CVR-2011-952
SUPPLEMENTARY MATERIAL
Arrhythmogenic Consequences of Myofibroblast-Myocyte Coupling
Thao P. Nguyen, Yuanfang Xie, Alan Garfinkel, Zhilin Qu, and James N. Weiss
Abbreviations and Acronyms
Cf
Fibroblast membrane capacitance
C
Myocyte membrane capacitance
CI
Confidence interval
DAD
Delayed afterdepolarization
EAD
Early afterdepolarization
Ef
Uncoupled fibroblast resting membrane potential
Ensc
Reversal potential of non-selective cation current Insc
Gf
Fibroblast conductance
Gj
Gap junction coupling conductance
GK
Maximum potassium current conductance
Gnsc
Conductance of non-selective cation current Insc
HypoK
Hypokalemia
Ib,Na
Background sodium current
ICa,L
L-type Ca current
If
Fibroblast membrane current density
Iion
Myocyte membrane current density
Ij
Gap junction current
IK1
Inward-rectifying potassium current
IK
Time- and voltage-dependent delayed-rectifier potassium current
INaK
Na-K pump current
Insc
Non-selective cation current
RMP
Myocyte resting membrane potential
VF
Ventricular fibrillation
Vm
Myocyte membrane potential
Vf
Fibroblast membrane potential
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Myofibroblast-myocyte coupling
Online Suppl. Material
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SUPPLEMENTARY METHODS
Solutions
The Standard Tyrode’s solution containing (in mmol/L) NaCl 136, KCl 5.4 (or 2.7 in hypokalemia
experiments), NaH2PO4 0.33, CaCl2 1.8, MgCl2 1, HEPES 10, and glucose 10 (pH 7.4 adjusted
with NaOH), was used for cell isolation and extracellular perfusion in patch clamp studies unless
otherwise indicated. The enzyme solution for myocyte isolation was a Ca2+-free Tyrode’s
solution containing 1.0 mg/mL collagenase (Type II, Worthington) and 0.1 mg/mL protease (type
XIV, Sigma). The pipette solution for whole cell recordings contained (in mmol/L): K-aspartate
110, KCl 30, NaCl 5, HEPES 10, EGTA 0.0-0.1, MgATP 5, creatine phosphate 5, cAMP 0.1 (pH
7.2 adjusted with KOH). The extracellular stressor employed in myocyte perfusion was either
hydrogen peroxide (H2O2, 0.1 or 1 mmol/L) or hypokalemia (HypoK, 2.7 mmol/L).
Dynamic Clamp
Our dynamic clamp employed the high-speed M series multifunction Data Acquisition Device NI
PCIe-6251 and NI-DAQmx driver software (National Instruments Corp.) to ensure 16-bit
accuracy even at speeds up to 1.25 MS/s. Additionally, real time control was achieved using the
Real-Time eXperiment Interface (RTXI), a real-time Linux based software system adapted by
Christini, White, and Butera for hard real-time data acquisition in biological applications such as
dynamic clamping and control of cardiac arrhythmia dynamics1,2. For excellent plug-ins and
tutorials on real-time applications, please refer to www.rtxi.org. During myofibroblast-myocyte
coupling using the dynamic clamp, gap-free recordings of virtual myofibroblast membrane
potential Vf and virtual gap junction current Ij were acquired simultaneously with gap-free
recording of real myocyte membrane potential Vm.
Virtual Ventricular Fibroblast or Myofibroblast with Gap Junction
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The electrophysiological model of the ventricular myofibroblast employed in our hybrid
biological-computational experiments was closely adapted from MacCannell et al’s ‘active’
fibroblast model. The original ‘active’ fibroblast had a membrane capacitance of 6.3 pF and 4
membrane ionic currents—a time- and voltage-dependent delayed-rectifier K+ current IK, an
inward-rectifying K+ current IK1 (both currents were identified in adult rat ventricular fibroblasts),
a Na+-K+ pump current INaK, and a background Na+ current Ib,Na to balance the efflux associated
with Na+-K+ pump activity (see MacCannell3 for formulations of those four currents). While the
uncoupled resting potential Ef of MacCannell’s ‘active’ fibroblast was fixed at -49.6 mV, our
myofibroblast had 2 possible Ef values of -50 or -25 mV. Therefore, to depolarize Ef to -25 mV
when needed, our myofibroblast model had the addition of a non-selective cation current Insc,
similar to those previously reported that were stretch-sensitive4-7. Formulation for the current Insc
is as follows:
I nsc  Gnsc (V f  Ensc )
where Gnsc is the constant, time- and voltage-independent conductance of Insc (0 when Ef = -50
mV or 0.17 mS/mF when Ef = -25 mV), Vf the myofibroblast membrane potential, and Ensc the
reversal potential of Insc (-10 mV). This Insc current was linear in the range of physiological
potentials and set to be constitutively active without inactivation or deactivation.
Additionally, our myofibroblast model included a programmable gap junction conductance
(Gj).
Mathematical simulations of EAD generation by myofibroblast-myocyte coupling
To explore the mechanisms underlying EAD promotion by myocyte-myofibroblast coupling, we
performed simulations using the Luo-Rudy 1 ventricular myocyte AP model8 and a simplified
‘passive’ myofibroblast model devoid of ionic currents9. The passive myofibroblast contained a
battery Ef (representing the uncoupling myofibroblast resting membrane potential), membrane
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conductance (Gf), capacitor (Cf) and coupling conductance (Gj), the values of which could be set
explicitly. The transmembrane voltage (V) of the myocyte was governed by the following
differential equation:
C
dV
  I ion  G j (V f  V )
dt
and that (Vf) of the myofibroblast by the following one:
Cf
dV f
dt
  I f  G j (V  V f )
where C is the myocyte membrane capacitance set as C = 1 F/cm2, Gj the gap junction
conductance between the myocyte and the myofibroblast, and Cf the myofibroblast membrane
capacitance.
Iion is the Luo-Rudy 1 myocyte membrane current density and If is the
myofibroblast membrane current density modeled by:
I f  G f (V f  E f )
To generate an EAD-prone condition for the Luo-Rudy 1 model, we set the maximum
conductance of L-type Ca current (ICa,L), delayed rectifier K current (IK), and inward-rectifying K
current (IK1) to 0.069, 0.331, and 0.54 mS/mF, respectively. We also changed the slope of the
steady-state activation and inactivation curves of ICa,L by fitting with a sigmoid function as
follows10:
d 
f 
1
1 e
 (V Vd ) / s d
1 e
(V V f ) / s f
1
where Vd = -25 mV, Vf = -20 mV, sd = 8.7, and sf = 3.8 were used. The time constants of
activation and inactivation of ICa,L were sped up by 10 and 2.8 times, respectively. The time
constant of IK activation was slowed down by 1.8 times. Differential equations were solved using
forward Euler method with a time step varied between 0.1~0.01 ms.
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Myofibroblast-myocyte coupling
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Under this parameter set, APD was prolonged, but EADs did not occur. However, when
G K was reduced from 0.331 mS/F to 0.323 mS/F or below, EADs occurred in the action
potential of the myofibroblast-uncoupled myocyte; therefore, the G K threshold of 0.323 mS/F
was used to define the ‘control’ EAD threshold. After coupling of the myocyte to the
myofibroblast, depending on the choice of the myofibroblast and gap junction coupling
parameter set (Cf, Gf, Ef, and Gj), the G K threshold for EAD formation of the myo/fibroblastcoupled myocyte could shift to a new value, either lower or higher than that of the control (0.323
mS/F, 0% EAD threshold shift in Fig. 5). If the G K threshold of the myofibroblast-coupled
myocyte was higher than the control value, the myofibroblast promoted EADs because EADs
could occur in the presence of a larger myocyte K current; in other words, the myofibroblast
lowered the myocyte EAD threshold (negative EAD threshold shift) and caused the myocyte to
become more sensitive to EAD induction. Vice versa, if the G K threshold of the myofibroblastcoupled myocyte was smaller the control value, the myofibroblast suppressed EADs, the
myocyte EAD threshold was raised (positive EAD threshold shift), and the myocyte became less
sensitive to EAD induction (Fig. 5).
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Myofibroblast-myocyte coupling
Online Suppl. Material
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SUPPLEMENTARY REFERENCES
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Ginneken AC. HERG channel (dys)function revealed by dynamic action potential clamp
technique. Biophys J 2005;88:566-578.
2. Berecki G, Zegers JG, Wilders R, Van Ginneken AC. Cardiac channelopathies studied with
the dynamic action potential-clamp technique. Methods Mol Biol 2007;403:233-250.
3. MacCannell KA, Bazzazi H, Chilton L, Shibukawa Y, Clark RB, Giles WR. A mathematical
model of electrotonic interactions between ventricular myocytes and fibroblasts. Biophys J
2007;92:4121-4132.
4. Kamkin A, Kiseleva I, Isenberg G. Activation and inactivation of a non-selective cation
conductance by local mechanical deformation of acutely isolated cardiac fibroblasts. Cardiovasc
Res 2003;57:793-803.
5. Kamkin A, Kiseleva I, Isenberg G, Wagner KD, Gunther J, Theres H, Scholz H. Cardiac
fibroblasts and the mechano-electric feedback mechanism in healthy and diseased hearts. Prog
Biophys Mol Biol 2003;82:111-120.
6. Kamkin A, Kiseleva I, Lozinsky I, Scholz H. Electrical interaction of mechanosensitive
fibroblasts and myocytes in the heart. Basic Res Cardiol 2005;100:337-345.
7. Hu H, Sachs F. Stretch-activated ion channels in the heart. J Mol Cell Cardiol 1997;29:15111523.
8. Luo CH, Rudy Y. A model of the ventricular cardiac action potential. Depolarization,
repolarization, and their interaction. Circ Res 1991;68:1501-1526.
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coupling: mechanistic insights from computational models. Am J Physiol Heart Circ Physiol
2009;297:H775-784.
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Myofibroblast-myocyte coupling
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10. Tran DX, Sato D, Yochelis A, Weiss JN, Garfinkel A, Qu Z. Bifurcation and chaos in a model
of cardiac early afterdepolarizations. Phys Rev Lett 2009;102:258103.
11. Dorval AD, Christini DJ, White JA. Real-Time linux dynamic clamp: a fast and flexible way to
construct virtual ion channels in living cells. Ann Biomed Eng 2001;29:897-907.
12. Berecki G, Zegers JG, Bhuiyan ZA, Verkerk AO, Wilders R, van Ginneken AC. Long-QT
syndrome-related sodium channel mutations probed by the dynamic action potential clamp
technique. J Physiol 2006;570:237-250.
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Myofibroblast-myocyte coupling
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SUPPLEMENTARY FIGURE
Mathematical model of
myo/fibroblast
(Cf, Ef, Gf)
with gap junction (Gj)
Isolated rabbit
myocyte
Current clamp
Patch clamp
amplifier
Myocyte Vm
Gap junction
Ij = Gj (Vm-Vf)
Dynamic clamp
computer
Supplemental Figure 1. Schema of the dynamic clamp technique, in which a real rabbit
ventricular myocyte is electrotonically coupled to a virtual myofibroblast with
programmable properties. Action potentials elicited in current clamp mode from a freshly
isolated patch-clamped adult rabbit ventricular myocyte were fed into a dynamic clamp
computer running a virtual myofibroblast model in real time. At each time point (5 KHz), the
dynamic clamp computer injected a gap junction current Ij proportional to the voltage difference
between the myocyte and the virtual myofibroblast. Cf, myofibroblast capacitance; Ef, uncoupled
myofibroblast resting membrane potential; Gf, myofibroblast conductance; Gj, gap junction
conductance; Vm, myocyte membrane potential; Vf, myofibroblast membrane potential.
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