Fig 1.
A schematic model of the main signaling pathways that regulate insulin secretion.
Glucose enters the cell through its glucose transporter, and is phosphorylated and metabolized in the mitochondrion as well free fatty acids (FFA). Glucose and FFA metabolism leads to an increase in the ATP/ADP ratio, closure of the ATP-sensitive potassium (KATP) channels leading to plasma membrane (PM) depolarization that increase a calcium influx through the voltage-gated calcium channels and an increase in cytoplasmic Ca2+. Other transmembrane channels can also regulate PM potential: K+Kr is the voltage gated K+ channel, SOC is the store operating channels, Nab is the Na+ background current, NALCN is the specific nonselective cation channel that can be modulated by acetylcholine through activation of M3 muscarinic receptors (M3R). Increase in cytoplasmic Ca2+ leads to the activation of several calcium dependent enzymes including adenylyl cyclase (AC) and phospholipase C (PLC). Phosphoinositides pathway: phosphatidylinositol-4-phosphate (P4P) is synthesized from phosphatidylinositol (PI) by phosphatidylinositol 4-kinases and its synthesis activates by PKC and Ca2+. Phosphotidylinositol-4,5-bisphosphate (PIP2) in turn is primarily formed from P4P by phosphatidylinositol-4-phosphate 5-kinase I. cAMP pathway: Ca2+/CaM is Ca2+-bound calmodulin, Synthesis and degradation of cAMP are catalyzed by adenylyl cyclase and phosphodiesterase (PDE), respectively. ACc is the soluble AC, ACP is the G-protein controlled AC on plasmalemma that can be activated by stimulatory Gαs type G-protein and Ca2+/CaM and deactivated by inhibitory Gi/o type G-protein. PDE activity can be enhanced by Ca2+/CaM, cAMP activates protein kinase A (PKA) and exchange protein (Epac). The incretins glucagon-like peptide-1 (GLP-1) and glucose-dependent insulinotropic polypeptide (GIP) bind to their respective receptors (GLP-1R and GIPR), activate ACP and increase intracellular levels of cAMP. Endogenous catecholamines adrenaline (epinephrine) and noradrenaline (norepinephrine) bound with G-protein-coupled α2A-adrenergic receptors (AdR) on plasma membrane and inhibit ACP. Phospholipase C (PLC) pathway. PLCC is the cytoplasmic calcium activated PLC and PLCP is plasma membrane bound PLC that can be activated by Gq type G-protein. Acetylcholine and FFA can bind to their respective receptors (M3R and FFAR1/GPR40) expressed at the cell surface and trigger a Gaq-mediated activation of PLCP. PLCC and PLCP generate inositol-3-phosphate (IP3) and diacylglycerol (DAG) by hydrolyzing membrane PIP2. DAG activates protein kinase C (PKC). Endoplasmic reticulum (ER): SERCA is the endoplasmic reticulum Ca2+ATPase, IP3R is the IP3 receptor; that can be activated by IP3 and PKA. Solid lines indicate fluxes, and dashed lines indicate inhibitory or stimulatory influences on currents or fluxes.
Fig 2.
A schematic model of interaction of G-proteins activated by receptors with PM bound adenylyl cyclase (ACp).
Activating G-protein can bind with ACp and their complex can accelerate cAMP production. ACp complex bounded with inhibiting G-protein cannot catalyze cAMP production.
Fig 3.
Modeling of spontaneous glucose-and GLP-1 stimulated changes of intracellular parameters.
(A) ATP/ADP and PM potentials (Vp); (B) Free cytoplasmic Ca2+ concentration ([Ca2+]c) and free Ca2+ concentration in ER ([Ca2+]ER); (C) Cytoplasmic cAMP and relative activated PKA (PKAa). (D) IP3 and DAG concentrations. (E) Concentrations of P4P and PIP2 on PM. Initially all coefficients were on basal level (see Tables in CM). Low glucose concentration (3 mM) was simulated initially (left part). An increased extracellular glucose level at 1000 sec (from 3 to 8 mM) stimulates ATP/ADP increase that blocks KATP channels. This inhibition allows the PM depolarization (Fig 3A) that activates the voltage-gated Ca2+ channels and increases cytoplasmic Ca2+. This activate SERCA and increase Ca2+ in the endoplasmic reticulum ([Ca2+]ER). Increased [Ca2+]c activates also PLC and correspondently increases IP3 and DAG, decreases PIP2 and increases P4P concentrations. Increase in GLP-1 (from 3.1e-7 μM to 6.2e-4 μM) with corresponding ACP activation was simulated at 4000 sec. This leads to a fast increase in cAMP concentration and PKA activation (Fig 3C). Rise in PKA activity increases Ca2+ discharge from the ER through the inositol 1,4,5 triphosphate receptor (IP3R) and decreases [Ca2+]ER (Fig 3B).
Fig 4.
Simulated response to block of KATP channel in type 2 diabetes (T2D).
(A) KATP channel current (IKATP), (B) PM potential (Vp); (C) [Ca2+]c. T2D conditions were simulated by a decrease of the coefficient that is responsible for glucose dependent saturated ATP/ADP ratio (ATDm, Eq 4). ATDm was decreased from 32 (basal level) to 15. In this case PM membrane potential does not increase up to the nessesary threshold and does not lead to [Ca2+]c increase as glucose is increased from 3 mM to 8 mM at 1000 sec. For simulation of KATP channel blocking the maximal conductance (gmKATP, Eq 9) was decreased from 24 nS (basal level) to 9 nS at 3000 sec. This induces additional PM depolarization and fast [Ca2+]c increase.
Fig 5.
Simulation of GLP-1 and GIP action at low and high glucose levels.
(A) Cytoplasmic [Ca2+]c and cAMP dynamics. (B) ACGLP, ACGIP and ACAR are the concentrations of complexes of AC on PM (ACP) bound with corresponding G-proteins activated by GLP-1R, GIPR and α2A adrenergic receptors. (C) VACp is G-protein and Ca2+ dependent AC activity on PM, VACc is the glucose and Ca2+-activated soluble AC activity that is independent on G-protein. At low glucose concentrations (3 mM) (left part) GLP-1 was increased from basal level (3.1e-7 μM) to 6.2e-4 μM at 1000 sec. Increased extracellular glucose level was simulated at 3000 sec (from 3 mM to 8 mM). Than GIP administration was modeled as the increased GIP from basal level (1.37e-6 μM) to 3.42e-3 μM at 5000 sec.
Fig 6.
Simulated response of GLP-1 action in T2D conditions.
T2D conditions were simulated by decreasing the glucose dependent saturated ATP/ADP ratio (ATDm, Eq 4). ATDm was decreased from 32 (basal level) to 15 as in Fig 4. In this case PM membrane potential is decreased and does not lead to [Ca2+]c increase as glucose increases from 3 mM to 8 mM at 1000 sec as well as in Fig 4. GLP-1 administration was simulated at 3000 sec ([GLP-1] was increased from 3.1e-7 μM to 6.2e-4 μM. This induces cAMP increase with additional PM depolarization and Ca2+ influx into cell. Corresponding PKA activation also increases Ca2+ flow from ER. These effects lead to significant [Ca2+]c and cAMP increase.
Fig 7.
Simulation of catecholamines and GLP-1 interaction at high glucose levels.
(A) Cytoplasmic cAMP and [Ca2+]c dynamics. (B) ACGLP, ACGIP and ACAR are the concentrations of complexes of AC on PM (ACP) bound with corresponding G-proteins activated by GLP-1R, GIPR and α2A adrenergic receptors. (C) VACp is G-protein and Ca2+ dependent AC activity on PM. The initial simulation was with low glucose (3 mM) as in Fig 3. Increase of glucose (8 mM at 1000 sec) induced changes of intracellular parameters. Catecholamine concentration (AR3) was increased from basal level (0.002 μM) to 3 μM at 3000 sec. Than GLP-1 was increased from basal level (3.1e-7 μM) to 6.2e-4 μM at 5000 sec.
Fig 8.
Effects of FFAR1/GPR40 activators and acetylcholine (Ach) on changes of intracellular parameters.
Two protocols were stimulated: 1. (---) glucose was increase from 3 mM to 8 mM at 3000 sec, than acetylcholine, M3R activator, (AM3 concentration in model) was added at 5000 sec (AM3 was increased from basal level 0.0022 μM to 2.2 μM) and 2. (- - - -) FFAR1/GPR40 agonist was added at 1000 sec (AR7 was increased from basal level 0.0506 μM to 82 μM), than glucose (3000 sec) and acetylcholine were added (5000 sec). (A) Free cytoplasmic Ca2+ concentration ([Ca2+]c. (B) Free Ca2+ concentration in ER ([Ca2+]ER); (C) IP3 concentration. (D) VPLP is the activity of PM bound PLC (Eq 78). (E) Concentrations of PIP2 on PM.
Fig 9.
Effects of Ach on changes of intracellular parameters at activated NALCN channels at low glucose.
(A) PM potential (Vp); (B) [Ca2+]c and [Ca2+]ER; (C) Cytoplasmic IP3 concentration and the activity of PM bound PLC (VPLP). For simulation of NALCN channel activity the maximal conductance (gmNM3, Eq 25, CM) was initially increased from 0 nS (basal level), to 35 nS. Addition of acetylcholine that opens NALCN channel was simulated at 1000 sec at the arrow (AM3 was increased from basal level 0.0022 μM to 2.2 μM). All simulations were performed at low glucose (3 mM).
Fig 10.
Simulated responses to GLP-1 and FFAR1/GPR40 activator at high glucose.
(A) [Ca2+]c and [Ca2+]ER; (B) Cytoplasmic cAMP and IP3 concentrations; (C) Concentrations of P4P and PIP2 on PM. Glucose (8 mM) induced changes of intracellular parameters were initially simulated as in Fig 3 up to steady state (left part). GLP-1 was simulated at 1000 sec as an increased GLP-1 from basal level (3.1e-7 μM) to 6.2e-4 μM. After that FFAR1/GPR40 activation was simulated at 4000 sec as increased AR7 from basal level (0.0506 μM) to 82 μM.
Fig 11.
Simulated response to FFAR1/GPR40 activator with following addition GLP-1 at high glucose.
(A) [Ca2+]c and [Ca2+]ER; (B) Cytoplasmic cAMP and IP3 concentrations; (C) Concentrations of P4P and PIP2 on PM. Glucose (8 mM) induced changes of intracellular parameters were initially simulated as in Fig 3 up to steady state (left part). FFAR1/GPR40 activator was simulated at 1000 sec as an increased AR7 from basal level (0.0506 μM) to 82 μM. After than GLP-1 action was simulated at 3000 sec (GLP-1 increased from basal level (3.1e-7 μM) to 6.2e-4 μM).
Fig 12.
Simulated response to Ach at activated NALCN channels and decreased phosphodiesterase (PDE) activity in low glucose.
(A) PM potentials (Vp); (B) [Ca2+]c and [Ca2+]ER; (C) Cytoplasmic cAMP and IP3 concentrations. For simulation of NALCN channel activity the maximal conductance (gmNM3, Eq 25, CM) was initially increased from 0 nS (basal level) to 35 nS. PDE activity (Vcpde, Eq 66) was decreased from 1.4 μmol s-1 (basal level) to 0.3 μmol s-1. All simulations were performed at low glucose level (3 mM).
Table 1.
Cell and physical parameters.
Table 2.
Cell metabolism and membrane current parameters.
Table 3.
Initial values and coefficients for receptors and G-proteins.
Table 4.
Initial values and coefficients for receptors and G-proteins (continuation).
Table 5.
Parameters and coefficients for calmodulin and cAMP pathways.
Table 6.
Parameters and coefficients for PLC pathway and Ca2+ handling.
Fig 13.
Diagram of the kinetic model of ligand, G protein and target enzyme interactions.
Rnd is the desensitized receptor, Rn is the free receptor, Ln is the ligand, LRn is the receptor bound with ligand, LRGnGDP is the receptor bound with ligand and G protein, GnGDP is the G proteins consisting of subunits α, β and γ. In this ground state the α-subunit is bound to GDP. GαnGTP is the GTP-bound α subunit of G protein, Gβγn is the β and γ subunit of G protein, GαnGDP is GDP-bound α subunit of G protein, GαnGTPEn is the complex of the α-subunit carries the GTP and effectors enzyme (En). Efn is the enzyme that is not bound with G protein. The constants can be identified by their subcripts, where n the forward transition and nr is the reverse transition. For reversible reactions (double arrows), forward reactions are in the direction of association. (A) Collision coupling model. (B). Pre-coupling of receptor and G-protein model.