Making Complex Arrhythmias from Simple
Mechanisms:
Exploring Anti- and Proarrhythmic Effects of Na Channel Blockade
with the Guarded Receptor Paradigm
C. Frank Starmer
Medical University of South Carolina
(monophasic cathodal truncated exponential shock, -100 V, 8 ms)
Dynamics of transmembrane potential
LA
RA
RV
LV
15.5 mm
tachycardia
shock
fibrillation
How To Initiate Reentry or Fibrillation:
The cardiac vulnerable period
refractory
conduction
Partial Conduction (arrhythmia)
Refractory: s1s2 = 2.1
Excitable: s1s2 = 2.3
Vulnerable: s1s2 = 2.2
Ion Channel Blockade Reduces Excitability (Antieffect) and Slows Conduction (Pro- effect)
Historical observations that provided a foundation for a
model of ion channel blockade:
Johnson and McKinnon (1957) (memory)
West and Amory (1960) (use-dependence)
Armstrong (1967) (open channel block)
Heistracher (1971) (frequency-dependence)
Carmeliet (1988) (trapping)
Steady-state Frequency-dependent
AP Alterations: Quinidine
dV/dt(max) decreases
with increased stim rate
AP amplitude decreases
with increased stim rate
Johnson and McKinnon JPET 460-468, 1957
Freq-dependent
Quinidine Block:
Alteration of AP
Duration
West and Amory: JPET 130:183-193,1960
Increased stim
rate slows
repolarization
An Early Model of Use-dependent Blockade
West and Amory: JPET 130:183-193,1960
Frequency- as well as Use-dependence:
Detailed Characterization of Ajmaline Blockade
dV/dt(max) reduced with
repeated stimulation: note approx
exponential decrease with stimulation
number
Steady-state dV/dt(max)
Reduced with faster stimulation
Heistracher. Naunyn-Schmeideberg’s Archiv Fur Pharmakologie 269:199-213, 1971
Voltage and Time-dependent TEA Block of K+
Channels
Control: no “inactivation”
+ TEA: Apparent “inactivation”
+90 mV
CP
IK
-46 mV
Armstrong. J. Gen Physiol 54:553-575, 1969
Once a Drug Molecule Blocks the Channel,
Can it Escape?
i.e. is it possible to trap it in the channel
From These Observations, One Wonders:
Is use-dependent channel blockade a “special”
process or is it simply a variant of ordinary
ligand-receptor interactions?
If it’s a variant - what variant?
Ordinary (not use-dependent) Chemistry:
Reacting with a Continuously Accessible Site
No possibility of use- or frequency dependence
Ligand + Receptor
a
LR-Complex
b
b = a/(a + b)
l=a+b
b(t) = b + (b0 - b) e-l t
(b- b0)/2 = Kd = b/a
How to Build a Model that Displays
use- and frequency dependence?
Unblocked + Drug
a(V)
Blocked
b(V)
A necessary condition:
Either a Real or Apparent Voltage-dependent
Equilibrium Dissociation Constant:
Kd = b(V) / a(V)
Modeling Apparent Voltage Dependence
Of the Equilibrium Dissociation Constant
Voltage-dependent Access to the Binding Site
(a+b)/b kD
Inaccessible
Blocked
l
Hypothesis: Control of Binding Site
Access by Channel Conformation
accessible
inaccessible
Blockade During Accessible and Inaccessible
Intervals:
Accessible Conformation
Channel + D
a
b
Blocked
Inaccessible Conformation
Channel + D
b
Blocked
Characterization of Access Control:
Guarded Receptor Model
(when channel transition time << drug binding time)
G*k
Unblocked Channel + Drug
T*l
Blocked Channel
where G and T act as “switches” that control binding site accessibility
G = “guard function” controls drug ingress: e.g. h, m, m3h, d, n, n4
T = “trap function” controls drug egress: e.g. m3h, h
In reality, the guard and trap functions are hypothesized to reflect specific
channel protein conformations, and not arbitrary model parameters
Starmer, Grant, Strauss. Biophys J 46:15-27, 1984
Starmer and Grant. Mol Pharm 28:348-356,1985
Starmer. Biometry 44:549-559, 1989
Combining Gated Access with Repetitive
Stimulation makes Use-dependent Blockade:
Switched Accessibility to a Binding Site
Starmer and Grant. Mol. Pharm 28:348-356, 1985
ta
tr
b(t) = b - (b0 - b) e-(k + l)*t
bactivated = ass - (a0 - ass) e-l*n
brecov = rss - (b0 - rss) e-l*n
la
l
l = la ta + lr tr
r
U
B
U
B
Dissecting the Mechanism of
Use-Dependent Blockade:
Using Voltage Clamp Protocols to Amplify or
Attenuate Blockade
Continuous Access Associated with
Channel Inactivation (shift in “apparent” h)
(1-h)a
Unblocked + Drug
b
Blocked
V(cond)
block
Starmer et. al. Amer. J Physiol 259:H626-H634, 1990
Transient Access Associated with
Channel Opening
Pulse duration: 2 ms
2 ms
150
350 ms
550
Gilliam et al Circ Res 65:723-739, 1989
Shift in Apparent Activation:
Evidence of Open (?) Channel Access Control
10 ms
Starmer et. Al. J. Mol Cell Cardiol 23:73-83, 1991
Exploring a Model of Use-Dependent Blockade
Are the Analytical Predictions Testable?
Analytical Description:
block associated with the nth pulse: bn = bss + (b0 - bss) e -(la ta + lr tr)n
Use-dependent rate: l = la ta + lr tr
Steady-state block: bss = a + g (r + a)
Steady-state slope: g = (1 - e-lr tr) / (1 - e-l )
Testing the Model
• Pulse-train stimulation evokes an exponential pattern of usedependent block
• There is a linear relation between exponential rate and stimulus
recovery interval
• There is a linear relation between steady-state block and a
function of the recovery interval (g)
• There is a shift in the midpoint of channel availability and / or
activation (depending on the access control mechanism)
Test 1. Frequency-dependent Lidocaine Uptake:
Exponential Pulse-to-pulse Blockade (50 ms)
.65
.35
.15
Gilliam et al Circ Res 65:723-739, 1989
Test 2: Linear Uptake Rate, Linear Steady State Block
ta constant and tr variable
Linear Uptake Rate
l = la t a + lr t r
Linear Steady-State Block
bss = a + g(r- a)
Test 3: Shifting Apparent Inactivation
(channel availability)
(1-h)a
Unblocked + Drug
b
Blocked
K = 3940 /M/s
l = .678 /s
KD = 18.8 mM
DV = s ln(1 + D/KD) = 10.76 mV
Obs DV = 9 mV
h =
1
(V Vh ) / s
1+ e
h = h (1  b )
*

h* =
1
1
=
(V Vh + DV ) / s
kD (V Vh ) / s 1 + e
1 + (1 +
)e
l
Test 4: Shifting Apparent Channel Activation
Nimodipine Blockade of Ca++ Channels
da
Unblocked + Drug
b
Blocked
DV = 40.1 mV KD = .38 nM
DV = k (1 + D/KD) = 43.4 mV
Exploiting the “Therapeutic” Potential of
Use-dependent Blockade
Cellular Antiarrhythmic Response
Multicellular Proarrhythmic Response
Therapeutic Potential: Cellular Effects of Blockade
(Antiarrhythmic)
Prolonging Recovery of Excitability:
Control and with Use-dependent Blockade
Therapeutic Potential: Multicellular Effects of Blockade
(Proarrhythmic)
Slowed Conduction, Increased Vulnerable Period
Why?
Propagation: Responses to Excitation
1) no response
2) front propagates away from stimulation site
3) front propagates in some directions and fails to
propagate in other direction (proarrhythmic)
Premature Excitation:
The Vulnerable Period
• Normal excitation: cells are in the rest state
• Premature excitation: Following a
propagating wave is a refractory region that
recovers to the resting state. Stimulation in
the transition region can be proarrhythmic
The Dynamics of Vulnerability
Using a simple 2 current model (Na: inward; K: outward) we can demonstrate
role of introducing a stimulus within and outside the interval of vulnerability:
We demonstrate the paradox of channel blockade: block extends the
refractory period, slows conduction and increases the VP
Here, we switch to Matlab, to demonstrate the dynamic
events defining the Vulnerable Period
Demonstrating the Vulnerable Period: Control
Refractory Period = 352 ms VP = 3 ms
Demonstrating Extension of the VP: Drug
Refractory Period = 668 ms VP = 59 ms
Use-dependent Extension of the VP
2-D Responses to Premature Excitation:
Note geometric distance between 1st and 2nd fronts
(refractory, unidirectional conduction, bidirectional conduction)
refractory
conduction
unidirectional conduction
Refractory: s1s2 = 2.1
Excitable: s1s2 = 2.3
Vulnerable: s1s2 = 2.2
Extending the VP with Na Channel Block:
Fact or Fantasy?
Starmer et. al. Amer. J. Physiol 262:H1305-1310, 1992
More Apparent Complexity: Monomorphic
and Polymorphic Reentry and ECG
Monomorphic
gNa = 2.25
Polymorphic
gna = 2.3
Polymorphic
gNa = 4.5
Major Lessons Learned From
Ideas Originating in Studies of
Johnson, Heistracher and
Carmaliet
Use caution when “repairing”
channels that aren’t broken:
Blockade of normal Na Channels
• Antiarrhythmic
– Extended refractory
interval and reduced
excitability leading to
PVC suppression
• Proarrhythmic
– Extends the vulnerable
period (increases the
probability of a PVC
initiating reentry)
– Slowed conduction
increase the probability
of sustained reentry
– Increases probability of
wavefront fractionation
Repairing Channels that are Broken (e.g.
SCN5A) may have Clinical Utility:
Blockade of “defective” channels diminishes EADs
in LQT Syndrome, Heart Failure, Epilepsy
Long QT Syndrome:
Links to Mutant Na and K Channels
QT
Stable and Unstable Action Potentials
Human Ventricular Cells
Beeler-Reuter Model
Yet Another Variant: Epilepsy
Summary
• Use- and Frequency Na channel block are consistent with
“ordinary” binding to a periodically accessible site
• Tonic block is compatible with block of inactivated
channels at the rest potential.
• Tests are available to validate the applicability of the
guarded-receptor paradigm to observations of drugchannel interactions
• For individual cells: use-dependent Na channel
block reduces excitability (prolongs the refractory
period (antiarrhythmic effect)
• For connected cells (tissue): reduced excitability
ALSO slows propagation which extends the
vulnerable period (proarrhythmic effect)
• The guarded receptor paradigm is a tool for “in
numero” exploration of channel blockade in both
cellular and multicellular preparations and direct
characterization of anti- and proarrhythmic effects
Apparent Trapping of Quinidine and Disopyramide
100 uM Diso
5 uM Quinidine
Zilberter et. Al. Amer. J. Physiol 266:H2007-H2017, 1994
Demonstrating the Trap
Zilberter et. Al. Amer. J. Physiol 266:H2007-H2017, 1994
Examples of Recent StateTransition Models
Balser et al J. Clin Invest. 98:2874-2886, 1996
Vedantham and Cannon J. Gen Physiol 113:7-16, 1999
Transforming a State-transition
Model to a Macroscopic Model:
The Importance of “Rapid Equilibration”
Unblocked Channel + Drug
Ga
Tb
Blocked Channel
Reducing a Complex State-Transition
Model to a Simple “Macro” GRH
Model
kD
a
R
b
I
l
B
Differential Equation Description:
dR
= b [ I ]  a [ R]
dt
dB
= kD[ I ]  l[ B]
dt
Conservation of Channels : R + I + B = Cmax
Guarded Receptor Formulation:
Rapid Equilibrat ion : aR = b I
I = C max - R - B = C max I=
a
b
I-B
a
(Cmax - B)
a+b
dB
a
=
kD(C max  B )  lB
dt a + b
db
= kD(1  h)(1  b)  lb
dt
Guard Function: 1-h
Spontaneous Oscillation: Mutant KVLQT1 and
HERG (K+) and SCN5A (Na+) Channels:
Altering Electrical Stability with Channel Blockade
Use- and Frequency-Dependent Blockade:
Central Features
Vclamp
Tclamp
Vhold
• Degree of Blockade Depends on Vclamp
• Degree of Blockade Depends on Tclamp
• Degree of Blockade Depends on Vhold
1. Frequency-dependent Lidocaine Uptake:
Exponential Pulse-to-pulse Blockade (2 ms)
Test 1: Exponential UDP Block, ta = constant
Gilliam et al Circ Res 65:723-739, 1989
Recovery of Excitability: Drug
Evolution of a Spiral Wave
T=0
T=5
T=1
T = 15
Monomorphic and Polymorphic
EKGs
Role of Wavefront Energy
Building a Model of “Discontinuous” (Usedependent) Drug-Channel Interaction:
Unblocked + Drug
a(V)
Blocked
b(V)
Apparent Voltage-dependent Equilibrium Dissociation Constant:
Kd = b(V) / a(V)
Why Does the Guraded Receptor
Model Work?
Comparing State-Transition and Macro Models
Macro Model: Unblocked + Drug
Ga
Tb
Blocked
Reduction in AP Duration:
C
L
C
Q
Colatsky Circ Res 50:17-27, 1982
Altering the Equilibrium Stability of a
Cell: Blockade of Na Current
Can be reversed by Na
blockade
EADs and Suppression via Na Channel
Blockade
Maltsev et al Circ 98:2545-2552, 1998
Frequency-dependent Lidocaine Uptake:
Access Controlled by “Inactivation”
Pulse duration: 50 ms
50 ms
150
250
350 ms
450
550
650
650
150
Gilliam et al Circ Res 65:723-739, 1989
Voltage-dependent Recovery
from Blockade
Starmer, et. al. J. Mol. Cell. Card 23;73-83, 1992
Two Modes of Na Channel Blockade:
Test 3: Linearity with variations in both ta and tr
l = la t a + lr t r
ta = 50 ms
ta = 10 ms
.45
.25
.15
tr = constant
tclamp
A Conformation-dependent Blockade Model
Closed <===> Open <===> Blocked
Armstrong. J. Gen Physiol 54:553-575, 1969
Binding to Accessible Sites at Sub-threshold Vm
A single mechanism for tonic and use-dependent block
Block independent of rate of
inactivation but dependent
on potential dependence of h
% block
-80 mV, t = 694 ms
block
2x (no evidence of 2 exp)
t : Channel Inactivation
V (mV) t (ms)
80
176
-70
94
65x
-40
9
-20
2.9
-20 mV, t = 373 ms
Gilliam et al Circ Res 65:723-739, 1989
Evidence that lidocaine does not
compete with fast-inactivation and
that slow recovery does not result
from accumulated fast inactivated
channels. Vedantham and Cannon
J. Gen. Physiol 113:7-16, 1999
Test 4: Exponential Binding to a Continuously
Accessible Site independent of “inactivation”
-20 mV
-80 mV
-120 mV
I = I + (I0 - I) e-2.95 t
Gilliam et al Circ Res 65:723-739, 1989
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