Ca-CaM-AMPK signaling models

Introduction

Calcium (Ca²⁺) plays a pivotal role in almost all cellular processes and ensures the functionality of an organism. In skeletal muscle fibers, Ca²⁺ is critically involved in the innervation of skeletal muscle fibers that results in the exertion of an action potential along the muscle fiber membrane, the prerequisite for skeletal muscle contraction. Furthermore and among others, Ca²⁺ regulates also intracellular processes, such as myosin-actin cross bridging, protein synthesis, protein degradation and fiber type shifting by the control of Ca²⁺-sensitive proteases and transcription factors, as well as mitochondrial adaptations, plasticity and respiration. These data highlight the overwhelming significance of Ca²⁺ ions for the integrity of skeletal muscle tissue. While the fast and acute oscillation of free Ca²⁺ levels in skeletal muscle is the major step in initiation of muscle contraction and relaxation, slower shifts of cytosolic Ca²⁺ levels are important contributors in the regulation of skeletal muscle plasticity by activation of specific signaling pathways such as the calmodulin/calcineurin signaling pathway (Gehlert et al., 2015) [1]. Computational modelling is likely to play an important role in analysing the quantitative behaviour of such pathways, in turn providing data for the basis of potential therapeutic drug design. On this page we would like to summarize all developed mathematical models dedicated to this topic of the research.

Ca-CaM-AMPK signaling pathway

The orchestra of Ca²⁺ signaling mechanisms in skeletal muscle determines a multitude of cellular processes. Already the initiation of muscle contraction at the neuromuscular junction is a Ca²⁺-dependent process at the motor endplate inducing a change in membrane polarization and a subsequent opening of L-type Ca²⁺ channels triggering the release of Ca²⁺ from the sarcoplasmatic reticulum (SR). This mechanism allows a distinct rise of cytosolic Ca²⁺ concentration that initiates actin/myosin interaction and movement of the myosin head. To facilitate the interplay of contraction and relaxation the SR is provided by several Ca²⁺ transport and binding molecules which are adjusted by a multitude of regulatory molecules. ATP production and hence energy supply of contracting muscle is also regulated by Ca²⁺-dependent enhancement of glycolytic enzyme activity and mitochondrial respiration. The high plasticity of skeletal muscle is enabled by Ca²⁺-dependent regulation of gene expression, translation and posttranslational processes including protein degradation (Gehlert et al., 2015) [1] (Figure 1).

Figure 1 from (Gehlert et al., 2015) [1] (A) Voltage-dependent activation of the dihidropyridine receptor (DHPR-Cav1.1) facilitates the release of Ca²⁺ ions out of the sarcoplasmatic reticulum (SR), which critically regulates skeletal muscle contraction. Reuptake of Ca²⁺ ions in the SR controls skeletal muscle relaxation and is mainly regulated by ATP-dependent sarcoplasmic/endoplasmic reticulum calcium ATPase pumps (SERCA1/2). Increased neuromuscular activity establishes an oscillating pattern of Ca²⁺ ion levels and causes elevated sarcoplasmic Ca²⁺ ion concentrations in the microenvironment of myofibrils; (B) Increasing levels of Ca2+ ions in the sarcoplasm bind to and activate calmodulin (CaM) which regulates activation of calcineurin and calmodulin kinase II and IV. Calmodulin kinase II (CaMKII) contributes to the phosphorylation of ryanodine receptor 1 (RyR1) which increases RyR1 channel activity and open probability. CaMKII further inhibits histone deacetylase II (HDACII) and increases nuclear abundance of myocyte enhancer factor 2 (MEF2). Calcineurin (CaN) dephosphorylates nuclear factor of activated T-cells (NFAT) hereby regulating its nuclear localization. NFAT and MEF2 facilitate the increased expression of “slow genes” coding protein isoforms of the oxidative fiber type; (C) CaMKIV increases the expression of mitochondrial genes, which contributes to mitochondrial adaptation. Free Ca²⁺ ions also directly stimulate or inhibit Ca²⁺ release via RyR1 in dependency of their luminal and sarcoplasmic Ca²⁺ concentration. Ca²⁺ ions further co-regulate the activation of energy metabolism by activating mitochondrial respiration and increasing the activity of glycolytic enzymes in sarcoplasm; and (D) store-operated calcium entry (SOCE) is regulated by stromal interaction molecule 1 (STIM1) which senses declined Ca²⁺ ion concentrations in the SR. Interaction of STIMP1 with Orai1 and canonical transient receptor potential channels (TRPC) leads to trans-sarcolemmal Ca²⁺ influx to increase intracellular Ca²⁺ levels upon declining Ca²⁺ content of the SR. Junctophilin maintains junctional triad integrity by overspanning the space between SR and plasma membrane and supports DHPR and RyR1 interaction. Ca²⁺ uptake and handling is enhanced by sarcalumenin which interacts with SERCA channels and calsequestrin.

To ensure sustained contractility of skeletal muscle, the generation of ATP has to match the demands during contraction. A major metabolic pathway in skeletal muscle that provides a high amount of ATP generation per time is the anaerobic glycolysis which converts one molecule glucose to two molecules pyruvate or lactate and two molecules ATP and, in case of glycogen utilization, three molecules ATP per molecule glycogen (Baker et al., 2010) [2]. The regulation of glucose or glycogen breakdown is relatively short-stepped and requires fewer enzymatic driven reactions when compared to aerobic oxidation (e.g., free fatty acids). Ca²⁺ ions contribute to the regulation of glycolysis as they affect the enzymatic speed of crucial enzymes of the glycolysis (Schonekess et al., 1995) [3]. Glycogen degradation to pyruvate requires glycogenphosphorylase (GP) which converts one molecule of glycogen to glucose-1-phosphate and primes its further degradation via glycolysis to lactate. The phosphorylation and activation of GPL depends on the activity of the enzyme phosphorylase kinase (PhK). Years ago, it was demonstrated that the important Ca²⁺-binding molecules CaM and troponin C regulate the activity of PhK in interplay with Ca²⁺ ions and the phosphorylation by PKA (Cohen, 1980) [4]. PhK in its unphosphorylated form (PhK b) form is relatively inactive when Ca²⁺ concentration is low. PKA can phosphorylate PLK on its β-subunit transforming it to its active form (PhK a). However, dependent on Ca²⁺ concentration, Ca²⁺ ions bind to the δ-subunit of PhK which has a high sequence homology to calmodulin. This mediates an important step in the activation of PhK, however, the additional interaction of PhK with sarcomeric troponin-c seems to be required for the further activation of PhK. The muscle specific isoform of phosphofructokinase (PFK-M) is the most important pacemaker of glycolysis rate. It catalyzes the reaction from fructose 6 phosphate to fructose 1–6 bisphosphate which together with AMP allosterically regulate PFK activity in contracting muscle. Ca²⁺ ions are able to modulate PFK activity by the Ca²⁺-dependent activation of CaM which interacts with PFK (Sola-Penna et al., 2010) [5]. PFK monomers have two binding sites for CaM. CaM binding to the high affinity site of PFK forms the generation of stable PFK dimers which exhibit increased catalytic activity of PFK, in part preventing allosteric inhibition of the enzyme, e.g., by ATP, citrate and lactate. The formerly described regulations facilitate the full activation of PhK and contribute to increased PFK activity via increased abundance of Ca²⁺. Hence, these Ca²⁺-dependent mechanisms serve as an important contribution to coordinate the onset of muscle contractions with mechanisms that augment energy metabolism in working muscle.

Ca²⁺ influx into mitochondria has been shown to result in increased energy conversion potential which is necessary in the maintenance of energetic homeostasis in contracting muscle (Korzeniewski, 2007) [6]. Recent data support this notion of Ca²⁺-activated muscle oxidative phosphorylation cascade. It could be shown that Ca²⁺ increased the conductance of complex IV, complexes I + III, ATP production/transport, and fuel transport/dehydrogenases (Glancy et al., 2013) [7]. Ca²⁺ concentration has also been shown to directly stimulate ATP production through activation of the F1F0-ATP synthase at least in cardiac muscle (Territo et al., 2000) [8]. Extrapolation of these data to the exercising muscle predicts a significant role of Ca²⁺ concentration in maintaining cellular energy homeostasis. The activation of the electron transport chain in mitochondria by Ca²⁺ concentration may significantly contribute to the Ca²⁺ stimulation of ATP production during exercise (Glancy et al., 2013) [7].

Peroxisome proliferator-activated receptor gamma coactivator 1-alpha (PGC-1α) is a key regulator of mitochondrial biogenesis, angiogenesis, as well as fat and carbohydrate metabolism in skeletal muscle (Olesen et al., 2010, Popov et al., 2015) [9] [10]. Mouse and human skeletal muscle expresses several PGC-1α (PPARGC1A) gene isoforms originating from the canonical (PGC-1α-a mRNA) and alternative (PGC-1α-b and PGC-1α-c mRNA) promoters (Miura et al., 2008, Yoshioka et al., 2009) [11] [12]. Alternative splicing at the intron between exons 6 and 7 can generate N-truncated (NT) PGC-1α isoforms (Zhang et al., 2009) [13], which possess unique properties, different to those of full-length isoforms (Thom et al., 2014) [14]. Thus, the PGC-1α gene has the potential to produce at least six transcripts (Chang et al., 2012) [15]. Acute endurance exercise leads to increased PGC-1α gene expression in skeletal muscle. AMP-activated protein kinase (AMPK), p38 mitogen-activated protein kinase (p38 MAPK), Ca²⁺/calmodulin-dependent protein kinase (CaMKII) and Ca2+/calmodulin-dependent protein kinase kinase β (CaMKKII) appear to be important for regulation of activity-induced PGC-1α gene expression from the canonical promoter (Zhang et al., 2014) [16]. Several groups (Norrbom et al., 2011, Ydfors et al., 2013, Popov et al., 2014) [17] [18] [19] have shown that in human skeletal muscle, acute exercise induces PGC-1α gene expression, mainly via the alternative promoter. Based on studies in rodent skeletal muscle, it was proposed that activation of exercise-induced expression via the alternative promoter is regulated by the beta-2 adrenergic receptor-protein kinase A (PKA)-cAMP response element-binding protein (CREB1) signalling pathway (Chinsomboon et al., 2009, Tadaishi et al., 2011) [20] [21]. Human myoblast (Norrbom et al., 2011) [17] and mouse (Wen et al., 2014) [22] studies showed that AMPK plays a role in the regulation of expression via the alternative promoter. However, another myoblast study (Yoshioka et al., 2009) [12] and a study in isolated rat muscle (Tadaishi et al., 2011) [21] did not confirm this finding. Furthermore, it has been demonstrated that constitutive expression PGC-1α gene occurs via the canonical promoter, independent of exercise intensity and exercise-induced increase of AMPK^Thr172 phosphorylation level. Expression of PGC-1α gene via the alternative promoter is increased of two orders after exercise. This post-exercise expression is highly dependent on the intensity of exercise. There is an apparent association between expression via the alternative promoter and activation of CREB1 (Popov et al., 2015) [23] (Figure 2).

Figure 2 Schematic diagramme of Ca-CaM-AMPK signaling pathway designed in SBGN standard using BioUML tool. All abbreviations for objects in the main text.

Published models

Regular physical activity leads to a number of adaptations in skeletal muscle that allow the muscle to more efficiently utilize substrates for ATP production and thus become more resistant to fatigue. Muscle contraction is a multifactorial process involving changes in cellular energy status (i.e. increased AMP:ATP), increases in intracellular Ca²⁺ levels, activation of protein kinase C (PKC), and so forth (Röckl et al., 2008) [24]. Not surprisingly, this has led many investigators to apply the mathematical modeling approach in order to decipher intracellular signaling pathways that coordinately act in response to physical activity.

So, in 2008, Cui and Kaandorp constructed a computational model of the complex calcium-calcineurin-MCIP-NFAT signaling network in cardiac myocytes totally based on biochemical principles (Cui and Kaandorp, 2008) [25]. As shown in the left-up corner of Figure 3, stress incurs the rise of the concentration of cytosolic Ca²⁺ (in normal cardiac myocytes, cytosolic Ca²⁺ concentration rests at a level of less than 200 nM and it becomes more than 700 nM under a very strong stress condition), which binds to CaM (4:1). Ca²⁺-bound CaM binds to CaN to activate it. CaN∗ (i.e., activated CaN) can bind to MCIP to form Complex1. CaN∗ can also work as the enzyme to help convert NFAT^p into NFAT. Another enzyme GSK3β works in the reverse conversion of NFAT into. NFAT^p, which can bind to 14-3-3 to form Complex3. Such conversion between NFAT and NFAT^p with the help of two enzymes (GSK3β and CaN∗) also happens in the nucleus. NFAT in the cytosol will be imported into the nucleus and NFAT^p in the nucleus will be exported into the cytosol. The nuclear NFAT can initiate the transcription of the hypertrophic genes and the gene encoding MCIP (more precisely, MCIP1, a form of MCIP). Both GSK3β and CaN∗ are shuttled between the nucleus and the cytosol. As shown in the rightup corner of Figure 3, particular stress such as pressure overload (PO) can activate BMK1, which catalyzes the conversion of MCIP into MCIP^p. MCIP^p can be converted into MCIP^pp by GSK3β. The reverse conversion of MCIP^pp into MCIP^p is again catalyzed by CaN∗. MCIP^pp will bind with 14-3-3 to form Complex2.

Figure 3 from (Cui and Kaandorp, 2008) [25] A schematic graph depicting the Ca²⁺-calcineurin-MCIP-NFAT signaling networks in cardiac myocytes (for details, please see the main text). Abbreviations are as follows: calmodulin (CaM); calcineurin (CaN); activated calcineurin (CaN∗); nuclear factor of activated T-cells (NFAT); phosphrylated NFAT(NFAT^p); modulatory calcineurin-interacting protein (MCIP); phosphorylated MCIP on serine 112 (MCIP^p); phosphorylated MCIP on both serine 112 and serine 108 (MCIP^pp); big mitogenactivated protein kinase 1 (BMK1); glycogen synthase 3β (GSK3β); the complex formed by MCIP and calcineurin (Complex1); the complex formed by MCIP^pp and protein 14-3-3 (Complex2); the complex formed by NFAT^p and protein 14-3-3 (Complex3); pressure overload (PO); hypertrophic stimuli (stress). The stress of PO is delivered by transverse aortic constriction (TAC).

MCIP1 seems to facilitate or suppress cardiac CaN signaling depending on the nature of the stress. In the case of CaN∗ transgenic mice, the knock-out of MCIP1 gene (i.e. MCIP1^−/− TG mice) exacerbated the hypertrophic response to CaN∗ overexpression. Paradoxically, however, cardiac hypertrophy in response to PO was blunted in normal MCIP1^−/− mice. In 2006, Shin et al. [26] published a paper in FEBS Letters using switching feedback mechanism to explain this dual role of MCIP in cardiac hypertrophy. The aim of the model developed by Cui and Kaandorp is to propose a much-extended version of Shin’s model by including more recent experimental findings (e.g., CaN∗ is imported into the nucleus to function there, MCIP^pp will associate with protein 14-3-3 and protein 14-3-3 competes with CaN∗ to associate with NFAT^p to form Complex3). The construction of the model was based on biochemical principles and they used an open source software (Cellerator^TM) to automatically generate the equations. After all, this model correctly predicted the mutant (MCIP1^−/−) behavior under different stress such as PO and CaN∗ overexpression.

For its part, Saucerman and Bers integrated another mechanistic computational models of CaM, CaMKII, and CaN with the Shannon-Bers model [27] of excitation-contraction coupling in the rabbit ventricular myocyte to assess when and where CaM, CaMKII, and CaN may be activated in the cardiac myocyte (Saucerman and Bers, 2008) [28]. This mechanistic model (Figure 4) predicted that CaMKII is responsive only when targeted to Ca release sites such as the dyadic cleft, CaN is only responsive to gradual changes in the lower-amplitude cytosolic Ca signals, and these diverging responses can be quantitatively explained by their different affinities for CaM. These results support the idea that diverse CaM binding affinities may facilitate selective regulation of Ca-dependent pathways by fine-tuning sensitivity to particular local Ca signals.

Figure 4 from (Saucerman and Bers, 2008) [28] Model of calmodulin (CaM)-dependent signaling in cardiac myocytes. (A) Compartmental model schematic of cardiac myocyte EC coupling [27] incorporating CaM, CaMKII, and CaN signaling in thedyadic cleft and cytosol; (B) Reaction map for cooperative Ca binding of 2 Ca to CaM sequentially to the C-terminal and then N-terminal EF hands, along with binding of CaM “buffers”; (C) Probabilistic model of CaMKIIδ subunit switching between inactive (P_i), inactive Ca₂CaM-bound (P_b2), active Ca₄CaM-bound (P_b), Thr²⁸⁷-autophosphorylated with Ca₄CaM trapped (P_t), and Thr²⁸⁷-autophosphorylated but CaM-autonomous (P_a) or Ca₂CaM-bound (P_t2) states. (D) Reaction map for reversible binding of CaM, Ca₂CaM, and Ca₄CaM to CaN.

This detailed biochemical model describing CaMKII activation (Saucerman and Bers, 2008) [28] was extended with a computational model describing spatiotemporal [Ca²⁺] dynamics in a half sarcomere of a fast-twitch mouse muscle (Groenendaal et al., 2008) [29] by group of Prof. Martin Flueck from the Institute for Biomedical Research into Human Movement and Health of Manchester Metropolitan University (Eilers et al., 2012, 2014) [30],[31]. Both models [28],[29] consist of coupled differential equations and contain no stochastic elements. The sarcomeric model describes a cylinder consisting of four radial layers, of which the inner three form the myoplasm and the outer layer forms the sarcoplasmic reticulum (SR). Longitudinally, the layers are divided into six parts of equal volume, to form 18 myoplasmic elements and six SR elements (Fig. 5A). The number of elements in the model was limited to 24 to prevent excessive computational times and remain within computer memory limits. The elements include buffering of calcium by troponin-C, parvalbumin (in fast-twitch muscle) and ATP in the myoplasm and calsequestrin in the SR. In the model, calcium is able to diffuse within the myoplasm and the SR, and is transported between these two compartments through the RyR and SERCA, which have distinct locations on the modelled SR (Fig. 5A). To each myoplasmic element in the model [30], authors added a CaMKII reaction scheme describing Ca²⁺ binding to calmodulin (CaM) (Fig. 5B) and subsequent binding of Ca²⁺-CaM to CaMKII (Saucerman and Bers, 2008) [28]. Unlike the previous model [28], CaM-buffering was removed from the model and only free CaM was considered.

Figure 5 from (Eilers et al., 2012) [30] Schematized calcium model and CaM-CaMKII reaction schemes. (A) Simplified visualisation of the different spatial elements in the computational model of calcium dynamics in a half-sarcomere, adapted from Groenendaal et al., 2008 [29]. The model is bordered by a z-line on one side and an m-line on the other side. The grey elements (top row) make up the SR and the white elements (bottom tree rows) make up the myoplasm. Note that the actual model is a cylinder, and the elements are actually rings, with the lower border of the bottom elements as their centre; (B) Reaction scheme for sequential binding of calcium to the C-terminal and then the N-terminal EF-hand of calmodulin.

To validate the CaMKII reaction scheme, Eilers and coauthors first compared modelled Ca²⁺-sensitivity of CaMKII autophosphorylation and the effect of phosphatase concentration on this relationship to that of an independent experimental dataset (Bradshaw et al., 2003) [32]. The model reproduced the concentration for half-maximal activation and steepness of the relationship between [Ca²⁺] and CaMKII autophosphorylation quite well (Fig. 6A). Furthermore, authors compared the modelled relation between [CaM] and CaMKII activity, and between [CaM] and CaMKII autophosphorylation, with another independent experimental dataset (Gaertner et al., 2004) [33]. The model properly described the experimentally determined [Ca²⁺] concentrations for half-maximal CaMKII activity and the steepness of the curve (Fig. 6B&C).

Figure 6 from (Eilers et al., 2012) [30] Validation of CaM-CaMKII reaction scheme. (A) Comparison of modelled [Ca²⁺] - phospho^Thr287-CaMKII relation (blue lines) with published data (red open circles: 0.5 μM PP1; green circles: 2.5 μM PP1) (Bradshaw et al., 2003) [32]; (B) Comparison of modelled [CaM] - CaMKII activity relation (blue line) with independent experimental data (Gaertner et al., 2004) [33]; (C) Comparison of modelled [CaM] - CaMKII autophosphorylation relation (blue lines) with independent experimental data (Gaertner et al., 2004) [33]. Experimental data points are estimated from graphs in cited papers. PP1: Protein phosphatase 1.

Eilers et al found that the modelled spatial gradient in cytoplasmic [Ca²⁺] results in a two-fold decrease in CaMKII activity between the Ca²⁺ release site (i.e. near the z-line) and the part of the sarcomere close to the m-line. This gradient existed during simulations of a single RyR opening and simulations of repeated trains of RyR opening (Fig. 3, 4 & 5). Furthermore, simulated CaMKII activity increased more in the FT (fast-twitch) model than in the ST (slow-twitch) model (Fig. 7 & 8).

Figure 7 from (Eilers et al., 2012) [30]. CaMKII activity during a single RyR opening. Total simulated CaMKII activity (the sum of Pb4, Pt2, Pt4 and Pa - see Fig. 4) during a simulated single RyR opening in the fast-twitch (FT) and slow-twitch (ST) model (see text for model details). Graphs on the left display development of total CaMKII activity over time (in milliseconds) during a single RyR opening in the FT and ST model as indicated. Blue lines represent CaMKII activity in different myoplasmic compartments. Black inverted triangles indicate the approximate time point at which the CaMKII activity gradient was analysed, and visualised in the grids on the right. Note that the scale of the y-axis differs in the FT and ST graph. Grids on the right visualise the spatial distribution of the maximal increase in total CaMKII activity during a single simulated RyR opening. Colours indicate the percentage increase compared to the initial total activity, and the scale is indicated above the figure. Grid layout is the same as in Fig. 5A. The locations of the z-line and m-line of the half-sarcomeric model are indicated by Z and M, respectively. NSR: nonjunctional sarcoplasmic reticulum. JSR: junctional sarcoplasmic reticulum. SERCA: sarco/endoplasmic reticulum Ca2+-ATPase. RyR: Ryanodine receptor. Figure 8 from (Eilers et al., 2012) [30]. CaMKII activity during repeated RyR openings. Total simulated CaMKII activity (the sum of Pb4, Pt2, Pt4 and Pa - see Fig. 4) during a simulation of ten RyR openings in the fast-twitch (FT) and slow-twitch (ST) model. Graphs on the left display development of total CaMKII activity over time (in milliseconds) during ten simulated RyR openings in FT and ST model as indicated, and at a RyR opening frequency of 100Hz (upper two graphs) or 10Hz (lower two graphs). Blue lines represent CaMKII activity in different myoplasmic compartments. In order to optimise visualisation of the graphs, the scale of the y-axis differs in each graph. Grids on the right visualise the spatial distribution of maximal total CaMKII activation during the simulation of ten RyR openings. Colours indicate the percentage increase compared to the initial total activity, and the scale is indicated above the figure. Note that colour scale in this figure is of larger magnitude compared to Fig. 7. Grid layout is the same as in Fig. 5A.

Finally, they found that CaMKII-dependent modulation of RyR and SERCA cannot explain CaMKII overexpression-induced decreases in twitch contraction and relaxation times (Fig. 9). Therefore, the location of CaMKII in sarcomere is likely to be of importance for its function and should be considered when evaluating potential CaMKII targets for physiological relevance.

Figure 9 from (Eilers et al., 2012) [30] A/C: Total CaMKII activity (the sum of P_b, P_t, P_t2 and P_a - see Fig. 4) during a simulation of a single RyR opening in the fast-twitch (FT; A) and slow-twitch (ST; C) model in which CaMKII concentration is increased. Lines indicate CaMKII activity in different myoplasmic compartments. Blue lines: [CaMKII] = 1 µM; Red lines: [CaMKII] = 50 µM. Note that the scales on the y-axes are different; B/D: Spatially averaged [Ca²⁺] (left graphs) and [Ca²⁺-TropC] (right graphs) during a simulation of one RyR opening in the FT (B) and ST (D) model. Blue lines: [CaMKII] = 1 µM; Red lines: [CaMKII] = 50 µM. Note that scales on the y-axes are different.

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