Transcript AIMS_12.ppt

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-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
Porksen et al.,
AJP, 273:E908,
1997
deconvolved
measured
Peripheral insulin measurements in the blood of humans
exhibits oscillations, suggesting that insulin is secreted
in a pulsatile manner.
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 Ca2+ enters
the cells, causing insulin to be released.
calcium
Gilon et al.,
JBC, 268:22265,
1993
insulin
Fast Bursting Oscillations
Simultaneous fast Ca2+ 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 Ca2+ and voltage
from an islet...
Smith et al., FEBS Lett., 261-187, 1990
A
Zhang et al., Biophys. J., 84:2852, 2003
B
…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
Ca2+  K(Ca) channels
Metabolic oscillator controls slower oscillation
ATP  K(ATP) channels
Metabolic Oscillations Can Occur
Through Oscillations in Glycolysis
Glycolytic
oscillations
in yeast
Dano et al., Nature, 402:320-322, 1999
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
V = -(ICa + I K (V ) + I K (Ca) + I K ( ATP) ) / Cm
n = (n¥ (V ) - n) / t n
c = - f (a ICa + kc c)
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
V  ( I Ca  I K  I K (Ca )  I K ( ATP ) ) / Cm
n  (n (V )  n) /  n
c   f (I Ca  kc c)
c = f (Jleak - J serca + Jin - Jout )
cER = fER (Vcyt VER ) (J serca - Jleak )
ER is the Endoplasmic Reticulum
Ca2+ enters the cell through L-type Ca2+ channels. The free
cytosolic Ca2+ activates K(Ca) channels. Thus, there is mutual
feedback between the electrical and Ca2+ components.
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.
Bertram and
Sherman, BMB,
66:1313, 2004
The ER acts as a slow Ca2+ filter, setting the period of
bursting through its interaction with the cytosol.
Glycolytic Component of the DOM
substrate
product
d F6P
= l (JGK - J PFK1 )
dt
d F1, 6BP
= J PFK1 - 0.5JGPDH
dt
Key feature: The product F1,6BP feeds
back positively onto the allosteric
enzyme PFK1 (phosphofructokinase 1).
Leads to oscillations due to substrate
depletion.
Glycolytic Oscillations Produced if
Glucokinase Rate is in the Right Range
Solid-F6P, Dashed-FBP
(A) Intermediate JGK
(B) High JGK
Bertram et al.,
BJ, 87:3074, 2004
Glycolytic oscillations in muscle
extracts (Tornheim, Diabetes,
46:1375, 1997)
Mitochondrial Component
Includes equations for mitochondrial NADH concentration, inner
membrane 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 glycolytic
oscillations
With glycolytic
oscillations
Experiment
Model
Model
Bertram et al., Am. J. Physiol., 293:E890, 2007
A Test for Glycolytic Oscillations
Idea: Modify the activity of the key enzyme PFK1 and
see if islet oscillations behave as predicted by the model.
Fructose-2,6-bisphosphate
(F2,6BP) is a high-affinity
activator of PFK1
Competes with F1,6BP
for binding to PFK1, thus
reducing the positive
feedback
Model Prediction
F16BP (mM)
A
40
F26BP=0
20
0
0.1 mM
0
F16BP (mM)
B
40
Merrins et al.,
PLoS One, 2012
50
0.2 mM
100
150
30
40
Time (min)
F6P
20
F1,6BP
0
10
20
F6P (mM)
F2,6BP should make metabolic oscillations smaller
and faster by changing the F1,6BP nullcline
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!