP dependency of IP3-dependent Ca2+ flux. The cGMP/PKG mediated phosphorylation of IP3R1 in microsomes was confirmed in the accompanying experiment by immunoprecipitation. Hence, Murthy and Zhou [20] measured Ca2+ release through the phosphorylated IP3R1 within smooth muscle microsomes at different IP3 concentrations. Prior to measurements, microsomes were either treated with 0.5 μM PKG-Iα holoenzyme and 10 μM cGMP or left intact (control). Ca2+ release was determined from the decrease in the steady-state microsomal radioactive Ca2+ isotope content. In this way, two dose–response curves were obtained [20]. Their best fits with a Hill function reveal almost the same Hill coefficients (0.49 and 0.42, for the control and cGMP/PKG treated case, respectively) and the same Vmax (100%) but significantly different half-saturation constants Km, 1.17 � <sup>10</sup>�<sup>3</sup> <sup>μ</sup>M and 2.35 <sup>μ</sup>M, for the control and the cGMP/PKG treated case, respectively. These two measured values represent two points to which any function could virtually be fitted. Since this is highly unrealistic, we propose the use of competitive, reversible enzyme inhibition kinetics, where cGMP represents an

**Parameter Description Value References** *gIR*<sup>1</sup> Maximal permeability rate of the channel 30 s�<sup>1</sup> [50]

*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular…*

*nIP*<sup>3</sup> Hill coefficient 4 [50] *nSR* Hill coefficient 2 [50]

*nIR*1,*cGMP* Hill coefficient 0.47 Recalculated by

*nA* Hill coefficient 4 [50] *τIR*1,*<sup>I</sup>* Characteristic transition time 6.0 s [50]

*nI* Hill coefficient 4 [50]

*Parameter values for the cGMP and IP3 -dependent open probability of IP3R1 – Variant a.*

0.65 μM [50]

<sup>2</sup> � <sup>10</sup><sup>3</sup> <sup>μ</sup>M [50]

0.645 Recalculated by

24.6 μM Recalculated by

0.13 μM [50]

0.35 μM [50]

fitting from [36]

fitting from [36]

fitting from [36]

*KIP*<sup>3</sup> Half saturation constant in the IP3-dependent

*DOI: http://dx.doi.org/10.5772/intechopen.97708*

*KCa*,*SR* Half saturation constant in the sarcoplasmic Ca2+-

*f IR*1,*cGMP* Additional fold decrease in the channel open

*KcGMP*,*IR*<sup>1</sup> Half saturation constant in the cGMP-dependent

*KCa*,*<sup>A</sup>* Half saturation constant in the cytosolic Ca2+-

*KCa*,*<sup>I</sup>* Half saturation constant in the cytosolic Ca2+-

regulatory Hill function

dependent regulatory Hill function

probability due to cGMP

regulatory Hill function

dependent regulatory Hill function

dependent regulatory Hill function

inhibitor in the IP3-dependent open probability function:

where *KIP*3,*cGMP* is:

**105**

**Table 8.**

*OPIP*3,*cGMP* <sup>¼</sup> ½ � *IP*<sup>3</sup> *nIP*<sup>3</sup>

*KIP*3,*cGMP* <sup>¼</sup> *KIP*3,0 <sup>1</sup> <sup>þ</sup> ½ � *cGMP*

½ � *IP*<sup>3</sup> *nIP*<sup>3</sup> <sup>þ</sup> *<sup>K</sup>nIP*<sup>3</sup>

*IP*3,*cGMP*

, (33)

*Ki*,*cGMP :* (34)

whereas the Ca2+-dependent IP3R1 inhibition is considered as slow and is therefore modeled with the first-order kinetics as in Eq. (3):

$$\frac{df\_{IR1,I}}{dt} = \frac{f\_{IR1,I} - f\_{IR1,I}}{\tau\_{IR1,I}},\tag{31}$$

where *f IP*31,*<sup>I</sup>* is the fraction of the inhibited state in equilibrium, which follows a Hill function:

$$\overline{f}\_{IR1,I} = \frac{\left[\text{Ca}^{2+}\right]\_i^{n\_I}}{\left[\text{Ca}^{2+}\right]\_i^{n\_I} + K\_{Ca,I}^{n\_I}}.\tag{32}$$

Description of all parameters and their values are presented in **Table 8**.

#### *4.8.2 Variant B*

Other results of Murthy and Zhou [20] provide another possible model description of cGMP-dependent IP3R1 inhibition. The experiment offers direct PKG or


*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular… DOI: http://dx.doi.org/10.5772/intechopen.97708*

#### **Table 8.**

the Ca2+ efflux via IP3R1 as proposed by [50]. That model is upgraded here according to the experimental data of [36], with an additional regulatory factor *RIR*1,*cGMP*, which accounts for the drop in Ca2+ release after IP3 stimulation with increasing cGMP levels [36]. General description of the Ca2+ flux across the SR

*JIR*<sup>1</sup> <sup>¼</sup> *gIR*1*PIR*<sup>1</sup> *Ca*2<sup>þ</sup>

*RIR*1,*cGMP*

function of cGMP concentration in isolated gastric SMC [36]:

*RIR*1,*cGMP* ¼ 1 � *f IR*1,*cGMP*

therefore modeled with the first-order kinetics as in Eq. (3):

*df IR*1,*<sup>I</sup>*

process, it is considered to be in the equilibrium:

Hill function:

*4.8.2 Variant B*

**104**

*SR* � *Ca*2<sup>þ</sup>

*IP*3

½ � *cGMP nIR*1,*cGMP* ½ � *cGMP nIR*1,*cGMP* <sup>þ</sup> *<sup>K</sup>nIR*1,*cGMP*

where *gIR*1is an overall maximal rate of the channel permeability and *PIR*1is the channel open probability, which is a biphasic bell-shaped function of [Ca2+]i, and is also dependent on the cytosolic IP3 and sarcoplasmic Ca2+ concentrations ([*IP3*] and

> ½ � *IP*<sup>3</sup> *nIP*<sup>3</sup> ½ � *IP*<sup>3</sup> *nIP*<sup>3</sup> <sup>þ</sup> *<sup>K</sup>nIP*<sup>3</sup>

The regulatory factor *RIR*1,*cGMP* is a decaying Hill function that depends on the cGMP concentration and is an upgrade from the previous model [50]. The proposed function is the best fit to the measured decay of IP3-induced Ca2+ release as a

where *f IR*1,*cGMP* is an additional fold decrease in the channel open probability due

*i*

*<sup>i</sup>* <sup>þ</sup> *<sup>K</sup>nA Ca*,*A*

to cGMP. *f IR*1,*<sup>A</sup>*, and *f IR*1,*<sup>I</sup>* in Eq. (29) are the fractions of the channel population occupied by [Ca2+]i at the activation sites and inactivation sites, respectively. In this way, the bell-shaped dependency on [Ca2+]i is achieved. Since activation is a fast

*<sup>f</sup> IR*1,*<sup>A</sup>* <sup>¼</sup> *Ca*<sup>2</sup><sup>þ</sup> *nA*

*Ca*<sup>2</sup><sup>þ</sup> *nA*

whereas the Ca2+-dependent IP3R1 inhibition is considered as slow and is

*dt* <sup>¼</sup> *<sup>f</sup> IR*1,*<sup>I</sup>* � *<sup>f</sup> IR*1,*<sup>I</sup> τIR*1,*<sup>I</sup>*

where *f IP*31,*<sup>I</sup>* is the fraction of the inhibited state in equilibrium, which follows a

*i*

*<sup>i</sup>* <sup>þ</sup> *<sup>K</sup>nI Ca*,*I*

*<sup>f</sup> IR*1,*<sup>I</sup>* <sup>¼</sup> *Ca*<sup>2</sup><sup>þ</sup> *nI*

Description of all parameters and their values are presented in **Table 8**.

*Ca*<sup>2</sup><sup>þ</sup> *nI*

Other results of Murthy and Zhou [20] provide another possible model description of cGMP-dependent IP3R1 inhibition. The experiment offers direct PKG or

*i*

*Ca*<sup>2</sup><sup>þ</sup> *nSR*

*Ca*2<sup>þ</sup> *nSR SR*

*cGMP*,*IR*1

, (30)

, (31)

*:* (32)

*SR* <sup>þ</sup> *<sup>K</sup>nSR Ca*,*SR*

, (27)

*:* (28)

, (29)

membrane through the IP3R1 channels (*JIR*1) follows [50]:

*Muscle Cell and Tissue - Novel Molecular Targets and Current Advances*

[*Ca2+*]*SR*, respectively). It is modeled as in [50, 80]:

*PIR*<sup>1</sup> ¼ *f IR*1,*<sup>A</sup>* 1 � *f IR*1,*<sup>I</sup>*

*Parameter values for the cGMP and IP3 -dependent open probability of IP3R1 – Variant a.*

cGMP dependency of IP3-dependent Ca2+ flux. The cGMP/PKG mediated phosphorylation of IP3R1 in microsomes was confirmed in the accompanying experiment by immunoprecipitation. Hence, Murthy and Zhou [20] measured Ca2+ release through the phosphorylated IP3R1 within smooth muscle microsomes at different IP3 concentrations. Prior to measurements, microsomes were either treated with 0.5 μM PKG-Iα holoenzyme and 10 μM cGMP or left intact (control). Ca2+ release was determined from the decrease in the steady-state microsomal radioactive Ca2+ isotope content. In this way, two dose–response curves were obtained [20]. Their best fits with a Hill function reveal almost the same Hill coefficients (0.49 and 0.42, for the control and cGMP/PKG treated case, respectively) and the same Vmax (100%) but significantly different half-saturation constants Km, 1.17 � <sup>10</sup>�<sup>3</sup> <sup>μ</sup>M and 2.35 <sup>μ</sup>M, for the control and the cGMP/PKG treated case, respectively. These two measured values represent two points to which any function could virtually be fitted. Since this is highly unrealistic, we propose the use of competitive, reversible enzyme inhibition kinetics, where cGMP represents an inhibitor in the IP3-dependent open probability function:

$$OP\_{IP3,cGMP} = \frac{[IP\_3]^{np\_3}}{[IP\_3]^{np\_3} + K\_{IP3,cGMP}^{np\_3}},\tag{33}$$

where *KIP*3,*cGMP* is:

$$K\_{IP3,cGMP} = K\_{IP3,0} \left( \mathbf{1} + \frac{[cGMP]}{K\_{i,cGMP}} \right). \tag{34}$$


**Table 9.**

*Parameter values for the cGMP and IP3 -dependent open probability of IP3R1 – Variant B.*

The parameter*Ki*,*cGMP* is recalculated from [20] according to:

$$K\_{i, \text{cGMP}} = \frac{K\_{IP3, \text{cGMP}} [\text{cGMP}]\_0}{K\_{IP3, \text{cGMP}, i} - K\_{IP3, \text{c}}},\tag{35}$$

where *kcat*,*MLCK* is [Ca2+]i dependent rate of phosphorylation (see [67]) and,

*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular…*

where *fcat*,*MLCP* is an additional fold-increase in the MLCP-mediated *Mp* dephos-

The model of Yang et al. [67] demonstrated cGMP-mediated Ca2+-desensitization by shifting the equilibrium MLC phosphorylation and force curves vs. [Ca2+]i to the right. However, the model was not used to simulate the time-dependent phosphorylation and force development. In this context, the model would not accurately predict the results since Ca2+-dependent MLCK activation could not be considered as a fast process [81, 82]. Also, the simplification from 4 to 2 states is neither reasonable nor relevant if the model would account for the time-dependent variables. Hence, we propose another modeling approach to tackle the cGMPdependent activation of MLCP. The proposed model considers the Michaelis– Menten-type of enzyme kinetics for the rate of MLC dephosphorylation within the 4-state latch bridge kinetic scheme [83], yielding the velocity of MLCP dependent dephosphorylation (*VMLCP*) of both phosphorylated myosin species, attached and

<sup>d</sup>*<sup>t</sup>* <sup>¼</sup> *RMLCP*,*cGMPkcat*,*MLCP*,*<sup>b</sup>*½ � *MLCP tot*

where ½ � *MLCP tot* is the total MLCP concentration, *KMLCP* is a Michaelis–Menten

A similar modeling approach for ROCK-dependent sensitization of the contractile apparatus was used in our previous work [64]. The whole model for all Ca2+/ CaM/MLCK interactions, all myosin species, and the time-dependent force development is presented in different variants elsewhere [64, 81, 82, 84] and it comprises more than 12 differential equations. That is a minor drawback of the model, but the model proved itself in describing time-dependent force generation in rat airway smooth muscle cells [64, 82]. Such an extended model would also allow the

**Parameter Description Value References** *kMLCP*,*<sup>b</sup>* Basal dephosphorylation rate 8 s�<sup>1</sup> [64] *f MLCP*,*cGMP* Additional fold increase in dephosphorylation rate due to cGMP 1 [64] *nMLCP* Hill ceofficient 2 [67]

*KcGMP*,*MLCP* Half saturation constant in a cGMP-dependent regulatory Hill

*Parameter values for cGMP-dependent Ca2+-desensitization of the contractile apparatus.*

function

*KMLCP* Michaelis–Menten constant 10 μM [81] ½ � *MLCP tot* Total MLCP concentration 2 μM [81]

<sup>þ</sup> *KMLCP*

*Mp* <sup>þ</sup> *AMp*

constant, and *kcat*,*MLCP* is a catalytic rate constant, for which we consider to be cGMP-dependent as proposed by [67] in Eq. (35). All current parameters are

phorylation rate due to cGMP. *KcGMP*,*MLCP* is a half-saturation constant within cGMP-dependent regulatory Hill function with a Hill coefficient *nMLCP*.

½ � *cGMP nMLCP* ½ � *cGMP nMLCP* <sup>þ</sup> *<sup>K</sup>nMLCP*

*cGMP*,*MLCP*

*Mp* <sup>þ</sup> *AMp* ,

5.5 μM [67]

(38)

, (37)

*kcat*,*MLCP*,*<sup>b</sup>* is a basal dephosphorylation rate that is multiplied by the cGMP-

*RMLCP*,*cGMP* ¼ 1 þ *f MLCP*,*cGMP*

detached to actin, *AMp,* and *Mp*, respectively:

d *AMp* 

þ

*VMLCP* <sup>¼</sup> <sup>d</sup> *Mp*

presented in **Table 10**.

**Table 10.**

**107**

 d*t*

dependent regulatory factor:

*DOI: http://dx.doi.org/10.5772/intechopen.97708*

where *KIP*3,*cGMP*,*<sup>i</sup>* = 2.35 μM, which is a measured half-saturation constant treated with ½ � *cGMP* <sup>0</sup> = 10 <sup>μ</sup>M, and *KIP*3,*<sup>c</sup>* = 1.17 � <sup>10</sup>�<sup>3</sup> <sup>μ</sup>M, which is the corresponding value at control experiment without added cGMP. Eq. (37) gives *Ki*,*cGMP* = 5.0 � <sup>10</sup>�<sup>3</sup> <sup>μ</sup>M. The same calculation in which PKG is replacing cGMP in Eqs. (32)– (34) with the value ½ � *PKG* <sup>0</sup> =0.50 <sup>μ</sup>M yields *Ki*,*PKG* = 0.25 � <sup>10</sup>�<sup>3</sup> <sup>μ</sup>M. The summary of parameter values accounting for *OPIP*3,*cGMP=PKG* as a function of either cGMP or PKG is presented in **Table 9**.

We offer here two different variants of the mathematical descriptions for the cGMP impact on the IP3R1. Variant A seems more realistic as it contains the description with saturating Hill function. On the other hand, variant B takes into account the linear relationship on cGMP concentration, which might be questionable at high cGMP concentrations. However, variant B offers an insight into the strength of the inhibition on IP3R1 exerted by cGMP. *Ki*,*cGMP* and *Ki*,*PKG* values indicate very strong inhibition. It is also worth mentioning that such an effect might also arise from the experimental conditions since they were performed on the isolated microsomes [20]. Before actual inclusion of either of both mechanisms into a whole-cell-like model of VSMC, their careful model evaluation at different dynamical levels of [Ca2+]i signaling, such as membrane potential, basal [Ca2+]i, different shapes and frequencies of [Ca2+]i signal, would be required.

#### **4.9 The model of cGMP-mediated Ca2+-desensitization of the contractile apparatus**

Modeling of cGMP/PKG- dependent Ca2+-desensitization was first introduced by Yang et al. [67], who considered that MLCP is directly activated by cGMP. They modified the 4-state latch bridge model introduced by Hai and Murphy [13] by considering a simple theoretical description of Ca2+/CaM-dependent MLCK activation and MLCP dependent dephosphorylation [67]. They also reduced the model from 4 to 2 states of myosin species, phosphorylated and dephosphorylated (*Mp* and *M*, respectively), being in equilibrium. Hence, the relative level of phosphorylated myosin (*Mp*) was expressed as:

$$M\_p = \frac{k\_{\text{cat,MLCKK}}}{k\_{\text{cat,MLCKK}} + R\_{\text{MLCP},\text{cfGMP}}k\_{\text{cat,MLCP},b}},\tag{36}$$

*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular… DOI: http://dx.doi.org/10.5772/intechopen.97708*

where *kcat*,*MLCK* is [Ca2+]i dependent rate of phosphorylation (see [67]) and, *kcat*,*MLCP*,*<sup>b</sup>* is a basal dephosphorylation rate that is multiplied by the cGMPdependent regulatory factor:

$$R\_{\rm MLCP,cGMP} = \mathbf{1} + f\_{\rm MLCP,cGMP} \frac{[c\,\text{GMP}]^{\rm NLCP}}{[c\,\text{GMP}]^{\rm NLCP} + K\_{c\,\text{GMP},\text{MLCP}}^{\rm NLCP}},\tag{37}$$

where *fcat*,*MLCP* is an additional fold-increase in the MLCP-mediated *Mp* dephosphorylation rate due to cGMP. *KcGMP*,*MLCP* is a half-saturation constant within cGMP-dependent regulatory Hill function with a Hill coefficient *nMLCP*.

The model of Yang et al. [67] demonstrated cGMP-mediated Ca2+-desensitization by shifting the equilibrium MLC phosphorylation and force curves vs. [Ca2+]i to the right. However, the model was not used to simulate the time-dependent phosphorylation and force development. In this context, the model would not accurately predict the results since Ca2+-dependent MLCK activation could not be considered as a fast process [81, 82]. Also, the simplification from 4 to 2 states is neither reasonable nor relevant if the model would account for the time-dependent variables. Hence, we propose another modeling approach to tackle the cGMPdependent activation of MLCP. The proposed model considers the Michaelis– Menten-type of enzyme kinetics for the rate of MLC dephosphorylation within the 4-state latch bridge kinetic scheme [83], yielding the velocity of MLCP dependent dephosphorylation (*VMLCP*) of both phosphorylated myosin species, attached and detached to actin, *AMp,* and *Mp*, respectively:

$$V\_{MLCP} = \frac{\mathbf{d}\left[\mathbf{M}\_p\right]}{\mathbf{d}t} + \frac{\mathbf{d}\left[AM\_p\right]}{\mathbf{d}t} = \frac{R\_{MLCP,\text{GMP}}k\_{\text{cat},\text{MLCP},\text{b}}\left[\text{MLCP}\right]\_{\text{tot}}}{\left[M\_p\right] + \left[AM\_p\right] + K\_{MLCP}}\left(\left[M\_p\right] + \left[AM\_p\right]\right),\tag{38}$$

where ½ � *MLCP tot* is the total MLCP concentration, *KMLCP* is a Michaelis–Menten constant, and *kcat*,*MLCP* is a catalytic rate constant, for which we consider to be cGMP-dependent as proposed by [67] in Eq. (35). All current parameters are presented in **Table 10**.

A similar modeling approach for ROCK-dependent sensitization of the contractile apparatus was used in our previous work [64]. The whole model for all Ca2+/ CaM/MLCK interactions, all myosin species, and the time-dependent force development is presented in different variants elsewhere [64, 81, 82, 84] and it comprises more than 12 differential equations. That is a minor drawback of the model, but the model proved itself in describing time-dependent force generation in rat airway smooth muscle cells [64, 82]. Such an extended model would also allow the


#### **Table 10.**

*Parameter values for cGMP-dependent Ca2+-desensitization of the contractile apparatus.*

The parameter*Ki*,*cGMP* is recalculated from [20] according to:

*KIP*3,0 Half-saturation constant in the IP3-dependent regulatory

*Muscle Cell and Tissue - Novel Molecular Targets and Current Advances*

*Ki*,*cGMP* Apparent inhibition constant for cGMP-dependent

*Ki*,*PKG* Apparent inhibition constant for PKG-dependent

Hill function

inhibition of IP3-dependent open probability of IP3R1

inhibition of IP3-dependent open probability of IP3R1

*Parameter values for the cGMP and IP3 -dependent open probability of IP3R1 – Variant B.*

PKG is presented in **Table 9**.

**Table 9.**

**apparatus**

**106**

myosin (*Mp*) was expressed as:

*Ki*,*cGMP* <sup>¼</sup> *KIP*3,*<sup>c</sup>*½ � *cGMP* <sup>0</sup>

**Parameter Description Value References**

*nIP*<sup>3</sup> Hill coefficient 4 [50]

*KIP*3,*cGMP*,*<sup>i</sup>* � *KIP*3,*<sup>c</sup>*

where *KIP*3,*cGMP*,*<sup>i</sup>* = 2.35 μM, which is a measured half-saturation constant treated with ½ � *cGMP* <sup>0</sup> = 10 <sup>μ</sup>M, and *KIP*3,*<sup>c</sup>* = 1.17 � <sup>10</sup>�<sup>3</sup> <sup>μ</sup>M, which is the corresponding value at control experiment without added cGMP. Eq. (37) gives *Ki*,*cGMP* =

5.0 � <sup>10</sup>�<sup>3</sup> <sup>μ</sup>M. The same calculation in which PKG is replacing cGMP in Eqs. (32)– (34) with the value ½ � *PKG* <sup>0</sup> =0.50 <sup>μ</sup>M yields *Ki*,*PKG* = 0.25 � <sup>10</sup>�<sup>3</sup> <sup>μ</sup>M. The summary of parameter values accounting for *OPIP*3,*cGMP=PKG* as a function of either cGMP or

We offer here two different variants of the mathematical descriptions for the

cGMP impact on the IP3R1. Variant A seems more realistic as it contains the description with saturating Hill function. On the other hand, variant B takes into account the linear relationship on cGMP concentration, which might be questionable at high cGMP concentrations. However, variant B offers an insight into the strength of the inhibition on IP3R1 exerted by cGMP. *Ki*,*cGMP* and *Ki*,*PKG* values indicate very strong inhibition. It is also worth mentioning that such an effect might also arise from the experimental conditions since they were performed on the isolated microsomes [20]. Before actual inclusion of either of both mechanisms into a whole-cell-like model of VSMC, their careful model evaluation at different dynamical levels of [Ca2+]i signaling, such as membrane potential, basal [Ca2+]i,

different shapes and frequencies of [Ca2+]i signal, would be required.

*Mp* <sup>¼</sup> *kcat*,*MLCK*

**4.9 The model of cGMP-mediated Ca2+-desensitization of the contractile**

Modeling of cGMP/PKG- dependent Ca2+-desensitization was first introduced by Yang et al. [67], who considered that MLCP is directly activated by cGMP. They modified the 4-state latch bridge model introduced by Hai and Murphy [13] by considering a simple theoretical description of Ca2+/CaM-dependent MLCK activation and MLCP dependent dephosphorylation [67]. They also reduced the model from 4 to 2 states of myosin species, phosphorylated and dephosphorylated (*Mp* and *M*, respectively), being in equilibrium. Hence, the relative level of phosphorylated

*kcat*,*MLCK* þ *RMLCP*,*cGMPkcat*,*MLCP*,*<sup>b</sup>*

, (35)

0.65 μM [50]

5.0 � <sup>10</sup>�<sup>3</sup> <sup>μ</sup>M Recalculated

0.25 � <sup>10</sup>�<sup>3</sup> <sup>μ</sup>M Recalculated

from [20]

from [20]

, (36)

modeling of other cGMP/PKG-mediated mechanisms of MLCP and MLCK regulation by considering several different microscopic states of these two enzymes, such as different phosphorylated states, interaction with telokin, CPI-17, etc. That would allow the interconnection of different signal pathways and, hence, the simulation of the effects of various agonists and inhibitors.

#### **5. Conclusion**

This work discusses previous and provides the novel cGMP/PKG-dependent mechanisms at the molecular level accounting for their potential use in comprehensive whole-cell-like models of vascular smooth muscle contraction. Much has been done in the fields of measurements and modeling of the cGMP/PKG effects on the individual [Ca2+]i encoding and decoding mechanisms implicated in VSMC contractility. However, especially in the modeling part, there is still room for improvement and upgrading the existing models and building even multi-cellular [85, 86] and systems-pharmacology based models [87]. We should also take into consideration the importance of coupling the models of vascular smooth muscle cells to endothelial cells that, in response to the shear stress of blood flow, produce NO and other contractile and relaxation mediators [88, 89]. Moreover, the models would enable simulations at the tissue and organ level [90]. However, many of such multi-scale models are weak in describing mechanisms at the molecular level. That is not an easy task since the number of variables and parameters and the model complexity can increase tremendously. The other possibility to tackle that web of interrelated interactions is by complex network approach [91]. However, a dynamic modeling approach, as presented here, which is currently presented only at the level of individual fluxes that need to be assembled into a comprehensive model, offers many more options for studying the temporal dynamical behavior of the system functioning, either under physiological or pathological conditions or after pharmacological intervention. The remarkable advantage and added value of such mathematical models is that they describe the processes as dynamic ones. They often do not consider only one single process but take into account mutual interactions between several highly interrelated variables. In this way, they reach beyond the intuitive thinking of direct and inverse proportions between certain variables, which is often the case when interpreting the experimental results. However, models hide other pitfalls, such as excessive simplicity or complexity, unfounded predictions, prejudging, unawareness of the model's limitations, and transfer of models between different cell types and organisms, and much more. Nevertheless, they represent a useful tool for in-depth insight into the system's dynamical functioning, distinguishing essential from nonessential mechanisms, and last but not least, for highlighting the targets of pharmacological intervention.

#### **Acknowledgements**

The author acknowledges the support of the Slovenian Research Agency (ARRS) grant P1–0055.

**Author details**

University of Maribor, Maribor, Slovenia

provided the original work is properly cited.

\*Address all correspondence to: ales.fajmut@um.si

Faculty of Natural Sciences and Mathematics and Faculty of Health Sciences,

*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular…*

*DOI: http://dx.doi.org/10.5772/intechopen.97708*

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

Aleš Fajmut

**109**

#### **Conflict of interest**

The author declares no conflict of interest.

*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular… DOI: http://dx.doi.org/10.5772/intechopen.97708*

### **Author details**

modeling of other cGMP/PKG-mediated mechanisms of MLCP and MLCK regulation by considering several different microscopic states of these two enzymes, such as different phosphorylated states, interaction with telokin, CPI-17, etc. That would allow the interconnection of different signal pathways and, hence, the simulation of

*Muscle Cell and Tissue - Novel Molecular Targets and Current Advances*

This work discusses previous and provides the novel cGMP/PKG-dependent mechanisms at the molecular level accounting for their potential use in comprehensive whole-cell-like models of vascular smooth muscle contraction. Much has been done in the fields of measurements and modeling of the cGMP/PKG effects on the individual [Ca2+]i encoding and decoding mechanisms implicated in VSMC contractility. However, especially in the modeling part, there is still room for improvement and upgrading the existing models and building even multi-cellular [85, 86] and systems-pharmacology based models [87]. We should also take into consideration the importance of coupling the models of vascular smooth muscle cells to endothelial cells that, in response to the shear stress of blood flow, produce NO and other contractile and relaxation mediators [88, 89]. Moreover, the models would enable simulations at the tissue and organ level [90]. However, many of such multi-scale models are weak in describing mechanisms at the molecular level. That is not an easy task since the number of variables and parameters and the model complexity can increase tremendously. The other possibility to tackle that web of interrelated interactions is by complex network approach [91]. However, a dynamic modeling approach, as presented here, which is currently presented only at the level of individual fluxes that need to be assembled into a comprehensive model, offers many more options for studying the temporal dynamical behavior of the system functioning, either under physiological or pathological conditions or after pharmacological intervention. The remarkable advantage and added value of such mathematical models is that they describe the processes as dynamic ones. They often do not consider only one single process but take into account mutual interactions between several highly interrelated variables. In this way, they reach beyond the intuitive thinking of direct and inverse proportions between certain variables, which is often the case when interpreting the experimental results. However, models hide other pitfalls, such as excessive simplicity or complexity, unfounded predictions, prejudging, unawareness of the model's limitations, and transfer of models between different cell types and organisms, and much more. Nevertheless, they represent a useful tool for in-depth insight into the system's dynamical functioning, distinguishing essential from nonessential mechanisms, and last but not

least, for highlighting the targets of pharmacological intervention.

The author declares no conflict of interest.

The author acknowledges the support of the Slovenian Research Agency (ARRS)

**Acknowledgements**

**Conflict of interest**

grant P1–0055.

**108**

the effects of various agonists and inhibitors.

**5. Conclusion**

Aleš Fajmut Faculty of Natural Sciences and Mathematics and Faculty of Health Sciences, University of Maribor, Maribor, Slovenia

\*Address all correspondence to: ales.fajmut@um.si

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Palmer LG, Weinstein AM. Volumeactivated chloride permeability can

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[68] Yang J, Clark Jr JW, Bryan RM, Robertson C. The myogenic response in isolated rat cerebrovascular arteries: smooth muscle cell model. Medical engineering & physics. 2003;25(8): 691-709. DOI:10.1016/s1350-4533(03)

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[65] Wu X, Haystead TA, Nakamoto RK, Somlyo AV, Somlyo AP. Acceleration of myosin light chain dephosphorylation and relaxation of smooth muscle by telokin: synergism with cyclic

*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular… DOI: http://dx.doi.org/10.5772/intechopen.97708*

nucleotide-activated kinase. Journal of Biological Chemistry. 1998;273(18): 11362-11369. DOI:10.1074/ jbc.273.18.11362.

[54] Wooldridge AA, MacDonald JA, Erdodi F, Ma C, Borman MA, Hartshorne DJ, et al. Smooth muscle phosphatase is regulated in vivo by exclusion of phosphorylation of threonine 696 of MYPT1 by phosphorylation of Serine 695 in

*Muscle Cell and Tissue - Novel Molecular Targets and Current Advances*

targeting subunit 1 (MYPT 1) and MYPT 1 isoform expression in NO/ cGMP mediated differential vasoregulation of cerebral arteries compared to systemic arteries. Acta Physiologica. 2018;224(1):e13079. DOI:

[60] Eto M. Regulation of cellular protein phosphatase-1 (PP1) by phosphorylation of the CPI-17 family, C-kinase-activated PP1 inhibitors. Journal of Biological Chemistry. 2009; 284(51):35273-35277. DOI:10.1074/jbc.

[61] Smolenski A, Lohmann SM, Bertoglio J, Chardin P, Sauzeau V, Le Jeune H, et al. Cyclic GMP-dependent protein kinase signaling pathway inhibits RhoA-induced Ca2+

sensitization of contraction in vascular smooth muscle. Journal of Biological Chemistry. 2000;275(28):21722-21729. DOI:10.1074/jbc.m000753200.

[62] Roux E, Mbikou P, Fajmut A. Role of protein kinase network in excitationcontraction coupling in smooth muscle cell. Protein Kinases. 2012:287-320. DOI:

[63] Butler T, Paul J, Europe-Finner N, Smith R, Chan E-C. Role of serinethreonine phosphoprotein phosphatases

[64] Mbikou P, Fajmut A, Brumen M, Roux E. Contribution of Rho kinase to the early phase of the calcium–

contraction coupling in airway smooth muscle. Experimental physiology. 2011;

[65] Wu X, Haystead TA, Nakamoto RK, Somlyo AV, Somlyo AP. Acceleration of myosin light chain dephosphorylation and relaxation of smooth muscle by telokin: synergism with cyclic

96(2):240-258. DOI:10.1113/ expphysiol.2010.054635.

in smooth muscle contractility. American Journal of Physiology-Cell Physiology. 2013;304(6):C485-C504. DOI:10.1152/ajpcell.00161.2012.

10.1111/apha.13079.

r109.059972.

10.5772/37805.

response to cyclic nucleotides. Journal of Biological Chemistry. 2004;279(33): 34496-34504. DOI:10.1074/jbc.

[55] Gao Y, Portugal AD, Negash S, Zhou W, Longo LD, Usha Raj J. Role of Rho kinases in PKG-mediated relaxation of pulmonary arteries of fetal lambs exposed to chronic high altitude hypoxia. American Journal of

Physiology-Lung Cellular and Molecular Physiology. 2007;292(3):L678-L684. DOI:10.1152/ajplung.00178.2006.

[56] Khromov A, Choudhury N, Stevenson AS, Somlyo AV, Eto M. Phosphorylation-dependent

DOI:10.1074/jbc.m109.019729.

10.1038/nature02582.

m112.398479.

**114**

[57] Terrak M, Kerff F, Langsetmo K, Tao T, Dominguez R. Structural basis of protein phosphatase 1 regulation. Nature. 2004;429(6993):780-784. DOI:

[58] Grassie ME, Sutherland C, Ulke-Lemée A, Chappellaz M, Kiss E, Walsh MP, et al. Cross-talk between Rho-associated kinase and cyclic nucleotide-dependent kinase signaling pathways in the regulation of smooth muscle myosin light chain phosphatase. Journal of Biological Chemistry. 2012; 287(43):36356-36369. DOI:10.1074/jbc.

[59] Lubomirov L, Papadopoulos S, Filipova D, Baransi S, Todorović D, Lake P, et al. The involvement of phosphorylation of myosin phosphatase

autoinhibition of myosin light chain phosphatase accounts for Ca2+ sensitization force of smooth muscle contraction. Journal of Biological Chemistry. 2009;284(32):21569-21579.

m405957200.

[66] Khromov AS, Momotani K, Jin L, Artamonov MV, Shannon J, Eto M, et al. Molecular mechanism of telokinmediated disinhibition of myosin light chain phosphatase and cAMP/cGMPinduced relaxation of gastrointestinal smooth muscle. Journal of Biological Chemistry. 2012;287(25):20975-20985. DOI:10.1074/jbc.m112.341479.

[67] Yang J, Clark JW, Bryan RM, Robertson CS. Mathematical modeling of the nitric oxide/cGMP pathway in the vascular smooth muscle cell. American Journal of Physiology-Heart and Circulatory Physiology. 2005;289(2): H886-H897. DOI:10.1152/ ajpheart.00216.2004.

[68] Yang J, Clark Jr JW, Bryan RM, Robertson C. The myogenic response in isolated rat cerebrovascular arteries: smooth muscle cell model. Medical engineering & physics. 2003;25(8): 691-709. DOI:10.1016/s1350-4533(03) 00100-0.

[69] Zhou X-B, Arntz C, Kamm S, Motejlek K, Sausbier U, Wang G-X, et al. A molecular switch for specific stimulation of the BKCa channel by cGMP and cAMP kinase. Journal of Biological Chemistry. 2001;276(46): 43239-43245. DOI:10.1074/jbc. m104202200.

[70] Mistry D, Garland C. Nitric oxide (NO)-induced activation of large conductance Ca2+-dependent K+ channels (BKCa) in smooth muscle cells isolated from the rat mesenteric artery. British journal of pharmacology. 1998; 124(6):1131-1140. DOI:10.1038/sj. bjp.0701940.

[71] Lee MR, Li L, Kitazawa T. Cyclic GMP causes Ca2+ desensitization in vascular smooth muscle by activating the myosin light chain phosphatase. Journal of Biological Chemistry. 1997; 272(8):5063-5068. DOI:10.1074/ jbc.272.8.5063.

[72] Stockand JD, Sansom SC. Mechanism of activation by cGMPdependent protein kinase of large Ca (2 +)-activated K+ channels in mesangial cells. American Journal of Physiology-Cell Physiology. 1996;271(5):C1669- C1677. DOI:10.1152/ajpcell.1996.271.5. c1669.

[73] Large WA, Wang Q. Characteristics and physiological role of the Ca (2+) activated Cl-conductance in smooth muscle. American Journal of Physiology-Cell Physiology. 1996;271 (2):C435-C454. DOI:10.1152/ ajpcell.1996.271.2.c435.

[74] Jacobsen JCB, Aalkjær C, Nilsson H, Matchkov VV, Freiberg J, Holstein-Rathlou N-H. A model of smooth muscle cell synchronization in the arterial wall. American Journal of Physiology-Heart and Circulatory Physiology. 2007;293 (1):H229-H237. DOI:10.1152/ ajpheart.00727.2006.

[75] Di Francesco D, Noble D. A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Philosophical Transactions of the Royal Society of London B, Biological Sciences. 1985;307 (1133):353-398. DOI:10.1098/ rstb.1985.0001.

[76] Fotis H, Tatjanenko LV, Vasilets LA. Phosphorylation of the α-subunits of the Na+/K+-ATPase from mammalian kidneys and Xenopus oocytes by cGMPdependent protein kinase results in stimulation of ATPase activity. European journal of biochemistry. 1999; 260(3):904-910. DOI:10.1046/ j.1432-1327.1999.00237.x.

[77] Strieter J, Stephenson JL, Palmer LG, Weinstein AM. Volumeactivated chloride permeability can

mediate cell volume regulation in a mathematical model of a tight epithelium. The Journal of general physiology. 1990;96(2):319-344. DOI: 10.1085/jgp.96.2.319.

[78] Lalli MJ, Shimizu S, Sutliff RL, Kranias EG, Paul RJ. [Ca2+] ihomeostasis and cyclic nucleotide relaxation in aorta of phospholambandeficient mice. American Journal of Physiology-Heart and Circulatory Physiology. 1999;277(3):H963-H970. DOI:10.1152/ajpheart.1999.277.3.h963.

[79] Parthimos D, Edwards DH, Griffith T. Minimal model of arterial chaos generated by coupled intracellular and membrane Ca2+ oscillators. American Journal of Physiology-Heart and Circulatory Physiology. 1999;277 (3):H1119-H1144. DOI:10.1152/ ajpheart.1999.277.3.h1119.

[80] Imtiaz MS, Smith DW, van Helden DF. A theoretical model of slow wave regulation using voltagedependent synthesis of inositol 1, 4, 5 trisphosphate. Biophysical journal. 2002;83(4):1877-1890. DOI:10.1016/ s0006-3495(02)73952-0.

[81] Fajmut A, Brumen M. MLC-kinase/ phosphatase control of Ca2+ signal transduction in airway smooth muscles. Journal of theoretical biology. 2008;252 (3):474-481. DOI:10.1016/j. jtbi.2007.10.005.

[82] Mbikou P, Fajmut A, Brumen M, Roux E. Theoretical and experimental investigation of calcium-contraction coupling in airway smooth muscle. Cell biochemistry and biophysics. 2006;46 (3):233-251. DOI:10.1385/cbb:46:3:233.

[83] Fajmut A, Dobovišek A, Brumen M. Mathematical modeling of the relation between myosin phosphorylation and stress development in smooth muscles. Journal of chemical information and modeling. 2005;45(6):1610-1615. DOI: 10.1021/ci050178a.

[84] Fajmut A, Brumen M, Schuster S. Theoretical model of the interactions between Ca2+, calmodulin and myosin light chain kinase. FEBS letters. 2005; 579(20):4361-4366. DOI:10.1016/j. febslet.2005.06.076.

mechanics/cell model. Journal of biomechanical engineering. 2008;130

[91] Gosak M, Markovič R, Dolenšek J, Rupnik MS, Marhl M, Stožer A, et al. Network science of biological systems at different scales: A review. Physics of life reviews. 2018;24:118-135. DOI:10.1016/

*DOI: http://dx.doi.org/10.5772/intechopen.97708*

*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular…*

(1). DOI:10.1115/1.2838026.

j.plrev.2017.11.003.

**117**

[85] Kapela A, Nagaraja S, Tsoukias NM. A mathematical model of vasoreactivity in rat mesenteric arterioles. II. Conducted vasoreactivity. American Journal of Physiology-Heart and Circulatory Physiology. 2010;298(1): H52-H65. DOI:10.1152/ ajpheart.00546.2009.

[86] Koenigsberger M, Sauser R, Meister J-J. Emergent properties of electrically coupled smooth muscle cells. Bulletin of mathematical biology. 2005; 67(6):1253-1272. DOI:10.1016/j. bulm.2005.02.001.

[87] Garmaroudi FS, Handy DE, Liu Y-Y, Loscalzo J. Systems Pharmacology and Rational Polypharmacy: Nitric Oxide Cyclic GMP Signaling Pathway as an Illustrative Example and Derivation of the General Case. PLoS computational biology. 2016;12(3): e1004822. DOI:10.1371/journal. pcbi.1004822.

[88] Koo A, Nordsletten D, Umeton R, Yankama B, Ayyadurai S, García-Cardeña G, et al. In silico modeling of shear-stress-induced nitric oxide production in endothelial cells through systems biology. Biophysical journal. 2013;104(10):2295-2306. DOI:10.1016/j. bpj.2013.03.052.

[89] Sriram K, Laughlin JG, Rangamani P, Tartakovsky DM. Shearinduced nitric oxide production by endothelial cells. Biophysical journal. 2016;111(1):208-221. DOI:10.1016/j. bpj.2016.05.034.

[90] Comerford A, Plank M, David T. Endothelial nitric oxide synthase and calcium production in arterial geometries: an integrated fluid

*Molecular Mechanisms and Targets of Cyclic Guanosine Monophosphate (cGMP) in Vascular… DOI: http://dx.doi.org/10.5772/intechopen.97708*

mechanics/cell model. Journal of biomechanical engineering. 2008;130 (1). DOI:10.1115/1.2838026.

mediate cell volume regulation in a mathematical model of a tight epithelium. The Journal of general physiology. 1990;96(2):319-344. DOI:

*Muscle Cell and Tissue - Novel Molecular Targets and Current Advances*

[84] Fajmut A, Brumen M, Schuster S. Theoretical model of the interactions between Ca2+, calmodulin and myosin light chain kinase. FEBS letters. 2005; 579(20):4361-4366. DOI:10.1016/j.

[85] Kapela A, Nagaraja S, Tsoukias NM. A mathematical model of vasoreactivity

in rat mesenteric arterioles. II. Conducted vasoreactivity. American Journal of Physiology-Heart and Circulatory Physiology. 2010;298(1):

[86] Koenigsberger M, Sauser R, Meister J-J. Emergent properties of electrically coupled smooth muscle cells. Bulletin of mathematical biology. 2005;

67(6):1253-1272. DOI:10.1016/j.

as an Illustrative Example and Derivation of the General Case. PLoS computational biology. 2016;12(3): e1004822. DOI:10.1371/journal.

[87] Garmaroudi FS, Handy DE, Liu Y-Y, Loscalzo J. Systems Pharmacology and Rational Polypharmacy: Nitric Oxide Cyclic GMP Signaling Pathway

[88] Koo A, Nordsletten D, Umeton R, Yankama B, Ayyadurai S, García-Cardeña G, et al. In silico modeling of shear-stress-induced nitric oxide production in endothelial cells through systems biology. Biophysical journal. 2013;104(10):2295-2306. DOI:10.1016/j.

Rangamani P, Tartakovsky DM. Shearinduced nitric oxide production by endothelial cells. Biophysical journal. 2016;111(1):208-221. DOI:10.1016/j.

[90] Comerford A, Plank M, David T. Endothelial nitric oxide synthase and calcium production in arterial geometries: an integrated fluid

H52-H65. DOI:10.1152/ ajpheart.00546.2009.

bulm.2005.02.001.

pcbi.1004822.

bpj.2013.03.052.

bpj.2016.05.034.

[89] Sriram K, Laughlin JG,

febslet.2005.06.076.

[78] Lalli MJ, Shimizu S, Sutliff RL, Kranias EG, Paul RJ. [Ca2+] ihomeostasis and cyclic nucleotide relaxation in aorta of phospholambandeficient mice. American Journal of Physiology-Heart and Circulatory Physiology. 1999;277(3):H963-H970. DOI:10.1152/ajpheart.1999.277.3.h963.

[79] Parthimos D, Edwards DH, Griffith T. Minimal model of arterial chaos generated by coupled intracellular

and membrane Ca2+ oscillators. American Journal of Physiology-Heart and Circulatory Physiology. 1999;277 (3):H1119-H1144. DOI:10.1152/ ajpheart.1999.277.3.h1119.

[80] Imtiaz MS, Smith DW, van

wave regulation using voltage-

s0006-3495(02)73952-0.

(3):474-481. DOI:10.1016/j.

jtbi.2007.10.005.

10.1021/ci050178a.

**116**

Helden DF. A theoretical model of slow

dependent synthesis of inositol 1, 4, 5 trisphosphate. Biophysical journal. 2002;83(4):1877-1890. DOI:10.1016/

[81] Fajmut A, Brumen M. MLC-kinase/ phosphatase control of Ca2+ signal transduction in airway smooth muscles. Journal of theoretical biology. 2008;252

[82] Mbikou P, Fajmut A, Brumen M, Roux E. Theoretical and experimental investigation of calcium-contraction coupling in airway smooth muscle. Cell biochemistry and biophysics. 2006;46 (3):233-251. DOI:10.1385/cbb:46:3:233.

[83] Fajmut A, Dobovišek A, Brumen M. Mathematical modeling of the relation between myosin phosphorylation and stress development in smooth muscles. Journal of chemical information and modeling. 2005;45(6):1610-1615. DOI:

10.1085/jgp.96.2.319.

[91] Gosak M, Markovič R, Dolenšek J, Rupnik MS, Marhl M, Stožer A, et al. Network science of biological systems at different scales: A review. Physics of life reviews. 2018;24:118-135. DOI:10.1016/ j.plrev.2017.11.003.

### *Edited by Kunihiro Sakuma*

The loss of skeletal muscle mass and strength substantially impairs physical performance and quality of life. This book details some approaches to the treatment of muscle wasting. It also reviews novel applications against pulmonary arterial hypertension such as cell reprogramming and the use of anticancer drugs that induce programmed cell death. Vascular smooth muscle cells (VSMCs) are the most prevalent cell types in blood vessels and serve critical regulatory roles. This publication also introduces mathematical models concerning the molecular mechanism and targets of cyclic guanosine 3′,5′-monophosphate (cGMP) in the contraction of VSMCs. This book will be of interest to professionals in clinical practice, medical and health care students, and researchers working in muscle-related fields of science.

Published in London, UK © 2021 IntechOpen © JOSE LUIS CALVO MARTIN & JOSE ENRIQUE GARCIA-MAURIÑO MUZQUIZ / iStock

Muscle Cell and Tissue - Novel Molecular Targets and Current Advances

Muscle Cell and Tissue

Novel Molecular Targets and Current Advances

*Edited by Kunihiro Sakuma*