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Mathematical models of electrical activity of the pancreatic β-cell: a physiological review.

Félix-Martínez GJ, Godínez-Fernández JR - Islets (2014)

Bottom Line: Almost all the models have been developed based on experimental data from rodents.However, given the many important differences between species, models of human β-cells have recently been developed.This review summarizes how modeling of β-cells has evolved, highlighting the proposed physiological mechanisms underlying β-cell electrical activity.

View Article: PubMed Central - PubMed

Affiliation: Department of Electrical Engineering; Universidad Autónoma Metropolitana-Iztapalapa ; México , DF , México.

ABSTRACT
Mathematical modeling of the electrical activity of the pancreatic β-cell has been extremely important for understanding the cellular mechanisms involved in glucose-stimulated insulin secretion. Several models have been proposed over the last 30 y, growing in complexity as experimental evidence of the cellular mechanisms involved has become available. Almost all the models have been developed based on experimental data from rodents. However, given the many important differences between species, models of human β-cells have recently been developed. This review summarizes how modeling of β-cells has evolved, highlighting the proposed physiological mechanisms underlying β-cell electrical activity.

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(A) Diagram of the models including ER as a secondCa2+ compartment and a non-specific calcium release-activatedcurrent (CRAC). During the silent phase (1), Ca2+ is released fromthe ER to the cytoplasm and is simultaneously extruded from the cell. This resultsin the activation of the CRAC current and the Ca2+-inactivatedCa2+ current, driving slow depolarization and initiation of aburst of action potentials (2). As [Ca2+]i increases andCa2+ is captured by the ER during the active phase, both the CRACand the Ca2+-inactivating Ca2+ currents areinhibited, resulting in membrane repolarization (3). (B and C)Simulations using the model of Chay111 including ER. Fast (B) and slow(C) bursting is produced by modifying the release rate ofCa2+ from the ER. In both cases, Vm (top, black curve),[Ca2+]i, and [Ca2+]ER(bottom, yellow and purple curves, respectively) are shown.
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f0005: (A) Diagram of the models including ER as a secondCa2+ compartment and a non-specific calcium release-activatedcurrent (CRAC). During the silent phase (1), Ca2+ is released fromthe ER to the cytoplasm and is simultaneously extruded from the cell. This resultsin the activation of the CRAC current and the Ca2+-inactivatedCa2+ current, driving slow depolarization and initiation of aburst of action potentials (2). As [Ca2+]i increases andCa2+ is captured by the ER during the active phase, both the CRACand the Ca2+-inactivating Ca2+ currents areinhibited, resulting in membrane repolarization (3). (B and C)Simulations using the model of Chay111 including ER. Fast (B) and slow(C) bursting is produced by modifying the release rate ofCa2+ from the ER. In both cases, Vm (top, black curve),[Ca2+]i, and [Ca2+]ER(bottom, yellow and purple curves, respectively) are shown.

Mentions: In contrast to the fast oscillations observed by Dean and Mathews,85,86 Smith et al.109 reported slow bursting activity with a periodicityof minutes. In order to explain the origin of the slow oscillations observedexperimentally in single cells, clusters of β-cells, and isolated islets,26,88,109 Bertramet al.110 and Chayet al.111 included theendoplasmic reticulum (ER) as a second Ca2+ compartment in β-cellmodels (Fig. 5A). As observedexperimentally, in these models, Ca2+ is transported into the ER by theSERCA pumps during the active phase of the electrical activity and is released during thesilent phase, mainly through the IP3 receptor channels and the ryanodinereceptor channels.41-43 One important aspect of these models is the presence ofnon-specific calcium release-activated currents (CRAC) in the β-cells. The main idea(depicted schematically in Fig. 5A)is that during the silent phase, Ca2+ is slowly released from the ER,preventing an abrupt drop of [Ca2+]i (Figs. 5B and C, bottom panel). As[Ca2+]i is extruded from the cell, the inactivation of theCa2+-inactivating Ca2+ current is removed.Simultaneously, as the Ca2+ concentration in the ER([Ca2+]ER) declines, the CRAC current increases. Eventually,the combination of these 2 currents becomes large enough to initiate a new burst. Then,[Ca2+]i is increased, driving the transport ofCa2+ into the ER, promoting inactivation of both theCa2+ and CRAC currents. Finally, when these currents are sufficientlysmall, the active phase terminates. In terms of periodicity, models including[Ca2+]ER as a second slow process were able to generate bothfast and slow bursting (Figs. 5B andC), in contrast to models that depend on a single slow process (e.g.,[Ca2+]i in the CK model or [ADP] in the SK model), which onlygenerated bursting with a periodicity of seconds (fast oscillations).16,112 The period of the oscillations in modelsincluding the ER is determined by the release rate of Ca2+ from the ER.When the release rate is low, [Ca2+]ER reaches a high levelduring the active phase, and because Ca2+ is released from the ER slowly,[Ca2+]i stays elevated (thus making theCa2+-dependent Ca2+ channels inactive), preventing theinitiation of a new burst of action potentials. By including the ER, it was possible tosimulate the effects of muscarinic agonists (e.g., acetylcholine) in the electricalactivity of β-cells, which are known to mediate Ca2+ release from theER.113Figure 5.


Mathematical models of electrical activity of the pancreatic β-cell: a physiological review.

Félix-Martínez GJ, Godínez-Fernández JR - Islets (2014)

(A) Diagram of the models including ER as a secondCa2+ compartment and a non-specific calcium release-activatedcurrent (CRAC). During the silent phase (1), Ca2+ is released fromthe ER to the cytoplasm and is simultaneously extruded from the cell. This resultsin the activation of the CRAC current and the Ca2+-inactivatedCa2+ current, driving slow depolarization and initiation of aburst of action potentials (2). As [Ca2+]i increases andCa2+ is captured by the ER during the active phase, both the CRACand the Ca2+-inactivating Ca2+ currents areinhibited, resulting in membrane repolarization (3). (B and C)Simulations using the model of Chay111 including ER. Fast (B) and slow(C) bursting is produced by modifying the release rate ofCa2+ from the ER. In both cases, Vm (top, black curve),[Ca2+]i, and [Ca2+]ER(bottom, yellow and purple curves, respectively) are shown.
© Copyright Policy - open-access
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4292577&req=5

f0005: (A) Diagram of the models including ER as a secondCa2+ compartment and a non-specific calcium release-activatedcurrent (CRAC). During the silent phase (1), Ca2+ is released fromthe ER to the cytoplasm and is simultaneously extruded from the cell. This resultsin the activation of the CRAC current and the Ca2+-inactivatedCa2+ current, driving slow depolarization and initiation of aburst of action potentials (2). As [Ca2+]i increases andCa2+ is captured by the ER during the active phase, both the CRACand the Ca2+-inactivating Ca2+ currents areinhibited, resulting in membrane repolarization (3). (B and C)Simulations using the model of Chay111 including ER. Fast (B) and slow(C) bursting is produced by modifying the release rate ofCa2+ from the ER. In both cases, Vm (top, black curve),[Ca2+]i, and [Ca2+]ER(bottom, yellow and purple curves, respectively) are shown.
Mentions: In contrast to the fast oscillations observed by Dean and Mathews,85,86 Smith et al.109 reported slow bursting activity with a periodicityof minutes. In order to explain the origin of the slow oscillations observedexperimentally in single cells, clusters of β-cells, and isolated islets,26,88,109 Bertramet al.110 and Chayet al.111 included theendoplasmic reticulum (ER) as a second Ca2+ compartment in β-cellmodels (Fig. 5A). As observedexperimentally, in these models, Ca2+ is transported into the ER by theSERCA pumps during the active phase of the electrical activity and is released during thesilent phase, mainly through the IP3 receptor channels and the ryanodinereceptor channels.41-43 One important aspect of these models is the presence ofnon-specific calcium release-activated currents (CRAC) in the β-cells. The main idea(depicted schematically in Fig. 5A)is that during the silent phase, Ca2+ is slowly released from the ER,preventing an abrupt drop of [Ca2+]i (Figs. 5B and C, bottom panel). As[Ca2+]i is extruded from the cell, the inactivation of theCa2+-inactivating Ca2+ current is removed.Simultaneously, as the Ca2+ concentration in the ER([Ca2+]ER) declines, the CRAC current increases. Eventually,the combination of these 2 currents becomes large enough to initiate a new burst. Then,[Ca2+]i is increased, driving the transport ofCa2+ into the ER, promoting inactivation of both theCa2+ and CRAC currents. Finally, when these currents are sufficientlysmall, the active phase terminates. In terms of periodicity, models including[Ca2+]ER as a second slow process were able to generate bothfast and slow bursting (Figs. 5B andC), in contrast to models that depend on a single slow process (e.g.,[Ca2+]i in the CK model or [ADP] in the SK model), which onlygenerated bursting with a periodicity of seconds (fast oscillations).16,112 The period of the oscillations in modelsincluding the ER is determined by the release rate of Ca2+ from the ER.When the release rate is low, [Ca2+]ER reaches a high levelduring the active phase, and because Ca2+ is released from the ER slowly,[Ca2+]i stays elevated (thus making theCa2+-dependent Ca2+ channels inactive), preventing theinitiation of a new burst of action potentials. By including the ER, it was possible tosimulate the effects of muscarinic agonists (e.g., acetylcholine) in the electricalactivity of β-cells, which are known to mediate Ca2+ release from theER.113Figure 5.

Bottom Line: Almost all the models have been developed based on experimental data from rodents.However, given the many important differences between species, models of human β-cells have recently been developed.This review summarizes how modeling of β-cells has evolved, highlighting the proposed physiological mechanisms underlying β-cell electrical activity.

View Article: PubMed Central - PubMed

Affiliation: Department of Electrical Engineering; Universidad Autónoma Metropolitana-Iztapalapa ; México , DF , México.

ABSTRACT
Mathematical modeling of the electrical activity of the pancreatic β-cell has been extremely important for understanding the cellular mechanisms involved in glucose-stimulated insulin secretion. Several models have been proposed over the last 30 y, growing in complexity as experimental evidence of the cellular mechanisms involved has become available. Almost all the models have been developed based on experimental data from rodents. However, given the many important differences between species, models of human β-cells have recently been developed. This review summarizes how modeling of β-cells has evolved, highlighting the proposed physiological mechanisms underlying β-cell electrical activity.

Show MeSH
Related in: MedlinePlus