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
Mar 27, 2015
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
LVRV
RA LA
15.5 mm
shock
tachycardia fibrillation
Dynamics of transmembrane potential
(monophasic cathodal truncated exponential shock, -100 V, 8 ms)
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)
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)
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
Freq-dependent Quinidine Block:
Alteration of AP Duration
West and Amory: JPET 130:183-193,1960
Increased stimrate 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
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
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
Once a Drug Molecule Blocks the Channel, Can it Escape?
i.e. is it possible to trap it in the channel
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:
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 =
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)
Modeling Apparent Voltage DependenceOf the Equilibrium Dissociation Constant
Voltage-dependent Access to the Binding Site
Inaccessible Blocked kD
l
Hypothesis: Control of Binding Site Access by Channel Conformation
accessible inaccessible
Blockade During Accessible and Inaccessible Intervals:
Channel + D BlockedChannel + D Blocked
Accessible Conformation Inaccessible Conformation
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
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
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)
V(cond)
Unblocked + Drug Blocked(1-h)
Starmer et. al. Amer. J Physiol 259:H626-H634, 1990
block
Transient Access Associated with Channel Opening
Pulse duration: 2 ms
2 ms150350 ms550
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 -(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-)
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)
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
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
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
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
Exploiting the “Therapeutic” Potential of Use-dependent Blockade
Cellular Antiarrhythmic ResponseMulticellular 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: ControlRefractory Period = 352 ms VP = 3 ms
Demonstrating Extension of the VP: DrugRefractory 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: s1s2 = 2.1
Vulnerable: s1s2 = 2.2
Excitable: s1s2 = 2.3
refractoryconduction
unidirectional conduction
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 PolymorphicgNa = 2.25 gNa = 4.5
Polymorphic gna = 2.3
Major Lessons Learned FromIdeas 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
Q T
Stable and Unstable Action Potentials
Beeler-Reuter ModelHuman Ventricular Cells
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 drug-channel 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
Zilberter et. Al. Amer. J. Physiol 266:H2007-H2017, 1994
100 uM Diso
5 uM Quinidine
Demonstrating the Trap
Zilberter et. Al. Amer. J. Physiol 266:H2007-H2017, 1994
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
Transforming a State-transition Model to a Macroscopic Model:
The Importance of “Rapid Equilibration”
Unblocked Channel + Drug Blocked ChannelG
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:
Spontaneous Oscillation: Mutant KVLQT1 and HERG (K+) and SCN5A (Na+) Channels:
Altering Electrical Stability with Channel Blockade
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
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 = 1
T = 5 T = 15
Monomorphic and Polymorphic EKGs
Role of Wavefront Energy
Building a Model of “Discontinuous” (Use-dependent) Drug-Channel Interaction:
Unblocked + Drug Blocked(V)
(V)
Apparent Voltage-dependent Equilibrium Dissociation Constant:Kd = (V) / (V)
Why Does the Guraded Receptor Model Work?
Comparing State-Transition and Macro Models
Macro Model: Unblocked + Drug BlockedG
Reduction in AP Duration:
CL
C Q
Colatsky Circ Res 50:17-27, 1982
Altering the Equilibrium Stability of a Cell: Blockade of Na Current
Can be reversed by Nablockade
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
650
150250350 ms450550650
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
ta = 50 ms
ta = 10 ms
tr = constant
= a ta + r tr
tclamp
.15
.25
.45
A Conformation-dependent Blockade ModelClosed <===> 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
-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
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