1. 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

2. shock tachycardiafibrillation Dynamics of transmembrane potential (monophasic cathodal truncated exponential shock, -100 V, 8 ms)

3. How To Initiate Reentry or Fibrillation: The cardiac vulnerable period Refractory: s1s2 = 2.1 Vulnerable: s1s2 = 2.2 Excitable: s1s2 = 2.3 refractory conduction Partial Conduction (arrhythmia)

4. 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)

5. Steady-state Frequency-dependent AP Alterations: Quinidine Johnson and McKinnon JPET 460-468, 1957 dV/dt(max) decreases with increased stim rate AP amplitude decreases with increased stim rate

6. Freq-dependent Quinidine Block: Alteration of AP Duration West and Amory: JPET 130:183-193,1960 Increased stim rate slows repolarization

7. An Early Model of Use-dependent Blockade West and Amory: JPET 130:183-193,1960

8. Frequency- as well as Use-dependence: Detailed Characterization of Ajmaline Blockade Heistracher. Naunyn-Schmeidebergs Archiv Fur Pharmakologie 269:199-213, 1971 dV/dt(max) reduced with repeated stimulation: note approx exponential decrease with stimulation number Steady-state dV/dt(max) Reduced with faster stimulation

9. 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 IKIK

10. Once a Drug Molecule Blocks the Channel, Can it Escape? i.e. is it possible to trap it in the channel

11. Is use-dependent channel blockade a special process or is it simply a variant of ordinary ligand-receptor interactions? If its a variant - what variant? From These Observations, One Wonders:

12. 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 + (b 0 - b ) e - t (b - b 0 )/2 = K d =

13. How to Build a Model that Displays use- and frequency dependence? Unblocked + Drug Blocked (V) A necessary condition: Either a Real or Apparent Voltage-dependent Equilibrium Dissociation Constant: K d = (V) / (V)

14. Modeling Apparent Voltage Dependence Of the Equilibrium Dissociation Constant Voltage-dependent Access to the Binding Site InaccessibleBlocked kD l

15. Hypothesis: Control of Binding Site Access by Channel Conformation accessibleinaccessible

16. Blockade During Accessible and Inaccessible Intervals: Channel + D Blocked Channel + D Blocked Accessible ConformationInaccessible Conformation

17. 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, m 3 h, d, n, n 4 T = trap function controls drug egress: e.g. m 3 h, 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

18. Combining Gated Access with Repetitive Stimulation makes Use-dependent Blockade: Switched Accessibility to a Binding Site b recov = r ss - (b 0 - r ss ) e - n b activated = a ss - (a 0 - a ss ) e - n b(t) = b - (b 0 - b ) e - k + l t = a t a + r t r t r tata U B a r Starmer and Grant. Mol. Pharm 28:348-356, 1985

19. Dissecting the Mechanism of Use-Dependent Blockade: Using Voltage Clamp Protocols to Amplify or Attenuate Blockade

20. 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

21. 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

22. Shift in Apparent Activation: Evidence of Open (?) Channel Access Control 10 ms Starmer et. Al. J. Mol Cell Cardiol 23:73-83, 1991

23. Exploring a Model of Use-Dependent Blockade Are the Analytical Predictions Testable? Analytical Description: block associated with the n th pulse: b n = b ss + (b 0 - b ss ) e -( a t a + r t r )n Use-dependent rate = a t a + r t r Steady-state block: b ss = a + (r + a ) Steady-state slope (1 - e - r tr ) / (1 - e - )

24. 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)

25. 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

26. Test 2: Linear Uptake Rate, Linear Steady State Block t a constant and t r variable = a t a + r t r b ss = a + (r - a ) Linear Uptake Rate Linear Steady-State Block

27. Test 3: Shifting Apparent Inactivation (channel availability) Unblocked + Drug Blocked (1-h) V = s ln(1 + D/K D ) = 10.76 mV K = 3940 /M/s l =.678 /s K D = 18.8 M Obs V = 9 mV

28. Test 4: Shifting Apparent Channel Activation Nimodipine Blockade of Ca ++ Channels Unblocked + Drug Blocked d V = 40.1 mV V = k (1 + D/K D ) = 43.4 mV K D =.38 nM

29. Exploiting the Therapeutic Potential of Use-dependent Blockade Cellular Antiarrhythmic Response Multicellular Proarrhythmic Response

30. Therapeutic Potential: Cellular Effects of Blockade (Antiarrhythmic) Prolonging Recovery of Excitability: Control and with Use-dependent Blockade

31. 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)

32. 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

34. 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 PeriodMatlab

35. Demonstrating the Vulnerable Period: Control Refractory Period = 352 ms VP = 3 ms

36. Demonstrating Extension of the VP: Drug Refractory Period = 668 ms VP = 59 ms

37. Use-dependent Extension of the VP

38. 2-D Responses to Premature Excitation: Note geometric distance between 1 st and 2 nd fronts (refractory, unidirectional conduction, bidirectional conduction) Refractory: s1s2 = 2.1 Vulnerable: s1s2 = 2.2 Excitable: s1s2 = 2.3 refractory conduction unidirectional conduction

39. Extending the VP with Na Channel Block: Fact or Fantasy? Starmer et. al. Amer. J. Physiol 262:H1305-1310, 1992

40. More Apparent Complexity: Monomorphic and Polymorphic Reentry and ECG MonomorphicPolymorphic gNa = 2.25gNa = 4.5 Polymorphic gna = 2.3

41. Major Lessons Learned From Ideas Originating in Studies of Johnson, Heistracher and Carmaliet

42. Use caution when repairing channels that arent 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

43. Repairing Channels that are Broken (e.g. SCN5A) may have Clinical Utility: Blockade of defective channels diminishes EADs in LQT Syndrome, Heart Failure, Epilepsy

44. Long QT Syndrome: Links to Mutant Na and K Channels Q T

45. Stable and Unstable Action Potentials Beeler-Reuter ModelHuman Ventricular Cells

46. Yet Another Variant: Epilepsy

47. 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

48. 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

50. Apparent Trapping of Quinidine and Disopyramide Zilberter et. Al. Amer. J. Physiol 266:H2007-H2017, 1994 100 uM Diso 5 uM Quinidine

51. Demonstrating the Trap Zilberter et. Al. Amer. J. Physiol 266:H2007-H2017, 1994

52. 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

53. Transforming a State-transition Model to a Macroscopic Model: The Importance of Rapid Equilibration Unblocked Channel + Drug Blocked Channel G

54. Reducing a Complex State-Transition Model to a Simple Macro GRH Model R I B kD l Differential Equation Description: Guard Function: 1-h Guarded Receptor Formulation:

55. Spontaneous Oscillation: Mutant KVLQT1 and HERG (K+) and SCN5A (Na+) Channels: Altering Electrical Stability with Channel Blockade

56. Use- and Frequency-Dependent Blockade: Central Features Degree of Blockade Depends on V clamp Degree of Blockade Depends on T clamp Degree of Blockade Depends on V hold V clamp V hold T clamp

57. 1. Frequency-dependent Lidocaine Uptake: Exponential Pulse-to-pulse Blockade (2 ms) Test 1: Exponential UDP Block, t a = constant Gilliam et al Circ Res 65:723-739, 1989

58. Recovery of Excitability: Drug

59. Evolution of a Spiral Wave T = 0 T = 1 T = 5T = 15

60. Monomorphic and Polymorphic EKGs Role of Wavefront Energy

61. Building a Model of Discontinuous (Use- dependent) Drug-Channel Interaction: Unblocked + Drug Blocked (V) Apparent Voltage-dependent Equilibrium Dissociation Constant: K d = (V) / (V)

62. Why Does the Guraded Receptor Model Work? Comparing State-Transition and Macro Models Macro Model: Unblocked + Drug Blocked G

63. Reduction in AP Duration: C L C Q Colatsky Circ Res 50:17-27, 1982

64. Altering the Equilibrium Stability of a Cell: Blockade of Na Current Can be reversed by Na blockade

65. EADs and Suppression via Na Channel Blockade Maltsev et al Circ 98:2545-2552, 1998

66. Frequency-dependent Lidocaine Uptake: Access Controlled by Inactivation Pulse duration: 50 ms 50 ms 150 650 150 250 350 ms 450 550 650 Gilliam et al Circ Res 65:723-739, 1989

67. Voltage-dependent Recovery from Blockade Starmer, et. al. J. Mol. Cell. Card 23;73-83, 1992

68. Two Modes of Na Channel Blockade: Test 3: Linearity with variations in both t a and t r t a = 50 ms t a = 10 ms t r = constant = a t a + r t r t clamp.15.25.45

69. A Conformation-dependent Blockade Model Closed Open Blocked Armstrong. J. Gen Physiol 54:553-575, 1969

70. Binding to Accessible Sites at Sub-threshold V m 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 Inactivation V (mV) (ms) -70 94 -40 9 -20 2.9 Block independent of rate of inactivation 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 Cannon J. Gen. Physiol 113:7-16, 1999 65x 2x (no evidence of 2 exp) block % block

71. 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 tctc I = I + (I 0 - I ) e -2.95 t