Cellular Electrophysiology Part 1: Resting and Action Potentials Cellular Electrophysiology Bioengineering 6000 CV Physiology Cardiac Electrophysiology Theory Simulation Experiment • The membrane: structure, channels and gates • The cell: resting potential, whole cell currents, cardiac cell types • The tissue: myocardial structure, propagation Scale • The heart: conduction system, extracellular electrograms • ECG and the volume conductor: the heart in the thorax Cellular Electrophysiology Bioengineering 6000 CV Physiology Membrane Composition Cellular Electrophysiology Bioengineering 6000 CV Physiology Proteins and the Membrane Cellular Electrophysiology Bioengineering 6000 CV Physiology Membrane Functions Control of solutes’ movement Compartmentalization Electrical Activity Cellular Electrophysiology Bioengineering 6000 CV Physiology Theory Simulation Experiment Background Physics = Theory Cellular Electrophysiology Bioengineering 6000 CV Physiology Current and Ohm’s Law 1 • Without potential difference there I = V = GV is no current! R • Without conductance, there is no current. v(0) v(x) • Ohm’s law: jx – linear relationship between current and voltage 0 x – not universal, especially not in living systems L Cellular Electrophysiology Bioengineering 6000 CV Physiology Electricity Basics: Resistance = Req = R1+ R2 + R3 R1 R2 R3 = 1/Req =1/R1+ 1/R2 + 1/R3 Geq = G1 + G2 + G3 I I-V Curve Slope = 1/R = G A V V I = V/R = VG Cellular Electrophysiology Bioengineering 6000 CV Physiology Electricity Basics: Rectification I-V Curve I A Slope = 1/R = G V V I = V/R = VG Cellular Electrophysiology Bioengineering 6000 CV Physiology Equilibrium Net Forces Equal Zero No change over time Cellular Electrophysiology Bioengineering 6000 CV Physiology Ion Channel Permeability An electron has a unitary charge of 1.6022x10-19 C Cation+ has a charge of qo= zeo where z is the valence The attractive force between ions is given by Coulombs law: ε is the Dielectric constant, a parameter related to the properties of the material capable of separating charge Cellular Electrophysiology Bioengineering 6000 CV Physiology Ion Transport Active transport (pump) Passive cotransport (symporter) Channels Cellular Electrophysiology Bioengineering 6000 CV Physiology Ion Transport Net K+ Cellular Electrophysiology Bioengineering 6000 CV Physiology Forces Diffusive Force @c J = D c = D 2c − r @t r Chemical Potential µ = µ0 + RT ln(c) Electrical Force q q F = k 1 2 e e r2 Electrical Potential φ = zFΦ Cellular Electrophysiology Bioengineering 6000 CV Physiology Resting Potential Cellular Electrophysiology Bioengineering 6000 CV Physiology Equilibrium Potential a) Membrane is impermeable b) Membrane becomes permeable to potassium only (semipermeable) c) Equilibrium established when electrostatic and chemical gradients balance. Cellular Electrophysiology Bioengineering 6000 CV Physiology Example Nernst Potentials Nernst Potential Ion External Internal (mV) Cellular Electrophysiology Bioengineering 6000 CV Physiology Resting Potential Electrostatic (Vm = 80mV) - + V m + - Chemical (Veq = 94mV) + + 61.5 log([K ]i / [K ]o) Net Gradient + + [K ]o [K ]i - + Electrostatic (Vm = 80mV) Vm - + Chemical (Veq = 70mV) + + 61.5 log([Na ]o / [Na ]i) Net Gradient + + [Na ]o [Na ]i What determines K+ Nernst Potential resting potential? Cellular Electrophysiology Bioengineering 6000 CV Physiology Resting Potential • All ions contribute • Goldman-Hodgkin-Katz Equation N + N + RT i PM + [Mi ]out + i PA+ [Ai ]in E = ln i i m N + N + F P + [M ]in + P + [A ]out i Mi i i Ai i Cellular Electrophysiology Bioengineering 6000 CV Physiology Cardiac Action Potentials Cellular Electrophysiology Bioengineering 6000 CV Physiology Driving Force Sign convention is inside relative to outside. - - - Vm Vm = -80 mV (electrical) - - -Veq - - Veq = -94 mV (chemical) - - + - + [K ]i VD = Vm - Veq = 14 mV (net) [K ]o - Driving Force = Vm - Veq is the potential available to drive ions across the membrane. Membrane resistance = Rm is the resistance of the membrane through a specific channel for a specific ion. V V I = m − eq Rm Ohm’s Law: links these parameters and describes the membrane current. Cellular Electrophysiology Bioengineering 6000 CV Physiology Action Potentials-Positive Feedback Increase in gNa Depolarization Na flux • What starts the positive feedback? • What stops the positive feedback? Cellular Electrophysiology Bioengineering 6000 CV Physiology Cardiac Action Potential 0 Ca threshold (-35mV) mV Na threshold (-65mV) -80 Na+ current K+ current = depolarizing = repolarizing Ca++ current 300-350 ms Cellular Electrophysiology Bioengineering 6000 CV Physiology Cardiac Cell Currents Chemical K+ ++ T2 Chemical Ca Chemical Na+ 0 Electrostatic Vm mV -80 T1 T3 Time - - - - - - - - - + + + + + - + [K ]o + [Na ]o [K ]o [K ]i [K ]i + - [Na ]i - - + ++ - [Ca ]o - ++ [Ca ]i ++ [Ca ]o - - ++ [Ca ]i - - - - - - + + - - - - - T1 T2 T3 Note: Only includes relevant currents, i.e., for which G > 0 Cellular Electrophysiology Bioengineering 6000 CV Physiology Driving Force: Sodium At AP peak: - - - - + Chemical Veq = 70 mV [Na ]o - - Electrical Vm= 10 mV + - [Na ]i Net Vd= -60 mV - - - - - - Is there ever a time when the Net Gradient (driving force) = 0? 0 What stops the Na-current? mV -80 Cellular Electrophysiology Bioengineering 6000 CV Physiology Sodium Channel Behavior Depolarization Inactivation Repolarization (voltage) (time) (voltage, time) Recovery (voltage, time) Note: voltage and time dependence Cellular Electrophysiology Bioengineering 6000 CV Physiology Summary: Membrane Channel Voltage dependence Time, voltage, and ligand dependent Cellular Electrophysiology Bioengineering 6000 CV Physiology Cardiac Ion Currents Na+ Ca2+ 2K+ 3Na+ 3Na+ Ca2+ + Na-K Na-Ca Ca K pump exchanger pump Ion channels Carrier mediated ion transport • Passive ion movement • Na-K and Ca pumps require ATP • Driven by concentration and • Capable of driving against electrostatic gradients concentration gradient • Channels are selective • Na-Ca exchange does not require ATP • Gates control opening Cellular Electrophysiology Bioengineering 6000 CV Physiology Summary: Cardiac Action Potential • Resting potential depends almost entirely on [K+]. • Na channels require time at potentials more negative than -65 mV in order to recovery. Without it, they will remain inactive. • Slow (Ca++) channels have a threshold of -35 mV • The plateau represents balance between Ca++ and K+ currents. • Some cardiac cells depolarize spontaneously; most do not. Nature Cell Biology 6, 1039 - 1047 (2004) Thomas J. Jentsch, Christian A. Hübner & Jens C. Fuhrmann Cellular Electrophysiology Bioengineering 6000 CV Physiology Theory Simulation Experiment Measurement = Experiment Cellular Electrophysiology Bioengineering 6000 CV Physiology Measuring Membrane Potential 1x Vm Unity Gain High Impedance Amplifier -80mV Ground Cellular Electrophysiology Bioengineering 6000 CV Physiology Optical Methods Cellular Electrophysiology Bioengineering 6000 CV Physiology Whole Cell Currents (Voltage Clamp) For each ion type: Vc Vm Outward A activation 0 Iv Iv Inward inactivation Vc [mV] 10 -40 Cellular Electrophysiology Bioengineering 6000 CV Physiology Voltage Clamp in HH [Na]e Simulation of Cell EP Bioengineering 6000 CV Physiology Voltage Clamp Results • Note use of Na Channel blocker to isolate Na current • IV curve is nonlinear Vc Cellular Electrophysiology Bioengineering 6000 CV Physiology Single Channel (Unitary) Currents Channel current (pA) 0 pA closed open 2 channels open Time Membrane voltage (mV) -10 mV -80 mV Cellular Electrophysiology Bioengineering 6000 CV Physiology Membrane Patch Clamp Cellular Electrophysiology Bioengineering 6000 CV Physiology Single Channel Examples Current/ Voltage Two different characteristic channels Current as function of voltage Cellular Electrophysiology Bioengineering 6000 CV Physiology Theory Simulation Experiment Simulations Cellular Electrophysiology Bioengineering 6000 CV Physiology Membrane Equivalent Circuit Channel Lipid Bilayer Charged Polar Head Rm Cm + − Em Cellular Electrophysiology Bioengineering 6000 CV Physiology Hodgkin-Huxley Formalism • Qualitative concepts • Quantitative formulation and simulation (see next lecture) • Sir Alan Hodgkin – 1914-1988 • Sir Andrew Huxley – 1917-2012 – brother of Aldous Huxley • Nobel Prize: 1963 Cellular Electrophysiology Bioengineering 6000 CV Physiology Single Channel Model Active γ α At Rest Recovering β α, β, γ: state transition probabilities, (functions of v and t) Cellular Electrophysiology Bioengineering 6000 CV Physiology HH Derivation and Homework Assignment Cellular Electrophysiology Bioengineering 6000 CV Physiology Control of Heart Rate - Pacemaking Cellular Electrophysiology Bioengineering 6000 CV Physiology Pacemaker Cells in the Heart • Note difference in basic AP shape: why? • Note unstable (depolarizing baseline): why? Pacemaker and ECC Bioengineering 6000 CV Physiology Regulation of Heart Rate SA Epi, Node NE ACh Epi/NE; • increases If (β1- adrenergic ACh: receptor) • increases pK • reduces If (muscarinic receptor) Pacemaker and ECC Bioengineering 6000 CV Physiology.