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Abstract We investigate the role of the ionic currents expressed in the human pancreatic β-cell in the generation of spiking electrical activity. The depolarization and repolarization segments of the action potential produced by a recent mathematical model were studied using the lead potential analysis method to estimate the contribution of the ionic channels to the generation and shape of the action potentials. It is well established that after being transported into the cell, glucose is metabolized, producing energy in form of ATP. The increased ATP concentration blocks ATP-sensitive K + channels (K ATP ) which results in membrane depolarization and voltage-dependent activation of Ca 2+ channels. The rise in cytosolic Ca 2+ triggers insulin secretion (Fig. 1). Electrical activity of β-cells and insulin secretion Introduction Figure 1. Consensus model of glucose-stimulated insulin secration. Adapted from: Henquin, J. C., Nenquin, M., Ravier, M. A., and Szollosi, A. (2009). Shortcomings of current models of glucose-induced insulin secretion. Diabetes, Obesity and Metabolism, 11, 168–179. doi:10.1111/j.1463-1326.2009.01109.x Action potential firing in human β-cells (Fig. 2) is driven by the interaction between ionic channels, whose activity is regulated by the membrane potential (Vm), metabolic variables and calcium ions. Mathematical models of the pancreatic β- cell Figure 2. Glucose-induced electrical activity in human β cells: action potential firing. Adapted from: Rorsman, P. and Braun, M. (2013). Regulation of Insulin Secretion in Human Pancreatic Islets. Annual Review of Physiology, 75(1), 155–179. doi:10.1146/annurev-physiol- 030212-183754 Methods Results As a complement to experimental work, mathematical models of β-cells have been used to elucidate how the cellular mechanisms involved in GSIS interact, providing feasible explanations and hypotheses to experimental observations. The lead potential analysis is a method proposed by Cha et al.[1] to quantify the contribution of an individual ionic channel to the changes in Vm. We analyzed the spiking electrical activity pattern produced with the model of Riz et al.[2] of the human β-cell (Fig. 3). Figure 3. Diagram of the mechanisms included in the model of Riz et al. of human β-cells. Reproduced with permission from Félix-Martinez, G. J., and Godínez-Fernández, J. R. (2014). Mathematical models of electrical activity of the pancreatic β-cell: a physiological review. Islets, e949195. doi:10.4161/19382014.2014.949195 1. Depolarization segment Conclusions The initial depolarization of the AP is provoked mainly by the inhibition of the IKv and ISK currents, being taken over by the activation of L- type Ca 2+ current (IL), which is counteracted by the activation of the Ca 2+ -dependent K + currents (IKCa and ISK) and the delayed rectifier K + current (IKv). The role of the ionic transport mechanisms in the human β-cell is still unclear. In this work we have shown how mathematical models can be used as a complement to the experimental work to contribute to a better understanding of the interaction between the ionic currents involved in the spiking electrical behavior in human β-cells. References Analysis of spiking electrical activity in human β-cells using mathematical models Gerardo J. Félix-Martínez and J. Rafael Godínez-Fernández Laboratory of Biophysics. Universidad Autónoma Metropolitana Unidad Iztapalapa, México. email: gjfelix2005@gmail.com

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Analysis of spiking electrical activity in human β-cells using mathematical models Gerardo J. Félix-Martínez and J. Rafael Godínez-Fernández Laboratory of Biophysics. Universidad Autónoma Metropolitana Unidad Iztapalapa, México. Abstract We investigate the role of the ionic currents expressed in the human pancreatic β-cell in the generation of spiking electrical activity. The depolarization and repolarization segments of the action potential produced by a recent mathematical model were studied using the lead potential analysis method to estimate the contribution of the ionic channels to the generation and shape of the action potentials. It is well established that after being transported into the cell, glucose is metabolized, producing energy in form of ATP. The increased ATP concentration blocks ATP-sensitive K + channels (K ATP ) which results in membrane depolarization and voltage-dependent activation of Ca 2+ channels. The rise in cytosolic Ca 2+ triggers insulin secretion (Fig. 1). Electrical activity of β-cells and insulin secretion Introduction Figure 1. Consensus model of glucose-stimulated insulin secration. Adapted from: Henquin, J. C., Nenquin, M., Ravier, M. A., and Szollosi, A. (2009). Shortcomings of current models of glucose-induced insulin secretion. Diabetes, Obesity and Metabolism, 11, 168–179. doi:10.1111/j.1463-1326.2009.01109.x Action potential firing in human β-cells (Fig. 2) is driven by the interaction between ionic channels, whose activity is regulated by the membrane potential (Vm), metabolic variables and calcium ions. Mathematical models of the pancreatic β- cell Figure 2. Glucose-induced electrical activity in human β-cells: action potential firing. Adapted from: Rorsman, P. and Braun, M. (2013). Regulation of Insulin Secretion in Human Pancreatic Islets. Annual Review of Physiology, 75(1), 155–179. doi:10.1146/annurev-physiol- 030212-183754 Methods Results As a complement to experimental work, mathematical models of β-cells have been used to elucidate how the cellular mechanisms involved in GSIS interact, providing feasible explanations and hypotheses to experimental observations. The lead potential analysis is a method proposed by Cha et al.[1] to quantify the contribution of an individual ionic channel to the changes in Vm. We analyzed the spiking electrical activity pattern produced with the model of Riz et al.[2] of the human β-cell (Fig. 3). Figure 3. Simulations of the electrical activity of the human β-cell with the Riz-Pedersen model. 1. Depolarization segment Conclusions The initial depolarization of the AP is provoked mainly by the inhibition of the IKv and ISK currents, being taken over by the activation of L- type Ca 2+ current (IL), which is counteracted by the activation of the Ca 2+ -dependent K + currents (IKCa and ISK) and the delayed rectifier K + current (IKv). email: gjfelix2005@gmail.com The role of the ionic transport mechanisms in the human β-cell is still unclear. In this work we have shown how mathematical models can be used as a complement to the experimental work to contribute to a better understanding of the interaction between the ionic currents involved in the spiking electrical behavior in human β-cells. For the membrane potential: Where each current is given by: References

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Abstract We investigate the role of the ionic currents expressed in the human pancreatic β-cell in the generation of spiking electrical activity. The depolarization and repolarization segments of the action potential produced by a recent mathematical model were studied using the lead potential analysis method to estimate the contribution of the ionic channels to the generation and shape of the action potentials. It is well established that after being transported into the cell, glucose is metabolized, producing energy in form of ATP. The increased ATP concentration blocks ATP-sensitive K + channels (K ATP ) which results in membrane depolarization and voltage-dependent activation of Ca 2+ channels. The rise in cytosolic Ca 2+ triggers insulin secretion (Fig. 1). Electrical activity of β-cells and insulin secretion Introduction Figure 1. Consensus model of glucose-stimulated insulin secration. Adapted from: Henquin, J. C., Nenquin, M., Ravier, M. A., and Szollosi, A. (2009). Shortcomings of current models of glucose-induced insulin secretion. Diabetes, Obesity and Metabolism, 11, 168–179. doi:10.1111/j.1463-1326.2009.01109.x Action potential firing in human β-cells (Fig. 2) is driven by the interaction between ionic channels, whose activity is regulated by the membrane potential (Vm), metabolic variables and calcium ions. Mathematical models of the pancreatic β- cell Figure 2. Glucose-induced electrical activity in human β cells: action potential firing. Adapted from: Rorsman, P. and Braun, M. (2013). Regulation of Insulin Secretion in Human Pancreatic Islets. Annual Review of Physiology, 75(1), 155–179. doi:10.1146/annurev-physiol- 030212-183754 Methods Results As a complement to experimental work, mathematical models of β-cells have been used to elucidate how the cellular mechanisms involved in GSIS interact, providing feasible explanations and hypotheses to experimental observations. The lead potential analysis is a method proposed by Cha et al.[1] to quantify the contribution of an individual ionic channel to the changes in Vm. We analyzed the spiking electrical activity pattern produced with the model of Riz et al.[2] of the human β-cell (Fig. 3). 1. Depolarization segment Conclusions The initial depolarization of the AP is provoked mainly by the inhibition of the IKv and ISK currents, being taken over by the activation of L- type Ca 2+ current (IL), which is counteracted by the activation of the Ca 2+ -dependent K + currents (IKCa and ISK) and the delayed rectifier K + current (IKv). The role of the ionic transport mechanisms in the human β-cell is still unclear. In this work we have shown how mathematical models can be used as a complement to the experimental work to contribute to a better understanding of the interaction between the ionic currents involved in the spiking electrical behavior in human β-cells. The “lead potential” is calculated as: While the contribution of each of the ionic currents is estimated by: is the temporal change in V L when the component of interest is fixed Where References Analysis of spiking electrical activity in human β-cells using mathematical models Gerardo J. Félix-Martínez and J. Rafael Godínez-Fernández Laboratory of Biophysics. Universidad Autónoma Metropolitana Unidad Iztapalapa, México. email: gjfelix2005@gmail.com

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Laboratory of Biophysics. Universidad Autónoma Metropolitana Unidad Iztapalapa, México. Abstract We investigate the role of the ionic currents expressed in the human pancreatic β-cell in the generation of spiking electrical activity. The depolarization and repolarization segments of the action potential produced by a recent mathematical model were studied using the lead potential analysis method to estimate the contribution of the ionic channels to the generation and shape of the action potentials. It is well established that after being transported into the cell, glucose is metabolized, producing energy in form of ATP. The increased ATP concentration blocks ATP-sensitive K + channels (K ATP ) which results in membrane depolarization and voltage-dependent activation of Ca 2+ channels. The rise in cytosolic Ca 2+ triggers insulin secretion (Fig. 1). Electrical activity of β-cells and insulin secretion Introduction Figure 1. Consensus model of glucose-stimulated insulin secration. Adapted from: Henquin, J. C., Nenquin, M., Ravier, M. A., and Szollosi, A. (2009). Shortcomings of current models of glucose-induced insulin secretion. Diabetes, Obesity and Metabolism, 11, 168–179. doi:10.1111/j.1463-1326.2009.01109.x Action potential firing in human β-cells (Fig. 2) is driven by the interaction between ionic channels, whose activity is regulated by the membrane potential (Vm), metabolic variables and calcium ions. Mathematical models of the pancreatic β- cell Figure 2. Glucose-induced electrical activity in human β cells: action potential firing. Adapted from: Rorsman, P. and Braun, M. (2013). Regulation of Insulin Secretion in Human Pancreatic Islets. Annual Review of Physiology, 75(1), 155–179. doi:10.1146/annurev-physiol- 030212-183754 Methods Results As a complement to experimental work, mathematical models of β-cells have been used to elucidate how the cellular mechanisms involved in GSIS interact, providing feasible explanations and hypotheses to experimental observations. The lead potential analysis is a method proposed by Cha et al.[1] to quantify the contribution of an individual ionic channel to the changes in Vm. We analyzed the spiking electrical activity pattern produced with the model of Riz et al.[2] of the human β-cell (Fig. 3). Figure 3. Diagram of the mechanisms included in the model of Riz et al. of human β-cells. Reproduced with permission from Félix-Martinez, G. J., and Godínez-Fernández, J. R. (2014). Mathematical models of electrical activity of the pancreatic β-cell: a physiological review. Islets, e949195. doi:10.4161/19382014.2014.949195 2. Repolarization segment Conclusions The repolarization phase is driven primarily by the inhibition of IL and IKCa, although the remaining inward and outward currents increased their contribution near the end of the repolarization segment. References The role of the ionic transport mechanisms in the human β-cell is still unclear. In this work we have shown how mathematical models can be used as a complement to the experimental work to contribute to a better understanding of the interaction between the ionic currents involved in the spiking electrical behavior in human β-cells. Analysis of spiking electrical activity in human β-cells using mathematical models Gerardo J. Félix-Martínez and J. Rafael Godínez-Fernández Laboratory of Biophysics. Universidad Autónoma Metropolitana Unidad Iztapalapa, México. email: gjfelix2005@gmail.com

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Abstract We investigate the role of the ionic currents expressed in the human pancreatic β-cell in the generation of spiking electrical activity. The depolarization and repolarization segments of the action potential produced by a recent mathematical model were studied using the lead potential analysis method to estimate the contribution of the ionic channels to the generation and shape of the action potentials. It is well established that after being transported into the cell, glucose is metabolized, producing energy in form of ATP. The increased ATP concentration blocks ATP-sensitive K + channels (K ATP ) which results in membrane depolarization and voltage-dependent activation of Ca 2+ channels. The rise in cytosolic Ca 2+ triggers insulin secretion (Fig. 1). Electrical activity of β-cells and insulin secretion Introduction Figure 1. Consensus model of glucose-stimulated insulin secration. Adapted from: Henquin, J. C., Nenquin, M., Ravier, M. A., and Szollosi, A. (2009). Shortcomings of current models of glucose-induced insulin secretion. Diabetes, Obesity and Metabolism, 11, 168–179. Action potential firing in human β-cells (Fig. 2) is driven by the interaction between ionic channels, whose activity is regulated by the membrane potential (Vm), metabolic variables and calcium ions. Mathematical models of the pancreatic β- cell Figure 2. Glucose-induced electrical activity in human β cells: action potential firing. Adapted from: Rorsman, P. and Braun, M. (2013). Regulation of Insulin Secretion in Human Pancreatic Islets. Annual Review of Physiology, 75(1), 155–179. Methods Results As a complement to experimental work, mathematical models of β-cells have been used to elucidate how the cellular mechanisms involved in GSIS interact, providing feasible explanations and hypotheses to experimental observations. The lead potential analysis is a method proposed by Cha et al.[1] to quantify the contribution of an individual ionic channel to the changes in Vm. We analyzed the spiking electrical activity pattern produced with the model of Riz et al.[2] of the human β-cell (Fig. 3). Figure 3. Diagram of the mechanisms included in the model of Riz et al. of human β-cells. Reproduced with permission from Félix-Martinez, G. J., and Godínez-Fernández, J. R. (2014). Mathematical models of electrical activity of the pancreatic β-cell: a physiological review. Islets, e949195. 1. Depolarization segment References The initial depolarization of the AP is provoked mainly by the inhibition of the IKv and ISK currents, being taken over by the activation of L- type Ca 2+ current (IL), which is counteracted by the activation of the Ca 2+ -dependent K + currents (IKCa and ISK) and the delayed rectifier K + current (IKv). 1.Cha, C. Y., Himeno, Y., Shimayoshi, T., Amano, A., and Noma, A. (2009). A Novel Method to Quantify Contribution of Channels and Transporters to Membrane Potential Dynamics. Biophysical Journal, 97(12), 3086– 3094. 2.Riz, M., Braun, M., and Pedersen, M. G. (2014). Mathematical modeling of heterogeneous electrophysiological responses in human β-cells. PLoS Computational Biology, 10(1), e1003389. Analysis of spiking electrical activity in human β-cells using mathematical models Gerardo J. Félix-Martínez and J. Rafael Godínez-Fernández Laboratory of Biophysics. Universidad Autónoma Metropolitana Unidad Iztapalapa, México. email: gjfelix2005@gmail.com

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