1. Molecular Medicine Program
Ιατρικη Σχολη Πανεπιστημιου Κρητης
Diomedes E. Logothetis
Electrochemical Forces and Ion Transport
Ion Channels: Voltage clamp, Basic Properties
November 13, 2007
Lecture goals:
This lecture will discuss transport through uniporters, the chemical and electrical forces determining the
direction and magnitude of ion movement through ion channels, the patch-clamp technique and the
molecular basis of the two fundamental properties of ion channel protein, selectivity and gating. The
“Learning Objectives” below define the topics and what students should know regarding each topic.
Learning Objectives
1. Know the classes of all membrane transport proteins and distinguish them according to rates of
transport.
2. Know methods of studying the transport process (e.g. the transporter reconstitution into
liposomes).
3. Describe Glucose transport through GLUT1 transporters as an example of a uniport-catalyzed
transport system. Know the mechanism thought to account for transport through uniporters.
4. Understand how distribution of unbalanced charges at the membrane boundary accounts for
membrane potentials.
5. Know the distribution (low vs. high) of the four major ions in most mammalian cells.
6. Know the thermodynamic derivation of the Nernst Equation and be comfortable explaining it
qualitatively.
7. Given a membrane potential be able to determine the flow of ions (for a particular distribution in
and out of the cell) considering the relative magnitude and direction of the chemical and
electrical forces.
8. Be able to use Ohm’s law to determine the currents flowing through the cell membrane.
9. Given a membrane potential be able to determine the flow of ions (for a particular distribution in
and out of the cell) considering Ohm’s Law.
10. Know the different types of Ion Channels and the major features they possess.
11. Understand how the balance of currents determines the membrane potential.
12. Know the voltage clamp and all modes of the patch clamp techniques.
13. Predict how ion flux through a particular ion channel will influence the membrane potential.
14. Understand how K ion selectivity, permeation and gating occurs.
Reading
See Lecture Notes and
Chapter 1 from Hille, 3rd
edition “Ion Channels of Excitable Membranes” pp. 1-22.
Chapter 15 from Lodish et al., 4th
edition “Molecular Cell Biology” pp. 578-585.
1

2. Transport Across Cell Membranes I
Diffusion of small molecules across phospholipid bilayers
A pure artificial phospholipid bilayer is permeable to gases (e.g O2 and CO2), small hydrophobic
molecules and small uncharged polar molecules. It is only slightly permeable to water and urea and
impermeable to ions and to large uncharged polar molecules. The movement of molecules across the
lipid bilayer can take place via a number of mechanisms that we will cover in the remaining lectures on
membrane transport. Ions and large polar molecules cross the lipid bilayer aided by transport proteins.
Molecules that cross the lipid bilayer without the help of transport proteins cross by passive diffusion,
from a high to a low concentration of the molecule, down their chemical concentration gradient. Their
relative diffusion rate is proportional to their concentration gradient across the bilayer and their
hydrophobicity. The hydrophobicity of a substance is measured by how easily the substance will
partition from the watery environment of the extracellular or intracellular compartments to the oily
environment of the lipid bilayer. Substances that cross the lipid bilayer have been assigned a partition
coefficient “K”, a number that provides a measure of the relative affinity of the substance for lipid versus
water: the higher the partition coefficient for a substance, the more lipid-soluble it is. The partition
coefficient is the major determining factor of another measure of transport across the membrane, the
permeability coefficient “P”, which takes into account the thickness of the membrane (2.5 to 3nM) and
the diffusion coefficient “D” a measure of diffusion that is rather similar for most substances. Thus,
P = KD/x eqn. 1
The rate of diffusion of small molecules through the membrane is given by the empirical relationship
known as Fick’s law, which states that the diffusion rate across the membrane is directly proportional to
P, to the difference in solution concentrations on either side of the membrane and to the membrane
area “A” where transport is taking place. Thus, for a substance “n” its diffusion rate in mol/sec is given
by:
dn/dt = PA (Cintracell. – Cextracell.) eqn. 2
Membrane Transport Proteins
Most molecules cross biological membranes with the aid of transport proteins. Even the
transport of water, which even when unaided crosses poorly membranes, can be dramatically
accelerated by transport proteins called water channels or aquaporins (we’ll discuss in more detail in a
later lecture). Three major classes of membrane transport proteins facilitate the transport of most
substances across the lipid bilayer: a) Transporters, b) Ion Channels and c) ATP-powered pumps.
The three classes of transporters are mainly differentiated on the ground of their relative rate of
transport and the utilization of chemical or electrical energy to carry out the transport function. Ion
Channels are the most efficient transport proteins (107
-108
ions/s) whose active state is very tightly
controlled and are thus used by nature to carry out much of the electrical signaling required for the
rapid communication between cells (e.g. neurons , cardiac and endocrine cells). They are followed by
transporters that transport at intermediate rates (102
-104
molecules/s) and whose active state may be
less tightly controlled and are used to aid in the movement of ions in different body compartments (such
as through the various parts of the kidney to regulate water and ion filtration). Transporters are
themselves divided into three types: i) uniporters (transport of a single molecule in a given direction), ii)
symporters (transport of two or more molecules in the same direction) and iii) antiporters (transport of
two or more molecules in opposite directions). The slowest transport proteins are the ATP-powered
2

3. pumps (100
-103
ions/s). As the name implies these transport proteins utilize the energy from splitting
ATP in order to perform their transport function and they need to do so because they transport ions
against their concentration gradient. Symporters and antiporters also utilize energy to transport one of
the ions against its concentration gradient but in contrast to the ATP-powered pumps, this energy does
not come directly from the hydrolysis of ATP but rather from the concentration gradient of one of the
transported ions which is transported down its concentration gradient. The remaining two forms of
transport proteins allow ion movement down a gradient (chemical for uniporters and electrochemical for
ion channels).
For charged molecules (e.g. ions) where there is a net amount of charge being transported, the
movement of charge as a function of time gives rise to an electrical current that can be monitored
experimentally to assess the function of the protein in transporting the charged substance. For non-
charged molecules, one needs to way to identify the transported molecules and measure them reliably.
A sensitive assay is to monitor the movement of non-charged molecules is to radiolabel them and
collect fluid where the radiolabeled substance is being transported to at different time points and
measure the radioactivity of the samples. To study the functional properties of different kinds of
membrane transport proteins, one needs experimental systems in which the particular transport protein
to be studied predominates. Two common ways to study transport proteins are the following: a) The
specific transport protein is extracted and purified; the purified protein then is reincorporated into pure
phospholipid bilayer membranes such as liposomes, where its function can be assayed. b) The gene
encoding a specific transport protein can be expressed at high levels in a cell that normally does not
express it or expresses it at very low levels; the difference in transport of the substance transported by
the expressed protein from the control cells allows assessment of the function of the protein of interest.
Uniporter-catalyzed transport
Uniporters catalyze the simplest type of transport, small molecules moving down their
concentration gradient. The type of molecules that utilize this form of transport are not only ions but
also amino acids, nucleosides, sugars, and others. One can think of transporters as enzymes that
catalyze the transport of molecules. One important distinction, however, is that unlike the substrates of
enzymatic reactions, transported substances do not undergo a chemical change during the reaction,
i.e. the process of moving across the membrane. Uniporter-catalyzed transport is sometimes referred
to as facilitated diffusion. This sort of diffusion should be distinguished from passive diffusion on the
following three grounds. a) The rate of facilitated transport by uniporters is far higher than predicted by
Fick’s equation which describes passive diffusion. Since the transported molecules travel through the
core of the protein and never enter the hydrophobic core of the phospholipid bilayer, the partition
coefficient K is irrelevant. b) Facilitated diffusion is specific through uniporters that transport only a
single species of molecules or a single group of closely related molecules. The specificity of transport
is in sharp contrast to passive diffusion, where any small hydrophobic molecule will be transported
through the membrane. c) Facilitated diffusion takes place via a limited number of uniporter molecules,
rather than throughout the phospholipid bilayer. Consequently, there is a maximum transport rate Vmax
that is achieved when the concentration gradient across the membrane is very large and each uniporter
is working at its maximal rate. The transport rate of a substance through a uniporter, shows Michaelis-
Menten kinetics, similar to those seen by a simple enzyme-catalyzed chemical reaction. Thus, there is
a characteristic Km for each transporter, that is the substrate concentration at which half-maximal
transport occurs across the membrane. The lower the value of Km the more tightly the substrate binds
to the transporter and the greater the transport rate.
A representative member of the sugar uniporters is GLUT1, a plasma membrane protein that
catalyzes the movement of glucose into cells such as erythrocytes. Glucose carried in the blood serves
3

4. as a major source of cellular energy for virtually all mammalian cells, including red blood cells (RBCs).
Blood glucose is 5 mM, or 0.9 g/L. For GLUT1 in the RBCs, the Km for glucose transport is 1.5 mM,
meaning that at this concentration half the transporters would have a bound glucose. At the blood
4
Figure 1. Comparison of the observed uptake rate of glucose by erythrocytes (red curve) with the
calculated rate, if glucose were to enter solely by passive diffusion through the phospholipid bilayer (blue
curve).
The rate of glucose uptake (measured as micromoles per milliliter of cells per hour) in the first few seconds
is plotted against the glucose concentration in the extracellular medium. In this experiment the initial
concentration of glucose in the erythrocyte is zero, so that the concentration gradient of glucose across the
membrane is the same as the external concentration. The glucose transporter in the erythrocyte membrane
clearly increases the rate of glucose transport, compared with that associated with passive diffusion, at all
glucose concentrations. Like enzymes, the transporter catalyzed uptake of glucose exhibits a maximum
transport rate Vmax and is said to be saturable. The Km is the concentration at which the rate of glucose
uptake is half-maximal.

5. 5
Figure 2. Model of the mechanism of uniport transport by GLUT1, which is believed to shuttle between two
conformational states. In one conformation (1), (2) and (5), the glucose-binding site faces outward; in the other (3),
(4), the binding site faces inward. Binding of glucose to the outward-facing binding site (1) to (2) triggers a
conformational change in the transporter (2) to (3), moving the bound glucose through the protein such that it is now
bound to the inward-facing binding site. Glucose can be released to the inside of the cell (3) to (4). Finally, the
transporter undergoes the reverse conformational change (4) to (5), inactivating the inward-facing glucose binding
site and regenerating the outward-facing one. If the concentration of glucose is higher inside the cell than outside,
the cycle will work in reverse (4) to (1), catalyzing net movement of glucose from inside to out.

6. glucose concentration GLUT1 in RBCs is functioning at 77% of the maximal rate Vmax. The isomeric
sugars D-mannose and D-galactose, which differ from D-glucose at only one carbon atom, are also
transported by GLUT1 at measurable rates but with Km values of 20 mM (D-mannose) and 30 mM (D-
galactose). The Km for the nonbiological isomer of glucose (L-glucose) is >3000 mM. Thus, GLUT1 is
quite specific for D-glucose than other substrates. After glucose is transported into the erythrocyte, it is
rapidly phosphorylated, forming glucose 6-phosphate, which cannot leave the cell. Because this
reaction is the first step in the metabolism of glucose, the intracellular concentration of free glucose
does not increase as glucose is taken up by the cell. Consequently, the glucose concentration gradient
across the membrane is maintained, as is the rate of glucose entry into the cell.
GLUT1 is an integral, transmembrane protein with a molecular weight of 45,000. It accounts for 2
percent of the protein in the plasma membrane of erythrocytes. Insertion of purified GLUT1 into
artificial liposomes dramatically increases their permeability to D-glucose. This artificial system exhibits
all the properties of glucose entry into erythrocytes: in particular, D-glucose, D-mannose, and D-
galactose are taken up, but L-glucose is not.
Amino acid sequence and biophysical studies on the glucose transporter indicate that it contains 12 α
helices that span the phospholipid bilayer. Although the amino acid residues in the transmembrane α
helices are predominantly hydrophobic, several helices bear amino acid residues (e.g., serine,
threonine, asparagines, and glutamine) whose side chains can form hydrogen bonds with the hydroxyl
groups on glucose. These residues are thought to form the inward-facing and outward-facing glucose-
binding sites in the interior of the protein.
The current model of the mechanism of uniport transport by GLUT1 is believed to involve shuttling
between two conformational states. Binding of glucose to the outward-facing binding site of GLUT1
triggers a conformational change in the transporter moving the bound glucose through the protein, such
that it is now bound to the inward-facing binding site. Glucose can then be released to the inside of the
cell. Finally, the transporter undergoes the reverse conformational change, in activating the inward-
facing glucose binding site and regenerating the outward-facing one. If the concentration of glucose is
higher inside the cell than outside, the cycle will work in reverse, catalyzing net movement of glucose
from inside to out.
Electrical signaling
Ion movement across the plasma membrane through ion channel proteins serves distinct
signaling roles such as changes in internal Ca2+
concentration or changes in the membrane potential,
thus allowing rapid communication of the cell with its external environment. Although electrical signals
are mainly thought to be the language of the nervous system, they are also generated in almost all cells
in response to a variety of stimuli. Thus, the stereotypic electrical signals called spikes or action
potentials serve as important signals in many non-neuronal types of cells: for example, eggs generate
an action potential when they meet the first sperm, macrophages respond with a kind of action potential
to certain factors in complement as part of their chemotactic reaction and secretory cells in many
glands --- pancreas, pituitary, adrenal medulla for example -- undergo action potentials when the
contents of their secretory granules are to be released.
Membrane Potential and Cell Capacitance
Sodium (Na+
), potassium (K+
), calcium (Ca2+
) and chloride (Cl-
) ions are unequally distributed on
either side of the plasma membrane (see next sections for specific ion distribution in a muscle cell).
Yet, electroneutrality is achieved in the bulk intracellular and extracellular solutions as positively and
negatively charged molecules screen the charge of each other. Suppose that we have some way of
6

7. taking individual positive ions (cations) out of the cytoplasm of a cell and placing them outside (we will
see later ways in which this can be done). As we move more and more cations out of the cell it
becomes more difficult (takes more work) to move each additional ion because the partners of the
cations, the negatively charged ions (anions) that are left behind, attract additional cations from leaving.
Moreover, we are building an excess of cations outside that repel more cations from coming out. The
amount of work to transport one ion with valence z out of the cell is:
Work = -ze0V eqn. 3
Where e0 is the elementary charge. This equation is the fundamental definition of the membrane
potential V. It is equal to the work that it takes to move a charge of valence z across the membrane.
Meanwhile, we just argued that the work increases the more ions we transport across the membrane.
The relationship between the work and the total charge that has been transported turns out to be a
simple proportionality, such that:
V = Q / C eqn. 4
where we say that Q is the net unbalanced charge left inside the cell, and C is a quantity called the
capacitance. From your physics courses you have learned that capacitance is simply the capability of
an insulator to separate electric charge. The capacitance of the cell membrane resides specifically in
the lipid bilayer, which insulates the extra- from the intracellular aqueous phase with its hydrophobic
core. Clearly, if a cell has a large capacitance, you can move a lot of charge before V changes very
much. The physical properties of a membrane, which determine its capacitance, are the dielectric
constant e, the membrane area A and the membrane thickness d.
C = εA/4πd eqn. 5
Let's remember from eqn. 5, that the membrane capacitance is proportional to the membrane
area (see below for the reason) and inversely proportional to the membrane thickness (the larger the
distance between the plates of the capacitor the weaker the attractive forces that keep the charges on
each side). As we shall see in later lectures, this has great significance for the understanding of the
pathophysiology of demyelinating diseases such as multiple sclerosis.
Below we see a diagram (Fig. 3) of what our negatively-charged cell is like: in both the interior and in
the exterior solution almost all the ions have balancing counter ions.
7

8. Figure 3
There are two things to notice about this picture. First, the unbalanced charges are at the membrane
boundary. That is because unbalanced charges repel each other; if two of them were somewhere in
the middle of the cell or out in the extracellular solution, they would repel each other and start to move
apart. Thus charges always congregate at boundaries, such as at the membrane, where they cannot
move any further. This is why the capacitance depends on the membrane area: if the area is larger,
the unbalanced charges are farther apart and there is less repulsion; that is, V is smaller.
The second thing to notice is that the ions that are next to the membrane are not necessarily the
same ones that we moved in the first place. Ions are always in motion, so they are often exchanging
places. Also, if you were to introduce an extra ion into the center of the cell, it would start repelling its
neighbors, causing them to move; they would repel their neighbors and so on, until the net effect occurs
that one unbalanced charge winds up at the membrane surface. This process (which is just the
conduction of electricity in an ionic solution) is much faster than diffusion. That is, it would take much
longer for the original ion to diffuse over to the membrane than it takes for its electrical influence to be
felt. This is the fundamental reason why electrical signaling is the fastest signaling process in cells.
To calculate the fraction of uncompensated ions on each side of the membrane required to
produce a specific membrane potential difference in a cell of a given geometry, consider the space-
charge neutrality principle. According to this principle, in a given volume, the total charge of cations is
approximately equal to the total charge of anions. The membrane capacitance of a typical cell is 1
µF/cm2
, which means that 10-6
uncompensated coulombs of charge on each side of the 1 cm2
membrane are needed to produce 1 V across the membrane.
The Nernst equation and the resting potential
In the previous section we created a negative membrane potential (fig. 3) by removing some
cations out of the cytoplasm and placing them outside the cell, thus creating a charge imbalance.
Indeed, when an experimenter records the potential difference across the membrane (potential
difference between two microelectrodes, one inserted into a resting cell while the other outside the cell
in the bath), (s)he records a constant ("resting") membrane potential difference of -80 to -90 mV
(defined as Vin-Vout). What is the basis for this resting potential?
8
Figure 3. The net excess
of positive charges
outside and negative
charges inside the
membrane of a cell at
rest represents a small
fraction of the total
number of ions inside and
outside the cell (the ratio
of the width of the region
of charge separation to
cell diameter is
exaggerated here for
purposes of illustration).

9. Imagine that we could have a pathway that selectively allows for positive ions, that is lets cations go
through but is impermeable to anions. As it turns out the negative resting potential of most cells, such
as a muscle cell is caused by the fact that the resting membrane is almost exclusively permeable to
potassium ions (i.e. specific proteins that allow potassium ions to leave the cell at rest). The membrane
potential develops because K ions, which are 30 times more concentrated inside the cell, have a
tendency to leave the cell (through specialized potassium permeable proteins). The resulting charge
separation (less positive charge inside) sets up the negative membrane potential.
The exact relation between concentration difference and membrane potential is given by the
Nernst equation, which we will now derive.
Let us start by remembering the extracellular and intracellular distribution of the main ions, in a
muscle cell, for example:
extracellular intracellular
Na+ 145 mM 15 mM
K+ 5 mM 145 mM
Cl- 125 mM 10 mM
Ca2+ 2 mM 0.0001 mM (!!)
We have already mentioned that ions cross membranes through specialized proteins that
provide a hydrophilic pathway. We will now consider WHY the ions move. Ion movement through
specialized proteins is energetically passive, that is, ions move towards a lower level of free energy.
The free energy of an ion is the sum of two components: Chemical and electrical.
The chemical energy varies with ion concentration and temperature and has the form:
Chemical energy =µo + RT ln [X]
Here µo is the standard free energy of a 1 molar solution, R is the universal gas constant, T the
absolute temperature and [X] the concentration of ion X. The chemical energy represents the fact that
random thermal motion tends to drive particles from regions where they are concentrated to regions
where they are dilute. For our muscle cell, this means that for instance for K- ions there exists a
chemical driving force for K-efflux from the cell. The magnitude of this chemical energy gradient is
simply the difference between the two free energies inside and outside of the membrane:
Chemical energy gradient = µo + RT ln [X]i - (µo + RT ln [X]o)
= RT ln ([X]i/[X]o)
The electrical energy is proportional to the potential and has the form:
Electrical energy = zFV (per mole of ion)
V is the potential, F the Faraday constant (96,500 coulombs/mole) and z the valence (+1 for
potassium). An ion will want to move towards a potential of opposite sign to its charge, thus a cation will
be attracted by a region of negative potential. The electrical driving force is the difference between the
electrical energies inside and outside:
Electrical energy gradient = zFVin - zFVout
9

10. = zF (Vin-Vout)
The sum of the chemical and electrical energy gradients is called the electrochemical gradient.
The transmembrane electrochemical gradient is the real driving force for ion movement through
specialized proteins. This driving force vanishes when the sum of the chemical and electrical gradient
equals zero. This condition is called the equilibrium condition, because there is no net transmembrane
flux anymore. At equilibrium, the concentration gradient is exactly counterbalanced by an electrical
gradient of opposite sign.
RT ln ([K]i/[K]o) + zF (Vin-Vout) = 0
Rearranging yields the familiar Nernst equation:
VX = Vin-Vout = (RT/zF) ln ([X]o/[X]i) (eqn. 6)
= (RT/zF) ln (10) log ([X]o/[X]i)
VX is called the Nernst potential for ion X. It is the potential that a membrane selective for ion X
would stabilize at. Other equivalent names for the Nernst potential are: equilibrium or reversal
potential. To distinguish the Nernst potential of a particular ion from the membrane potential or the
resting potential we will designate it with the letter “E”. With the physiological extra- and intracellular
concentrations listed above, we can now calculate the Nernst potentials for the major ions. This will tell
us, at what value of the transmembrane potential the net driving force for a particular ion would vanish.
At 37oC, the expression RT/F ln (10)= 61 mV.
ENa = 61 log (145/15) = 60 mV
EK = 61 log (5/145) =-89 mV
ECl =-61 log (125/10) =-67 mV
ECa =30.5 log (2/.0001) =131 mV
Thus, the measured value of the membrane resting potential in our muscle cell (-80 to -90 mV) is very
close to the Nernst potential for K- ions. It is as if the cell membrane is K-selective. This is confirmed by
the fact that changes in extracellular K lead to predictable changes in the membrane potential, while
changes in the other ions have little effect on the resting potential. The resting muscle membrane
behaves like a K-selective membrane because specific K-permeable proteins are the only pathway for
ions to move under resting conditions. It is worth noting that at the resting potential there exists a large
inwardly directed electrochemical driving force for both Na and Ca ions. It can therefore be anticipated,
that if Na and/or Ca pathways were to be permeable abruptly, this would lead to a large inward current
which would make the inside of the cell more positive than before this change in permeability. We will
see in a later lecture that this is precisely the mechanism that leads to the generation of an action
potential.
Ohm's law is central
Electrical phenomena arise whenever charges (denoted as Q, measured in Coulombs) of opposite
sign are separated or can move independently. Any net flow of charges (or a change of charge with
time, dQ/dt) is called a current (I), measured in Amperes. For our discussion of cellular excitability we
10

11. will mainly study the mechanisms determining current flow across the plasma membrane of a cell. The
magnitude of a current flowing between two points (for instance from extracellular to intracellular) is
determined by the potential difference (or "voltage", or "voltage difference") between the two points
(denoted as V, in Volts) and the resistance to current flow, R, measured in Ohms.
I=V/R OHM'S LAW (eqn. 7a)
(For those who are uncomfortable with electricity: try the hydraulic equivalent F=P/R. Here the potential
difference corresponds to the pressure difference P and the current corresponds to the flow F).
When Ohm's law is applied to biological cell membranes, it is often advantageous to replace the
electrical resistance by its reciprocal, the conductance g, measured in reciprocal Ohms, or Siemens.
I=gV OHM's LAW (eqn. 7b)
For simplicity, we will assume that all resistive elements in the cell membrane behave in an "ohmic
way", i.e. that their current voltage relationship (abbreviated as I-V) is described by eqn. 7b: the I-V
relation is linear with a slope given by the conductance g. This is shown graphically by the solid line in
Fig. 4a, which represents the transmembrane current (I) measured at different transmembrane
potentials (V) in a hypothetical cell. Fig. 4b shows the experimental arrangement, the so called
“voltage-clamp technique”, which enables us to construct I-V relationships and to study the
conductance characteristics of the cell membrane. Using this technique, we have inserted two
microelectrodes into our cell (glass microelectrodes have tip diameters of 0.1-0.5 microns and can be
inserted into many cells without apparent damage to the membrane). One is connected to a voltmeter
to measure the transmembrane potential. The second microelectrode is hooked up to a tunable current
source (battery of variable output), which allows us to inject current into the cell. These electrodes are
then connected to a feedback circuit that compares the measured voltage across the membrane with
the voltage desired by the experimenter. If these two values differ, then current is injected into the cell
to compensate for this difference. This continuous feedback cycle, in which the voltage is measured
and current is injected, effectively “clamps” the membrane at a particular voltage. If specialized
proteins that can offer a hydrophilic path to ions (called ion channels, see below) were to open (allowing
ions to flow through them), then the resultant flow of ions into or out of the cell would be
11

12. Figure 4a Figure 4b
compensated for by the injection of positive or negative current into the cell through the current-
injection electrode. The current injected through this electrode is necessarily equal to the current
flowing through. It is the injected current that is measured by the experimenter. mThe convention used
in Fig.4a is that the voltage is expressed as the difference between the intracellular and the
extracellular potential (V=Vin-Vout). At negative values of V the cell is said to be hyperpolarized,
whereas at positive membrane potentials it is said to be depolarized. Positive charge moving from
inside to outside is called outward current and is represented as an upward (positive) current, while
inward current is shown as a negative current deflection.
12
Figure 4. Measuring the resistive properties of the plasma membrane to the flow of specific ions. (a) A current-voltage
relationship showing ohmic (linear) characteristics. Conventions are also shown, i.e. negative current means negative
inside with respect to the outside, outward current means positive ions (e.g. K) moving from the inside to the outside. (b) A
voltage clamp experiment using two electrodes. One measures voltage (inside with respect to the outside) and compares
it to the voltage that the experimenter desires to hold (or clamp) the cell membrane at. To adjust the voltage to the desired
level the experimenter injects through the second electrode (the current electrode) either positive or negative current. The
current injected in order to keep the membrane voltage from changing is precisely matching the amount of current entering
or leaving the cell through conducting pathways (at the desired membrane potential).

13. Ion channels carry transmembrane current
How does current actually flow through the cell membrane via the channel protein? The answer to
this question is not obvious, since we know that cell membranes are composed of a lipid bilayer with a
very highly hydrophobic center, which is practically totally impermeable to charged particles like ions.
Thus, in electrical terms, a lipid bilayer presents an almost infinite resistance to ionic current flow. For
this reason, over the last ~50 years the presence of specialized membrane structures called ion
channels was postulated. Today we know that ion channels are large transmembrane protein
molecules embedded in the lipid bilayer. Each channel forms a relatively hydrophilic central pore, which
allows ions to cross from one side of the membrane to the other. Many different channel proteins exist
and we will discuss some of them in detail. The two most important functional properties of ion
channels are (1) the fact that the channels fluctuate between open (conducting) and closed (non-
conducting) states. This property is called channel gating and its importance will become obvious when
we will consider the factors that control it, and (2) their ability to distinguish between different ions
(channel selectivity). The nomenclature of ion channels is based upon these two most important
functional properties. Thus, they are classified into distinct categories according to the stimuli that
cause them to open. Ion channels
Fig. 5a Fig. 5b
that open in response to changes in voltage across the membrane are called voltage-gated (see Fig 5a
and 1b), those that open in response to binding of a ligand are called ligand-gated, those that open in
response to mechanical stress are called mechanically gated or mechanosensitive channels (see Fig
5b). A class of potassium channels that are thought to be active at resting membrane potentials and as
such to be major contributors to the negative resting potentials of cells are starting to be recognized as
PIP2--gated (as they seem to be opened by interactions with the membrane phospholipid
13
Figure 5. Schematic representation of the various types of Ion Channels. (a) Depiction of a voltage
gated channel showing three key features. A voltage sensor that somehow is coupled to the
movement of a gate that opens the channel so that ions can flow down the electrochemical gradient.
Ions are selected (e.g. K versus Na) through the selectivity filter. (b) Four classes of ion channels:
voltage gated, intra- or extracellular ligand gated and mechanically gated channels.

14. phosphatidylinositol-bis-phosphate). Within these categories ion channels that are selective for K+
ions
are called potassium channels, for Ca2+
ions, calcium channels and so on. Thus, we have distinct K+
channels that are voltage-gated, ligand-gated, or mechanosensitive. Always keep in mind, that for
each channel type there are several to many forms (e.g. the count is over 100 for K+
channels)
The benefit of the voltage-clamp technique can be appreciated for voltage-gated currents in
particular. These ionic currents are both voltage and time dependent; they become active at certain
membrane potentials and do so at a particular rate. Keeping the voltage constant in the voltage clamp
allows these two variables to be separated; the voltage dependence and the kinetics of the ionic
currents flowing through the plasma membrane can be directly measured.
The balance of currents determines the potential
The current-voltage relation we drew in Fig. 6 does not apply to a real cell since as we said there is a
negative resting potential (i.e. at equilibrium where the net current is zero, the membrane potential is
negative). Figure 6 draws the correct relation for a K-selective channel. It will now intersect the current
axis at VK. Ohm's law still describes the I-V relation, but we have to introduce the voltage offset, and
eqn. 4b becomes:
IK = gK (V-EK) (eqn. 1)
V-EK is of course just the electrochemical driving force at any potential V. If K-channels are the only
channels open, then as stated above, the membrane potential will be EK. However, if the cell
membrane also has some other measurable conductance, then V will deviate from EK. Let us assume
for instance, that the cell also has a measurable Na-conductance, with gNa:gK = 1:5.
INa= gNa (V-ENa)
INa will be zero at ENa and have a slope of 1/5 that of IK (see Fig. 6). The resting potential VR in this
case will settle at a value between ENa and EK where net K efflux is exactly balanced by net Na influx.
This point can easily be determined graphically from Fig. 6.
Figure 6.
Since INa=-IK
gNa (VR-ENa) = - gK (VR-EK)
14
Figure 6. Two linear (for the
sake of simplicity) resting
conductances are shown. One
conducts K ions while the other
Na (gNa : gK = 1:5). The dashed
line shows the sum of the two
conductances or the “net”
conductance. Resting membrane
potential can be appreciated
graphically as the potential where
inward and outward currents are
equal or they add up to zero. VK
and VNa are the same as EK and
ENa.

15. rearranging VR = (ENa gNa)/(gK+gNa)+(EK gK)/(gK+gNa) (eqn. 2)
So VR can have any value between ENa and EK. The actual value of VR
becomes a weighted average of the two Nernst potentials for Na and K, where the weight is given by
the relative conductances. In our example with the above values for ENa, EK and gNa:gK, VR = -64
mV.
As expected, if gNa>>gK then VR=ENa
and, if gK >>gNa then VR=EK
V will however only stay constant as long as the ionic gradients do not change. If there was no
independently operating, active transport system which maintains the ionic gradients (we will discuss
this in the last lecture) these gradients would indeed run down, since at VR there is a constant K-efflux
and Na-influx.
The patch clamp technique
The patch clamp technique (see Fig. 7), a variant of the voltage clamp technique described earlier, has
revolutionized the study of ion channels. Erwin Neher and Bert Sakmann who are primarily responsible
for this technique, received the Nobel Prize in 1991. This technique allows one to record current flow
not only from hundreds to thousands of channels present in the plasma membrane but also ionic
currents from a single channel protein. With this technique, a fire-polished glass micropipette with a tip
diameter of around 1 µm is pressed against the plasma membrane of a cell. Application of a small
amount of suction to the pipette greatly tightens the seal between the pipette and the membrane. The
result is a seal with extremely high resistance between the inside and outside of the pipette. Thus ion
flow through open ion channels offers much less resistance than through the pipette-membrane seal.
Figure 7
15
Figure 7. All modes of the patch clamp technique
start with a clean pipette pressed against an intact
cell to form a gigaohm seal (the resistance to ion
flow between and the membrane is in the order of
gigaohms). Currents can be recorded in this “on-
cell” or “cell-attached” mode as minute currents
passing between the pipette solution and the
cytoplasm. Additional suction can break the
isolated patch without affecting the gigaohm seal,
giving access to the cell cytoplasm and measuring
currents from the “whole-cell” membrane (minus the
small ripped patch). Pulling the patch pipette away
from the cell can rip a small patch of membrane
giving rise to the “outside-out” patch where the
experimenter has easy access to the solution on the
external side of the patch. Finally, an alternative
configuration is the “inside-out” mode of recording,
where the pipette is pulled away from the “on-cell”
mode, exposing the inner surface of the membrane
to the bath, where the experimenter can easily
manipulate the internal solutions.

16. This dramatically improves the signal to noise ratio and extends the utility of the technique to the whole
range of channels involved in electrical excitability, including those with small conductance. The patch
clamp technique is highly versatile, as one can record channel activity in different arrangements. The
"cell-attached" recording records microscopic (from just one or a few ion channel) currents, while the
intracellular environment of the cell is intact. Pulling away from the cell, a small patch of the membrane
can be ripped away (inside-out or outside-out patch) allowing recording of single-channel currents
under absolute control of the intracellular solution that can now be easily changed through the bath
solution (e.g. for the inside-out patch). If one would like to record from many ion channels further
suction can be applied to the cell attached mode to break the patch under the electrode and allow
access to the remaining cell membrane containing many ion channels (whole cell). Since there are
many different types of ion channels in the membrane, one has to take cautious care of adjusting the
composition of the solutions and including pharmacological agents that will allow isolation of the current
type that needs to be studied.
Ionic currents recorded by the patch clamp technique
Figure 8 shows single channel records of a K channels found in cardiac cells. 150 mM K bathed the
patch from each side. At 0 mV no single channel openings were observed (EK = 0 mV). As the
membrane potential was held to increasingly more and more negative levels, the channel openings
became larger and larger (difference from the dotted zero line). When the single channel currents
obtained at each membrane voltage was plotted (for both the negative potentials shown, as well as the
positive potentials not shown) a linear ohmic relationship was obtained (labeled control). If the external
K concentration was adjusted to 30 mM or the internal K concentration was changed to 45 mM, while
leaving the K concentration on the other side to 150 mM, the I-V curves shown were obtained. Do the
EK values obtained experimentally match the values predicted by the Nernst equation?
16
Figure 8. left: Single-channel currents recorded from an inwardly rectifying K channel in the open cell-
attached configuration. Numbers to the left of each current trace refer to holding potential. The
electrode was filled with Ca-free, high-K solution. The dotted line indicates zero-current level. right:
Single-channel I-V relationships obtained from similar patches as those shown on the left. From: H.
Matsuda, A. Saigusa & H. Irisawa, 1987 Nature 325: 156-159 and H. Matsuda, 1991, Journal of

17. Figure 9 shows whole cell records from a cation selective (Na, Ca and Mg), cyclic nucleotide-gated
channel from the rod outer segment membrane (see next lecture). 1 mM cGMP activated this current
linearly at both negative and positive membrane potential changes.
17
Figure 9. Macroscopic current-voltage relation at a saturating cyclic GMP concentration. A, recordings
from one patch. The membrane potential was held at 0, and positive/negative voltage steps of +/- 10
mV increments and lasting 1 s were delivered, in the absence and the presence of 1000 µM-cyclic
GMP. The steady-state current amplitude at the end of each voltage step was measured. The current
measurements in the two runs without cyclic GMP were averaged and then subtracted from the
corresponding measurements with cyclic GMP. B, averaged current-voltage relation from seven
patches. The current in each experiment was normalized to unity at –60 mV before averaging was
done. Black circles show averaged current values; the horizontal bars show standard deviations of the
currents, which are very small. The straight line is drawn through points between 0 and –60 mV, and is
extrapolated linearly to positive voltages. From L. W. Haynes and K. –W. Yau, 1990, Journal of
Physiology (London) 429: 451-481.

18. 18

19. Potassium channels involved in the generation and maintenance of the resting potential: There
exist specific potassium channels that are active at negative membrane potentials (unlike most voltage-
gated channels that require depolarization in order to open) and as such allow potassium efflux. It is
precisely through this pathway that positive ions leave the cytoplasm, whenever the membrane
potential is more positive than EK and create a negative membrane potential at rest, as we discussed in
the last lecture. Since EK has a negative value (~-90 mV in the muscle cell of the previous lecture) K
flux would tend to bring the membrane towards EK. There are some distinguishing features that
members of this potassium channel family possess.
(1) On the basis of hydrophobicity analysis, there are two closely related varieties of K channels, those
containing two membrane-spanning segments per subunit and those containing six. In all cases,
the functional K channel protein is a tetramer, typically of four subunits that are either identical
(homotetramers) or different (heterotetramers). In all cases the N- and C- terminal ends of the
proteins are in the cell cytoplasm. Subunits of the two membrane-spanning variety appear to be
shortened versions of their larger counterparts, as if they simply lack the first four membrane-
spanning segments. Members of the family of K channels that control the resting potential contain
two membrane-spanning segments.
(2) When the membrane potential is above EK the K+
outward current is smaller than when Vm is more
negative than EK and K+
flows in the inward direction. This property of preferred conduction in the
inward direction is called inward rectification, and many times these channels are referred to as
inward rectifiers. The physiological importance of this design of inward rectification is not fully
appreciated yet, although it is clear that it is the outward current these channels carry that serves
their physiological role in keeping the membrane potential near EK (it is rare that the membrane
potential of a cell becomes more negative than EK). Although not important for our purposes in this
course, the molecular basis of the rectification property that inwardly rectifying K+
channels show is
block of outward K+
currents by internal Mg2+
and polyamines.
Fig. 10a (left) and 10b (right)
19

20. 20
Figure 10 a and b. (a.) Stereoview of a ribbon representation illustrating the three-dimensional fold of
the KcsA tetramer viewed from the extracellular side. The four subunits are distinguished by color. (b.)
Mutations in the voltage-gated Shaker K+
channel that affect function are mapped to the equivalent
positions in KcsA based on the sequence alignment. Two subunits of KcsA are shown. The residues
colored red (GYG, main chain only) are absolutely required for K+
selectivity.
Figure 10 c and d. (c.) A cutaway stereoview displaying the solvent-accessible surface of the K+ channel colored
according to physical properties. The surface coloration varies smoothly from blue in areas of high positive charge
through white to red in negatively charged regions. The yellow areas of the surface are colored according to carbon
atoms of the hydrophobic (or partly so) side chains of several semi-conserved residues in the inner vestibule. The green
CPK spheres represent K+ ion positions in the conduction pathway. (d.) Stereoview of the entire internal pore. Within a
stick model of the channel structure is a three-dimensional representation of the minimum radial distance from the center
of the channel pore to the nearest van der Waals protein contact.
c.
…...
d.

21. Selectivity and permeation mechanism
In 1998 the transmembrane region of a related bacterial K+
channel (with two membrane-spanning
transmembrane segments) from Streptomyces lividans (KcsA) was crystallized in detergent and
provided structural evidence at ~3 Å resolution for the selectivity and permeation mechanism of K+
channels. The KcsA channel is a tetramer with four-fold symmetry about a central pore (Fig. 10a). Like
several other membrane proteins, it has two layers of aromatic amino acids positioned to extend into
the lipid bilayer, presumably near the membrane-water interfaces. Each subunit has two
transmembrane α-helices connected by the roughly 30 amino acid pore region, which consists of a
helix and a loop that forms the selectivity filter (Fig. 10b). A subunit is inserted into the tetramer such
that
one transmembrane helix (inner helix) faces the central pore while the other (outer helix) faces the lipid
membrane. The inner helices are tilted with respect to the membrane normal by about 25° and are
slightly kinked, so that the subunits open like an inverted teepee or the petals of a flower facing the
outside of the cell. The open petals house the structure formed by the pore region near the extracellular
surface of the membrane at the wide end of the structure.
This region contains the K channel signature sequence (TV/IGYG), which is invariant among all K
channel sequences known, and forms the selectivity filter. The K selectivity filter is lined by carbonyl
oxygen atoms of the main chain atoms (GYG) (not the side chain ones). When an ion enters the
selectivity filter, it evidently dehydrates (nearly completely). To compensate for the energetic cost of
dehydration, the carbonyl oxygen atoms must take the place of the water oxygen atoms, come in very
close contact with the ion, and act like surrogate water. Thus, the main chain atoms create a stack of
sequential oxygen rings, which afford numerous closely spaced sites of suitable dimensions for
coordinating a dehydrated K ion. The K ion thus has only a very small distance to diffuse from one site
to the next within the selectivity filter. The narrow selectivity filter is only 12 Å long. The Val and Tyr side
chains from the V-G-Y-G sequence point away from the pore and make specific interactions with amino
acids from the tilted pore helix. Together with the pore helix Trp residues, the four Tyr side chains form
a massive sheet of aromatic amino acids, twelve in total, that is positioned like a cuff around the
selectivity filter. The filter is thus constrained in an optimal geometry so that a dehydrated K ion fits with
proper coordination but the Na ion is too small. The structure reveals the presence of two K ions near
opposite ends of the selectivity filter, which mutually repel each other. Thus, when the second ion
enters, the attractive force between a K ion and the selectivity filter becomes perfectly balanced by the
repulsive force between ions, and this is what allows conduction to occur. This picture accounts for both
21
Figure 10e. A section of the model
perpendicular to the pore at the level of
the selectivity filter and viewed from the
cytoplasm. The view highlights the
network of aromatic amino acids
surrounding the selectivity filter. Tyrosine-
78 from the selectivity filter (Y78) interacts
through hydrogen bonding and van der
Waals contacts with two Trp residues
(W67, W68) from the pore helix.

22. a strong interaction between K ions and the selectivity filter and a high throughput mediated by
electrostatic repulsion. The remainder of the pore is wider and has a relatively inert hydrophobic lining.
These structural and chemical properties favor a high K throughput by minimizing the distance over
which K interacts strongly with the channel. A large water-filled cavity and helix dipoles help to
overcome the high electrostatic energy barrier facing a cation in the low dielectric membrane center.
Although the crystal structure of the KcsA channel has provided the structural basis for selectivity
and permeation that is likely to prove a guiding model for many channels, the structural basis of gating
mechanism remains unclear. Both the absence of the plasma membrane in these structures (quite
important for gating as we’ll see later) and the static nature of crystal structures are likely to prove
limiting for understanding the dynamic process of ion channel gating via this technique.
Gating mechanism
In 2002 the crystal structure of another bacterial K+
channel, MthK was determined. This channel is
activated by intracellular calcium, which binds to its cytosolic domains and exerts a force that is
transduced to the transmembrane domains to open the channel gate. Unlike the KcsA structure, which
depicted a picture of the closed channel conformation, the MthK structure reflected a snapshot of the
open channel conformation. Comparison of the closed and open conformations of these two highly
related K+
channels gave rise to a model of what happens during gating (Fig. 11). The TM2 helices
cross each other to form a narrow opening that seem to constrict ion flow. Ca2+
binding exerts a force
through a region below the TM2 helix bundle crossing to bend the helix in the middle at a hinge
position, produced by a conserved glycine; the structural change produced by this force leads to an
enlargement of the helix bundle crossing and thereby to gating of the channel. Different channels may
utilize different strategies to generate the force required for this pivoted gating mechanism. So,
intracellular ligand-gated channels (e.g. Ca2+
, cAMP, βγ subunits of G proteins, etc.) may bing to
different cytosolic domains in their respective ion channel proteins but the net effect seems to be very
similar in forcing the TM2 helix to bend at the Gly residue that serves as a hinge point. Even voltage-
gated channels that we will consider in great detail at a later lecture couple the movement of a sensor
that senses changes in transmembrane voltage to the lower half of this pore-lining helix to bend it and
gate the channel open.
Our molecular understanding of how the gate is coupled to the conformational changes caused by
the gating stimulus is poor and is a very active area of research. In the last couple of years it has been
appreciated that phosphoinositides, and in particular PIP2, (which are minor components of the plasma
membrane) are crucial elements to the gating of inwardly rectifying K channels. These channels
22

23. interact directly with PIP2 (electrostatically, i.e. positive residues on the channel protein interact with the
negatively charged PIP2), a property that appears crucial to their activity. Thus, constitutively active K
channels experience strong interactions with PIP2, while other members of this K channel family show
weaker and varying degrees of interaction with PIP2. Channels that show intermediate to weak
interactions with PIP2 can have their activity modulated (usually inhibited) when PIP2 is hydrolyzed
through receptor mediated signaling (i.e. receptors coupling to Gq to stimulate PLC). Both examples
listed below as members of the inwardly rectifying K channel family are gated by interactions with PIP2
and both are inhibited during agonist-induced hydrolysis of PIP2. We imagine that channel-PIP2
interactions exert a tangential force onto the channel gate to cause it to open.
23
Figure 11. The crystal structure of the
open state of MthK, a Ca2+
-activated K+
channel that is related to GIRK4 and KcsA,
was recently published (Jiang et al.,
2002a) Comparison of the open state of
MthK to the closed state of KcsA (Jiang et
al., 2002b) provided a picture of K+
channel
gating. The crystal structures showed that
the TM2 helices of the closed channel
(KcsA) are straight and form a narrow
bundle crossing close to the cytosolic end
of the permeation pathway. In contrast, in
the open channel (MthK) the TM2 helices
are bent at position G83 by 30o
and their
narrow bundle crossing widens, consistent
with the notion that the TM2 helix bundle
crossing serves as a gate and the glycine
residue serves as a hinge point during
gating (Jiang et al., 2002b).