The Dual Oscillator Model for Pancreatic Islets Richard Bertram Department of Mathematics and 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-DMS

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 humans exhibits oscillations, suggesting that insulin is secreted in a pulsatile manner. Porksen et al., AJP, 273:E908, 1997 measured deconvolved

Central Question: What is the mechanism for oscillations in insulin secretion from pancreatic β-cells?

Islets are Electrically Excitable Islets are like nerve cells in that they produce electrical impulses. During an upstroke of an impulse Ca 2+ enters the cells, causing insulin to be released. insulin calcium Gilon et al., JBC, 268:22265, 1993

Fast Bursting Oscillations Simultaneous fast Ca 2+ and voltage measurements from a mouse islet in 11.1 mM glucose. From Zhang et al., Biophys. J., 84:2852, 2003

Slow Bursting Oscillations Slow oscillations of Ca 2+ and voltage from an islet... Zhang et al., Biophys. J., 84:2852, 2003Smith et al., FEBS Lett., , 1990 …have period similar to slow insulin oscillations measured from a mouse in vivo (Nunemaker et al., Diabetes, 54:3517, 2005)

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 coupled oscillators. Calcium oscillator controls fast bursting Ca 2+  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: , 1999 Glycolytic oscillations in yeast

Modeling Approach Cells within an islet are electrically coupled, leading to synchronization within an islet. Our model therefore describes a single cell within the synchronized cell 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 + activation variable n. This depends on the voltage.

Electrical/Calcium Components of the DOM Ca 2+ enters the cell through L-type Ca 2+ channels. The free cytosolic Ca 2+ activates K(Ca) channels. Thus, there is mutual feedback between the electrical and Ca 2+ components. ER is the Endoplasmic Reticulum

Fast Oscillations with the DOM When glycolysis is non-oscillatory, the DOM produces fast bursting oscillations, due to the electrical/calcium components of the model. The ER acts as a slow Ca 2+ filter, setting the period of bursting through its interaction with the cytosol. Bertram and Sherman, BMB, 66:1313, 2004

Glycolytic Component of the DOM Key feature: The product F1,6BP feeds back positively onto the allosteric enzyme PFK1 (phosphofructokinase 1). Leads to oscillations due to substrate depletion. substrate product

Glycolytic Oscillations Produced if Glucokinase Rate is in the Right Range (A)Intermediate J GK (B) High J GK Glycolytic oscillations in muscle extracts (Tornheim, Diabetes, 46:1375, 1997) Solid-F6P, Dashed-FBP Bertram et al., BJ, 87:3074, 2004

Mitochondrial Component Includes equations for mitochondrial NADH concentration, inner membrane potential, Ca 2+ 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 glycolytic oscillations With glycolytic oscillations Bertram et al., Am. J. Physiol., 293:E890, 2007 Experiment 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 and see if islet oscillations behave as predicted by the model. Competes with F1,6BP for binding to PFK1, thus reducing the positive feedback

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 overexpress the Bifunctional Enzyme 2 (BIF2) into islets. Then use molecular tagging to degrade either the kinase or phosphatase action of the enzyme. Kinase makes F2,6BP from F6P Phosphatase converts F2,6BP back to F6P

Prediction Confirmed With kinase the oscillations in calcium are faster and smaller Merrins et al., PLoS One, 2012

Prediction Confirmed With phosphatase oscillations are slower and larger Merrins et al., PLoS One, 2012

Next Step Use a FRET sensor to directly measure oscillations in the concentration of a molecule that is in the glycolytic pathway and downstream of PFK1. Do these oscillations exist?

Thank You!