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