Bioelectric phenomena

2013/2014, lecturer: Martin Zápotocký

4 lectures:

1. Electric quantities and their measurement,

components of electric circuits

2. Electrode potential, Nernst equation, galvanic and

electrolytic cell

3. Electric phenomena at the cell membrane, ion channels,

Donnan equilibrium, resting membrane potential

4. Action potential, effects of electric current on the organism

Warning: figures and equations

drawn on the blackboard are not

included in these slides

Electric charge

• Electric phenomena are due to the interaction and motion of electric

charges

• The net electric charge Q of a physical body is given by the total

contained number of electrons 𝑁𝑒 and number of protons 𝑁𝑝:

𝑄 = 𝑁𝑒 −𝑒 + 𝑁𝑝𝑒

where 𝑒 = 1.6 × 10−19𝐶 is the elementary quantum of electric charge

• Example: calcium ion Ca2+ has net charge 18 −𝑒 + 20𝑒 = +2𝑒

• Unit of electric charge: 1 Coulomb (C)

• Total charge of one mole of univalent cations: the Faraday constant

𝐹 = 𝑒𝑁𝐴 = 96.5 𝑘𝐶/𝑚𝑜𝑙

• The net electric charge of an isolated body is conserved

Electrostatic force, electric field

• Coulomb law: the electrostatic force between charges q and Q

separated by distance r has magnitude

𝐹 =1

4𝜋𝜖

𝑞𝑄

𝑟2

and points in the direction connecting the charges

(repulsive for like charges, attractive for opposite charges)

• The permittivity constant 𝜖 is characteristic of the given material

(medium); it is lowest in the vacuum, 𝜖0 = 8.85 × 10−12C V−1m−1

• Two charges of +1 C, one meter apart, will repel each other with force

of 9 × 109 N! Macroscopic objects are nearly neutral.

• The interaction is mediated by the electric field. The charge Q creates

the electric field intensity 𝐸 = 𝐹 /𝑞. The electric field lines of a

positive point charge point radially outwards.

Electric dipole, polarization, dielectric screening

• Inside a molecule with net zero electric charge, positive and negative

charges can spatially separate, giving the molecule a dipole moment

• A dipole placed in an external electric field will rotate to align with the

field lines (parallel to intensity 𝐸 )

• A material composed of molecular dipoles will get polarized and

reduce (screen) the effect of the external electric field

• The force between two charges placed inside a dielectric material is

reduced compared to their interaction in vacuum: 𝐹 =1

4𝜋𝜖

𝑞𝑄

𝑟2, 𝜖 > 𝜖0

• Relative permittivity 𝜖/𝜖0 for some materials:

air: 1.0006, glass: 5-10, lipid membrane: 8, water: 78.5

Solvation, hydration

• Polar solvents (water, ethanol, ammonia,…) efficiently

solvate ions

• The dielectric screening helps to dissociate ionic bonds

(e.g. Na+Cl- dissolved in water)

• Hydration number: the number of molecules of water

with which an ion forms a complex. Effective radius of

ion: the size of ion together with its hydration shell.

Smaller ions can fit more water molecules. Cations

polarize water stronger than anions.

Ion

Ionic

Radius

(Å)

Approx.

hydrated

radius

Approx.

hydration

number

Li+ 0.90 3.40 25

Na+ 1.16 2.76 17

K+ 1.52 2.32 11

Electric potential

• Electric potential U at a given location 𝑟 : defined as the amount of

work needed to bring a unit electric charge from the reference location

(with zero potential) to the given location

• In the field of a point charge Q located at 𝑟 = 0 :

𝑈 𝑟 =𝑄

4𝜋𝜖𝑟

In this case U=0 at 𝑟 = ∞.

• Note that 𝑊 = 𝑞𝑈 is the potential energy of charge q in the electric

field of charge Q

• Unit of electric potential: 1 Volt (V); note V=J/C

• Equipotential lines for the field of a point charge: concentric circles

• Only the potential difference (voltage) is measurable

• In a reactive medium, the notion of electrochemical potential is

necessary (next lecture)

Electric current, Ohm’s law

• A positive electric charge which is mobile will move in the direction of

the electric field, i.e. to locations with lower electric potential.

• Conductors: materials in which (some) electric charges are mobile.

Examples: metals, ionic solutions. Note: dielectrics are insulators;

water is a conductor as it contains a fraction of OH- and H+

• Electric current through a conductor: defined as amount of charge

passing per unit time. Units: 1 Ampere (A) = C/sec.

• Ohm’s law: relates the magnitude I of (direct) electric current passing

through a conductor with the applied electric potential difference U

𝑈 = 𝑅𝐼 where R is the resistance of the conductor; units: 1 Ohm (Ω) = V/A

Resistivity, molar conductivity

• Resistance of conductor of length L and cross-section A:

𝑅 = 𝜌 𝐿𝐴

where ρ is the resistivity of the material (units: Ω m)

• Typical resistivity for metal conductors: 10-8 Ω m, for insulators: wood

1010 Ω m, teflon 1014 Ω m. Resistivity depends on temperature.

• For ionic solutions, the specific conductivity is defined as

𝜅 =1

𝜌

units: Ω-1 m-1 = S m-1 , S=Siemens=Ω-1

• Molar conductivity: Λ = 𝜅/𝑐 , where c is the molar ionic concentration.

Typical values: 10-3 S m2 mol-2

• In dilute solutions, molar conductivities add:

Λ = Λ𝑖 (Law of independent migration of ions)

Direct / alternating current, effective value

• Direct current (DC): electrons move only in one direction. Example:

constant current.

• Alternating current (AC): direction of motion alternates. Example:

periodic harmonic current,

𝐼 = 𝐼0 sin𝜔𝑡 where 𝐼0 is the amplitude of the current, 𝜔 = 2𝜋𝑓 is the angular frequency

• In a (linear) electric circuit, both current and voltage are harmonic with

identical frequency (but can be mutually phase-shifted)

• Effective value of current (or voltage): 𝐼eff =𝐼0

2

Meaning: energy dissipated in resistor through which a DC current of

magnitude 𝐼eff flows = energy dissipated in resistor through which an

AC current of amplitude 𝐼0 flows

Components of electric circuits, impedance

• Electric circuits are combinations of the 3 ideal components: resistors,

capacitors, inductors. Circuit is driven by a voltage source, e.g. a

battery (device using chemical energy to separate positive and negative

charges – see next lecture).

• In general, applying an alternating voltage 𝑈0sin𝜔𝑡 results in an

alternating current with same frequency 𝜔 and with amplitude 𝐼0,

related to 𝑈0 by electric impedance Z

𝑈0 = 𝑍 𝐼0

Capacitor

• A capacitor consists of two conductors separated

by an insulator (dielectric).

• The capacitor stores separated electric charges. The

capacitance C relates the potential difference U

across capacitor and stored charge Q:

𝑄 = 𝐶𝑈

• Units: 1 Farad (F) = Coulomb / Volt

• For capacitor made of two plates of area A

separated by distance d, dielectric of permittivity ε:

𝐶 =𝜖𝑆

𝑑

• When alternating voltage 𝑈0sin𝜔𝑡 is applied,

current with amplitude 𝐼0 = 𝜔𝐶𝐼0 will flow

• Impedance 𝑍 =1

𝜔𝐶= capacitive reactance

Inductor

• An inductor opposes changes in electric current, stores magnetic

energy. Typically made as a coil of wire.

• The inductance L relates the potential difference U across inductor and

the rate of change 𝐼 =𝑑𝐼

𝑑𝑡 of current I flowing through inductor:

𝑈 = 𝐿𝐼 • Units: 1 Henry (H) = V A-1

• When alternating voltage 𝑈0sin𝜔𝑡 is applied, current with amplitude

𝐼0 = 𝑈0/𝜔𝐿 will flow

• Impedance 𝑍 = 𝜔𝐿 = inductive reactance

Connection in series and in parallel

• Two components of a circuit can be connected in series or in parallel.

• Components in series have common current:

• Components in parallel have common voltage:

Impedance of biological tissue

• In general, materials have resistance,

capacitance and inductance, can be viewed as

RCL circuit in series

• Total impedance of the circuit is

𝑍 = 𝑅2 + 𝜔𝐿 −1

𝜔𝐶

2

• For biological tissues, inductance is usually

negligible. For skin at freq< 1 kHz, 𝑅 ≪1

𝜔C , so

𝑍 = 𝑅2 +1

𝜔𝐶

2

≃1

𝜔𝐶

(only high-frequency currents will pass easily)

Measurement of electric quantities

• Analog voltmeter, ammeter: based on electric or magnetic force

deflecting a needle. Ideal voltmeter has very high internal resistance,

ideal ammeter very low resistance.

• Measuring range can be increased by:

– Adding resistor (shunt) in series to voltmeter

– Adding resistor (shunt) in parallel to ammeter

• Ohmmeter: resistance from Ohm’s law

• Conductometry : measure specific conductance of electrolyte solution,

use to determine the ionic concentration: 𝑐 = 𝜅/Λ

• Measuring the specific conductance κ: place electrolyte in vessel with

two platinum electrodes. Measure the total resistance R. “Capacity” C

of the vessel (depends on volume, geometry) relates κ and R:

𝜅 =𝐶

𝑅

• Determining C: first, measure R for standard solution with known κ

The oscilloscope

• Used to visualize the time course

of electric quantities

• Most common type: based on the

cathod ray tube (electron gun)

• Electrons emitted by heated wire

filament (cathode), accelerated

through anode (high voltage),

collimated into narrow beam

• Beam passes through horizontal

pair of plates (deflection in

vertical direction, signal) and

vertical pair of plates (deflection

in horizontal direction, time basis)

• Used e.g. in heart and breathing

activity monitors

Electrode potential

• Consider a metal electrode in contact with

its electrolyte. For each type of electrode,

the redox equilibrium is established at the

electrode / electrolyte boundary: 𝑀𝑔2+(𝑎𝑞) + 2𝑒− ⇌ 𝑀𝑔(𝑠)

C𝑢2+(𝑎𝑞) + 2𝑒− ⇌ 𝐶𝑢(𝑠)

• Electric double layer on electrode surface

• Mg more reactive than Cu, so a higher

electrode potential develops at the Mg

electrode boundary. How to measure it?

• Must compare to reference electrode:

2𝐻+(𝑎𝑞) + 2𝑒− ⇌ 𝐻2(𝑔)

and measure the difference of the

unknown electrode potential and

reference electrode potential ≡ standard electrode potential,

assuming unit concentration of solvent

Measuring the standard electrode potential

• To measure the standard electrode potential

(for Mg), connect with the standard electrode

in a cell configuration, which will close the

circuit (two half cells make a full cell)

• Electrons flow through wire connecting

electrodes (and voltmeter)

• Ions flow through the salt bridge (glass tube

filled with another, non-reactive electrolyte)

• The electrochemical series is ranked by 𝐸0.

Metals higher in the series loose electrons

more readily.

metal / metal ion E°

(volts)

Mg2+ / Mg -2.37

Zn2+ / Zn -0.76

Cu2+ / Cu +0.34

Ag+ / Ag +0.80

Reminder: chemical potential, activity

• Consider a system composed of substances i = 1,2,3,..., with number of

moles 𝑛1, 𝑛2, 𝑛3, … Chemical potentials 𝜇𝑖 give the change in energy

of the system if composition is slightly altered.

• At given p,T, 𝑛1, 𝑛2, 𝑛3, … : change in free enthalpy is

Δ𝐺 = 𝜇1Δ𝑛1 + 𝜇2Δ𝑛2 +⋯

where Δ𝑛1, Δ𝑛2, ... are the changes in number of moles

• The dependence of chemical potential on state variables is expressed

through the dimensionless activity a. By definition:

𝜇 = 𝜇𝑜 + 𝑅 𝑇 ln a

where 𝜇𝑜 is the chemical potential in a reference state

• For ideal gas, 𝜇 𝑝, 𝑇 = 𝜇𝑜(𝑇) + 𝑘𝐵𝑇 ln𝑝

𝑝0, therefore 𝑎 = 𝑝/𝑝0

• For ideal (dilute) solution, 𝑎 = 𝑐/𝑐0, where c is the concentration of

solute

Electrochemical potential

• Consider the boundary of two phases (e.g. solid electrode / electrolyte

solution). We define the following potentials:

• External (Volt) potential: work needed to bring unit charge from ∞ to 10-8 m

within the phase boundary. (This is the usual electrostatic potential)

• Internal (Galvani) potential Φ: the external potential + work needed to bring

unit charge across the boundary surface

• Electrochemical potential (of specific component): work required to

transport 1 mole of molecules into the given phase

𝜇𝑖 = 𝜇𝑖0 + 𝑅𝑇 𝑙n𝑎𝑖 + 𝑧𝐹𝜙

where F=Faraday’s constant, z = net number of elementary charges on

each molecule

Nernst equation for the electrode potential

• At redox equilibrium, the electrochemical potentials for the metal in

the electrode and in the electrolyte must be equal. Otherwise, one

would gain energy by transporting matter to lower 𝜇𝑖

• The Nernst equation gives the electrode potential corresponding to

redox equilibrium:

𝐸 = 𝐸0 −𝑅𝑇

𝑛𝐹ln𝐾

where T = absolute temperature (in Kelvins), n = number of

electrons transferred in the redox reaction, K = equilibrium

constant of redox reaction. R = 8.3 JK−1 mol−1 , F=96.5 kC/mol.

• Example: for hydrogen electrode reaction 2𝐻+ 𝑎𝑞 + 2𝑒− ⇌ 𝐻2 𝑔 ,𝐾 = 𝑎𝐻+

2/𝑎𝐻2, so

𝐸 = 𝐸0 −𝑅𝑇

2𝐹𝑙n

𝐻+ 2

𝑝𝐻2= −

𝑅𝑇

𝐹𝑙n[𝐻+]

𝑝𝐻2

Electrochemical cell as current source

• Any cell made of two half-cells with

different 𝐸 can act as steady source of

current (active circuit component)

• Electromotive force (EMF) ℰ : the voltage

measured with a very weak current,

ℰ = difference of electrode potentials =

difference of Galvani potentials

• Example: Daniell cell, Zn and Cu,

ℰ = 1.1 V (for standard concentrations, at

room temperature)

• When current is allowed to flow:

– measured voltage decreases

– redox equilibrium is disturbed,

eventually zinc anode is dissolved

while the copper electrode is plated

with copper

• Can increase electromotive force by

connecting cells in series

The Daniell cell

Galvanic cell vs. electrolytic cell

• Galvanic cell: converts chemical energy

into electrical energy. Spontaneous redox

reaction separates + and – charges, creates

potential difference (electromotive voltage

/ force).

• Electrolytic cell: requires an external

source of electrical energy, which is

converted into chemical energy

(electrolytic reaction).

• Rechargeable battery (e.g. lead-acid battery

in cars, Pb / H2SO4): works alternatively as

Galvanic cell and electrolytic cell.

Cathode (reduction): Na+ + e- → Na

Anode (oxidation): 2 Cl- → Cl2 + 2 e-

Electrolysis of NaCl

Electric phenomena in biological cells

• Every living cell maintains an electric potential difference across its

plasma membrane. Usually, inside is negative compared to outside, by

40 to 90 mV.

• The cell membrane acts as capacitor and as highly variable resistor

• A living cell functions as a battery, i.e. uses chemical energy (ATP) to

recharge the membrane capacitor

• Signaling (information transmission) in the neural system is based on

electric excitations traveling along the membrane

• Muscle activity, heart rhythm also controlled by electric excitations

The plasma membrane is a selectively permeable

interface of distinct ionic environments

• Lipid bilayer gives capacitance 10 nF/mm2

• Charge neutrality in bulk, + and – charge on

membrane. It is enough to move 1/105 of total

K+ ions to set up V=-60 mV.

• Resistance: highly variable, depends on

number and state of ion channels. Typical

value 1 MΩ/mm2

• Ion concentrations for typical neuron:

Outside

[mol/m3]

Inside

[mol/m3]

Na+ 150 15

K+ 5.5 150

Cl- 125 9

Ion channels

• Conformational transitions between open state and closed state.

Control of transition rates: ligand-gated vs. voltage-gated channels.

• Most ion channels are selective mainly for one type of ion.

• A single channel behaves like a resistor, but with modified Ohm’s law:

𝐼channel = 𝑔(𝑉 − 𝐸)

g is the single-channel conductance, 𝑔 = 0 or 𝑔 = 𝑔open ≃ 10 pS

V = transmembrane voltage, E = reversal potential

• Conductance for given ion type: 𝐺 = 𝑛 𝑝open 𝑔open

n = No. of channels / unit area, 𝑝open= open probability

Nernst equation for reversal potential

• For the given ion type, no net flow through channel when the two sides

are in electrochemical equilibrium, 𝜇𝑖𝑛 = 𝜇𝑜𝑢𝑡: 𝜇0 + 𝑅𝑇 𝑙n 𝑐𝑖𝑛 + 𝑧𝐹𝜙𝑖𝑛 = 𝜇0 + 𝑅𝑇 𝑙n 𝑐𝑜𝑢𝑡 + 𝑧𝐹𝜙𝑜𝑢𝑡

• Nernst – Donnan potential:

𝐸 = 𝜙𝑖𝑛 − 𝜙𝑜𝑢𝑡 =𝑅𝑇

𝑧𝐹𝑙n𝑐𝑜𝑢𝑡𝑐𝑖𝑛

• When 𝑉 = 𝐸, gradient of concentration is balanced by electrical

potential gradient. Net electrochemical driving force is zero.

• Note: 𝑅𝑇

𝐹= 27 mV. Typical values:

𝐸𝐾 = −80𝑚𝑉, 𝐸𝑁𝑎 = +50 𝑚𝑉, 𝐸𝐶𝑙 = −60𝑚𝑉

Donnan equilibrium

• Can we achieve equilibrium with two ion types?

• Consider K+ and Cl-: reversal potentials identical if

(Donnan equilibrium rule)

𝐾+𝑖𝑛 𝐶𝑙

−𝑖𝑛 = 𝐾+

𝑜𝑢𝑡 𝐶𝑙−

𝑜𝑢𝑡

• Will the in and out concentrations equilibrate? No,

due to impermeant anions (proteins) inside the cell

(the Donnan effect):

𝐾+𝑖𝑛 > 𝐾+

𝑜𝑢𝑡

𝐶𝑙− 𝑖𝑛 < 𝐶𝑙−

𝑜𝑢𝑡

• Neurons do not satisfy the Donan equilibrium rule!

Exchangers and pumps (ATPases) maintain system

out of equilibrium.

Example of Donnan equilibrium

• Consider these concentrations of K+, Cl-, A- [μM]:

• The Donnan equilibrium condition is satisfied:

80 × 20 = 40 × 40

• The reversal potentials are:

𝐸𝐾 =𝑅𝑇

𝐹𝑙n

40

80= −17mV, 𝐸𝐶𝑙=

𝑅𝑇

(−1)𝐹𝑙n

40

20= −17mV

• If transmembrane voltage is 𝑉 = −17mV, no K+ current and

no Cl- current flows through the open channels.

Deviation from Donnan equilibrium

• Donnan equilibrium rule for K+, Cl- is well

satisfied in some muscles.

• Donnan equilibrium is broken in neurons.

Resting potential is in between the distinct

reversal potentials.

• This is the result of Donnan equilibrium,

+ influence of other ions (Na+, Ca2+)

+ action of pumps and echangers (ATP used,

deviation from thermodynamic equilibrium).

• In general, the “resting” membrane is

maintained in a non-equilibrium steady state.

Concentrations have to be maintained by

pumps and exchangers.

• Na-K pump: 3 Na+ out, 2 K+ in (to the side

with higher concentration) – chemical energy

is used to restore the concentration gradient

Resting potential, hyperpolarization, depolarization

• By convention, the potential outside the cell is 0.

• The living cell can indefinitely maintain a “resting state”, with the

cell interior at the resting potential, usually -40 mV to -90 mV

• Perturbations (channel gating or injection of current by electrode)

lead to hyperpolarization or depolarization

• Current injection (of positive ions) leads to depolarization, i.e. less

negative potential inside the cell

• Outflux of positive ions or influx of negative ions leads to

hyperpolarization, i.e. more negative potential (below the resting

potential).

Resting membrane potential

• When K, Na, Cl ions have different reversal potentials, their

thermodynamic equilibria cannot be achieved simultaneously.

• At the resting membrane potential, currents will flow across channels,

but total current = 0. The Hodgkin-Horowitz equation expresses the

net balance of currents:

0 = 𝐺𝐾 𝐸rest − 𝐸𝐾 + 𝐺𝑁𝑎 𝐸rest − 𝐸𝑁𝑎 + 𝐺𝐶𝑙(𝐸rest − 𝐸𝐶𝑙)

therefore

𝐸𝑟𝑒𝑠𝑡 =𝐺𝐾𝐸𝐾 + 𝐺𝑁𝑎𝐸𝑁𝑎 + 𝐺𝐶𝑙𝐸𝐶𝑙

𝐺𝐾 + 𝐺𝑁𝑎 + 𝐺𝐶𝑙

• Goldman equation for rest membrane potential (reduces to Nernst eq.

if only one ion type present) :

𝐸𝑟𝑒𝑠𝑡 =𝑅𝑇

𝐹𝑙n𝑃𝐾 𝐾+

out + 𝑃𝑁𝑎 𝑁𝑎+

out + 𝑃𝐶𝐿 𝐶𝑙+

out

𝑃𝐾 𝐾+𝑖𝑛 + 𝑃𝑁𝑎 𝑁𝑎

+𝑖𝑛 + 𝑃𝐶𝐿 𝐶𝑙

+𝑖𝑛

P = permeability = ion diffusion const. across membrane

divided by membrane thickness

The neuron

• Morphologically and functionally

distinct parts: dendritic tree, soma, axon

• Dendrite receives input from sensory

stimulus or other neurons

• Soma: integration of input, generation

of action potential (at axon hillock)

• Axon: conducts action potentials.

Myelinated vs. non-myelinated. Up to

1 m in length.

• Membrane in dendrite, soma, axon

differs by distinct types of ion channels

Neuron

• Hlavní části neuronu:

– tělo (integrace)

– dendrity (vstup)

– axon (výstup, až 1m)

• Komunikace mezi neurony: skrz kontaktní body, synapse

Electric activity in pyramidal neuron of brain cortex

Action potentials

Passive spread of depolarization

• Used for signal transmission in the dendrites and within myelinated axon

segments. Depolarization decays exponentially with distance from point of

steady current injection:

𝑉(𝑑) = 𝑉0𝑒−𝑑/𝜆

where the electrotonic length λ = 0.1 to 5 mm (smaller in narrow neurites).

• Equivalent circuit:

The action potential (“neural spike”)

• Short propagating pulse, generated when

depolarization exceeds a threshold

• The pulse is always the same (“all or

nothing”), does not depend on details of

stimulus (if big enough)

• Basis for all neural communication,

coding by spike frequency

• Only in excitable membranes

• Mechanism explained by A. L. Hodgkin

and A. Huxley (1952), Nobel Prize 1963.

Electrode through giant axon of the squid

(1 mm diameter). Mathematical model.

Properties of ion channels predicted,

confirmed only in 1970.

Mechanism of excitability

• In the resting state, for squid axon:

𝑉 = 𝐸𝑟𝑒𝑠𝑡 = −60𝑚𝑉, 𝐸𝐾= −75𝑚𝑉, 𝐸𝐶𝑙 = −40𝑚𝑉, 𝐸𝑁𝑎 = +55𝑚𝑉

• In the resting state, G(K) >> G(Na)

• Voltage-gated ion channels:

conductivity G depends on V

• Depolarization stage:

if 𝑉 > 𝑉𝑡ℎ𝑟𝑒𝑠ℎ = −45𝑚𝑉,

Na channels open (gated by voltage)

→ further depolarization

→ further opening → ... (positive

feedback loop)

• After a few msec: inactivation of Na

channels, delayed activation of K

channels. Leads to repolarization.

• Refractory period: time before next

action potential can be initiated

(several msec). Determines maximum

spike frequency (several hundred Hz).

Hodgkin-Huxley model of action potential

• Matematical model (1952), predicting the existence of voltage-gated

ion channels. The predicted properties of these channels were verified

by experiments in 1970.

• The gating variables m, h, n correspond to structural units of the

ion channel proteins.

• In 1950s, numerical solution of the model took 1 week of computer

time. It took 10 years before the model was generally accepted.

• The model is (just for illustration, not on exam):

n h

Propagation of action potential

• Spatial shape of the action potential:

width of 1-2 mm

• Travels on the axon with v = 1m/sec

to 100 m/sec, faster in bigger axons

• Mechanism: enough voltage spreads

passively from center of spike to

neighboring region to exceed

threshold there

• Refractory period ensures that spike

keeps traveling in one direction

(usually away from soma, starting at

axon hillock). Backpropagation of

spikes also possible.

Myelinated vs. non-myelinated axons

• Long axons are usually myelinated

• Myelin sheath increases transmembrane

resistance and reduces capacitance →

better passive conduction along axon

• It is enough to generate action potential

only at the gaps, Nodes of Ranvier,

separated by ~ 1mm. This is saltatory

conduction.

• More efficient transmission of spikes:

smaller diameter without loss of velocity,

smaller energetical requirements

Electric control of muscle activity

• Neuromuscular junction: motor neuron

terminates on muscle fiber

• Separate action potentials on motor neuron and

muscle. In the muscle, the action potential

leads to release of Ca2+ from intracellular

stores, activation of motor proteins (myosin).

• For skeletal muscles, tension is controlled by

a) frequency of action potentials sent from

motor neuron to each fiber, b) recruitment of

additional fibers.

• For cardiac muscle, the action potential lasts

~200 msec. Extended plateau, which is due to

long-lasting opened Ca2+ channels. Pacemaker

cells spontaneously generate action potentials.

Cardiac action potentials

Action potential in ventricular myocyte

Antiarrhythmic agents

Effect of electric current on the organism

• DC current: electrolytic effects, result in change in tissue excitability.

• Stimulatory effect following a change in DC current, such as the pulse

stimulus. Rheobase: minimum amplitude of pulse which will

eventually result in an excitation (action potential, muscle twitch).

Chronaxie: pulse duration needed to induce excitation when pulse

amplitude = 2 rheobase. Typically msec. Rheobase depends strongly

on location of stimulation.

• AC current at intermediate frequency (10-500 Hz): strong stimulatory

effect. Above 100 Hz, stimulatory threshold increases as f 2, i.e. effect

is weaker. Current densities used in electrotherapy: 1-10 mA/cm2.

Review Lab No. 4b!

• AC current at high frequency: weak stimulatory effect up to 100 kHz,

strong thermal effect. Can be used to generate heat deep in tissue.