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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
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LVRV
RA LA
15.5 mm
shock
tachycardia fibrillation
Dynamics of transmembrane potential
(monophasic cathodal truncated exponential shock, -100 V, 8 ms)
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How To Initiate Reentry or Fibrillation:The cardiac vulnerable period
Refractory: s1s2 = 2.1
Vulnerable: s1s2 = 2.2
Excitable: s1s2 = 2.3
refractoryconduction
Partial Conduction (arrhythmia)
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Ion Channel Blockade Reduces Excitability (Anti- effect) 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)
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Steady-state Frequency-dependent AP Alterations: Quinidine
Johnson and McKinnon JPET 460-468, 1957
dV/dt(max) decreaseswith increased stim rate
AP amplitude decreaseswith increased stim rate
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Freq-dependent Quinidine Block:
Alteration of AP Duration
West and Amory: JPET 130:183-193,1960
Increased stimrate slows repolarization
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An Early Model of Use-dependent Blockade
West and Amory: JPET 130:183-193,1960
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Frequency- as well as Use-dependence: Detailed Characterization of Ajmaline Blockade
Heistracher. Naunyn-Schmeideberg’s Archiv Fur Pharmakologie 269:199-213, 1971
dV/dt(max) reduced withrepeated stimulation: note approxexponential decrease with stimulationnumber
Steady-state dV/dt(max)Reduced with faster stimulation
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Voltage and Time-dependent TEA Block of K+
Channels
Armstrong. J. Gen Physiol 54:553-575, 1969
+90 mV
-46 mV
CP
Control: no “inactivation” + TEA: Apparent “inactivation”
IK
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Once a Drug Molecule Blocks the Channel, Can it Escape?
i.e. is it possible to trap it in the channel
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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?
From These Observations, One Wonders:
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Ordinary (not use-dependent) Chemistry:Reacting with a Continuously Accessible Site
No possibility of use- or frequency dependence
Ligand + Receptor LR-Complex
b =
b(t) = b + (b0 - b) e- t
(b- b0)/2 = Kd =
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How to Build a Model that Displaysuse- and frequency dependence?
Unblocked + Drug Blocked(V)
(V)
A necessary condition:Either a Real or Apparent Voltage-dependent
Equilibrium Dissociation Constant:Kd = (V) / (V)
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Modeling Apparent Voltage DependenceOf the Equilibrium Dissociation Constant
Voltage-dependent Access to the Binding Site
Inaccessible Blocked kD
l
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Hypothesis: Control of Binding Site Access by Channel Conformation
accessible inaccessible
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Blockade During Accessible and Inaccessible Intervals:
Channel + D BlockedChannel + D Blocked
Accessible Conformation Inaccessible Conformation
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Characterization of Access Control:Guarded Receptor Model
(when channel transition time << drug binding time)
Unblocked Channel + Drug Blocked Channel
where G and T act as “switches” that control binding site accessibility
G*k
l
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 specificchannel protein conformations, and not arbitrary model parameters
Starmer, Grant, Strauss. Biophys J 46:15-27, 1984Starmer and Grant. Mol Pharm 28:348-356,1985
Starmer. Biometry 44:549-559, 1989
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Combining Gated Access with Repetitive Stimulation makes Use-dependent Blockade:
Switched Accessibility to a Binding Site
brecov = rss - (b0 - rss) e-n
bactivated = ass - (a0 - ass) e-n
b(t) = b - (b0 - b) e-k + lt
= a ta + r tr
tr
ta
U B
U B
a
r
Starmer and Grant. Mol. Pharm 28:348-356, 1985
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Dissecting the Mechanism of Use-Dependent Blockade:
Using Voltage Clamp Protocols to Amplify or Attenuate Blockade
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Continuous Access Associated with Channel Inactivation (shift in “apparent” h)
V(cond)
Unblocked + Drug Blocked(1-h)
Starmer et. al. Amer. J Physiol 259:H626-H634, 1990
block
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Transient Access Associated with Channel Opening
Pulse duration: 2 ms
2 ms150350 ms550
Gilliam et al Circ Res 65:723-739, 1989
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Shift in Apparent Activation:Evidence of Open (?) Channel Access Control
10 ms
Starmer et. Al. J. Mol Cell Cardiol 23:73-83, 1991
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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 -(a ta + r tr)n
Use-dependent rate = a ta + r tr
Steady-state block: bss = a + (r + a)
Steady-state slope(1 - e-r tr) / (1 - e-)
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Testing the Model
• Pulse-train stimulation evokes an exponential pattern of use-dependent 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 ()
• There is a shift in the midpoint of channel availability and / or activation (depending on the access control mechanism)
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Test 1. Frequency-dependent Lidocaine Uptake:Exponential Pulse-to-pulse Blockade (50 ms)
Gilliam et al Circ Res 65:723-739, 1989
.15
.65
.35
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Test 2: Linear Uptake Rate, Linear Steady State Block ta constant and tr variable
= a ta + r tr
bss = a + (r- a)
Linear Uptake Rate
Linear Steady-State Block
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Test 3: Shifting Apparent Inactivation(channel availability)
Unblocked + Drug Blocked(1-h)
V = s ln(1 + D/KD) = 10.76 mV
K = 3940 /M/sl = .678 /sKD = 18.8 M
sVVVsVV
sVV
hh
h
eel
kDh
bhh
eh
/)(/)(
*
*
/)(
1
1
)1(1
1
)1(
1
1
Obs V = 9 mV
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Test 4: Shifting Apparent Channel ActivationNimodipine Blockade of Ca++ Channels
Unblocked + Drug Blockedd
V = 40.1 mV
V = k (1 + D/KD) = 43.4 mV
KD = .38 nM
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Exploiting the “Therapeutic” Potential of Use-dependent Blockade
Cellular Antiarrhythmic ResponseMulticellular Proarrhythmic Response
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Therapeutic Potential: Cellular Effects of Blockade (Antiarrhythmic)
Prolonging Recovery of Excitability:Control and with Use-dependent Blockade
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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)
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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
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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
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Demonstrating the Vulnerable Period: ControlRefractory Period = 352 ms VP = 3 ms
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Demonstrating Extension of the VP: DrugRefractory Period = 668 ms VP = 59 ms
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Use-dependent Extension of the VP
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2-D Responses to Premature Excitation:Note geometric distance between 1st and 2nd fronts
(refractory, unidirectional conduction, bidirectional conduction)
Refractory: s1s2 = 2.1
Vulnerable: s1s2 = 2.2
Excitable: s1s2 = 2.3
refractoryconduction
unidirectional conduction
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Extending the VP with Na Channel Block:
Fact or Fantasy?
Starmer et. al. Amer. J. Physiol 262:H1305-1310, 1992
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More Apparent Complexity: Monomorphic and Polymorphic Reentry and ECG
Monomorphic PolymorphicgNa = 2.25 gNa = 4.5
Polymorphic gna = 2.3
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Major Lessons Learned FromIdeas Originating in Studies of
Johnson, Heistracher and Carmaliet
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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
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Repairing Channels that are Broken (e.g. SCN5A) may have Clinical Utility:
Blockade of “defective” channels diminishes EADs in LQT Syndrome, Heart Failure, Epilepsy
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Long QT Syndrome:Links to Mutant Na and K Channels
Q T
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Stable and Unstable Action Potentials
Beeler-Reuter ModelHuman Ventricular Cells
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Yet Another Variant: Epilepsy
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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 drug-channel interactions
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• 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
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Apparent Trapping of Quinidine and Disopyramide
Zilberter et. Al. Amer. J. Physiol 266:H2007-H2017, 1994
100 uM Diso
5 uM Quinidine
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Demonstrating the Trap
Zilberter et. Al. Amer. J. Physiol 266:H2007-H2017, 1994
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Examples of Recent State-Transition Models
Balser et al J. Clin Invest. 98:2874-2886, 1996
Vedantham and Cannon J. Gen Physiol 113:7-16, 1999
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Transforming a State-transition Model to a Macroscopic Model:
The Importance of “Rapid Equilibration”
Unblocked Channel + Drug Blocked ChannelG
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Reducing a Complex State-Transition Model to a Simple “Macro” GRH
Model
R I B
kD
l
Differential Equation Description:
maxC B I R :Channels ofon Conservati
][][
][][
BlIkDdt
dB
RIdt
dR
lbbhkDdt
db
lBBkDdt
dB
)1)(1(
)C(
B) -(C I
B - I - C B - R -C I
I R :ionEquilibrat Rapid
max
max
maxmax
Guard Function: 1-h
Guarded Receptor Formulation:
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Spontaneous Oscillation: Mutant KVLQT1 and HERG (K+) and SCN5A (Na+) Channels:
Altering Electrical Stability with Channel Blockade
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Use- and Frequency-Dependent Blockade:Central Features
• Degree of Blockade Depends on Vclamp
• Degree of Blockade Depends on Tclamp
• Degree of Blockade Depends on Vhold
Vclamp
Vhold
Tclamp
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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
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Recovery of Excitability: Drug
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Evolution of a Spiral Wave
T = 0 T = 1
T = 5 T = 15
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Monomorphic and Polymorphic EKGs
Role of Wavefront Energy
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Building a Model of “Discontinuous” (Use-dependent) Drug-Channel Interaction:
Unblocked + Drug Blocked(V)
(V)
Apparent Voltage-dependent Equilibrium Dissociation Constant:Kd = (V) / (V)
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Why Does the Guraded Receptor Model Work?
Comparing State-Transition and Macro Models
Macro Model: Unblocked + Drug BlockedG
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Reduction in AP Duration:
CL
C Q
Colatsky Circ Res 50:17-27, 1982
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Altering the Equilibrium Stability of a Cell: Blockade of Na Current
Can be reversed by Nablockade
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EADs and Suppression via Na Channel Blockade
Maltsev et al Circ 98:2545-2552, 1998
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Frequency-dependent Lidocaine Uptake:Access Controlled by “Inactivation”
Pulse duration: 50 ms
50 ms
150
650
150250350 ms450550650
Gilliam et al Circ Res 65:723-739, 1989
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Voltage-dependent Recovery from Blockade
Starmer, et. al. J. Mol. Cell. Card 23;73-83, 1992
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Two Modes of Na Channel Blockade:Test 3: Linearity with variations in both ta and tr
ta = 50 ms
ta = 10 ms
tr = constant
= a ta + r tr
tclamp
.15
.25
.45
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A Conformation-dependent Blockade ModelClosed <===> Open <===> Blocked
Armstrong. J. Gen Physiol 54:553-575, 1969
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Binding to Accessible Sites at Sub-threshold Vm
A single mechanism for tonic and use-dependent block
-80 mV, = 694 ms
-20 mV, t = 373 ms
Gilliam et al Circ Res 65:723-739, 1989
: Channel InactivationV (mV) (ms) -70 94 -40 9 -20 2.9
Block independent of rate ofinactivation but dependent
on potential dependence of h
Evidence that lidocaine does not compete with fast-inactivation and that slow recovery does not result from accumulated fast inactivated channels. Vedantham and CannonJ. Gen. Physiol 113:7-16, 1999
65x2x (no evidence of 2 exp)
block
% block
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Test 4: Exponential Binding to a Continuously Accessible Site independent of “inactivation”
Gilliam et al Circ Res 65:723-739, 1989
-20 mV
-80 mV-120 mV
tc
I = I + (I0 - I) e-2.95 t