ohms law explained

The plasma membrane separates two media of different ionic composition
K+ are the predominant cations in the
intracellular fluid
Na+ are the predominant cations in the
extracellular fluid.
The main anions of the intracellular fluid are
organic molecules (P-): negatively charged
amino acids (glutamate and aspartate),
proteins, nucleic acids, phosphates, etc…
In the extracellular fluid the predominant
anions are ClA marked difference between cytosolic and
extracellular Ca2+ concentrations is also
observed
The plasma membrane separates two media of different ionic composition
Intracellular and extracellular media are neutral ionic solutions: in each
medium, the concentration of positive ions is equal to that of negative ions.
Extracellular:
[Na+]e + [K+]e + 2[Ca2+]e = 140 +3 + (2 x 1.5) = 146 mM and [Cl-]e = 146 mM
Intracellular:
[Na+]i + [K+]i + 2[Ca2+]i = 7 + 140 + 0.0002 = 147 mM but [Cl-]i = 7 mM
In the intracellular compartment, other anions than chloride ions are present
and compensate for the positive charges (HCO3-, PO42-, aminoacids, proteins,
nucleic acids, etc …).
The unequal distribution of ions across the neuronal plasma
membrane is kept constant by active transport of ions
Concentration gradients for Na+, K+, Ca2+ and Cl- ions are constant in the
external and cytosolic compartments.
Two hypotheses can explain this constancy:
Na+, K+, Ca2+ and Cl- ions cannot cross the plasma membrane. In that
case, concentration gradients need to be established only once in the
lifetime.
Plasma membrane is permeable to Na+, K+, Ca2+ and Cl- ions but
there are mechanisms that continuously re-establish the gradients
and maintain constant the unequal distribution of ions.
The unequal distribution of ions across the neuronal plasma
membrane is kept constant by active transport of ions
When proteins are absent from a synthetic lipid bilayer, no movements of
ions occur.
The lipid bilayer is a barrier for the diffusion of ions and most polar
molecules.
When a axon is immerged in a bath containing a control concentration of
radioactive *Na+ (24Na+), *Na+ constantly appear in the cytoplasm.
This *Na+ influx is not affected by dinitrophenol (DNP), a blocker of ATP
synthesis in mitochondria. It does not require energy expenditure.
This is passive transport.
But what are the mechanisms that maintain concentration gradients across
neuronal membranes?
The unequal distribution of ions across the neuronal plasma
membrane is kept constant by active transport of ions
When the reverse experiment is conducted, the axon is passively loaded
with radioactive *Na+, and is transferred to a bath containing cold Na+.
Measuring the quantity of *Na+ that appears in the bath per unit of time
(d*Na+/dt, expressed in counts per minute) allows quantification of the efflux
of *Na+.
In the presence of dinitrophenol (DNP) this *Na+ efflux quickly diminishes to
nearly zero.
The process can be started up again by intracellular injection of ATP.
Therefore the *Na+ efflux is active transport.
Ionic composition of cytosol and
extracellular compartments are
maintained at the expense of a
continuous basal metabolism that
provides energy (ATP) utilized to
actively transport ions and thus to
compensate for their passive
movements.
(a) Effect of dinitrophenol on the outflux of *Na+ as a function of time
(b) Passive and active Na+ fluxes are in opposite directions
Ionic channels
Ionic channels have a 3D structure that delimits an aqueous pore through
which certain ions can pass.
Each channel may be regarded as an excitable molecule as it is
specifically responsive to a stimulus and can be in at least two
different states: closed and open.
Channel opening, the switch from the closed to the open state, is tightly
controlled by:
1. a change in the membrane potential – these are voltage-gated
channels;
2. the binding of an extracellular ligand, such as a neurotransmitter –
these are ligand-gated channels, also called receptor channels or
ionotropic receptors;
3. the binding of an intracellular ligand such as Ca2+ ions or a cyclic
nucleotide;
4. mechanical stimuli such as stretch – these are mechanoreceptors.
Membrane potential (Vm)
The cell interior shows a negative
potential (between –60 and –80 mV)
with respect to the outside, which is
taken as the zero reference potential.
Membrane potential (Vm) is by
convention the difference between
the potential of the internal and
external faces of the membrane (Vm
= Vi - Vo).
In the absence of ongoing electrical
activity, this negative potential is
termed the resting membrane
potential (Vrest)
Membrane potential (Vm)
Vm varies: it can be more negative or
hyperpolarized or less negative
(depolarized) or even positive (also
depolarized, the internal face is
positive compared to the external
face).
At rest, Vm is in the range -80/ -50
mV. But when neurons are active, Vm
varies between –90 mV and +30 mV.
Since nerve cells communicate
through rapid (ms) or slow (s)
changes in their membrane potential,
it is important to understand Vrest first.
The electrochemical gradient
To predict the direction of the passive diffusion of ions
through an open channel, both the concentration gradient of
the ion and the membrane potential have to be known.
The resultant of these
electrochemical gradient.
two
forces
is
called
the
To understand what the electrochemical gradient is for a
particular ion, the concentration gradient and the electrical
gradient will first be explained separately.
Ions passively diffuse down their concentration gradient
If Vm = 0 mV, ions will diffuse
according to their concentration
gradient only.
Na+, Ca2+ and Cl- will diffuse
passively towards the
intracellular medium (when Na+,
Ca2+ or Cl- permeable channels
are open) as a result of their
concentration gradient.
In contrast, K+ will move from the
intracellular medium to the
extracellular one (when K+
permeable channels are open).
Equation de Nernst : gradient de concentration
Sous l’influence du gradient de concentration, un cation passe du
compartiment A vers B produisant un excès de charges +
dans le compartiment B et un excès de charges – dans le
compartiment A
Le travail (W) nécessaire pour le déplacement d’un ion dépend
de la constante des gaz parfaits
R = 8,314 joules/mole/°K
de la température absolue
T° Kelvin = T° Celsius + 273
des concentrations dans chaque compartiment
[cation]A & [cation]B
W1 = R x T x Ln
[cation]B
[cation]A
Equation de Nernst : gradient électrique
Le transfert des cations de A vers B polarise la membrane
et crée un gradient électrique (ou électrostatique) de B vers A
qui tend à s’opposer au gradient de concentration
Le travail (W) électrostatique s’opposant à la diffusion de l’ion dépend :
de la valence de l’ion : Z
de la quantité d’électricité que représente un ion gramme
F = Faraday = 96500 coulombs
de la force électromotrice générée : E
W2 = z.F.E
Le flux ionique né d’un gradient de concentration est
auto-limité par le gradient électrique qu’il génère
Equation de Nernst : potentiel d’équilibre
Le flux ionique, né d’un gradient de concentration, est auto-limité par le gradient électrique qu’il génère
[cation]B
W1 = R.T.Ln
W2 = z.F.E
[cation]A
z.F.E =
[cation]Ext
R.T
Eion =
R.T.Ln
Ln
z.F
[cation]B
B = EXTERNE
A = INTERNE
[cation]A
Ln = 2,3 log10
ou
Eion = 2,3
[cation]Int
A 20°C : 2,3
R.T
z.F
[cation]Ext
R.T
log
z.F
[cation]Int
[cation]Ext
= 58,2
Eion = 58,2 x
log
[cation]Int
Equation de Nernst : gradient de diffusion
Le déplacement d’une molécule chargée (ion inorganique) entre deux compartiments C1 et C2 génère un
potentiel électrique E.
L’équilibre ou il n’y a pas de mouvement net de la molécule chargée est décrit par l’équation de Nernst
Equation de Nernst:
C1
C2
= e EZF/RT
E: différence de potentiel
Z: charge de l’ion
F: constante de Faraday
(96520 Coulombs)
T: température absolue
(273+C)
R: Constante des gaz
parfaits, égale à 8,314570
J.K-1.mol-1
La somme du gradient de concentration et du gradient électrique =
Gradient électrochimique ou de diffusion (driving force)
C’est la résultante des forces ou gradients qui déterminent le sens de
passage d’un ion à travers le membrane
Equation de Nernst : potentiel d’équilibre d’un ion
Equation de Nernst:
RT
E=
Ln
ZF
C1
Potentiel d’équilibre :
le flux passif net d’un ion à travers
la membrane est nul.
C2
A 20°C: RT/F = 25 mV; En base 10 avec Z = +1
RT/ZF= 58
Pour le K : EK = 58 log 3/140 = - 96mV
Pour le Na: ENa = 58 log 140/14 = + 58 mV
Pour le Cl:
ECl
= -58 log144/14 = - 58 mV
Pour le Ca: ECa = 29 Log 1/10-4 = + 116mV
The passive diffusion of ions through an open channel creates a current
– To know the direction of passive diffusion of a
particular ion and how many of these ions diffuse
per unit of time, the direction and intensity of the
net flux of ions (number of moles per second)
through an open channel have to be measured.
Usually the net flux (fnet) is not measured.
– The electrical counterpart of this net flux, the ionic
current, is measured instead.
The passive diffusion of ions through an open channel creates a current
• Passive diffusion of ions through an open channel is
a movement of charges through a resistance
(resistance here is a measure of the difficulty of ions
moving through the channel pore).
• Movement of charges through a resistance is a
current. Through a single channel the current is
called ‘single-channel current’ or ‘unitary current’, iion.
The relation between fnet and iion is: iion = fnet zF
Loi d’Ohm
• The amplitude of iion is expressed in ampères
(A) which are coulombs per seconds (C s–1).
F is the Faraday constant (96 500 C)
• z is the valence of the ion (+1 for Na+ and K+,
–1 for Cl–, +2 for Ca+); and fnet is the net flux
of the ion in mol s–1.
Loi d’Ohm
A current is expressed following Ohm’s law:
U = RI
I is the current through a resistance
R and U is the difference of potential between the two ends
of the resistance.
For currents carried by ions, I is called iion, the current that
passes through the resistance of the channel pore which has
a resistance R (called rion).
Loi d’Ohm
• But what is U in biological systems?
• U is the force that makes ions move in a
particular direction; it is the electrochemical
gradient for the considered ion and is also
called the driving force: U = Vm – Eion
Loi d’Ohm
Loi d’Ohm
According to Ohm’s law, the current iion through a single
channel is derived from: (Vm – Eion) = rion . iion
so: iion = (1/rion)( Vm - Eion) = gion (Vm - Eion)
Loi d’Ohm
gion is the reciprocal of resistance: it’s the conductance of the
channel.
It is a measure of the ease of flow of ions (flow of current)
through the channel pore.
Whereas resistance is expressed in ohms (Ω), conductance
is expressed in siemens (S).
Loi d’Ohm
iion is negative when it represents an inward flux of positive charges (cations)
iion is positive when it represents an outward flux of positive charges.
Passive diffusion of ions according to (a) their concentration gradient only, or (b) to membrane potential
(electrical gradient) only (Vm = –30 mV).
Loi d’Ohm
In fact, several channels of the same type are open at the same
time.
e.g.: the total current of Na+ channels INa that crosses the
membrane at time t is the sum of the unitary currents iNa at time t:
INa = Npo iNa
Npo is therefore the number of open Na+ channels in the membrane
at time t); and
iNa is the unitary Na+ current.
More generally:
Iion = Npo iion
Loi d’Ohm
By analogy, the total conductance of the membrane for a particular ion is:
Gion = Npo gion
and from iion = gion (Vm - Eion) :
Iion = Gion (Vm - Eion)
Iion and iion can be measured experimentally :
• iion is the current measured from a patch of membrane where only
one channel of a particular type is present.
• Iion is the current measured from a whole cell membrane where N
channels of the same type are present.
Roles of ionic currents
Ionic currents have two main functions:
• Ionic currents change the membrane potential:
– either they depolarize the membrane
– or repolarize it or hyperpolarize it, depending on the charge carrier.
• These terms are in reference to resting potential.
Roles of ionic currents
Roles of ionic currents
• Changes of membrane potential are signals.
– A depolarization can be an action potential or a postsynaptic excitatory
potential (EPSP).
– An hyperpolarization can be a postsynaptic inhibitory potential (IPSP).
Ionic currents increase the concentration of a
particular ion in the intracellular medium.
• Example of Ca2+ current :
– It is always inward. It transiently and locally increases the intracellular
concentration of Ca2+ ions and contributes to the triggering of Ca2+dependent events such as secretion or contraction.
A particular membrane potential, the resting membrane
potential Vrest
• In the absence of ongoing electrical activity (when the neuron is
not excited or inhibited by the activation of its afferents) its
membrane potential is termed the resting membrane potential
(Vrest).
• For some neurons, Vrest is stable (silent neurons) for others it is
not (pacemaker neurons for example).
The theory of Vrest : Julius Bernstein (1902)
1.
Vrest is due to selective permeability of the membrane to one ionic species only
and that nerve excitation developed when such selectivity was transiently lost.
2.
under resting conditions the cell membrane permeability is minimal to Na+, Cland Ca2+ while it is high to K+.
3.
K+ moves outwards following its concentration gradient ([K+]i is 50 times higher
than [K+]e): positive charges are thus subtracted from the intracellular medium
and there is an accumulation of negative charges at the intracellular side of
the membrane and positive charges at the external side of the membrane.
4.
These positive charges will oppose further outward movements of K+ until an
equilibrium is reached when the concentration gradient for K+ cancels the drive
exerted by the electrical gradient.
5.
This is by definition the equilibrium potential EK. Hence, at Vm = EK, although
K+ keeps moving in and out of the cell, there is no net change in its
concentration across the membrane.
Establishment of Vrest in a cell
where most of the
channels open are K+ channels.
Suppose that at t = 0 and cell
potential Vm = 0 mV (a),
K+ ions will move outwards due to
their concentration gradient (b).
Loss of intracellular K+ induces a
negative potential (Vm) as Vm = EK
(c).