The Dual Oscillator Model for Pancreatic Islets

Richard Bertram

Department of Mathematicsand

Programs in Neuroscience and Molecular Biophysics Florida State University, Tallahassee, FL.

AIMS Conference, 2012

Collaborators

Arthur Sherman (NIH)Leslie Satin (U. Michigan)Matthew Merrins (U. Michigan)

Funding: NSF-DMS0917664

What is an Islet of Langerhans?

Cluster of electrically coupled hormone-secreting cells,located throughout the pancreas. The human pancreas has about 1 million islets.

Courtesy of Rohit Kulkarni

Immunostained for glucagon (green) and insulin (red)

Insulin Secretion is Pulsatile

Peripheral insulin measurements in the blood of humansexhibits oscillations, suggesting that insulin is secretedin a pulsatile manner.

Porksen et al.,AJP, 273:E908,1997

measured

deconvolved

Central Question:

What is the mechanism for oscillations ininsulin secretion from pancreatic β-cells?

Islets are Electrically Excitable

Islets are like nerve cells in that they produce electricalimpulses. During an upstroke of an impulse Ca2+ entersthe cells, causing insulin to be released.

insulin

calcium

Gilon et al.,JBC, 268:22265,1993

Fast Bursting Oscillations

Simultaneous fast Ca2+ and voltage measurements from a mouseislet in 11.1 mM glucose. From Zhang et al., Biophys. J., 84:2852, 2003

Slow Bursting Oscillations

Slow oscillations of Ca2+ and voltage from an islet...

Zhang et al., Biophys. J., 84:2852, 2003Smith et al., FEBS Lett., 261-187, 1990

…have period similar to slowinsulin oscillations measuredfrom a mouse in vivo (Nunemaker et al., Diabetes,54:3517, 2005)

A BA B

Compound Bursting Oscillations

Henquin et al., Eur. J. Physiol., 393:322, 1982

Bursting oscillations superimposed on a slow wave of activity

The Dual Oscillator Model

Central Hypothesis

Fast, slow, and compound oscillations can all be produced by a mechanism with two coupledoscillators.

Calcium oscillator controls fast bursting

Ca2+ K(Ca) channels

Metabolic oscillator controls slower oscillation

ATP K(ATP) channels

Metabolic Oscillations Can Occur Through Oscillations in Glycolysis

Dano et al., Nature, 402:320-322, 1999

Glycolyticoscillationsin yeast

Modeling Approach

• Cells within an islet are electrically coupled, leading to synchronization within an islet. Our modeltherefore describes a single cell within the synchronizedcell population.

• A β-cell is very small and spherical (diameter ≈10 microns). Modeled as a single compartment;equations depend on time only.

Electrical Component of the DOM

Voltage equation reflects Kirchoff’s current law

Second equation describes dynamics of the K+ activationvariable n. This depends on the voltage.

Electrical/Calcium Components of the DOM

)(

/))((

/)( )()(

ckIfc

nVnn

CIIIIV

cCa

n

mATPKCaKKCa

Ca2+ enters the cell through L-type Ca2+ channels. The freecytosolic Ca2+ activates K(Ca) channels. Thus, there is mutualfeedback between the electrical and Ca2+ components.

ER is the Endoplasmic Reticulum

Fast Oscillations with the DOM

When glycolysis is non-oscillatory, the DOM produces fast burstingoscillations, due to the electrical/calcium components of the model.

The ER acts as a slow Ca2+ filter, setting the period ofbursting through its interaction with the cytosol.

Bertram andSherman, BMB,66:1313, 2004

Glycolytic Component of the DOM

Key feature: The product F1,6BP feedsback positively onto the allostericenzyme PFK1 (phosphofructokinase 1).Leads to oscillations due to substratedepletion.

substrate

product

Glycolytic Oscillations Produced if Glucokinase Rate is in the Right Range

(A) Intermediate JGK

(B) High JGK

Glycolytic oscillations in muscleextracts (Tornheim, Diabetes,46:1375, 1997)

Solid-F6P, Dashed-FBP

Bertram et al.,BJ, 87:3074, 2004

Mitochondrial Component

Includes equations for mitochondrial NADH concentration, innermembrane potential, Ca2+ concentration, and ADP/ATP concentrations.

Final 3-compartment model:

Bertram et al.,BJ, 92:1544, 2007

ATP acts on K(ATP) channels to affect V

The Three Types of Activity can be Reproduced by the Model

No glycolytic oscillations

With glycolyticoscillations

With glycolyticoscillations

Bertram et al., Am. J. Physiol., 293:E890, 2007

Experiment

Model

Model

A Test for Glycolytic Oscillations

Fructose-2,6-bisphosphate(F2,6BP) is a high-affinity activator of PFK1

Idea: Modify the activity of the key enzyme PFK1 andsee if islet oscillations behave as predicted by the model.

Competes with F1,6BP for binding to PFK1, thusreducing the positivefeedback

Model Prediction

F2,6BP should make metabolic oscillations smaller and faster by changing the F1,6BP nullcline

Merrins et al.,PLoS One, 2012

F6P

F1,6BP

Experimental Test of the Prediction

Use an adenovirus to overexpressthe Bifunctional Enzyme 2 (BIF2)into islets. Then use moleculartagging to degrade either thekinase or phosphatase action of theenzyme.

Kinase makes F2,6BP from F6P

Phosphatase converts F2,6BP backto F6P

Prediction Confirmed

With kinase theoscillations incalcium arefaster and smaller

Merrins et al.,PLoS One, 2012

Prediction Confirmed

With phosphataseoscillationsare slower and larger

Merrins et al.,PLoS One, 2012

Next Step

Use a FRET sensor to directly measure oscillationsin the concentration of a molecule that is in theglycolytic pathway and downstream of PFK1. Dothese oscillations exist?

Thank You!