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Cellular Electrophysiology

Part 1: Resting and Action Potentials

Cellular Electrophysiology Bioengineering 6000 CV

Cardiac Electrophysiology

Theory Simulation

Experiment

• The membrane: structure, channels and gates • The : , whole cell currents, cardiac cell types • The tissue: myocardial structure, propagation Scale • The : 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 ’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 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 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 = zF

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

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

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 () 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 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

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 – 1914-1988 • Sir – 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