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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

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tutorial electrophysiology of pancreatic islets
Tutorial: Electrophysiology of Pancreatic Islets

Richard Bertram

Department of Mathematics

and

Programs in Neuroscience and Molecular Biophysics

Florida State University

outline
Outline
  • Background on islets
  • Genesis of bursting oscillations
  • The Phantom Bursting Model
  • Modulators
  • Coupling among b-cells
the pancreas and liver interact
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
What are Pancreatic Islets?

Most of the cells in an islet are insulin-secreting b-cells

why study islets
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
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
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.

relaxation oscillations
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.

relaxation oscillations10
Relaxation Oscillations

This figure was made with l=0.01. More typically l=1 and

the separation of time scales is not as great as it is here.

changing c translates the v nullcline
Changing c Translates the V-Nullcline

c=0.1

c=0.2

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.

dynamics of c introduced by incorporating ion fluxes
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.

fast slow analysis of bursting
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
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
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 endoplasmic reticulum
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
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

er slows down bursting
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
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.

how does this happen
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

modulators of b cell activity
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
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

g s pathway
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.
g q pathway
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
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
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.

b cells are coupled through gap junctions
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
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