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  -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  -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 Oscillations in insulin secretion from and calcium concentration in a mouse islet. From Gilon et al. (1993), JBC 268: Ca Ins

 -Cells Exhibit Electrical Bursting Electrical impulses or action potentials are generated in bursts when the bath or blood glucose level is in the stimulatory range. Electrical recording from a mouse islet (courtesy L. Satin and M. Zhang)

The Genesis of Bursting 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  -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 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=0.1c=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 where influxefflux 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. Increasing the Ca 2+ pump rate k pmca raises the c-nullcline (from A to B) and increases the plateau fraction. This simulates the effect of increasing the glucose concentration in islets. k pmca

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 Ca 2+ store that maintains a free Ca 2+ in the hundreds of micromolar. It uptakes or releases Ca 2+, depending on the cytosolic Ca 2+. Spiking cell Silent cell

Modified Calcium Equations cytosolic Ca 2+ concentration ER Ca 2+ concentration where and into ERout of ER Important: c er affects the c nullcline, translating it to the right as c er increases

ER Slows Down Bursting Bursting without an ER Bursting with an ER Notice that the cytosolic Ca 2+ concentration no longer has a sawtooth shape. It is similar to experimental data. The ER Ca 2+ 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 Ca 2+ influx/efflux or the flux into/out of the ER.

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 c er 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 c er 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

Modulators of  -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

G s 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 Ca 2+ channels, changing the activation properties of the channels. (3) Activated PKA phosphorylates ATP-dependent K + channels. Bottom Line: PKA increases insulin secretion from  -cells.

G q Pathway This pathway is activated by the parasympathetic neurotransmitter ACh. This results in the production of Inositol Triphosphate (IP 3 ) and Diacylglycerol (DAG). ER IP 3 activates channels that release Ca 2+ from the ER. This changes the electrical and Ca 2+ activity pattern in the cell. DAG co-activates, along with Ca 2+, protein kinase C (PKC). This sensitizes the exocytotic machinery, increasing insulin release. Gomperts et al., Signal Transduction, 2003.

ACh Converts Bursting to Fast Bursting 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. Henquin et al., Endocrinology, 122:2134, 1988

ACh Conversion is Reproduced by the Phantom Bursting Model IP 3 opens channels in the ER, so Ca 2+ 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  -Cells

 -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  -cells.

Electrical Coupling Can Synchronize  -Cells and Overcome Noise Numerical simulations with model  -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!