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Modeling Ca cycling in cardiac cells: from ion channels to whole cell dynamics

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Title: Modeling Ca cycling in cardiac cells: from ion channels to whole cell dynamics


1
Modeling Ca cycling in cardiac cells from ion
channels to whole cell dynamics
  • Yohannes Shiferaw
  • UCLA

Collaborators Alain Karma, Daisuke Sato,
Northeastern Univ. Robert Rovetti, Alan
Garfinkel, Zhilin Qu, and James Weiss, UCLA
2
Outline
  • Overview of some important features of Ca
    cycling
  • in cardiac cells.
  • Developing a phenomenological model of Ca
    cycling
  • Some features of the nonlinear dynamics of
    paced cells.
  • Relating whole cell properties to Ca
    signalling at
  • the ion channel level.
  • Summary

3
Cardiac tissue and cells
Cardiac tissue
(Guinea-pig ventricular cell)
Function
  • Conduct electrical waves
  • Contract in response to an electrical stimulus

4
Basic Cell physiology
Action potential regulates intracellular calcium
Membrane Voltage
Intracellular Calcium (average)
APD
200 ms
Calcium
Contraction
5
Spatial distribution of Ca release
SR
JSR
T-tubule
NaCa exchange channels
Dyadic cleft
High Ca concentration
L-type Ca channels
uptake channels
RyR channels
Signaling via Ca induced Ca release
6
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
7
Calcium sparks are correlated with whole cell ICa
Cleeman et al., 1995
Release is induced by calcium entry (CICR)
Single channel current
8
Graded release
Peak Ca
ICa Current
Wier et al (1994), J Physiol 474(3)
Wier et al (1994), J Physiol 474(3) adapted
Release of Ca is graded with respect to Ca current
9
Paced cardiac cells exhibit nonlinear dynamical
properties
Ca transient alternans observed in
rabbit Ventricular, when cell is paced with
periodic voltage clamp.
From lab of J. Weiss, UCLA
Diaz et al. 2002
10
Concordant electro-mechanical alternans
L
L
L
S
S
S
L
(Rabbit)
Chudin et al. 1999
Discordant electro-mechanical alternans
L
S
S
L
(guinea pig)
J. Hüser, et al. 2000
L
S
L
S
11
Quasiperiodic dynamics
Otani et al, 1997
(dog Purkinje)
12
Why are alternans relevant to the heart?
13
Can we construct a model of Ca cycling where
  • Release is triggered by Ca entry via a CICR
    mechanism
  • operative within 104 dyadic cleft.
  • Release occurs via discrete release events called
    Ca
  • sparks.
  • Release mirrors the whole cell Ca entry (graded
  • release).
  • Can be used to understand the rich dynamical
  • behavior of Ca cycling.

14
A Phenomenological approach
Phenomenological model of Ca release at the
dyadic cleft (spark)
Concentration of JSR
Duration of spark
15
Spark recruitment rate
Sparks are recruited at a rate roughly
Proportional to the Ca entry
16
Summing discrete release events
Whole cell current due to summation of discrete
Ca fluxes
Satisfies
17
Full Model Equations for Ca cycling
Biophys J., 2003
18
Instability Mechanism
Load dependence of release
19
Nonlinear map reduction
D (NaCa exchanger and L-type Ca current)
R (release)

y
x
Calcium cycling dynamics
U (uptake)
Shiferaw et al., 2005
Alternans occurs when
20
Experimental Validation
Diaz et al., 2004
21
Nonlinear dynamics of voltage and Ca cycling
Two coupled nonlinear systems
Voltage
Calcium
coupling
Due to kinetics of gates
22
Bi-directional coupling
Fox et al., 2002
V(t)
3 Na
Ca2
Ca release enhances INaCa
INaCa
Ca2
ICa
Ca release inhibits Ica via Ca-induced
inactivation
Ca2
23
Positive coupling
V
Ca2
INaCa dominant
-100
time
Negative coupling
V
Ca2
ICa dominant
0
100
200
0
100
200
time
time
24
Voltage on calcium
Larger diastolic interval
Larger Ca transient
t (ms)
t (ms)
Consequence of graded release
25
Stability diagrampositive coupling
Nonlinearity of the Voltage system
T300ms
Concordant
stable
Nonlinearity of the Calcium system
26
Stability diagramnegative coupling
concordant
Nonlinearity of the Voltage system
Quasiperiodic
Concordant
quasi-periodic
stable
discordant
Discordant
Nonlinearity of the Calcium system
27
Discrete maps
The restitution slope.
Degree of instability of Ca cycling.
Degree of coupling between voltage and Ca
systems.
28
Limitations
Model does not yield insight on the role of
ion channels.
Can we understand the basic whole cell
properties in terms of the kinetics and
interaction of ion channels?
For example, can we explain graded release
in terms of Ca signaling between Ion
channels in the dyadic cleft??
29
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30
Modified from Stern (1999), J Gen Physiol 113(3)
Ca2
Ca2
Ca2
31
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40
Main points
  • Rich nonlinear dynamics of voltage-calcium of
    cardiac cells. Dynamics can
  • be understood in terms of basic features
    of Ca release, and bi-directional
  • coupling.
  • Whole cell properties dependent on local ion
    channel signaling in the
  • dyadic cleft.
  • Stochasticity at the ion channel level is
    critical to understanding whole
  • cell properties.
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