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The Structure of the Cell

Membrane

Resting Membrane Potential

10.09.2013.

� Structure of the cell membrane.

� Resting membrane potential.

• The Nernst equation.

• Donnan potential.

• The Goldman-Hodgkin-Katz equation

Phospholipids

Polar – head(hydrophilic)

Non-polar – tail

(hydrophobic)

⇒⇒⇒⇒ „water soluble fat”

phosphatidil – cholin0

The main component of the biological membranes.

Phospholipid = diglyceride (glycerine+fatty acid) + phosphate group + organic molecule (e.g. choline).

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Irving LangmuirAmerican physico-chemist

1932 Nobel-price in chemistry

• 1917 – lipids form a monolayer on thesurface of the water� polar heads (hydrophilic) – oriented

toward the water� nonpolar tails (hydrophobic) – oriented

away from waterwater

Irving Langmuir, "The Constitution and Fundamental Properties of Solids and Liquids. II," Journal of the American Chemical Society 39 (1917): 1848-1906.

Lipid bilayer

1925 – Evert Gorter & F. Grendel (University of Leiden, Holland)

• Compared the measured surface area of the erythrocytes and the surface area

calculated from the lipid content of them.

• Gorter E, Grendel F. On Bimolecular Layers of Lipoids on the Chromocytes of the

Blood. J Exp Med. 1925 Mar 31;41(4):439-43.

Gortel, E. & Grendel, F. (1925) On bimolecular layers of lipoid on the chromocytes of the blood. J. Exp. Med. 41, 439–443.

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Lipid bilayer

• twice as much lipid in the membrane of the red blood cells than needed for a monolayer → lipid bilayer

IC

EC

Polar heads toward the intra- and extracellular

space

Apolar tails in the middle

Gortel, E. & Grendel, F. (1925) On bimolecular layers of lipoid on the chromocytes of the blood. J. Exp. Med. 41, 439–443.

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Gibbs free energy [Joule]

G = H - TSA spontaneous process is accompanied bya decrease in the Gibbs energy at constanttemperature and pressure.

At constant temperature and pressure thechange in the Gibbs energy is equal to themaximum non-expansion workaccompanying a process.

Hydrophobic interaction

• hydrophobic = water-repelling; low affinity (solubility) for water

• Walter Kauzmann (American chemist) - Nonpolar molecules in polar

environment (solvents) are trying to minimize their contact with water

• 1”cage” formation → 2clustering

• Factors affecting the strength of hydrophobic interaction

– Temperature (T ↑ ⇒ Strength ↑)

– Number of carbons in the hydrophobic molecule (Length ↑ ⇒ Strength ↑)

– Number of “non single” bonds (e.g. double, triple bonds…) in the hydrophobic molecule

(shape) ( # “non single” bonds ↑ ⇒ Strength ↓)

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Thermodynamic changes

hydrophobic

molecule

H2O

+ hydrophobic

molecule

H2O

→

H2O H2O

hydrophobic

molecule

hydrophobic

molecule

Clustering

(forming hydrophobic interactions)

∆H = small positive

∆S = large positive

∆∆∆∆G = negativeSPONTANEOUS PROCESS

Cage formation

(no interaction between hydrophobic molecules)

∆H = small positive

∆S = large negative

∆∆∆∆G = positiveNON SPONTANEOUS PROCESS

„Fluid mosaic” model

• phospho-lipid bilayer

• Fluid – lateral movement of the components („floating”)

• Mosaic – the mosaic-like arrangement of themacromolecules

http://www.molecularexpressions.com/cells/plasmamembrane/plasmamembrane.html

• 1972 - Singer and Nicholson „fluid mosaic” model

Singer SJ, Nicolson GL. The fluid mosaic model of the structure of cell membranes. Science. 1972 Feb 18;175(23):720-31.

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Structure of the cell membrane

rotation

Polar

(hydrophilic) head

Non-polar

(hydrophobic) tail

Lateral diffusion

Flip-flop~ 5 nm

Protein molecule (~30-50%)

Phospholipide molecule (~40-60%)

Functions of the membrane poteins

• Ion channels (Na+/K+ ATPase; K+ channel…)

• Transporters (Aquaporin-H2O transport)

• Structural elements

• Intracellular connections (anchoring – cytoskeleton)

• Extracellular connection (gap junction: cell to cellcontact between cardiac cell)

• Signal transduction (action potential)

• Receptors (insulin receptor)

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The main components of the intra- and extracellular space

• water

• Ions

– Kations (K+, Na+, Ca2+)

– Anions (Cl-, H2PO4− and HPO4

2− ions)

• proteins

– Mainly intracellular localisation

– Negatively charged polyvalent (having more than one

valence) macromolecules (pH! – isoelectric point)

Membrane potential

The electrical potential difference (voltage)

across a cell's plasma membrane.

Extracellular space

Intracellular space

0V

Microelectrode

-100 mV > Uresting < -30 mV

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Ionic concentrations inside and outside of a muscle cell

Na+ : 120 mMK+ : 2.5 mM

Cl- : 120 mM

Na+ : 20 mM

K+ : 139 mM

Cl- : 3.8 mM

Forces controlling the movements of charged particles

Chemical potential energy:

� The chemical potential of a thermodynamic system is the amount of energy

(Joule) by which the system would change if an additional particle were

introduced (~ number of the particles!).

� Concentration gradient → diffusion: moving the particles through the

permeable membrane from a high concentration area to a low

concentration area → diffusion potential.

Energy: Capacity for doing work.

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Electric potential energy

• the result of conservative Coulomb forces

• associated with the configuration of a particular

set of point charges within a defined system

• work required by an electric field to move

electric charges (Joule).

• Electrical gradients: The sum of the “+” and “-”

are not the same at the different points in space.

• An electric field creates a force that can move

the charged particles (the work of the electric

field) → moving charged particles = electric

current.

K+ : 100 mM

Cl- : 100 mM

K+ : 5 mM

Cl- : 5 mM

Force controlling the movements of ions through the cell membrane

Electro-chemical potential

= the combination (sum) of the chemical and the electric

potential energy.

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Julius Bernstein (1839 - 1917) - German physiologist

1./ The cell membrane is selectively permeable to potassium• Ca2+ sensitive potassium channels• Inwardly rectifying potassium channels• Voltage-gated potassium channels• “Tandem pore domain potassium channel” – “leak channel” (K2p)

1952: Hodgkin and Huxley suggested the leakage of current etchum, KA; Joiner, WJ; Sellers, AJ; Kaczmarek, LK; Goldstein, SA. (1995) A

new family of outwardly rectifying potassium channel proteins with two poredomains in tandem. Nature, 376 (6542): 690-5.

2./ The intracellular potassium cc. is high

3./ The extracellular potassium cc. is low

Bernstein’s potassium

hypothesis (1902)

Bernstein,J.(1902).Untersuchungen zur Thermodynamik der bioelektrischen Strome. Pflugers Arch.ges. Physiol. 92, 521–562.

Bernstein’s potassium hypothesis

K+ : 100 mM

Cl- : 100 mM

K+ : 5 mM

Cl- : 5 mM

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Bernstein’s potassium hypothesis

K+ gradient (chemical potential)

electric gradient

(electrical potential)

The side with

high

concentration of

positive ions

becomes the

negative side !!!!

[K+] [K+]

[Cl-] [Cl-]

- +

How is it possible to quantify the Bernstein’s hypothesis ?

(calculating the electrical potencial (value, number)

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Walther Hermann NernstGerman physical chemist

(June 25, 1864 – November 18, 1941)

Calculating the electrical potential at which

there is no longer a net flux (movement) of a

specific ion across a membrane.

N = number of moles associated with the concentration gradient

R = gas constant

T = absolute temperature

X1 / X2 = concentration gradient

N = number of moles of the charged particles

z = valency (number of + or – charges (e.g. K+ : monovalent))

F = Faraday’s number

E = strength of the electric field = electric potential or electrostatic potential

= The work needed to move a unit electric charge from one point to another

against an electric field (Joule/Coulomb = Volt).

Electric potential energy ⇒ Welectr=NZFE

Chemical potential energy ⇒ Wchem=NRTln��

��

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Equlibrium (resting) condition

2

1ln

X

XNRTNzFE =

2

1ln

X

XRTzFE =

2

1lnX

X

zF

RTE =

Electrical potential energy Chemical potential energy

Equlibrium potential

Nernst equation: What membrane potential

(E) can compensate (balance) the

concentration gradient (X1/X2).

2

1lnX

X

zF

RTE =

The inward and outward flows of the ions are balanced

(net current = zero → equilibrium = stable, balanced, or unchanging

system).

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Nernst equation

( )( )out

inmV

C

C

zE log

58−=

2

1ln

X

X

zF

RTE =

Ionic concentrations inside and outside of a muscle cell

[K+] ⇒ EmV = -58/1 log (139/2.5) = - 101.2 mV

[Na+] ⇒ EmV = -58/1 log (20/120) = + 45.1 mV

[Cl-] ⇒ EmV = -58/1 log (3.8/120) = + 86.9 mV

Na+ : 120 mMK+ : 2.5 mM

Cl- : 120 mM

Na+ : 20 mM

K+ : 139 mM

Cl- : 3.8 mM

EmV=-92mV= 30.8 mV

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What happens if the cell

membrane is permeable to

more than one type of ion?

Frederick George Donnan

Donnan equilibrium: characterising the equlibrium

situation when the membrane is not permeable for

some ionic components.

- non-moving charged component (e.g. intracellular

proteins) → equlibrium concentration difference

- more than one diffusible ion (K+, Cl-)

(1870-1956; Irish chemist)

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Donan equlibrium - at start

[K+]

[Pr -] [Cl-]

[K+]

K+=x K+=x

Pr-=x Cl-=x

Cl- concentration gradient

K+ concentration gradient

Cl- electrical gradient

K+ electrical gradient

A B

A B

Donan equlibrium - at equlibrium

[K+]

[Pr -] [Cl-]

[K+]

K+=x+y K+=x-y

Cl-=y Cl-=x-y

Pr-=x

A (-) B (+)

[Cl-]

A B

- +

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Donnan rule of equilibrium

• Diffusible ions: K+, Cl-

• In equlibrium the elektro-chemical potentials are equal.

[ ][ ]

[ ][ ]

in

out

out

in

Cl

Cl

zF

RTE

K

K

zF

RTlnln ==

[ ][ ]

[ ][ ]

in

out

out

in

Cl

Cl

K

K=

[ ][ ] [ ][ ]outoutinin

ClKClK =

The Donnan rule is valid only when the ions are passively distributed.!

The Gibbs–Donnan equilibrium is a phenomenon that contributes to the formation of

an electrical potential across a cell membrane.

What happens if the Donnan rule is not obeyed?

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Goldman-Hodgkin-Katz Constant

field equation (Goldman equation)

To determine the potential across a cell's membrane taking intoaccount all of the ions with different permeabilities through themembrane.

David E. Goldman (USA)

Alan Lloyd Hodgkin (England)

Bernard Katz (England).

The Goldman equation for M positive ionic species and A negative:

•Em = The membrane potential•Pion = the permeability for that ion•[ion]out = the extracellular concentration of that ion•[ion]in = the intracellular concentration of that ion•R = The ideal gas constant•T = The temperature in kelvins•F = Faraday's constant

Goldman equation

A "Nernst-like" equation with terms for each permeant ion.- All the ions are involved.- Good agreement with the measured values (muscle cell: Umeasured=-92mV_Ucalc.=-89.2mV).

[ ] [ ]

[ ] [ ]

+

+=

∑∑

∑∑−+

−+

−+

−+

M

j outjA

N

i iniM

M

j injA

N

i outiM

m

APMP

APMP

F

RTE

ji

ji

ln

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The membrane potential is the result of a„compromise” between the various equlibriumpotentials, each weighted by the membranepermeability and absolute concentration of theions.

Goldman equation

The end!