Tutorial: Electrophysiology of Pancreatic Islets

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Tutorial Electrophysiology of Pancreatic Islets
Richard Bertram Department of Mathematics and Prog
rams in Neuroscience and Molecular
Biophysics Florida State University
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Outline

• Background on islets
• Genesis of bursting oscillations
• The Phantom Bursting Model
• Modulators
• Coupling among b-cells

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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.
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What are Pancreatic Islets?
Most of the cells in an islet are
insulin-secreting b-cells
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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.

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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 26822265.
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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.
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The Genesis of Bursting Oscillations
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Relaxation Oscillations
Modified Morris-Lecar model for a barnacle muscle
fiber
We add the K(Ca) and K(ATP) currents, since these
are present in b-cells.
The activation variable n changes more slowly
than voltage V, and the V-nullcline is cubic, so
this model produces a relaxation oscillation.
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Relaxation Oscillations
This figure was made with l0.01. More typically
l1 and the separation of time scales is not as
great as it is here.
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Changing c Translates the V-Nullcline
c0.1
c0.2
For small c the system spikes continuously. For
large c the system is at rest.
For intermediate c the system is bistable, with a
stable steady state and a stable limit cycle.
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Dynamics of c Introduced by Incorporating Ion
Fluxes
where
influx
efflux
Bistability is evident, since system may be
oscillating (O) or silent (S) for the same
value of c.
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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.
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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.
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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
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The Phantom Bursting Model
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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
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Modified Calcium Equations
cytosolic Ca2 concentration
ER Ca2 concentration
where
and
into ER
out of ER
Important cer affects the c nullcline,
translating it to the right as cer increases
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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.
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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.
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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.
smaller
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Modulators
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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
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Several Types of G-Protein
The a 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
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Gs Pathway

• This pathway is activated by GLP-1. The activated
  Gas
• activates adenylyl cyclase, which produces cAMP.
  This activates
• the enzyme protein kinase A (PKA), which may have
  one or
• more of the following effects
• 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.

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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.
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ACh Converts Bursting to Fast Bursting
Henquin et al., Endocrinology, 1222134, 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.
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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.
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Coupling Among b-Cells
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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.
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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., 59547, 1991
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Thats All Folks!