1. May 27, 2005 Control of stability of intracellular Ca-oscillations and electrical activity in a network of coupled cells. Stan Gielen Dept. of Biophysics Martijn Kusters Wilbert van Meerwijk Dick Ypey Lex Theuvenet

2. May 27, 2005 Overview Summary of Ca-dynamics in NRK cell Dynamics of Ca-oscillations and action potentials coupling between Ca-oscillations and action potentials Stability of Ca-dynamics in the cell Alternative model for cells with IP3-oscillations Coupling between two oscillators Propagation of electrical activity in network of layers –oscillators as pacemakers which initiate propagation ? –instability due to coupling ?

3. May 27, 2005 Model for Normal Rat Kidney Cell NRK-cell = fibroblast similar to Cells of Cajal NRK cells form a network coupled by gap- junctions

4. May 27, 2005 Model for Membrane NRK cell

5. May 27, 2005 Components of the model Ca cyt BCa cyt B Ca ex G CaL Cl ex G Cl(Ca) K cyt G Kir G leak ATP PMCA Ca ER (0.1 μM) (1000 μM)

6. May 27, 2005 This model focusses on the dynamics of the cell membrane, including the L-type Ca-channel and other ion channels with the following components: PMCA pump : pump Ca out of cytosol into extracellular space Ca 2+ L-type channel: V ca-L = +55 mV Cl(Ca) channel: V Cl = -20 mV Leak channel K ir channel : V K = -75 mV Ca-buffer in the cytosol Ca cyt BCa cyt B Ca ex G CaL Cl ex G Cl(Ca) K cyt G Kir G leak PMCA Ca ER

7. May 27, 2005 Components of the model for the NRK Membrane Leak current Potassium channel PMCA-pomp

8. May 27, 2005 Components of the model for the NRK Membrane Ca 2+ L type channel Cl(Ca) kanaal

9. May 27, 2005 Current clamp Ipulse=6 pA When we current clamp, the activation gate of the Ca L type opens, giving rise to an inflow of Ca through the Ca L type channel. As a consequence, an action potential will be generated Ca cyt BCa cyt B Ca ex G CaL G Cl(Ca) K G Kir G leak PMCA Ca ER

10. May 27, 2005 Current clamp I pulse =6 pA Action potential Ca cyt Buffered Ca PMCA current IKIK I Cl I Leak

11. May 27, 2005 Current clamp I pulse =6 pA Action potential Ca cyt Buffered Ca PMCA current IKIK I Cl I Leak Inflow of Ca through L-type Ca channel Plateau due to Nernst potential of Ca-dependent Cl-channel

12. May 27, 2005 Current clamp I pulse =6 pA Action potential Ca cyt Buffered Ca PMCA current IKIK I Cl I Leak Important !

13. May 27, 2005 Adding a Ca 2+ buffer eliminates the plateau De Roos et al. 1998

14. May 27, 2005 The effect of a Ca-buffer With Ca bufferWithout Ca buffer Shorter plateau- phase

15. May 27, 2005 Model for intracellular Ca 2+ - oscillations

16. May 27, 2005 Model for Ca-oscillations from ER G lek Ca ER Ca cyt BCa cyt B G lk G lek ATP PMCA IP3 receptor ATP SERCA SERCA pump IP3-receptor leakage of Ca from the ER into the cytosol PMCA pump leakage of Ca from extracellular space into the cytosol Ca-buffer in the cytosol (0.1 μM) (1000 μM)

17. May 27, 2005 This model focusses on the dynamics of Ca in the ER and cytosol by transport through the IP3 receptor. The model has the following components: SERCA pump IP3-receptor leakage of Ca from the ER into the cytosol PMCA pump leakage of Ca from extracellular space into the cytosol Ca-buffer in the cytosol

18. May 27, 2005 Components of the model for the IP3-oscillator IP3-receptor Leakage from ER SERCA-pomp A conversion factor of 0.1 transforms an increase/decrease of Ca ER into a decrease/increase of Ca cyt.

19. May 27, 2005 Intracellular Ca-oscillations Harks et al., 2004

20. May 27, 2005 Stability analysis of IP3 receptor

21. May 27, 2005 Ca-oscillations as a function of IP 3

22. May 27, 2005 IP 3 -mediated calcium oscillations Ca ER Buffered Ca Ca cyt Ca ER J PMCA,J SOC,J Leak J SERCA, J IP3

23. May 27, 2005 Concentration IP3 lowhigh IP 3 -mediated calcium oscillations Ca ER Ca cyt Buffered Ca J SERCA, J IP3 J PMCA,J SOC,J Leak

24. May 27, 2005 Overview Summary of Ca-dynamics in NRK cell Dynamics of Ca-oscillations and action potentials coupling between Ca-oscillations and action potentials Stability of Ca-dynamics in the cell Alternative model for cells with IP3-oscillations Coupling between two oscillators Propagation of electrical activity in network of layers –oscillators as pacemakers which initiate propagation ? –instability due to coupling ?

25. May 27, 2005 Stability of Ca-dynamics in the cell Whole cell model Action potentials Ca-oscillations

26. May 27, 2005 Ca cyt BCa cyt B IP3 Ca ex G CaL Cl ex G Cl(Ca) K cyt G Kir G lk G Calk PMCA Ca er SERCA IP3R J Calker Complete Model

27. May 27, 2005 steady-state behavior Without IP3, the steady-state is easily found by solving J SERCA =J leak,ER and J PMCA =J leak,membrane This gives a single, stable solution for Ca cyt and Ca ER : Ca cytosol = 0.1 μM; Ca ER = 1300 μM ER/cytosol: membrane/cytosol:

28. May 27, 2005 Stability of Ca 2+ concentrations Ca cyt Ca ex (1000 μM) G Calk PMCA Ca er SERCA J Calker Ca cyt G Calk PMCA Ca er SERCA J Calker Action potential triggers Ca oscillationCa oscillation triggers action potential Ca ex (1000 μM)

29. May 27, 2005 Ca cyt BCa cyt B IP3 Ca ex G CaL Cl ex G Cl(Ca) K cyt G Kir G lk G Calk PMCA Ca er SERCA IP3R J Calker Additional channel to stabilize Ca-dynamics G SOC

30. May 27, 2005 Whole cell model with SOC/CRAC channel Action potentials Ca-oscillations

31. May 27, 2005 Components of the model Membrane potential Ca cytosol (μMol) dV/dt = 0 dCa cyt /dt=0 IP 3 = 0 Stable attractor

32. May 27, 2005 Components of the model Membrane potential dV/dt = 0 dCa cyt /dt=0 IP 3 receptor oscillates No stable attractor Ca cytosol (μM)

33. May 27, 2005 Components of the model dV/dt = 0 dCa cyt /dt=0 IP 3 high Stable attractor at – 20 mV Membrane potential Ca cytosol (μMol)

34. May 27, 2005 Stability analysis of IP3 receptor

35. May 27, 2005 Summary Stability of Ca-dynamics for all possible natural conditions requires a coupling between Ca-concentration in ER and extracellular Ca. Without IP3: stable condition corresponds to V=-70 mV; Ca cyt =0.1 μM Higher IP3 concentrations provide oscillations or stable point at V= -20 mV

36. May 27, 2005 Overview Summary of Ca-dynamics in NRK cell Dynamics of Ca-oscillations and action potentials coupling between Ca-oscillations and action potentials Stability of Ca-dynamics in the cell Alternative model for cells with IP3-oscillations Coupling between two oscillators Propagation of electrical activity in network of layers –oscillators as pacemakers which initiate propagation ? –instability due to coupling ?

37. May 27, 2005 Alternative model for coupling between IP3-oscillator (Ca-oscillations) and membrane oscillator (action potentials)

38. May 27, 2005 Problem Many cell types do not oscillate in isolation, but do so in a synchronized manner only when electrically coupled in a network (e.g. β-pancreatic cells in islets of Langerhans and aortic smooth muscle cells). –Cells in isolation are quiet or oscillate at lower frequencies. Paradox: If identical cells oscillate in phase, there are no currents ! How then can electrical coupling be crucial for the synchronous oscillations ? Moreover: if there are phase differences, they will be eliminated by the electrical coupling !

39. May 27, 2005 Basic mechanism J(Ca cyt,Ca ER ) = interaction term between Ca concentrations with reflecting Ca-induced Ca-release KCa cyt = efflux of Ca from cell U = constant, Ca-mediated electrical current Loewenstein & Sompolinsky, PNAS, 2001

40. May 27, 2005 Calcium and Voltage oscillations in non-excitable cell Cytosolic Ca (μM)Ca in stores (μM) Rest-state is unstable fixed-point Small perturbations in cytosolic Ca cause oscillations Loewenstein et al., PNAS 98, 2001

41. May 27, 2005 Calcium and Voltage oscillations Cytosolic Ca (μM)Ca in stores (μM) Non-excitable cell Excitable cell with Voltage- dependent Ca- current en K ca channel I K_Ca hyperpolarizes membrane potential, which de-activates Ca- influx into cell However, adding a shunt conductance destabilizes the fixed point Hyperpolarization decreases by electrical coupling

42. May 27, 2005 Calcium and Voltage oscillations Cytosolic Ca (μM)Ca in stores (μM) Excitable cell with Voltage- dependent Ca- current en K ca channel Addition of ashunt conductance 1.Reduces the effect of Ca cyt on membranbe potential 2.Suppresses efficacy of negative feedback by I K_Ca 3.Enables oscillations with Voltage- dependent Ca- current en K ca channel but with shunt conductance

43. May 27, 2005 Voltage and Ca oscillations in network of two electrically coupled cells Ca oscillations out-of-phase; electrical oscillations in- phase at double frequency Hyperpolarization due to Ca-influx Hyperpolarization due to electrical coupling

44. May 27, 2005 Multi-stability in network with 6 coupled cells. Cell 123456123456 123456123456 In a large network different realizations of out-of-phase calcium oscillations are possible and therefore the network possesses many stable states. The stable state in which the system will eventually settle is determined by the initial conditions. Note the differences in membrane potential !

45. May 27, 2005 Summary Cells are –intrinsically stable (near –70 mV ; Loewenstein et al. PNAS 2001) or –intrinsically oscillating ? Electrical coupling –enables oscillations and propagation of activity to otherwise silent cells or –disables oscillations and propagating activity in a network of pacemaker cells ? Ca oscillations out of phase ! Why ?

46. May 27, 2005 Overview Summary of Ca-dynamics in NRK cell Dynamics of Ca-oscillations and action potentials coupling between Ca-oscillations and action potentials Stability of Ca-dynamics in the cell Alternative model for cells with IP3-oscillations Coupling between two oscillators Propagation of electrical activity in network of layers –oscillators as pacemakers which initiate propagation ? –instability due to coupling ?

47. May 27, 2005 Coupling between two oscillators Inhibition and electrical coupling

48. May 27, 2005 Neuronal synchronization due to external input T ΔT Δ(θ)= ΔT/T Synaptic input

49. May 27, 2005 Neuronal synchronization T ΔT Δ(θ)= ΔT/T Phase shift as a function of the relative phase of the external input. Phase advance Hyperpolarizing stimulus Depolarizing stimulus

50. May 27, 2005 Neuronal synchronization T ΔT Δ(θ)= ΔT/T Suppose: T = 95 ms external trigger: every 76 ms Synchronization when ΔT/T=(95-76)/95=0.2 external trigger at time 0.7x95 ms = 66.5 ms

51. May 27, 2005 Inhibitory coupling for two identical leaky-integrate-and-fire neurons Out-of-phase stableIn-phase stable Lewis&Rinzel, J. Comp. Neurosci, 2003

52. May 27, 2005 Phase-shift function for inhibitory coupling for stable attractor Increasing constant input to the LIF- neurons I=1.2 I=1.4 I=1.6

53. May 27, 2005 Bifurcation diagram for two identical LIF-neurons with inhibitory coupling

54. May 27, 2005 Bifurcation diagram for two identical LIF-neurons with inhibitory coupling Time constant for inhibitory synaps

55. May 27, 2005 Electrical coupling for spiking neurons by gap junctional coupling Out-of-phase stableIn-phase stable

56. May 27, 2005 Phase-shift function for electrical coupling effect of supra- threshold part of spike tends to synchronize activity effect of sub- threshold part of spike tends to desynchronize activity -70 mV 0 mV +40 mV 1. 2. 1.2.

57. May 27, 2005 Phase-shift function for electrical coupling I=1.05 I=1.15 I=1.25 effect of supra- threshold part of spike tends to synchronize activity effect of sub- threshold part of spike tends to desynchronize activity effect of both components

58. May 27, 2005 Bifurcation diagram for two identical LIF-neurons with electrical coupling

59. May 27, 2005 Bifurcation diagram for two identical LIF-neurons with electrical coupling

60. May 27, 2005 If natural frequencies do not match Time courses of hypathocyte x1 (solid line) and of x2 (dashed line) at P1=1.5 μM and P2=2.5 μM. (a) Harmonic locking of 1:3 (γCA=0.025 s -1 ); (b) harmonic locking of 1:2 (γCA=0.05 s -1 ); (c) phase locking of 1:1 (γCA=0.09 s -1 ). (d) Devil’s staircase, a ratio N/M (where N is the spike number of x1 and M is the spike number of x2) as a function of the coupling strength γCA at given IP3 level: P1=1.5 μM, P2=2.5 μM. Wu et al., Biophys. Chem. 113, 2005 Coupling strength

61. May 27, 2005 Bifurcation diagram for two identical LIF-neurons with inhibitory and electrical coupling Inhibitory coupling only Electrical coupling only

62. May 27, 2005 Electrical coupling in addition to synaptic (inhibitory) interactions anti-phase, weak electrical coupling in-phase, strong electrical coupling no electrical coupling anti-phase, weak electrical coupling in-phase, strong electrical coupling Brem & Rinzel, J. Neurophysiol. 91, 2004

63. May 27, 2005 Anti-phase and in- phase both stable Stable in- phase Stable anti- phase Electrical coupling in addition to synaptic interactions The stronger is the synaptic inhibition, the larger is the electrical coupling required to stabilize in-phase behavior

64. May 27, 2005 Summary Gap-junctions between two cells tend to synchronize the two oscillators synchronizing effect is stronger when there is a plateau phase in the action potential

65. May 27, 2005 Overview Summary of Ca-dynamics in NRK cell Dynamics of Ca-oscillations and action potentials coupling between Ca-oscillations and action potentials Stability of Ca-dynamics in the cell Alternative model for cells with IP3-oscillations Coupling between two oscillators Propagation of electrical activity in network of layers –oscillators as pacemakers which initiate propagation ? –instability due to coupling ?

66. May 27, 2005 What happens for two pacemaker cells with excitatory and gap- junctional coupling ?

67. May 27, 2005 Two pacemaker cells

68. May 27, 2005 Synchronization of two oscillators No coupling Small conductance gap junction

69. May 27, 2005 Simple result for excitatory and electrical coupling Two pacemaker cells synchronize easily

70. May 27, 2005 Synchronization of activity in a network of cells

71. May 27, 2005 Network of NRK-cells

72. May 27, 2005 One pacemaker, surrounded by 6 followers

73. May 27, 2005 Two pacemaker cells RiRi R gap R cell V

74. May 27, 2005 Network of NRK-cells RiRi R gap R cell R gap R cell R gap R cell Experimental observation: a single pacemaker cell cannot initiate propagation of action potential firing

75. May 27, 2005 Resistance of gap-junction should not be too high and not too low ! RiRi R gap R cell R gap R cell R gap R cell In the heart: R cell is high !

76. May 27, 2005 Synchronization in a network of different coupled oscillators

77. May 27, 2005 Spontaneous oscillations and synchronization in NRK networks Ca er Ca syst Membrane potential NRK cell with intracellular (IP3) oscillator and plasma membrane Network with NRK cells Oscillations and synchronization

78. May 27, 2005 Standing problems Cells are intrinsically stable, but become unstable due to coupling in a network ? Or: cells are unstable but synchronize in a network to act as pacemakers for propagating activity ? What is the role of electrical/gap-junctional coupling and Ca-diffusion through gap junctions in propagation of action potential firing ? How to recognize pacemakers and followers ? Pace-makers seem to “move” in a network

79. May 27, 2005

80. Ca cyt BCa cyt B IP3 Ca ex G CaL Cl ex G Cl(Ca) K cyt G Kir G lk G Calk PMCA Ca er SERCA IP3R J Calker Complete model G SOC

81. May 27, 2005 Further topics for study Compartimentalization: –coupling of ER with cell membrane for store-operated channels –discrete sources and sinks (stores) –discrete channels : distance between channel clusters is larger than the diffusion length of free Ca 2+ stability of intracellular Ca 2+ control relation between stochastic character of channel dynamics and deterministic periodic behavior of Ca-oscillations

82. May 27, 2005 References Falcke (2004) Reading the patterns in living cells —the physics of Ca 2+ signaling. Advances in Physics, 53, 255–440 Loewenstein, Yarom, Sompolinsky (2001) The generation of oscillations in networks of electrically coupled cells. PNAS 98, 8095-8100.

83. May 27, 2005 Components of the model for the NRK Membrane CRAC kanaal Ca 2+ L type channel Cl(Ca) kanaal

84. May 27, 2005 Components of the model in the cell membrane CRAC channel Leakage into cytosol PMCA-pomp

85. May 27, 2005 Overview of parameter values for membranefor ER

86. May 27, 2005 Dynamics of IP 3 regulated Ca 2+ release

87. May 27, 2005 Ca-oscillations as a function of IP 3

88. May 27, 2005 Oscillations in a large network

89. May 27, 2005 -150-100-50050100150 0 0.2 0.4 0.6 0.8 1 m  (V) -150-100-50050100150 0 2 4 6 8 x 10 -3  m (V)  m (s) -150-100-50050100150 0.2 0.4 0.6 0.8 1 1.2 h  (V) V clamp (mV) -100-50050100 0 2 4 6 8 10  h (V) V clamp (mV)  h (s) Parameter fitting

90. May 27, 2005 Ca-action potentials triggered by Ca-release from the ER G Ca L 20 mV G Cl(Ca) -20 mV G K IR -70 mV

91. May 27, 2005 Phase diagram for closed-cell model Sneyd et al., PNAS, 2004

92. May 27, 2005 Ca 2+ is involved in the control of Muscle contraction memory storage egg fertilization enzyme secretion by acinar cell in pancreas coordination of cell behavior in the liver cell apoptosis second messenger : coding and transfer of information from cell membrane to nucleus etc., etc., etc. Yet, high cytosolic concentrations prohibit normal functioning of the cell. How can this be made compatibel ? See Martin Falcke, Advances in Physics, 53, 2004

93. May 27, 2005 Different forms of Ca 2+ oscillations hepatocyte stimulated with norepinephrine endothelial cell stimulated with histamine sinusoidal oscillations in a parotid gland

94. May 27, 2005 Ca-dynamics Ca-oscillations in non-excitable cells Ca-inflow in excitable cells (action- potential generation) without intracellular Ca-oscillations. Ca-oscillations in cells with action- potentials and with IP3-mediated Ca- oscillations.

95. May 27, 2005 Overview Summary of Hodgkin-Huxley model Dynamics of Ca-oscillations and action potentials coupling between Ca-oscillations and action potentials Stability of Ca-dynamics in the cell Propagation of electrical activity in network of layers –oscillators as pacemakers which initiate propagation ? –instability due to coupling ?

96. May 27, 2005 V mV 0 mV V mV 0 mV ICIC I Na Membrane voltage equation -C m dV/dt = g max, Na m 3 h(V-V na ) + g max, K n 4 (V-V K ) + g leak (V-V leak ) K

97. May 27, 2005 V (mV) mm mm Open Closed mm mm m Probability: State: (1-m) Channel Open Probability: mm mm Gating kinetics m.m.m.h=m 3 h

98. May 27, 2005 Actionpotential

99. May 27, 2005 Simplification of Hodgkin-Huxley Fast variables membrane potential V activation rate for Na + m Slow variables activation rate for K + n inactivation rate for Na + h -C dV/dt = g Na m 3 h(V-E na )+g K n 4 (V-E K )+g L (V-E L ) + I dm/dt = α m (1-m)-β m m dh/dt = α h (1-h)-β h h dn/dt = α n (1-n)-β n n

100. May 27, 2005 Phase diagram for the Morris-Lecar model

101. May 27, 2005 Phase diagram

102. May 27, 2005 Phase diagram of the Morris- Lecar model

103. May 27, 2005 Buffer dynamics with K on = 0.032 (μMol s) -1 K off = 0.06 s -1

104. May 27, 2005 Phase-plane plot for membrane dynamics (Morris-Lecar model)

105. May 27, 2005 Ca L type channel activation (m ∞ ) and inactivation (h ∞ ) m∞m∞ h ∞ V (mV)

106. May 27, 2005 The effect of Kon on the action potential Kon = 3.2 (μMol.s) -1 Kon = 0.032 (μMol.s) -1 Kon = 0.32 (μMol.s) -1 Shorter AP More Ca buffered Longer AP All Ca buffered