Transcript Model for IP3-oscillator

Intracellular and extracellular
oscillations in NRK cells
Model for Membrane NRK cell
This model only focusses on the dynamics of the cell
membrane, including the L-type Ca-channel and other ion
channels. The model has the following components:
•
•
•
•
•
•
•
PMCA pump
Ca L type channel
Cl(Ca) channel
CRAC channel
Leak channel
Kir channel
Ca-buffer in the cytosol
Components of the model
CaER
GCRAC
Gleak
Kcyt
GKir
Cacyt
GCl(Ca)
Clex
BCacyt
B
ATP
GCaL
Caex
PMCA
Components of the model for the NRK Membrane
I leak  Gleak (V  Eleak )
I K  GK
KO  K
(V  EK )
5.4  K   K
• Lek vanuit het
membraan
• Kalium kanaal
0.1
K 
1  exp(0.06{V  EK  50})
 K  3 exp(0.0002(V  EK  100))  exp
K
RT
1000ln( O )
F
120
Cacyt
J PMCA  C PMCA
Cacyt  K PMCA
0.0002(V  EK  10)
1  exp(0.06(V  EK  50))

EK 
• PMCA-pomp
Components of the model for the NRK Membrane
I CRAC  1 /(convflux)  CCRAC
1
(V  ECa )
Ca ER  K CRAC
I Ca ( L )  GCa ( L ) m  h  wCa (V  ECa ( L ) )
1
1  exp((V  15) / 5.24)
m 0.01(1  exp((V  10) / 5.9))
m  
0.035(V  10)
1
h 
1  exp((V  37) / 5.24)
0.01
h 
0.02  0.0197exp({0.0337(V  10)}2 )
1
wCa 
Cacyt
1
1
Cacyt
I Cl ( Ca )  GCl ( Ca )
(V  ECl (Ca ) )
Cacyt  K Cl
• CRAC kanaal
• Ca L type kanaal
m 
• Cl(Ca) kanaal
Buffer dynamics
Cacyt  B  CaB
with
Kon = 0.032 (microMol s)-1
Koff = 0.06 s-1
Steady state behavior without current
The previous plot and following plots show
• Upper left panel: Cacyt (red trace), BCa
(buffered complex, blue trace) and J_PMCA
(green trace)
• Upper right panel: VM (blue trace)
• lower left panel: ICl (red trace), ICa (black
trace), IK (green trace), Ileak(blue trace), ICRAC
(cyan trace) and Ipulse (magenta trace)
• All traces as a function of time (10 seconds
along horizontal axis)
Current clamp Ipulse=6 pA
• When we current clamp, the activation gate
of the Ca L type opens, giving rise to a
constant inflow of Ca through the Ca L type
channel.
• As a consequence, an action potential will
be generated
Current clamp Ipulse=6 pA
Current clamp Ipulse=3 pA
Effect van aanwezigheid buffer
Removing the buffer does affect
• Cacyt (smaller concentrations with buffer)
• AP (smaller AP with buffer)
Current clamp Ipulse=6 pA
Current clamp Ipulse=6 pA without
buffer
Increasing Kon from 0.032 to 0.32
Increasing Kon from 0.032 to 3.2
Overview of parameter values
Cell membrane
Nernst
leak
E
 0V
Nernst
ECa
( L )  0.05V
EClNernst
( Ca )  0.02V
Gleak  0.05nS
GK  2.2nS
R  8.31m 2 kg s -2 K -1mol-1
T  293K
F  96480C / m ol
TB  20M
K on  0.032( M  s ) 1
GCa ( L )  0.50nS
K off  0.06s 1
GCl ( Ca )  10.0nS
C PMCA  1.27Ms 1
K Cl  35M
K PMCA  0.2 M
Cm  20 pF
CCRAC  0.55Ms 1
K O  35M
K CRAC  10M
convflux 2  0.001231000
Model for IP3-oscillator
This model only focusses on the dynamics of Ca in the ER
and cytosol by transport through the IP3 receptor and by the
cell membrane, excluding the L-type Ca-channel and K- or Cl
ion channels. The model has the following components:
•
•
•
•
•
•
SERCA pump
IP3-receptor
leakage of Ca from the ER into the cytosol
PMCA pump
leakage of Ca from extracellular space into the cytosol
Ca-buffer in the cytosol
We will investigate the effect of various concentrations of IP3 on Caoscillations. Within each simulation, the IP3 concentration will be
considered to be constant.
Components of the model
CaER
P
L
C
GCRAC
SERCA
Glek
Glek
ATP
BCacyt
IP3
IP3
Glk
Cacyt
B
receptor
ATP
PMCA
Components of the model for the IP3-oscillator
• IP3-receptor
f 
Cacyt
Cacyt  K fIP3
IP3
IP3  K wIP 31
IP3
IP3  K wIP 32
w 
IP3
Kw
 Cacyt
IP3  K wIP 32
Kw
20
w 
Kw
• Leakage from ER
• SERCA-pomp J
IP3
 0.1Cacyt
IP3  K wIP 3
J IP3  CIP3 f 3w3 (CaER  Cacyt )
lek
 Clek (CaER  Cacyt )
A conversion factor of 0.1 transforms an increase/decrease of
CaER into a decrease/increase of Cacyt.
Components of the model in the
cell membrane
• CRAC channel
J CRAC
1
Nernst
 CCRAC
(V  ECa
)
CaER  KCRAC
• Leakage into cytosol
• PMCA-pomp
J
J lk  Clk (1000  Cacyt )
PMCA  CPMCA
Cacyt
Cacyt  K PMCA
Buffer dynamics
Cacyt  B  CaB
with
Kon = 0.032 (microMol s)-1
Koff = 0.06 s-1
steady-state behavior
Without IP3, the steady-state is easily found
by solving the two equations, with two
unknown variables Cacyt and CaER:
Clek (CaER  Cacyt )  CSERCA
CPMCA
Cacyt
Cacyt  K PMCA
Cacyt
Cacyt  K SERCA
 Clk (1000  Cacyt )  CCRAC
1
(V  ECa )
CaER  K CRAC
This gives a single, stable solution for Cacyt and CaER
Steady state behavior without IP3
It may take a long time, but the system always converges to a stable state,
irrespective of various parameters, as long as JCRAC is large enough .
The previous plot and following plots show
• Upper left panel: Cacyt (red trace) and BCa
(buffered complex, blue trace)
• Upper right panel: CaER
• lower left panel: JSERCA (red trace), Jlek (blue trace)
and JIP3 (green trace)
• lower left panel : JPMCA (red trace), Jlk (blue trace),
and JCRAC (green trace).
• All traces as a function of time (1000 seconds
along horizontal axis)
Concentration IP3=5
M
• When the concentration of IP3 increases above zero, the
activation gate of the IP3 receptor opens, giving rise to a
constant inflow of Ca through the IP3 receptor.
• As a consequence, CaER decreases relative to the situation
for IP3=0 M .
• Note that bear the end we have JPMCA= JCRAC + Jlk and
JSERCA=Jlek + JIP3
• Note that JIP3 does not oscillate: the system goes to a stable
steady state with a steady state value for activation f and
inactivation w of the IP3 receptor.
• A similar result is found for IP3= 8 M
IP3 concentration = 5
Concentration IP3=8
IP3 oscillations
• When IP3 concentration is increased to 10 M we obtain
oscillations of the IP3-receptor. A more detailed analytical
analysis is necessary to understand why f and w reach
steady state values (like for IP3 is 0,5 or 8) or start
oscillating.
• Averaged over time we find that JPMCA= JCRAC + Jlk and
JSERCA=Jlek + JIP3
• Note that the mean CaER concentration decreases to smaller
values for higher IP3 concentrations.
• Raising the IP3 concentration to higher values increases
the oscillation frequency.
Concentration IP3=10
Concentration IP3=12
What happens at higher IP3
concentrations ?
• Increasing the IP3- concentration to higher values
increases the oscillation frequency.
• Notice that the first peak of JIP3 is large, but subsequent
flux peak values are much smaller. This can be understood
from the following: After the first Ca-release from the ER,
the SERCA pump starts relaoding the ER. Since the next
IP3-release comes earlier for higher IP3 concentrations, the
Cacyt is higher at the following peak. As a consequence
CaER-Cacyt is smaller; giving rise to smaller IP3 outflow.
Moreover, the inactivation closes faster due to the higher
IP3 concentration (see equations on sheet 4).
Concentration IP3=20
Concentration IP3=50
Effect of buffer
Removing the buffer does affect
• Cacyt (smaller concentrations with buffer)
• JPMCA (saturates without a buffer)
but does not affect
• the frequency of oscillation
• CaER
Concentration IP3=12
Concentration IP3=12 without buffer
Increasing Kon from 0.032 to 0.32 eliminates
oscillations of the IP3 receptor (IP3=12)
Overview of parameter values
IP3-oscillator
Cell membrane
V  0.07V
C IP 3  10s 1
C SERCA  0.6 M / s
Clek  0.002s 1
K SERCA  0.2 M
K w  1s 1
K wIP 31  5M
K wIP 32  15M
K fIP3  0.5M
Nernst
ECa
 0.05V
C PMCA  0.6 M / s
CCRAC  55M 2 / s
Clk  0.0002s 1
K PMCA  0.25M
K CRAC  10M
TB  20M
K on  0.032( M  s ) 1
K off  0.06s 1
Conv  0.1