Analysis of spiking electrical activity in
human β-cells using mathematical models
Gerardo J. Félix-Martínez and J. Rafael Godínez-Fernández
email: gjfelix2005@gmail.com
Laboratory of Biophysics. Universidad Autónoma Metropolitana Unidad Iztapalapa, México.
Abstract
Methods
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.
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).
Introduction
Electrical activity of β-cells and insulin
secretion
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
(KATP) which results in membrane depolarization
and voltage-dependent activation of Ca2+ channels.
The rise in cytosolic Ca2+ triggers insulin secretion
(Fig. 1).
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
Results
1. Depolarization segment
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.
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-physiol030212-183754
Mathematical models of the pancreatic βcell
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 initial depolarization of the AP is provoked
mainly by the inhibition of the IKv and ISK
currents, being taken over by the activation of Ltype Ca2+ current (IL), which is counteracted by
the activation of the Ca2+-dependent K+ currents
(IKCa and ISK) and the delayed rectifier K+
current (IKv).
Conclusions
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
email: gjfelix2005@gmail.com
Laboratory of Biophysics. Universidad Autónoma Metropolitana Unidad Iztapalapa, México.
Abstract
Methods
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.
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).
Introduction
For the membrane potential:
I SK + I KCa + I Kv + I HERG + I Na + I L + IT + I PQ + I KATP + I Leak
dVm
=dt
Cm
Where each current is given by:
Electrical activity of β-cells and insulin
secretion
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
(KATP) which results in membrane depolarization
and voltage-dependent activation of Ca2+ channels.
The rise in cytosolic Ca2+ triggers insulin secretion
(Fig. 1).
I X = GX (Vm - EX )
Figure 3. Simulations of the electrical activity of the human β-cell with the
Riz-Pedersen model.
Results
1. Depolarization segment
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.
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-physiol030212-183754
Mathematical models of the pancreatic βcell
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 initial depolarization of the AP is provoked
mainly by the inhibition of the IKv and ISK
currents, being taken over by the activation of Ltype Ca2+ current (IL), which is counteracted by
the activation of the Ca2+-dependent K+ currents
(IKCa and ISK) and the delayed rectifier K+
current (IKv).
Conclusions
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
email: gjfelix2005@gmail.com
Laboratory of Biophysics. Universidad Autónoma Metropolitana Unidad Iztapalapa, México.
Abstract
Methods
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.
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).
The “lead potential” is calculated as:
å X GX E X
VL =
å X GX
Introduction
Electrical activity of β-cells and insulin
secretion
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
(KATP) which results in membrane depolarization
and voltage-dependent activation of Ca2+ channels.
The rise in cytosolic Ca2+ triggers insulin secretion
(Fig. 1).
While the contribution of each of the ionic
currents is estimated by:
dVL dVL - Fix
dt
dt
rc =
dVL
dt
Where
dVL - Fix
dt
Results
is the temporal change
in
VL
when
the
component of interest is
fixed
1. Depolarization segment
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.
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-physiol030212-183754
Mathematical models of the pancreatic βcell
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 initial depolarization of the AP is provoked
mainly by the inhibition of the IKv and ISK
currents, being taken over by the activation of Ltype Ca2+ current (IL), which is counteracted by
the activation of the Ca2+-dependent K+ currents
(IKCa and ISK) and the delayed rectifier K+
current (IKv).
Conclusions
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
email: gjfelix2005@gmail.com
Laboratory of Biophysics. Universidad Autónoma Metropolitana Unidad Iztapalapa, México.
Abstract
Methods
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.
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).
Introduction
Electrical activity of β-cells and insulin
secretion
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
(KATP) which results in membrane depolarization
and voltage-dependent activation of Ca2+ channels.
The rise in cytosolic Ca2+ triggers insulin secretion
(Fig. 1).
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
Results
2. Repolarization segment
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.
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-physiol030212-183754
Mathematical models of the pancreatic βcell
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 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.
Conclusions
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
email: gjfelix2005@gmail.com
Laboratory of Biophysics. Universidad Autónoma Metropolitana Unidad Iztapalapa, México.
Abstract
Methods
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.
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).
Introduction
Electrical activity of β-cells and insulin
secretion
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
(KATP) which results in membrane depolarization
and voltage-dependent activation of Ca2+ channels.
The rise in cytosolic Ca2+ triggers insulin secretion
(Fig. 1).
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.
Results
1. Depolarization segment
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.
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.
Mathematical models of the pancreatic βcell
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 initial depolarization of the AP is provoked
mainly by the inhibition of the IKv and ISK
currents, being taken over by the activation of Ltype Ca2+ current (IL), which is counteracted by
the activation of the Ca2+-dependent K+ currents
(IKCa and ISK) and the delayed rectifier K+
current (IKv).
References
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.