Background 1

1
Calcium Release, Subcellular Microdomains, and
Stochastic Signaling in Cardiac Myocytes
Yohannes Shiferaw Departments of
Physics California State University Northridge
2
Cardiac tissue and cells
Cardiac tissue
Cardiac tissue
(Guinea-pig ventricular cell)
Function

• Conduct electrical waves
• Contract in response to an electrical stimulus

3
Ion channels regulate voltage drop across the
cell membrane
Concentration gradient? voltage drop
KClo 100mM
electrostatic
K
KCli10mM
Cell membrane
K selective Ion channels
4
The cardiac action potential
Membrane voltage set by chemical gradients and
regulated by ion channels
Properties

• Excitable system. Allows for electrical wave
  propagation.

• Serves to regulate intracellular processes.

5
Basic Cell physiology
Action potential regulates intracellular calcium
Membrane Voltage
Intracellular Calcium (average)
APD
200 ms
Calcium
Contraction
6
Calcium
Contraction
7
Calcium
Contraction
T-tubules
Sarcoplasmic Reticulum (Ca store)
8
Calcium released at microdomain junctions
Cleemann et al (1998), PNAS 95. Bars are 10 mm.
9
Microdomain Ca Release Sparks
Cleemann et al (1998), PNAS 95
10
Spatial distribution of Ca release
SR
JSR
T-tubule
NaCa exchange channels
microdomain
micodomains
500nm
High Ca concentration
L-type Ca channels
uptake channels
RyR channels
Signaling via Ca induced Ca release
11
Calcium signaling in the dyadic cleft
The dyadic cleft
Wang et al. 2001
Calcium spark
Local calcium transient
Stochastic single L-type Ca channel (LCC) current
Sparks activated by the calcium entry due to
single LCCs
12
RyR receptor and clusters
20nmx20nm 2x106 daltons
Open probability regulated by Ca binding and a
host of other regulatory proteins
Form clusters of 50-100 RyR
13
In the last 2 years researchers have identified
binding sites the RyR which are directly linked
to cardiac arrhythmias.
Open probability Of RyR channel
0.1
1
10
Ca concentration
Mice with a well defined gene defect which leads
to defective RyR have a much greater propensity
for arrhythmia.
14
Close relation between Ca entry and release
SR Release(RyR)
Ca Entry(LCC)
Wier et al (1994), J Physiol 474(3) adapted
Cleemann et al (1998), PNAS 95
15
Can we explain the relationship between total Ca
entry into the cell and the release of Ca?
Need a theory of the stochastic interaction of
LCC channels and RyR receptors.
16
Markov state model of interacting channels
Ca 2
L-type Ca channel
Cell membrane
Micro-domain
RyR cluster
Ca 2 stores(SR)
kCa 2
C
O
k-
kCa 2
a1(V)
a
Ca
50-100 RyR channels
C
O
1-5 LCC channels
C1
O
C2
k-
b
b1(V)
kCa 2
O
C
k-
17
Number of sparks recruited in a small time
interval Dt
How do we find PS??
18
RyR Cluster state can be described using
birth-death process
n0
n1
n2
n3
nN
19
RyR Cluster state can be described using
birth-death process
n0
n1
n2
n3
nN
Transition rates are (1) state-dependent, (2)
nonlinear, and (3) modified by trigger current
(ica)
20
Master equation for discrete process
n0
n1
n2
n3
nN
21
The continuum limit (for large N) leads to a
Fokker-Plank equation
Master equation for discrete process
FP equation for continuous process
Macro term
Diffusion term
22
Can map the Fokker-Planck to a Langevin Eq.
Ca Channel CLOSED
Spark
U(x)
x Fraction of cluster open
23
Using the potential well to visualize dynamics
Ca Channel CLOSED
Spark
U(x)
x Fraction of cluster open
24
Barrier disappears when trigger current activates
Ca Channel CLOSED
Spark
Potential
Ca Channel OPEN
x Fraction of cluster open
25
Barrier reappears when trigger current turns off
3
2
1
Ca Channel CLOSED
Potential
Ca Channel OPEN
x Fraction of cluster open
26
Barrier reappears when trigger current turns off
3
2
1
Ca Channel CLOSED
Potential
Ca Channel OPEN
x Fraction of cluster open
27
Must pass this barrier BEFORE Ca channel closes
Potential
Ca Channel CLOSED
Ca Channel OPEN
x Fraction of cluster open
28
Distribution of times to first reach barrier
FIRST PASSAGE TIME DIST. P(xa, xb t)
x
Potential
xa
xb
29
Distribution of times to first reach barrier
FIRST PASSAGE TIME DIST. P(xa, xb t)
x
Potential
Distribution of times for Ca Channel to remain
open P(tO) b exp(-b tO) P(tOgtt) exp(-b
tO)
xa
xb
30
Distribution of times to first reach barrier
FIRST PASSAGE TIME DIST. P(xa, xb t)
x
Potential
Distribution of times for Ca Channel to remain
open P(tO) b exp(-b tO) P(tOgtt) exp(-b
tO)
xa
xb
Prob of sparking Prob of passing barrier
31
Finding a tractable Fokker-Planck Equation
3rd order polynomials
Linearize
Potential
xa
xb
32
Finding a tractable Fokker-Planck Equation
3rd order polynomials
Linearize
Potential
xa
xb
33
First passage time problem solved by Darling and
Siegert 1953
u solution to LT of adjoint FPE
confluent hypergeometric differential eq
34
confluent hypergeometric differential eq
Kummers Function
35
Computed solutions yield accurate predictions of
spark rate
Symbols Monte Carlo simulations
VaryingRyR conductance
Curves Analyticalfunction
Kummers Function
36
Assymptotics
Strong trigger current (ica)
Weak trigger current (ica)
37
Features of experimental data are explained
38

Summary Points
Related macroscopic behavior directly to
microdomain stochastic signaling. Predicted
macroscopic behavior was consistent with
experimental results.