Tutorial: Electrophysiology of
Pancreatic Islets
Richard Bertram
Department of Mathematics
and
Programs in Neuroscience and Molecular Biophysics
Florida State University
Outline
• Background on islets
• Genesis of bursting oscillations
• The Phantom Bursting Model
• Modulators
• Coupling among b-cells
The Pancreas and Liver Interact
The pancreas has both endocrine and exocrine functions.
The endocrine pancreas consists of clusters of cells called
islets of Langerhans. Insulin is the primary hormone
secreted from islets.
What are Pancreatic Islets?
Most of the cells in an islet are insulin-secreting b-cells
Why Study Islets?
• Malfunctioning islets are linked to late-onset or type II
diabetes.
• Diabetes is the fourth leading cause of death in the US.
• Diabetes is a major cause of blindness, kidney failure, and
amputation.
• Diabetes-related problems cost more than $100 billion per
year in the US.
in vitro Oscillatory Insulin Secretion
Ca
Ins
Oscillations in insulin secretion from and calcium
concentration in a mouse islet. From
Gilon et al. (1993), JBC 268:22265.
b-Cells Exhibit Electrical Bursting
Electrical recording from a mouse islet (courtesy L. Satin and M. Zhang)
Electrical impulses or action potentials are generated in
bursts when the bath or blood glucose level is in the
stimulatory range.
The Genesis of Bursting Oscillations
Relaxation Oscillations
Modified Morris-Lecar model for a barnacle muscle fiber:
Cm
dV
 [ I Ca  I K  I K (Ca )  I K ( ATP ) ]
dt
dn
 [n (V )  n] /  n
dt
We add the K(Ca) and K(ATP) currents, since these are present in
b-cells.
 c3 
(V  VK )
I K ( Ca )  g K ( Ca )  3
3 
 c  Kd 
I K ( ATP )  g K ( ATP ) (V  VK )
The activation variable n changes more slowly than voltage V, and
the V-nullcline is cubic, so this model produces a relaxation oscillation.
Relaxation Oscillations
This figure was made with =0.01. More typically =1 and
the separation of time scales is not as great as it is here.
Changing c Translates the V-Nullcline
c=0.1
c=0.2
For intermediate c
the system is bistable,
with a stable steady state
and a stable limit cycle.
For small c the system spikes
continuously. For large c the
system is at rest.
Dynamics of c Introduced by Incorporating
Ion Fluxes
dc
 f cyt J mem
dt
where
J mem  ( I Ca  k pmcac)
influx
efflux
Bistability is evident, since
system may be oscillating (O)
or silent (S) for the same value
of c.
Fast/Slow Analysis of Bursting
Treat c as a parameter and
construct a bifurcation diagram
for the fast subsystem. Then
superimpose c-nullcline (A,B)
and burst trajectory.
kpmca
Increasing the Ca2+ pump rate
kpmca raises the c-nullcline
(from A to B) and increases
the plateau fraction. This
simulates the effect of increasing
the glucose concentration in islets.
Bursting is Similar to a Relaxation Oscillation
The z-curve is similar in shape to the cubic V-nullcline of the
Morris-Lecar model when c is the slow variable and the periodic
branch is represented by the average voltage curve.
Problem with the “Chay-Keizer” Model
A key prediction of the model just described, the “Chay-Keizer model”,
is that c exhibits a slow rise during the active phase and a slow fall during
the silent phase of bursting. Calcium imaging data shows that this is in
fact not the case:
Courtesy of C. Nunemaker and L. Satin
The Phantom Bursting Model
The Endoplasmic Reticulum
The ER is an organelle that participates in the folding of proteins after
translation. It is also a Ca2+ store that maintains a free Ca2+ in the
hundreds of micromolar. It uptakes or releases Ca2+, depending on the
cytosolic Ca2+.
Spiking cell
Silent cell
Modified Calcium Equations
dc
 f cyt ( J mem  J er )
dt
 vcyt 
dcer
 J er
 fer 
dt
 ver 
cytosolic Ca2+ concentration
ER Ca2+ concentration
where
J er  J serca  J leak
into ER
and
J serca  ksercac
J leak  pleak (cer  c)
out of ER
Important: cer affects the c nullcline, translating it to the right as cer increases
ER Slows Down Bursting
Bursting without
an ER
Bursting with
an ER
Notice that the cytosolic Ca2+ concentration no longer has a
sawtooth shape. It is similar to experimental data. The
ER Ca2+ concentration now has the sawtooth shape.
With an ER, Bursting Can Be Slowed Down
Even More
Bursting can be slowed down by decreasing the size of the K(Ca)
conductance. This parameter has no direct influence on the Ca2+
influx/efflux or the flux into/out of the ER.
g K (Ca )  1000 pS
g K (Ca )  500 pS
g K (Ca )  370 pS
How Does This Happen?
Lowering K(Ca) conductance stretches the z-curve. If stretched sufficiently,
the lower branch will intersect the c-nullcline. The phase point will get stuck
and cer will have to change (moving the c-nullcline) so that the phase point is
released. Burst period then depends primarily on the time constant of cer and
the extent to which the phase point is stuck in the silent and/or active phase.
This type of bursting is called Phantom Bursting.
g K (Ca )  1000 pS
smaller g K (Ca )
Modulators
Modulators of b-Cell Activity
Factors released through the autonomic nerves or from the gut
modulate islet activity. These include epinephrine and acetylcholine
(ACh) from nerves and glucagon-like peptide 1 (GLP-1) from the
gut. These bind to receptors on the plasma membrane and activate
G-proteins.
Hille, Ion Channels of Excitable Membranes, 2001
Several Types of G-Protein
The  subunit of the G-protein determines the type of G-protein. There
are 4 types or families. Each has different downstream intracellular targets.
Hille, Ion Channels of Excitable Membranes, 2001
Gs Pathway
This pathway is activated by GLP-1. The activated Gs
activates adenylyl cyclase, which produces cAMP. This activates
the enzyme protein kinase A (PKA), which may have one or
more of the following effects:
(1) Activated PKA translocates into the nucleus, regulating gene
transcription, including transcription of the insulin gene.
(2) Activated PKA phosphorylates L-type Ca2+ channels, changing
the activation properties of the channels.
(3) Activated PKA phosphorylates ATP-dependent K+ channels.
Bottom Line: PKA increases insulin secretion from b-cells.
Gq Pathway
This pathway is activated by the parasympathetic neurotransmitter
ACh. This results in the production of Inositol Triphosphate (IP3)
and Diacylglycerol (DAG).
Gomperts et al., Signal
Transduction, 2003.
ER
IP3 activates channels that release Ca2+ from the ER. This changes
the electrical and Ca2+ activity pattern in the cell.
DAG co-activates, along with Ca2+, protein kinase C (PKC).
This sensitizes the exocytotic machinery, increasing insulin release.
ACh Converts Bursting to Fast Bursting
Henquin et al., Endocrinology, 122:2134, 1988
When ACh is added to the islet in the presence of a stimulatory
glucose concentration the normal bursting pattern is converted
to fast bursting with a depolarized silent phase.
ACh Conversion is Reproduced by the
Phantom Bursting Model
IP3 opens channels in the ER, so Ca2+
leaves the ER and enters the cytosol.
The increased efflux from the
ER changes the shape of the
c-nullcline, so that it no
longer intersects the bottom
branch of the z-curve. Subsequent
bursting is fast.
Coupling Among b-Cells
b-Cells are Coupled Through Gap Junctions
Gap junctions are formed by connexin proteins. Six of these
combine to form a Connexon, and two connexons combine to
form a gap junction. These junctions electrically couple neighboring
b-cells.
Electrical Coupling Can Synchronize b-Cells
and Overcome Noise
Numerical simulations with
model b-cells with electrical
connections. Cells arranged
in a cube, of two different
dimensions. Two cells from
each cube are shown.
weak
coupling
strong
coupling
Sherman and Rinzel, Biophys. J., 59:547, 1991
That’s All Folks!