Transcript MRB History

The Chay-Keizer Model:
A Twenty-Year Retrospective
Arthur Sherman
Laboratory of Biological Modeling
[email protected]
http://mrb.niddk.nih.gov/sherman
Collaborators
• Theoretical – Mentors
– John Rinzel
– Joel Keizer
• Theoretical – Postdocs
–
–
–
–
–
–
–
–
Cindy Stokes
Paul Smolen
Hsiu-rong Zhu
Richard Bertram
Gerda de Vries
Andrew LeBeau
Victor Matveev
Pete Roper
• Graduate Students
– Chip Zimliki
– Camille Daniel
• Experimental – NIH
–
–
–
–
–
Illani Atwater
Eduardo Rojas
Stanko Stojilkovic
Fred van Goor
Elise Stanley
• Experimental - USUHS
– David Mears
• Experimental –Alicante
– Bernat Soria
– Franz Martin
• Experimental – Richmond
– Les Satin
– Tracie Kinard
– Paula Goforth
Outline
• Background on Pancreatic b-Cells
– Role in glucose homeostasis
– Role in diabetes
– Paradigm for bursting oscillations
• The First Model – Chay-Keizer
• Adding the Endoplasmic Reticulum
• Emergent bursting – single cells vs. islets
Notkins, Sci. Am. Nov. 1979
b-Cells in the Endocrine Network
Schuit et al, Diabetes. 2001 Jan;50(1):1-11
b-Cells Secrete Insulin, Which:
• Promotes uptake of glucose by muscle, fat
• Promotes storage of energy as fat
• Allows use of protein to build tissues
instead of burning for energy
Type I Diabetes
• Auto-immune attack that kills the b-cells
• Requires insulin injections (insulindependent)
• Usually strikes children (juvenile)
Life Without b-Cells
Courtesy of Eli Lilly and Company Archives
Type II Diabetes
• Associated with age and obesity (adultonset)
• Usually does not require insulin, at least at
first (non-insulin dependent)
• Associated with hypertension, high
cholesterol, and inflammation (“Metabolic
Syndrome”)
Type II Diabetes (cont’d)
• Obesity causes insulin resistance
• If b-cells OK, compensate with exaggerated
insulin secretion
• If b-cells deficient, get hyperglycemia
• Complications
–
–
–
–
Atherosclerosis
Kidney damage
Blindness
Peripheral neuropathy
Nature of b-Cell Defect
• Mass (number of b-cells)?
• Function (secretion per b-cell)?
Approaches to Modeling
• Data mining – look for correlations
• Simulate every molecule and relationship
• Model modular subsystems
– Develop detailed understanding of dynamics
From molecular to modular cell biology
LELAND H. HARTWELL, JOHN J. HOPFIELD, STANISLAS LEIBLER & ANDREW W. MURRAY
Nature 402, C47 - C52 (1999)
Box 1 Phenomenological analysis of action potentials in nerve cells
Experimental Setup
Islet Bursting Pattern
And Glucose Sensitivity
Courtesy of I. Atwater
ICa(V)
Vm
IK(V)
[Ca2+]i
Mutations: Diabetes, Hyperinsulinism
IKATP
Mom’s Pills
Glucose
Transporter
(GLUT2)
IK-Ca
Equivalent Circuits
Equivalent Circuits
C
g
dV
Kirchhoff 's Law: C
 gV  0
dt
Equivalent Circuits II
C
gCa
dV
Kirchhoff 's Law: C
 gCa (V  VCa )  0
dt
Equivalent Circuits III
C
gCa
gK
dV
C
 g Ca (V  VCa )  g K (V  VK )  0
dt
gCa
gK
dV
C
 gCa (V  VCa )  g K (V  VK )  0
dt
gK  gK n
dn n (V )  n

dt
 n (V )
Morris-Lecar Model
(Hodgkin-Huxley)
dV
Cm
  I Ca  I K (V )  I leak
dt
dn n (V )  n

dt
 n (V )
 I K (V )  g K n(V  VK )
Morris-Lecar Can Account for Spiking
Chay-Keizer Model
K+
KCa channel
Ca2+
PMCA
Na+
Ca2+
Chay-Keizer Model
dV
Cm
  I Ca  I K (V )  I K ( Ca )
dt
dn n (V )  n

dt
 n (V )
dCa
 f (I Ca  k  Ca)
dt
 I K (V )  g K n(V  VK )
 I KCa  g KCa
Ca
(V  VK )
Ca  K
Chay-Keizer Bursting
Geometry of Bursting
Ca-V Relation
Ca Nullcline
“Calcium”
“Spike amplitude”
Glucose Dose Response – Chay-Keizer
Geometry of Glucose Response
High G
Intermediate G
Low G
Calcium Timecourse is NOT Sawtooth Shape
Santos et al, Pfluegers Arch. 418:417-422, 1991
Let’s Kick it Up a Notch
Chay-Keizer with ER
K+
KCa channel
VSCC
2+
Ca
ER
PMCA
Na+
SERCA
Ca2+
Chay-Keizer Model with ER
dV
Cm
  I Ca  I K (V )  I K ( Ca )  I K ( ATP )
dt
dn n (V )  n

dt
 n (V )
dCa
f
 f (I Ca  kc  Ca)  ( J SERCA  J RELEASE )
dt

dCaER
f

( J SERCA  J RELEASE )
dt

Chay-Keizer with ER
In Chay-Keizer with ER, Raising Glucose Raises Mean
Calcium
Geometry of Bursting
Ca-V Relation
Ca Nullcline
Geometry of Bursting with ER
ER Fills
ER Empties
Reorient View of Calcium
• Cytosolic calcium is not very slow (a few
seconds)
• ER imparts very slow dynamics (tens of
seconds)
Potentiation of Insulin Secretion by Acetylcholine
David Mears, USUHS
V
Gilon and Henquin, Endocrine Reviews, 22:565 2001
Response to Acetylcholine
Adding Store-Depletion
Operated Current (SOC)
or ACh-Activated Na+
Current
Calcium Can Fall at End of Active
Phase
Let’s Kick it Up Another Notch
K+
Kslow channel
VSCC
ER
SERCA
Ca2
+
PMCA
thapsigargin
or insulin
Na+
Ca2+
Further Refinements can Explain
Drop in Calcium
• A third, hidden, calcium compartment
(“calcium subspace”; Goforth et al, J. Gen.
Physiol. 120:307 2002)
• Slow feedback of calcium on metabolism
(Keizer and Magnus, 1987, 1998; Bertram
and Sherman, in review)
Dual Impalement
Eddlestone et al, J. Membr. Biol., 77:1-14, 1984
Single b-cell
Bursting
Patterns
Bertram et al, Biophys. J.
79:2880 2000
Among bursting cells:
•Most are fast
•A few are intermediate
• A few are slow
Single Cells
are Noisy
Zhang et al,
Biophys. J.
84:2852
2003
Dynamic Clamp Experiment
Geometry of Bursting
After Dclamp
Conclusions
• The Chay-Keizer model (negative feedback
from calcium) has gone through several
iterations of prediction and correction.
• KCa channel is governed by combined
effects of cystosolic and ER calcium.
• Interaction of slow cytosolic calcium and
very slow ER calcium determines time scale
of oscillation – “phantom bursting”
• Phantom model also helps explain
differences between single cells and islets
Future Directions - Experimental
• Measure ER calcium – differential
predictions vs. other models
• Assess contribution of calcium feedback on
KATP channels
• Study insulin feedback on electrical activity
and insulin secretion
Future Directions - Theoretical
• Bridge gap between calcium and insulin
secretion (vesicle dynamics)
• Comparative models
– Species (rat vs. mouse vs. human)
– Cell types (b vs.  vs. pituitary)
• Development of b cells (stem cells)
• Role in diabetes with other tissues (liver,
muscle, fat, hypothalamic neurons)
Acknowledgements
Experimental
• Les Satin
-VCU, Richmond
• Paula Goforth
-VCU, Richmond
• Farrukh Khan
- VCU,
Richmond
• Min Zhang
- VCU, Richmond
Theoretical
• Richard Bertram
– FSU, Tallahassee
• Camille Daniel
– VT, Blacksburg
References
Older models reviewed in:
Sherman, AJP 271:E362-E372 1996
Chay-Keizer with ER:
Chapter 5, “Whole Cell Models,” in
Computational Cell Biology, Springer, 2002
Subspace Model:
Goforth et al, J. Gen. Physiol. 120:307-322 2002