Carmel M. McNicholas, Ph.D.
MCLM 868, 934 1785
Sept. 6-7 2011
BIOLOGICAL MEMBRANES AND PRINCIPLES OF SOLUTE AND WATER MOVEMENT
3 Lectures and 1 Review with sample questions
OBJECTIVES
At the conclusion of this block of lectures you will be able to:
PART 1: INTRODUCTION AND BASIC CONCEPTS
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List the various fluid compartments of the body and their approximate relative sizes
State the major anions and cations of each compartment and their approximate concentrations
Appreciate the constancy of osmolality across the various fluid compartments
Understand the importance of the selective permeability of cellular membranes
Describe the role of the cytoskeleton, extracellular matrix, structural and gap junctions and the glycocalyx
State Fick’s first law of diffusion and explain how changes in the concentration gradient, surface area,
time and distance will influence the diffusional movement of a solute
Explain how the relative permeability of a cell to water and solutes will generate an osmotic pressure
and define the van’t Hoff equation and reflection coefficient.
Explain the significance in colloid osmotic (oncotic) and hydrostatic pressure gradients
Describe isotonic (iso-osmolar), hypotonic (hypo-osmolar) and hypertonic (hyper-osmolar) solutions in
terms of their effects on body cells
PART 2: PRINCIPLES OF ION MOVEMENT
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Understand the concept of the law of electroneutrality
Describe how chemical and electrical forces govern the movement of electrolytes
Describe the concept of a how a diffusion potential is generated
Write the Nernst equation and understand how this accounts for both the chemical and electrical driving forces that act on an ion
Use the Nernst Equation to calculate the equilibrium potential for monovalent and divalent ions
List the approximate values for a typical mammalian cell for ENa, EK, ECl and ECa
Understand the principle for how the resting membrane potential is calculated using the GoldmanHodgkin-Katz (GHK) equation (memorization of equation not necessary).
Given an increase or decrease in the permeability of Na+, K+ or Cl-, predict how the resting membrane
potential would change
PART 3: MEMBRANE TRANSPORT MECHANISMS
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Differentiate the following terms based on the source of energy driving the process and the molecular
pathway for: diffusion, facilitated diffusion, secondary active transport, and primary active transport
Describe how the energy derived from ATP hydrolysis is used to transport ions such as Na+, K+, H+ and
Ca2+ against their electrochemical gradient
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Explain how the energy derived from the Na+ gradient across cell membranes is used to drive the
“uphill” movement of solutes
Describe the following properties of ion channels: gating, activation and inactivation
Describe Gibbs-Donnan equilibrium and the transport processes involved in maintaining cell volume
Describe the pump-leak model and the generation of cell membrane potentials
Describe the properties of the epithelial monolayers. Identify the apical and basolateral membranes.
Understand the role of the tight junction in maintaining epithelial polarity. Identify transcellular and
paracellular routes of solute and water movement
Understand how voltage-gated ion channels are involved in the nerve action potential. Understand the
concept of threshold, depolarization, hyperpolarization and after-hyperpolarization in terms of movement of charge and the shape of the action potential.
Explain the refractory period in excitable cells and the its molecular basis
PART 4: REVIEW
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Several examples will be used to reiterate important concepts from the lectures and provide practice
in the use of the Nernst equation to calculate electrochemical equilibrium potentials and predict
whether solute movement occurred via an active or passive transport mechanism
Slide 1
BIOLOGICAL MEMBRANES
AND PRINCIPLES OF
SOLUTE AND WATER
MOVEMENT
Carmel M. McNicholas, Ph.D.
Department of Physiology & Biophysics
Contact Information:
MCLM 868
934 1 785
cbevense@uab. edu
Slide 2
Sept. ‘11
OUTLINE
•Biological Membranes and Principles of Solute
and Water Movement
•Diffusion and Osmosis
•Principles of Ion Movement
•Membrane Transport
•Nerve Action Potential
•HANDOUT AND PROBLEM SET
Slide 3
The Cell: The basic unit of life
(i) obtaining food and
oxygen, which are used
to generate energy
(ii) eliminating waste
substances
(iii) protein synthesis
(iv) responding to
environmental changes
(v) controlling exchange
of substances
(vi) trafficking
materials
(vii) reproduction.
Slide 4
The fluid compartments of a 70kg adult human
EXTRACELLULAR (~40%)
BLOOD
PLASMA
~3 L
[Na+] = 142 mM
[K+] = 4.4 mM
[Cl-] = 102 mM
[protein] = 1 mM
Osmolality =
290 mOsm
Capillary endothelium
INTERSTITIAL FLUID
~13 L
[Na+] = 145 mM
[K+] = 4.5 mM
[Cl-] = 116 mM
[protein] = 0 mM
Osmolality = 290 mOsm
TRANSCELLULAR FLUID
~1 L
Composition:
variable
Epithelial cells
INTRACELLULAR (~60%)
INTRACELLULAR
FLUID
~25 L
[Na+] = 15 mM
[K+] = 120 mM
[Cl-] = 20 mM
[protein] = 4 mM
Osmolality = 290
mOsm
Plasma membrane
TOTAL BODY WATER (~42 L)
Modified from: Boron & Boulpaep, Medical Physiology, Saunders, 2003.
The cell is the smallest unit capable of carrying out life processes. These
processes include: (i) obtaining food and oxygen, which are used to generate
energy, (ii) eliminating waste substances, (iii) protein synthesis, (iv) responding
to environmental changes (v) controlling exchange of substances between cells
and their environment (vi) trafficking materials (vii) reproduction. None of these
processes could occur, nor life for that matter, if cell membranes had not
evolved.
The principal fluid medium of the cell is water. The cells of the human body
live in a carefully controlled fluid environment divided into the extracellular
compartment and the intracellular compartment. A large percentage of total
body weight in humans is water - for a male this is approximately 60% (1/3
extracellular and 2/3 intracellular) and for a female 50%, infants have up to 75%
total body water. The lower value for females is because they tend to have
more adipose tissue and fat cells have a lower water content than muscle. In
this diagram the arrows denote the movement of water between various compartments.
The 42L of total body water is distributed between two compartments as
shown here: (i) the fluid inside the cell, the intracellular fluid (ICF), occupies the
intracellular compartment and (ii) the fluid outside the cells, the extracellular
fluid (ECF), occupies the extracellular compartment. Approximately 60% of the
total body water (TBW) is contained within the cells. The remaining 40% is contained within the ECF, which is further divided into two compartments: the
plasma and the interstitial fluid. Cell membranes separate the ICF and ECF compartments. There is a further sub-compartment of the extracellular fluid called
transcellular fluid (e.g. synovial fluid, CSF) which is approx. 1L. Water and solutes move between the interstitial fluid and plasma across the capillary walls
and between the intracellular fluid (the cytoplasm) and the ECF by crossing the
plasma membrane.
Slide 5
Solute composition of key fluid compartments
•Osmolality
constant
•Cell proteins –
10-20% of the
cell mass
•Structural and
functional
Slide 6
Membranes are selectively permeable
Gas molecules are
freely permeable
Small uncharged
molecules are freely
permeable
The composition of the various body fluid compartments are strikingly different. The most important ions inside the cell are potassium, magnesium, phosphates, bicarbonate and in lesser amounts sodium, calcium and chloride. Typically, substances found in high concentration in the ECF are low in the ICF and
vice versa. Remarkably, the osmolality remains constant. Indeed, any transient
changes in osmolality that occur are quickly dissipated because of the free
movement of water into or out of cells. 10-20% of the cell mass is constiuted by
proteins. There are two types of proteins, structural and functional.
The composition of cellular membranes determines the permeability to various solutes and water. We will discuss the mechanisms that have evolved to
allow for the transport of molecules across cellular membranes, however specializations within the cell have evolved to allow for movement of substances
into and out of cells.
Large / charged
molecules need
‘assistance’ to
traverse the plasma
membrane
Slide 7
Structure of the Plasma Membrane
The plasma membrane consists of both lipids and proteins. The fundamental
structure of the membrane is the phospholipid bilayer which separates the
intracellular and extracellular fluid compartments. The proteins embedded
within this bilayer carry out specific membrane functions.
This figure is an adaptation of the Singer and Nicolson fluid mosaic model for
membrane structure: this model is generally accepted as the basic paradigm for
the organization of all biological membranes. According to this model, membrane proteins come in two forms: peripheral proteins, which are dissolved in
the cytoplasm and relatively loosely associated with the surface of the membrane, and integral proteins, which are integrated into the lipid matrix itself, to
create a protein-phospholipid mosaic. The updated view of the original model
“dynamically structured mosaic model” has the following characteristics: emphasis is shifted from fluidity to mosaicism, which, in our interpretation, means
nonrandom codistribution patterns of specific kinds of membrane proteins
forming small-scale clusters at the molecular level and large-scale clusters
(groups of clusters, islands) at the submicrometer level. The cohesive forces,
which maintain these assemblies as principal elements of the membranes, originate from within a microdomain structure, where lipid–lipid, protein–protein,
and protein–lipid interactions, as well as sub- and supramembrane (cytoskeletal, extracellular matrix, other cell) effectors play equally important roles.
Slide 8
The Extracellular Matrix
Epithelial cell
Basement
membrane
Capillary
endothelium
Connective
tissue and
ECM
Slide 9
Fibroblast
The extracellular matrix
(ECM) of animal cells
functions in support,
adhesion, movement and
regulation
The Extracellular Matrix
The ECM is an organized meshwork of polysaccharides
and proteins secreted by fibroblasts. Commonly
referred to as connective tissue.
COMPOSITION:
Proteins: Collagen (major protein comprising the ECM),
fibronectin, laminin, elastin
Two functions: structural or adhesive
Polysaccharides: Glycosaminoglycans, which are mostly
found covalently bound to protein backbone
(proteoglycans).
Cells attach to the ECM by means of transmembrane
glycoproteins called integrins
• Extracellular portion of integrins binds to collagen,
laminin and fibronectin.
• Intracellular portion binds to actin filaments of the
cytoskeleton
Slide 10
The Cytoskeleton
Intracellular network of protein filaments
Role
Supports and stiffens
the cell
Provides anchorage for
proteins
Contributes to dynamic
whole cell activities (e.g.,
dividing and crawling of
cells and moving vesicles
and chromosomes)
Three Types Of
Cytoskeletal
Fibers
Microtubules (tubulin - green)
Microfilaments (actin-red)
Intermediate filaments
The extracellular matrix (ECM) is the extracellular structure that provides
structural support to cells in addition to performing various other important
functions. The extracellular matrix is the defining feature of connective tissue in
animals. The extracellular matrix is an organized meshwork of polysaccharides
and proteins secreted locally by fibroblasts. Different tissues have different
combinations of molecules in the matrix according to their functional requirements. The matrix may be calcified and hard as in bone and teeth or may be
strong and flexible as in tendons. In the eye, it maintains a jelly like consistency.
The extracellular matrix includes the interstitial matrix and the basement
membrane. The interstitial matrix is present in the intercellular spaces between
various animal cells. Gels of polysaccharides and fibrous proteins fill the interstitial space and act as a compression buffer against the stress placed on the ECM.
Basement membranes are sheet-like depositions of ECM on which various epithelial cells rest.
Due to its diverse nature and composition, the ECM can serve many functions,
such as providing support and anchorage for cells, segregating tissues from one
another, and regulating intercellular communication. The ECM regulates a cell's
dynamic behavior. In addition, it sequesters a wide range of cellular growth factors, and acts as a local depot for them. Changes in physiological conditions can
trigger protease activities that cause local release of such depots. This allows
the rapid and local growth factor-mediated activation of cellular functions,
without de novo synthesis.
Proteins have two functional types - they can be either structural (e.g. collagen or elastin) or adhesive (e.g. laminin).
Collagen is secreted into the extracellular matrix where it provides strength
and resistance to pulling forces. Many types have been described. All collagen
molecules are trimers, which can be wound round each other to form a rod like
triple helix which can in turn assemble into thicker fibers.
Fibronectin and laminin are proteins that function to mediate cell attachment
and adhesion. Elastin provides flexibility through maintenance of their polypeptide backbone as an unfolded random coil that always allows it to stretch and
recoil, for example in skin. Polysaccharides are found covalently linked to protein in the form of proteoglycans.
The cytoskeleton is an important, complex, and dynamic cell component. The
cytoskeleton maintains cell shape, anchors organelles in place, and moves parts
of the cell in processes of growth, motility and cell division.
There are many types of protein filaments make up the cytoskeleton primarily
microtubules (tubulin), microfilaments (actin) and intermediate filaments (various subunits). Intermediate filaments form a flexible scaffolding for the cell and
help resist external pressure.
The cyotoskeleton represents the cell's skeleton. Like the bony skeletons that
give us stability, the cytoskeleton gives our cells shape, strength, and the ability
to move, but it does much more than that. The cytoskeleton is made up of three
types of fibers that constantly shrink and grow to meet the needs of the cell:
microtubules, microfilaments, and actin filaments. Each type of fiber looks,
feels, and functions differently. Microtubules consist of a strong protein called
tubulin and they are the 'heavy lifters' of the cytoskeleton. They do the tough
physical labor of separating duplicate chromosomes when cells copy themselves
and serve as sturdy railway tracks on which countless molecules and materials
shuttle to and fro. They also hold the ER and Golgi neatly in stacks and form the
main component of flagella and cilia. Microtubules are made up of alpha and
beta tubulin which form dimers and are dynamic structures which are constantly being assembled and disassembled.
Microfilaments are unusual because they vary greatly according to their location and function in the body. For example, some microfilaments form tough
coverings, such as in nails, hair, and the outer layer of skin. Others are found in
nerve cells, muscle cells, the heart, and internal organs. In each of these tissues,
the filaments are made of different proteins. Microfilaments are made of actin
subunits and polymerized and depolymerized in vivo.
Actin filament are made up of two chains of the protein actin twisted together. Although actin filaments are the most brittle of the cytoskeletal fibers, they
are also the most versatile in terms of the shapes they can take. They can gather
together into bundles, weblike networks, or even three-dimensional gels. They
shorten or lengthen to allow cells to move and change shape. Together with a
protein partner called myosin, actin filaments make possible the muscle contractions necessary for everything from your action on a sports field to the beating of your heart.
Slide 11
Structural Junctions
Tight
Junctions
Adhering
Junctions
Desmosome
Slide 12
Zonula Adherens
(belt)
Gap Junctions
ROLE: Passage of solutes (MW<1000) from cell to cell.
• Cell- cell communication
• Propagation of electrical signal
Slide 13
The Membrane Glycocalyx - cell coat
Alberts et al., Molecular Biology of the
Cell, 4th Ed. Garland Science, 2002)
Carbohydrates are:
• Covalently attached to membrane proteins and lipids
• Sugar chains added in the ER and modified in the golgi
 Oligo and polysaccharide chains absorb water and form a
slimy surface coating, which protects cell from mechanical and
chemical damage.
 Membrane Carbohydrates and Cell-Cell Recognition
– crucial in the functioning of an organism. It is the
basis for:
> Sorting embryonic cells into tissues and organs.
> Rejecting foreign cells by the immune system.
There are three major types of cell junctions found in cells. Shown here are
tight junctions and adhering junctions.
Tight junctions are found exclusively in epithelial cells and serve to partition
regions of the cells and to form a selective seal between cells. Tight junctions
also restrict the diffusion of membrane components — proteins and lipids —
between the apical and basolateral membranes. Tight junctional proteins also
have specialized functions and are not all simply structural elements. For example a protein named Paracellin-1 is found in the kidney where it is involved in
paracellular Mg2+ absorption. The “tightness” of tight junctions varies considerably from one kind of epithelium to another.
Adhering or anchoring junctions are not restricted to epithelial cells and are
found both between contiguous cells and their substrate. These also serve as an
anchoring point for cytoskeletal elements. Such junctions are found both in epithelial cells and also connect heart cells. Adhering Junctions: Epithelial cells are
held together by strong adhering or anchoring junctions that are two distinct
types. One extends like a belt around the entire perimeter of each cell and is
called the Zonula adherens. The second, termed the desmosome or macula adherens, are spot-like structures that serve to maintain strong cell-cell adhesion.
Hemidesmosomes can anchor cells to the basement membrane.
A third type of junction is called the gap junction. Gap junctions are in a class
by themselves because there are no other structures in vertebrate membranes
that form closed channels that cross the extracellular space. Gap junctions are
comprised of units called connexons and each connexon is made up of six protein subunits called connexins. Two connexons in adjacent cells line up and form
a channel that allows the passage of ions, sugars and other solutes from cell to
cell. Gap junctions are not simply passive non-specific conduits, there are at
least 20 genes which encode for connexins in humans and mutations of certain
of these proteins can lead to disease. The composition of the connexons determines their permeability and selectivity.
The glycocalyx, also known as the cell coat, is a carbohydrate rich zone on the
cell surface. The cell surface is coated with carbohydrate covalently attached to
membrane proteins (glycoprotein) and membrane lipids (glycolipid). The carbohydrates are sugar chains that are added in the ER and modified in the golgi. A
chain composed of several sugar molecules is an oligosaccharide. There are also
polysaccharide chains linked to an integral membrane protein core – known as
proteoglycans which are either retained as integral proteins or secreted out of
the cell and attached to the bilayer. The oligo- and polysaccharide chains absorb
water and give the cell a slimy surface coating, which can protect from mechanical and chemical damage to the cell. The membrane glycocalyx is also important in specific cell-cell recognition and interactions between different cells.
Slide 14
Transport of large molecules
EXOCYTOSIS: Transport molecules migrate to the
plasma membrane, fuse with it, and release their
contents.
ENDOCYTOSIS: The incorporation of materials from
outside the cell by the formation of vesicles in the plasma
membrane. The vesicles surround the material so the cell
can engulf it.
If a cell is to live, it must obtain nutrients and other substances from the surrounding fluids. Most substances pass through the cell membrane itself by active transport and diffusion. The mechanisms involved in this will be discussed
later. Waste substances must also be removed from the cell. The means that
cells use to transfer small molecules are not sufficient for transporting macromolecules, which include proteins, polynucleotides and polysaccharides. To
transport these macromolecules, cells rely on active transport. There are two
basic means of active transport - by exocytosis and by endocytosis. Exocytosis
involves sending macromolecules out of the cell, while the opposite applies to
endocytosis.
Slide 15
Exocytosis
Some molecules are secreted continually from the cell, but others are selectively secreted. To control secretion, specific substances are stored in secretory
vesicles, which are released when triggered by an extracellular signal. The signal, hormones being an example, binds to its specific cell surface receptor. Then
the concentration of free Ca2+ is increased in the cell. The increased concentration of the Ca2+ triggers exocytosis, causing the secretory vesicles to fuse with
the cellular membrane, releasing the substances outside the cell.
Slide 16
Endocytosis
Endocytosis is required for a vast number of functions that are essential for
the well being of cell. It intimately regulates many processes, including nutrient
uptake, cell adhesion and migration, receptor signaling, pathogen entry, neurotransmission, receptor downregulation, antigen presentation, cell polarity, mitosis, growth and differentiation, and drug delivery. Endocytosis pathways can
be subdivided into four categories: namely, phagocytosis, pinocytosis, clathrinmediated endocytosis, and caveolae.
Phagocytosis is the process by which cells bind and internalize particulate
matter, such as small-sized dust particles, cell debris, micro-organisms and even
apoptotic cells, which only occurs in specialized cells.
Pinocytosis is the invagination of the cell membrane to form a pocket, which
then pinches off into the cell to form a vesicle filled with large volume of extracellular fluid and molecules within it. The filling of the pocket occurs in a nonspecific manner. The vesicle then travels into the cytosol and fuses with other
vesicles such as endosomes and lysosomes.
Clathrin-mediated endocytosis is mediated by small vesicles that have a morphologically characteristic crystalline coat made up of a complex of proteins
that mainly associated with the cytosolic protein clathrin. Clathrin-coated vesicles are found in virtually all cells and from domains of the plasma membrane
termed clathrin-coated pits. Coated pits can concentrate large extracellular molecules that have different receptors responsible for the receptor-mediated endocytosis of ligands, e.g. low density lipoproteins, antibodies, growth factors
and many more.
Caveoli are the most common reported non-clathrin coated plasma membrane buds, which exist on the surface of many, but not all cell types. They consist of the cholesterol-binding protein caveolin with a bilayer enriched in cholesterol and glycolipids. Caveolae are small flask-shape pits in the membrane that
resemble the shape of a cave (hence the name caveolae). They can and can
constitute approximately a third of the plasma membrane area of the cells of
some tissues, being especially abundant in smooth muscle, type I pneumocytes,
fibroblasts, adipocytes, and endothelial cells. Uptake of extracellular molecules
is also believed to be specifically mediated via receptors in caveolae.
Slide 17
Principles of Solute
and Water Movement
Slide 18
Diffusion and Osmosis
Slide 19
Membranes are selectively permeable
Gas molecules are
freely permeable
Small uncharged
molecules are freely
permeable
Large / charged
molecules need
‘assistance’ to
traverse the plasma
membrane
Slide 20
Diffusion
Diffusion is the net movement of a substance (liquid
or gas) from an area of higher conc. to one of lower
conc. due to random thermal motion.
Because of the cell membrane’s hydrophobic interior, the lipid bilayer serves
as a barrier to charged molecules. This is imperative in maintaining the composition of the various fluid compartments of the body. While some molecules can
pass through the lipid bilayer, others require a little help. For example small
non-polar molecules, such as O2, readily dissolves in the lipid bilayer and thus
can traverse. Some other small uncharged polar molecules such as water and
urea can also diffuse across the bilayer. Lipid bilayers are virtually impermeable
to charged molecules and so specialized proteins have evolved to allow translocation of these ions. These specialized proteins are known as membrane transport proteins and channels. Regardless of the process through which any of
these pass across the membrane, some biophysical concepts are common. We
are going to begin with very simple concepts, but even though simple are extremely important.
Diffusion is simply the net movement of a substance from an area of high concentration to an area of low concentration. Provided you are above absolute
zero (0°K = -273°C), molecules of any substance, (solid, liquid or gas) are in constant and random motion, bouncing in all directions. An example of liquid is
shown here. If we add a cube of dye into a beaker of water. Initially there is a
sharp demarcation between the two solutions, however with time the solutions
closest to where the drop of dye was placed becomes progressively lighter as
the molecules move away from the center of concentration, until eventually the
beaker achieves a uniform color. The molecules of dye will move randomly – the
majority will move from high to low, but because of the random nature of the
movement of solute as molecules move independently, some will move from
low to high concentration. Although the substance is moving in either direction,
we consider the net movement. At the point where there is uniform color the
system has achieved a state of equilibrium.
Slide 21
Slide 22
Diffusion of molecules from the extracellular side to the intracellular space is
demonstrated is this slide. Eventually when there is no net movement the concentration is at equilibrium.
Kinetic characteristic of diffusion
of an uncharged solute
Model: compartments separated by permeable glass
∆x
C s1
C s2
compartment 1
compartment 2
A = cross sectional area of the glass disc
Cs = concentration of uncharged solute
∆x = thickness
Slide 23
∆x
C s1
compartment 1
C s2
compartment 2
According to kinetics, the rate of movement can be
described as follows:
rate of diffusion from 1 → 2 = kCs1
-{rate of diffusion from 2 → 1 = kCs2}
----------------------------------------------------------------------------
net rate of diffusion across barrier
= k(Cs1-Cs2) = k∆Cs
where k is a proportionality constant.
Slide 24
Diffusion is proportional to the surface area
of the barrier (A) and inversely proportional
to its thickness (∆x).
k can thus be expressed as ADs/∆x, where Ds
is the diffusion coefficient of the solute.
Consider what happens to an uncharged solute, S, in a closed system with two
compartments separated by a permeable glass disc of thickness ∆x and cross
sectional area A. In this model the solute is the same on both sides of the disc or
membrane, but has different concentrations. The barrier is completely permeable to the solute therefore the solute can move either from compartment 1 to
compartment 2, or vice versa. Because the solute molecules are in constant
random motion due to the thermal energy of the system, there is a continual
motion of solute in both directions. Our question here is in which direction will
there be net movement of solute.
Using kinetics, we can evaluate the rate of movement of S from 1 to 2.
The rate of diffusion from 1 to 2 is given by kCs1, and likewise the rate of diffusion from 2 to 1 is kCs2. The different between these two will yield the net
rate of diffusion. The net rate of diffusion is k(∆Cs), where k is a proportionality
constant. Thus, the net flow of an uncharged solute is directly proportional to
the concentration difference across the barrier.
The factors that contribute to this proportionality constant, k, relate both to
properties of the membrane itself and the solute that is to traverse the membrane. Properties of both contribute to the movement of the solute.
One factor is the surface area of the barrier. The larger the area, the more
chance an S molecule has of “bouncing through”. Another is the thickness of the
barrier. The greater the thickness, the less chance the molecule has of “bouncing cleanly through”. Finally, the ability of the molecule to diffuse through the
medium is important. With more diffusability, the faster the molecules can get
across the membrane. This diffusability is given by the diffusion coefficient, Ds.
The concentration gradient across the
membrane is the driving force for net
diffusion.
Slide 25
FLUX (Js) describes how fast a solute moves, i.e. the
number of moles crossing a unit area of membrane per
unit time (moles/cm2.s)
Therefore, net diffusion rate = ADs∆Cs/∆x.
Dividing both sides by A (to obtain flux), we obtain:
Fick’s first law of diffusion:
Flux = Js = Ds∆Cs/∆x
“The rate of flow of an uncharged solute due to
diffusion is directly proportional to the rate of change
of concentration with distance in direction of flow”
When the concentration gradient of a substance is zero
the system must be in equilibrium and the net flux must
also be zero.
If we plug in these components of k, we arrive at a new expression for net diffusion. Physiologists describe solute movements across barriers in units of flux
(moles/surface area/unit of time). The rate of diffusion can be converted into a
flux by dividing by the area, A. Thus, we obtain a familiar form of Fick’s first law
of diffusion: flux = Js = Ds(∆Cs)/(∆X). Fick’s first law simply states that the rate of
flow of an uncharged solute due to diffusion is directly proportional to the rate
of change of concentration with distance in the direction of flow.
When the concentration gradient of a substance is zero the system must be in
equilibrium and the net flux must also be zero.
Slide 26
Diffusion of an uncharged solute
Model: compartments separated by a lipid
bilayer
∆x
Cs1
compartment 1
Cs2
The problem with our last model is that a biological membrane’s true composition makes things much more complicated. In particular, a biological membrane is comprised of a lipid bilayer of phospholipids interspersed with integral
and peripheral proteins. Because the phospholipids contain a water-soluble
head group and two lipid-solution tails, solutes of different hydrophobicity will
partition differently across the bilayer.
compartment 2
Biological membranes are composed of a lipid bilayer of
phospholipids interspersed with integral and peripheral
proteins (“Fluid Mosaic Model”).
Slide 27
Partitioning of an uncharged solute
across a lipid bilayer
The partition coefficient, Ks will increase or decrease the
driving force of the solute S across the membrane:
Cs 1
Js = KsDs∆Cs/∆x
Lipophilic
Ks > 1
Ks lies between
0 and 1
Cs 2
Hydrophilic
Ks < 1
Because it is difficult to measure Ks, Ds and ∆x, these
terms are often combined into a permeability coefficient,
Ps = KsDs/∆x.
It follows that:
Js = Ps∆Cs
This is a representation of the lipid bilayer. Again, recall that the concentration
on side 1 is greater than side 2 and the net movement of solute will be from 1
to 2.
Because of the lipid nature of the bilayer, the more lipophilic the solute, the
more it will accumulate on the inside of the membrane. Thus, its concentration
will be higher than in the corresponding bulk solution. The exact opposite will
be true for a hydrophilic solute: it will accumulate less on the inside of the
membrane. The result is that there will be a change in the driving force for S
across the membrane: larger for a more lipophilic S and smaller for a more hydrophilic S.
Thus, our flux equation must take this into account. To do so, we add an additional (unitless) term to the equation: the partition coefficient Ks. Ks can be empirically determined in somewhat of a straight-forward fashion by placing a
known amount of S in a mixture of water and a lipid (e.g., olive oil), shaking the
cocktail, and evaluate the distribution of S. Ks = 1 if all goes into the lipid phase,
and 0 if all goes into water. Obviously, most solutes are somewhere between 0
and 1.
Incorporating Ks into our flux equation, we now have J = KsD(∆C)/(∆x). In
practice, it is not easy to determine Ks,Ds and ∆x. Thus, they are usually lumped
together into a permeability coefficient, Ps that is much easier to determine
experimentally. We arrive at Js=Ps∆Cs.
Slide 28
Solute movement across a lipid
bilayer through entry into the lipid
phase occurs by simple diffusion.
This movement occurs downhill and
is passive.
Slide 29
Osmosis: The flow of volume
Osmosis refers to the net movement of water across
a semi-permeable membrane (or displacement of
volume) due to the solute concentration difference.
The movement of a solvent, in our case water, is referred to as osmosis. Thus
osmosis is the net movement of water (or displacement of volume) due to a
concentration difference. The transport of water across biologic membranes is
always passive. So far no water pumps have ever been described. To a certain
extent water can traverse the lipid bilayer by simple diffusion. The ease of
movement is determined by the phospholipid composition of the bilayer.
Because biologic systems are relatively dilute aqueous solutions, in which water comprises more than 95% of the volume, osmotic flow across biological
membranes has come to imply the displacement of volume resulting from an
area of high water concentration to an area of low water concentration.
Slide 30
Osmosis. The flow of volume
The solute concentration difference causes water to
move from compartment 2 → 1. The pressure
required to prevent this movement is the osmotic
pressure.
Time
1
Slide 31
2
1
2
Osmosis. The flow of volume
AN IDEAL MEMBRANE
(Meniscus)
Piston
(The piston applies
pressure to stop
water flow)
H2O
C s1
Compartment 1
Cs2
(Compartment 2
is open to the
atmosphere)
Compartment 2
Here the membrane is only permeable to water which will
flow down its concentration gradient from 2 → 1.
The volume flow can be prevented by applying pressure to
the piston. The pressure required to stop the flow of
water is the osmotic pressure of solution 1.
In this example two compartments open to the atmosphere are separated by
a semi-permeable membrane which allows only water to traverse. Solute is
present only in compartment 1. With time the flow of water causes the volume
of solution in compartment 1 to increase and 2 to decrease. Let’s consider why.
Osmosis takes place because the presence of solute decreases the chemical
potential of water. Water moves from where its chemical potential is higher to
where its chemical potential is lower.
Note: Addition of solute reduces the free energy of water and thus the chemical potential of water is reduced. Free energy is generated by the random
movement of the water molecules. Solute reduces this random motion.
In this example, a rigid-walled container is separated by a membrane. The
membrane is permeable to water rather than to the solute which occupies
compartments 1 and 2. The membrane is considered “ideal” because we are
making it only permeable to water (semi-permeable).
Second, we have a pressure-measuring piston attached to the left-hand side
of 1. Finally, the right-hand side of compartment 2 is open to the atmosphere.
Similar to our example in the previous slide, the difference in concentration of
solute in compartment 1 versus 2 creates an osmotic pressure difference across
the membrane and the pressure difference is the driving force for water to flow.
In this example, water will flow down its concentration gradient from the less
concentrated solute side (1) to the more concentrated solute side (2). This
movement will create pressure on the piston.The osmotic pressure (∆Π) that
must be applied to prevent the diffusion of water can be determined using the
van’t Hoff equation: ∆Π=RT(∆ Cs). At 37C (=310K), the product RT is ~25 atm.
Slide 32
The osmotic pressure (∆π) required is
determined from the van’t Hoff equation:
∆π = RT∆CS = (25.4)∆CS atm at 37°C.
Where, R = the gas constant (0.082 L.atm.K-1.mol-1),
T = absolute temperature (310 K @ 37 ºC) and ∆CS (mol.L-1)
is the concentration difference of the uncharged solute
Slide 33
Osmosis. Importance of osmolarity
φic = osmotically effective concentration
φ is the osmotic coefficient
‘i’ is the number of ions formed by
dissociation of a single solute molecule
‘c’ is the molar concentration of solute
(moles of solute per liter of solution)
e.g. what is the osmolarity of a 154
mM NaCl solution, where φ = 0.93
→
154 x 2 x 0.93 = 286.4 mOsm/l
The osmotic pressure depends upon the number of particles in solution.
Furthermore, the degree of ionization of solute must be taken into account:
e.g. 1 M soln. glucose, 0.5 M soln. NaCl and 0.333 M soln. MgCl2 all have ~ the
same osmotic pressure assuming complete dissociation of the salt solution
However, typically there is some deviation from ideal and hence the osmotic
coefficient (φ, phi) must be taken into account. We can calculate the effective
osmotic concentration by multiplying the molar concentration of the solute, the
number of ions formed by the dissociation of the solute and the osmotic coefficient. Here for example we can calculate the osmolarity of a 154 mM NaCl solution. Values for Φ can be obtained from handbooks.
Slide 34
Osmosis. The flow of volume
A NONIDEAL MEMBRANE
Piston
Cs 1
S
H2O
Cs 2
The osmotic pressure depends on the ability of the
membrane to distinguish between solute and solvent.
If the membrane is entirely permeable to both, then
intercompartmental mixing occurs and ∆π = 0.
The ability of the membrane to “reflect” solute S is
defined by a reflection coefficient σS that has values
from 0 (no reflection) to 1 (complete reflection).
Thus, the effective osmotic pressure for nonideal
membranes is:
∆πeff = σSRT∆CS
Slide 35
Osmotic and hydrostatic pressure
differences in volume flow
Volume flow across a membrane is described by:
JV = Kf∆P
where Kf is the membrane’s hydraulic conductivity and ∆P
is the sum of pressure differences.
These pressure differences can be hydrostatic (∆PH),
osmotic (∆πeff) or a combination of both. There is
equivalence of osmotic and hydrostatic pressure as
driving forces for volume flow, hence Kf applies to both
forces.
Thus, JV = Kf(∆πeff – ∆PH) (Starling equation)
and (∆πeff – ∆PH) is the driving force for volume flow.
Slide 36
Starling Forces
Arteriole
Interstitial fluid
pressure under
normal conditions
~0 mmHg
Venule
Interstitial
space
= fluid
movement
Filtration dominates
Absorption dominates
Osmotic (oncotic) pressure
Importance of plasma proteins!
Typically, membranes are not only permeable to water, but they also exhibit
some permeability to the solute as well. Thus the osmotic pressure depends on
two factors, (i) the concentration of the osmotically active particles and (ii)
whether the osmotically active particles can cross the membrane or not. Imagine such a nonideal membrane in which the membrane was equally permeable to water and the solute - intercompartmental mixing would occur and ∆Π
would equal zero.
Thus, the osmotic pressure developed will depend on the membrane’s ability
to ‘reflect’ the solute. This is termed the reflection coefficient, sigma. The reflection coefficient is a dimensionless number ranging between 0 and 1 that describes the ease with which a solute crosses the membrane. If σ (sigma) equals
zero, the membrane is freely permeable to the solute and the solute will diffuse
down its concentration gradient until the solute concentration on either side of
the membrane is equal. A solute of this kind will exert no osmotic effect and no
thus net water movement. If σ equals 1, the membrane is impermeable to the
solute and will be contained within its original compartment and thus exert its
full osmotic effect. Most solutes lie within the range 0 - 1.
Thus, for nonideal membranes, the effective osmotic pressure for is determined using the equation ∆πeff = σSRT∆CS.
Water or volume flow (Jv) across the membrane can also be generated by applying pressure to the piston and creating a hydrostatic pressure difference (∆P)
across the membrane. Under such conditions, volume flow will equal the product of (∆P) and the membrane’s hydraulic conductivity (Kf: also termed filtration
coefficient). Thus there is a linear relationship between a flow and the driving
force, which in the case of volume flow across a barrier. In fact, ∆P can be the
difference in hydrostatic pressure, the difference in osmotic pressure or a combination of both. Because pressure differences can be hydrostatic or osmotic in
nature, and the hydraulic conductivity coefficient is the same for either, total
volume flow equals K times the driving force for volume flow (osmotic minus
hydrostatic pressure difference). This equation is commonly known as the Starling equation, which can be used to determine volume flow as fluid flows from
the arterial to the venous end of a capillary and there are graded colloid and
hydrostatic pressure changes as illustrated on the next slide.
At the arterial end of a capillary bed, the hydrostatic pressure is relatively
higher than at the venous end. This leads to fluid movement out of the capillary.
As the colloid osmotic pressure this is due to the presence of plasma proteins
that are not freely permeable across the capillary membrane (hence σ= 1) remains constant and hydrostatic pressure decreases, water tends to be pulled
back into the capillary lumen. Starling deduced that the amount of fluid filtering
outward at the arterial end of the capillaries must almost equal the amount
reabsorbed at the venous end.
Slide 37
Tonicity
The red blood cell membrane is freely permeable to water and changes in the
extracellular osmolarity result in net movement of water into and out of the
cell. The cell is placed in a hypotonic solution; that is the solute concentration
outside the cell is less than inside. Water will move from outside to inside the
cell and eventually the cell will burst. Conversely, if we place the cells in a
hypertonic solution, as demonstrated on the left. Water will move from the
inside to the outside and the cells will shrink. Plasma solute concentrations are
kept within a very close range to keep the cells of the body functioning normally.
Slide 38
Principles of Ion Movement
Slide 39
Diffusion of Electrolytes
K+
AcCs1=100mM
Cs2=10mM
–
V
+
For charged species, both electrical and
chemical forces govern diffusion.
Slide 40
The Principle of Bulk Electroneutrality
All solutions must obey the principle of bulk
electroneutrality: the number of positive charges in a
solution must be the same as the number of negative
charges.
We’ve discussed the factors that influence the diffusion of uncharged solutes,
as well as water. Now let’s move on to electrolytes.
Again, let’s consider our model system. Here the solute is K-acetate, and the
concentration is 100 mM on the left-hand side and 10 mM on the right-hand
side. We also have a voltmeter present to measure potential differences across
the membrane.
Previously for uncharged solutes, we only needed to consider the concentration difference across the membrane, for a charged solute, we need to consider,
in addition, electrical forces.
An important point to remember is that all solutions must obey the law or
principle of electroneutrality. That is a bulk solution must contain equal positive
and negative charges.
Diffusion of Electrolytes
Slide 41
Cs1=100mM
K+
Cs2=10mM
AcAc-
– V +
K+
Law of electroneutrality (for a bulk solution) must be
maintained. In the above model in which the membrane
becomes permeable to sodium (K+) and acetate (Ac–), both ions
will move from side 1 → 2.
The concentration gradient between compartment 1 and 2 is
the driving force.
K+ (with the smaller radius) will move slightly ahead of Ac–,
thereby creating a diffusing dipole. A series of dipoles will
generate a diffusion potential.
Eventually, equilibrium is reached and Cs1 = Cs2 = 55mM
Diffusion of Electrolytes
Slide 42
Cs1=100mM
K+
Cs2=10mM
Ac– V +
When the membrane is permeable to only one of the ions (e.g.,
K+) an equilibrium potential is reached. Here, the chemical and
electrical driving forces are equal and opposite.
Equilibrium potentials (in mV) are calculated using the Nernst
equation:
Eion
=
C1
2.3RT
× log S2
zF
CS
Eion =
C1
60
× log S2
z
CS
R = gas constant; T = absolute temp.; F = Faraday’s constant; z = charge
on the ion (valence); 2.3RT/F = 60 mV at 37ºC
Slide 43
Let’s say the membrane --initially impermeable to everything-- is suddenly
made permeable to the solute. What will happen?
First of all, the law of electroneutrality for a bulk solution must be maintained
at all times. In other words, anions and cations have to balance on each side of
the membrane.
However, potassium is smaller than acetate and will therefore move faster
across the membrane. As potassium begins to move away from its paired acetate, electrostatic attraction reunites the pair. Thus, the pair will move together
through the membrane, but in an oriented fashion termed a dipole. A series of
dipoles will generate what is known as a diffusion potential.
The orientation of the dipole is such as to retard the diffusion of the ion having the greater mobility and to accelerate the movement of the ion having the
lower mobility so as to maintain electroneutrality.
The diffusion potential doesn’t last indefinitely. Shortly, intermixing of the
compartments leads to an equilibrium where Cs1=Cs2=55 mM and V = 0.
One can calculate the diffusion potential arising from the diffusion of a salt
that dissociated into a monovalent cation and monovalent anion if one has
knowledge of the diffusion coefficient of each of the monovalent ions and the
concentration of the ions.
An important result occurs when the membrane is made permeable to only of
of the ions-- potassium in our example. Recall that the law of electroneutrality
must be maintained at all times. Thus, when the membrane is permeable to one
of the ions, it cannot cross by itself because that would violate the law of electroneutrality.
This equation is also called the Nernst equation for a monovalent cation. The
Nernst equilibrium potential is the potential at which the electrical and chemical
driving forces for an ion exactly balance each other and there is no net movement of that ion. That is, at equilibrium.
The Nernst Equation is satisfied for ions at
equilibrium and is used to compute the electrical
force that is equal and opposite to the
concentration force.
Eion =
C1
60
× log S2
z
CS
At the Nernst equilibrium potential for an ion,
there is no net movement because the electrical
and chemical driving forces are equal and
opposite.
• Even when there is a potential difference
across a membrane, charge balance of the bulk
solution is maintained.
• This is because potential differences are
created by the separation of a few charges
adjacent to the membrane.
Slide 44
Calculating a Nernst Equilibrium Potential
Cs1 = 100mM
Na+
Cs2 = 10mM
Ac– V +
Eion =
C1
60
× log S2
z
CS
For the model above, the Nernst potential for Na+,
ENa = 60 log(100/10) = +60 mV
Let’s use this equation to calculate the Nernst potential for the Na+ ion. Here
the valence is +1. The equation can be simplified as follows: At 37C, RT/F ~60
mV The log of 100/10 equals 1, therefore 60*1=60. In this case the Nernst potential is positive. We will discuss the significance of the polarity of the potential
in due course.
It is important to remember that there is no net change in the BULK concentration of the cation between the two compartments.
Slide 45
Taking valence of the ion into account
in calculating a Nernst potential
Here, z = -1
ECl = −60 × log
Cl o
Cl i
[Cl-]i = 10 mM [Cl-]o = 100 mM
ECl = −60 × log
100
= − 60 mV
10
Slide 46
EK = 60 × log
[ K ]o
[K ] i
[K+]i = 100 mM [K+]o = 10 mM
EK = 60 × log
10
= − 60 mV
100
Equilibrium potentials of various ions for a mammalian cell
ION Extracellular
Conc. (mM)
Na+
145
Cl
116
K+
4.5
Ca2+
1
Slide 47
Let’s consider what happens when we take a negative valence into account.
Here our example is for Cl- , using the same concentrations as for Na in the previous example. Here the valence is –1. We plug in the numbers into the equation and arrive at a Nernst potential of –60mV, the same magnitude as that determined in our previous example but of opposite polarity.
Intracellular
Conc. (mM)
12
4.2
155
1x10-4
As a final example, let’s use K+ as our monovalent cation. The K+ concentration
inside the cell is higher than the outside. A table is given outlining the relative
concentrations of the various ions. We calculate a Nernst potential of –60mV.
Nernst potentials are also termed equilibrium potentials. Here I list a few using
concentrations that would be found in a mammalian cell. Notice for Ca2+ the
valence we would use to calculate the potential is +2.
Equilibrium
Potential (mV)
+67
-89
-95
+123
Remember:
Log 10/100 = log 0.1 = –1
Log 100/10 = log 10 = +1
A 10-fold concentration gradient
of a monovalent ion is equivalent,
as a driving force, to an electrical
potential of 60 mV.
Slide 48
Membrane potential vs. equilibrium potential
When a cell is permeable to more than one ion then
all permeable ions contribute to the membrane
potential (Vm).
Of course nothing in life is so simple, and cells are permeable to many ions not
just one. The Nernst potential allows us to calculate the equilibrium potential
for one ion only. If the cell were permeable to one ion this equilibrium potential
would also be called the membrane potential. This is the point at which there is
no net flow of current because the electrical and chemical driving forces for an
ions are equal and there is no net ionic movement.
Slide 49
Membrane Transport
Mechanisms I
Slide 50
1. Most biologic membranes are virtually impermeable to:
 Hydrophilic molecues having molecular radii > 4Å
e.g. glucose, amino acids)
 Charged molecules
2. The intracellular concentration of many water soluble
solutes differ from the medium in which they are bathed.
Thus, mechanisms other than simple diffusion across
the lipid bilayer are required for the passage of
solutes across the membrane.
The plasma membrane is a selectively permeable barrier between the cell and
the extracellular environment which allows the cell to maintain a constant internal environment. Two sets of observations led investigators to believe there
were additional transport mechanisms. One observation was that most biological membranes are virtually impermeable to hydrophilic molecules greater than
4 angstrom in diameter. These include glucose and amino acids, therefore, the
nutrients and building blocks we require to sustain life would be excluded from
the cell. Similarly, charged molecules are excluded. A second observation was
that the composition of many water soluble substances are different inside versus outside the cell. Recall the concentration of potassium is greater inside the
+
+
cell than outside and the opposite holds true for Na , that is the [Na ] concentration is higher in the ECF than in the ICF. This assymetry is essential for many
processes including nerve conduction and muscle contraction. Thus, diffusion
processes alone cannot account for the assymetries.
Slide 51
Transport across cell membranes
We know that some molecules such as water and gases can diffuse across the
cell membrane. Ions and hydrophilic solutes partition poorly into the lipid bilayer, thus simple passive diffusion of these solutes is negligible. Integral membrane proteins we talked about in the first lecture have evolved into specialized
proteins that serve to transport or aid the movement of specific molecules.
There are two principal types of passive diffusion via integral membrane proteins: simple and facilitated. One key property of this type of transport is that
these molecules do not directly require energy from the cell. Molecules will
move from an area of high concentration to that of low concentration, that is
down their concentration gradient. Three types of protein pathway through the
membrane are recognized: pores, channels and carriers. Certain carrier proteins transport solute against the electrochemical gradient, these require energy input and require ATP hydrolysis.
Slide 52
Transport through pores
Some intrinsic proteins form pores that are always open. Two physiological
examples are given here.
First, porins are found in the outer membrane of mitochondria, They Allow
≤5-kDa solutes to pass from cytosol to intermembrane space of mitochondria.
Second perforin which is a protein utilized by T lymphocytes which kill target
cells by permeabilizing the target cell membrane to granzymes, ions, water, etc.
A general characteristic of pores
is that they are always open.
Examples:
1) Porins are found in the outer
membrane of gram-negative
bacteria and mitochondria..
2) Monomers of Perforin are
released by cytotoxic T
lymphocytes to kill target cells
from: Boron, W.F. & Boulpaep, E.L., eds., Medical Physiology, 2003.
Slide 53
Transport Through Channels
General Characteristics of
ion channels:
1) Gating determines the
extent to which the
channel is open or
closed.
2) Sensors respond to
changes in Vm, second
messengers, or ligands.
Ion channels are similar to pores in that they form a hollow tube through the
membrane, but they differ in that they are gated. These proteins have specially
adapted structures that allow them to open and close. Conformational changes
within the protein molecule either allows, or blocks, the transport of ions. Specialized structures within the protein form selectivity filters, that is, they allow
passage of certain ions over others.
3) Selectivity filter
determines which ions
can access the pore.
Source: Boron, W.F. & Boulpaep, E.L., eds., Medical Physiology, 2003.
Slide 54
4) The channel pore
determines selectivity.
Why do we need to know how ion channels
influence cells……..?
Macular degeneration
Na+ channel blocker
Slide 55
Solute movement through pores
and channels occurs via simple
diffusion, is passive and
downhill. Metabolic energy is not
required.
Slide 56
Transport through carriers
Carriers never display a continuous transmembrane path.
Transport is relatively slow (compared to pores and channels)
because solute movement across the membrane requires a
cycling of conformation changes of the carrier to allow the
binding and unbinding of a limited number of solutes.
Slide 57
Carrier mediated transport
Cotransporter Exchanger
Facilitated diffusion: the carrier transports solute from a
region of higher to lower concentration. No additional energy
sources are required.
In the case of carrier proteins, there is never a continuous conduit between
the inside and outside of the membrane. There are generally two gates that
never open at the same time. Within the translocation path, there are binding
sites for the solute that is transported and under certain conformational
changes in the protein molecule the transiting particle can be trapped within
the path. The fundamental transport event for a channel to function is “opening’ whereas for a transporter the transport event is a complete cycle of conformational changes. Because the number of binding sites is limited the rate of
movement of solute is orders of magnitude lower than that for a channel. This is
an example of a carrier in which only one solute is translocated and is the simplest form of carrier protein that mediates facilitated diffusion.
Slide 58
Carrier-mediated transport:
Facilitated diffusion
 Such proteins are important for:
1) the transport of cell nutrients and multivalent ions
2) ion and solute asymmetry across membranes
 While diffusion processes display a linear relationship between
flux and solute concentration, carrier transport exhibit saturation
kinetics.
 Hyperbolic plots of transport activity Jx vs. [X] are indicative
of Michaelis-Menten enzyme kinetics.
 Carrier-mediated transporters display competitive inhibition
Jx =
Fick’s 1st law
Slide 59
J max ⋅ [ X ]
Km + [ X ]
Carrier mediated transport:
Active Transport
• Movement of an uncharged solute from a region of lower
concentration to higher concentration (uphill)
• Movement of a charged solute against combined chemical
and electrical driving forces
• Requires metabolic energy
• Two classes: primary and secondary
Slide 60
Primary Active Transport – Na-K ATPase
• ATP-dependent
• Electrogenic
• Important for maintaining ionic gradients (conduction,
nutrient uptake)
• Important for maintaining osmotic balance
Slide 61
Secondary Active Transport-Symport
An example of a secondary active transporter is the
electroneutral Na/Cl cotransporter.
Na+
Cl-
Na+
The energy released from Na+ moving down its electrochemical gradient is
used to fuel the transport of Cl– against its electrochemical gradient. Note
that the Na+ pump plays an important role in maintaining a continual Na+
gradient.
Carrier mediated transporter systems are important for the translocation of
solutes and multivalent ions either into or out of the cell, and secondly for generating assymetry across the cell membrane. Typically diffusion processes, such
as the movement of potassium through a K channel, display a linear relationship
between flux and solute concentration (described by the Fick equation), carriermediated transporter processes exhibit saturation kinetics. That is the rate of
transport gradually approaches a maximum as the concentration of the solute
transported by the carrier increases. Once this maximal rate, Jmax, or plateau
has been reached, any further increase in concentration elicits no further
change on the transport rate. Plots of the rate of transport against concentration often closely resembles the hyperbolic plots characteristic of MichelisMenten enzyme kinetics, and under these conditions, the kinetics of the transport can be described by defining the maximum transport rate Jx, equals Jmax
times [X] divided by (Km + [X]) where [X] is the solute concentration. Km is the
solute concentration at which Jx is half of the maximal flux (Jmax). The lower
the Km, the higher the apparent affinity of the transporter for the solute. In
order to be transported solute must first bind to the transporter, binding sites
are finite, so if two or more solutes are present that can be carried by the transporter in question, each will compete for binding. They thus display competitive
inhibition.
There are two classes of carrier-mediated transporters, those that are involved in facilitated diffusion and those that are involved in active transport. For
facilitated diffusion the carrier transports solute from an area of high to low
concentration, and no additional energy input is required. Active transport involves ATP hydrolysis, either directly or indirectly, and the transporter can move
solute from an area of low to high concentration, that is against its concentration gradient. Active transport can be further subdivided into primary or secondary. Primary active transport directly involves ATP hydrolysis. Secondary
active transport refers to processes that mediate the uphill movement of solutes but are not DIRECTLY coupled to metabolic energy. Instead the transporter
derives its energy by coupling the movement of one of the transported solutes
to the downhill movement of another solute.
The classic example a of primary active transporter is Na-K ATPase found in all
mammalian cells also known as the Na+ pump. All primary active transporters
are capable of hydrolyzing ATP and use the chemical energy released to perform the work of transport. The precise mechanism whereby the chemical
energy of the terminal phosphate bond of ATP is converted into transport in not
clearly understood. Notice that 3 Na+ ions are exchanged for 2 K+ ions and is
thus an electrogenic transporter. That is it has a 3:2 stoichiometry. The movement of solute generates a high intracellular K+ concentration and low Na+ Concentration inside the cell. Note, if there was a 1 for 1 exchange, it would be
termed electroneutral. This transporter is extremely important for maintaining
ionic gradients, and is involved in establishing gradients for nutrient uptake and
membrane potentials for example. Furthermore the Na+ pump is important for
maintaining osmotic balance.
One example of a secondary active transport mechanism is the NaCl cotransporter. The NaCl transporter utilizes the Na+ gradient established by the Na+
pump. Recall the Na+ pump moves Na+ out of the cell and K+ into the cell, thus
inside the cell, the concentration of Na+ is low, outside it is high. The NaCl cotransporter uses this gradient to translocate Cl- into the cell against its electrochemical gradient. Note sometimes multiple ions are transported as is the case
for the NaKCl cotransporter found in a variety of cells. Remember these are cotransporters because they move all solutes in the same direction. Others that
move one solute in one direction and another in the opposite direction are
termed exchangers or antiporters. Some examples include Na/H, Na-Ca etc.
Slide 62
Comparison of Pores, Channels, and Carriers
PORE
CHANNEL
CARRIER
Conduit through
membrane
Always open
Intermittently
open
Never open
Unitary event
None
(Continuously
open)
Open/close
Cycle of
conformational
changes
Particles
translocated
per ‘event’
---
60,000 *
1-5
Particles
translocated
per second
Up to 2
billion
1-100 million
200-50,000
* Assuming a 100 pS channel, a driving force of 100 mV and an open time of 1 ms
Slide 63
The “pump-leak” model
(generating the membrane potential)
Na+
K+
~
Na+
K+
Cl–
Pr–
The Na-pump that pumps 2 K+ into the cell in exchange for 3 Na+ out.
Under steady-state conditions, the diffusion of each ion in the opposite
direction through its channel-mediated “leak” must be equal to the amount
transported.
For most cells, however, PK > Pna. In the absence of a membrane potential, K+
would diffuse out of the cell faster than Na+ would diffuse in, thereby
violating the law of electroneutrality. Thus, a Vm is generated that reduces
the diffusion of K+ out of the cell and simultaneously increases the
diffusion of Na+ in.
Vm is generated by the ionic asymmetries across the membrane, which are
established by the Na-pump.
Slide 64
Gibbs-Donnan Membrane
Equilibrium
•Proteins are not only large, osmotically active
particles but they are also negatively charged
anions
•Proteins can influence the distribution of other
ions so that electrochemical equilibrium is
maintained
The plasma membranes surrounding cells of higher animals not only contain
Na+- pumps, but are also traversed by channels that allow the diffusion or leak
of Na+ and K+. There are other examples of pump-leak systems, but we use this
system because it is fairly ubiquitous and is essential in energizing a variety of
other secondary active pumps and bioelectric processes and the maintenance of
cell volume. As we now know, the Na pump uses energy derived from ATP hydrolysis to pump 3 Na+ ions out of the cell and 2 K+ ions into the cell. This results
in a low intracellular Na+ concentration and high K+ concentration and sets the
stage for movement of Na+ and K+ through their respective channels or leak
pathways down their concentration gradients. At steady state the movements
of Na+ and K+ through the pump must be precisely balanced by the leak of Na+
and K+ in the opposite directions. For most cells, however, the permeability of
the membrane to K+ is greater than to Na+ and in the absence of the pump, K+
would tend to diffuse out of the cell faster than Na+ could move in, this would
violate the law of electroneutrality. Thus a negative Vm is generated that slows
down the movement of K+ out of the cell and increases the diffusion of Na+ into
the cell. Thus the cell membrane potential is generated by the ionic assymetries
– the Vm is dependent on the individual permeability and concentrations of the
ions.
Slide 65
Gibbs-Donnan Equilibrium
Na+
Cl–
Na+
P–
1
Na+
Cl–
2
Na+
Cl–
P–
1
Initially
2
Equilibrium
In the simple model system above, Cl– will diffuse from 1
→ 2, and Na+ will follow to maintain electroneutrality. In
compartment 2 then, Cl– will be present and [Na+]equil. >
[Na+]initial at Donnan equilibrium.
Because of the asymmetrical distribution of the
permeant ions, there must be a Vm that simultaneously
satisfies their equilibrium distributions.
Slide 66
Gibbs-Donnan equilibrium
(the tendency for cells to swell)
At equilibrium, the increase in osmotically active particles
leads to the flow of water into compartment 2.
Na+
Cl–
Equil.:
Na+
Cl–
H 2O
1
P–
2
In animal cells, the presence of large impermeant
intracellular anions tends to lead to cell swelling due to
Donnan forces. However, the Na+ pump actively extrudes
osmotic solutes and counteracts the cell swelling.
We have discussed the role of the Na-pump in generating the membrane potential and also in solute movement. Another important role for the Na-pump is
to maintain intracellular osmolarity and prevent osmotic flow of water into the
cell and therefore prevent cell swelling. That is the Na-pump is involved in cell
volume regulation. We are back to our two-compartment model with a semipermeable membrane. Here the membrane is freely permeable to Na+, Cl- and
water but is impermeable to negatively charged proteins (P-). The macromolecules themselves contribute very little to the osmolarity of the cell because despite their large size, each one only counts as a single molecule and there are
relatively few of them compared with the number of small molecules inside the
cell. However, most biological macromolecules are highly charged and they
attract many inorganic ions of the opposite charge. Because of their large numbers these ions make a major contribution to the intracellular osmolality. A NaCl
solution is added to compartment 1 and Na salt of a protein to compartment 2.
Let’s assume initially that the Na concentration initially on both sides of the
membrane is equal. After a certain length of time the system reaches a state of
equibilrium known as Gibbs-Donnan equilibrium. Because Cl- can permeate the
membrane it will move down its concentration gradient, but because the protein molecules cannot cross the membrane, if left unchecked the system would
+
violate the law of electroneutrality, thus Na must also move in this case from
compartment 1 to 2. Eventually, the NaCl concentration in 2 will exceed that in
1. As we have learned if there is an asymmetrical distribution of charge across a
membrane there must also be an electrochemical potential difference, or Vm
that balances the concentration gradient and is given by the Nernst equation. A
cell that does nothing to control its osmolarity will have a higher concentration
of solutes on the inside than the outside of the cell. As a result the water concentration will be higher outside the cell than inside. The difference in the water
concentration across the plasma membrane will cause water to move continuously into the cell by osmosis causing it to rupture.
As we now know, the cell membrane is also permeable to water, thus at equilibrium the number of osmotically active particles in compartment 2 will exceed
those in 1 and thus water will move from 1-2. If the membrane were distensible, it would bulge into compartment 1. In mammalian cells, the presence of
large impermeant anions inside the cell would lead to cell swelling and ultimately bursting due to Donnan forces. However, to prevent this occurring, the Na
pump actively extrudes osmotically active solutes and thus plays a role in cell
+
volume regulation. There is an active extrusion of 3 Na in exchange for influx of
+
+
2 K that is balanced by the passive influx of 3Na and passive efflux of 2K+. The
net flux of Cl- is zero. If the Na+ pump is inhibited (e.g. by ouabain), there is a
net gain of 1 intracellular cation accompanied by a slight depolarization. This
depolarization leads to passive influx of 1 Cl to maintain electroneutrality. Thus
there is a net intracellular gain of one anion and 1 cation that increases the
number of osmotically active particles and hence the osmotic gradient leads to
cell swelling. Of course in a ‘real’ cell this is a gross oversimplification because
there are a host of transporters and channels to consider.
Note: The presence of impermeant anions in the cytoplasm contribute only ~10mV to the resting membrane potential.
Slide 67
The Na-pump (Na-K pump) is essential
for maintaining cell volume
Na+
2K+
ClH 2O
~
K+
Na+
K+
P[Na+]
+]
[K
3Na+ [Cl ]
P-
~
↑[Na+]
↓[K+]
↑[Cl-]
ClH2 O
Equal number of +ve and
–ve charges move:
Equilibrium
Inhibition of the Napump (ouabain) → cell
swelling
Because plasma membranes are not rigid, the cell cannot generate a hydrostatic pressure gradient. Thus cells would tend to swell and burst in their attempt
to achieve GD equlibrium. To balance the effect of the negatively charged macromolecules the cell must actively extrude Na, so the net effect is that NaCl is
largely excluded from the cell. The importance of the Na pump in controlling cell
volume is indicated by the observation that many cells swell and often burst if
they are treated with oubain (pump inhibitor). Cells contain a high concentration of solutes, including numerous negatively charged organic molecules that
are confined to the inside of the cell (fixed anions) and their accompanying cations are required for charge balance. This tends to create a large osmotic gradient that, unless balanced would tend to pull water into the cell. For animal
cells this effect is counteracted by an opposite osmotic gradient due to a higher
concentration of inorganic ions chiefly Na and Cl in the extracellular fluid. The
Na pump maintains osmotic balance by pumping the Na that leaks down its
steep electrochemical gradient. The Cl is kept out by the membrane potential.
As the intracellular K concentration declines the cell depolarizes, and as the
cell becomes less negative Cl is again allowed to enter the cell.
Slide 68
Membrane Transport
Mechanisms II
and the Nerve Action
Potential
Slide 69
Apical
Epithelia
Microvilli
Tight junction
Basal Lamina
Basolateral
• Lie on a sheet of connective tissue (basal lamina)
• Tight Junctional Complexes:
 Structural
 Allow paracellular transport
• Apical membrane; brush border (microvilli) –
increases surface area
• Apical (mucosal, brush border, lumenal) and
basolateral (serosal, peritubular) membranes have
different transport functions
• Capable of vectorial transport
An epithelium is an uninterrupted sheet of cells joined together by a continuous hoop, called the tight junction. Epithelial sheets line the inner and outer
surfaces of the body. For example, the GI tract is lined in its entirety by epithelial cells. There are a variety of types of epithelial cell, but they all have a common feature in that they lie on a sheet of connective tissue, termed the basal
lamina shown here in pink. The tight junctional complexes serve two purposes.
First, they are attachment points and maintains the integrity of the cell sheet
and also will allow the movement of water, solutes and even cells from one
body compartment to another. The apical surface of almost all epithelial cells
have at least a few short finger-like extensions, called microvilli ("tiny hairs").
Epithelia that are specialized for absorption, like that of the small intestine,
have a brush border, which consists of a large number of these microvilli on
each cell. The apical surface of other epithelial cells, like some of the ones lining
the trachea, have cilia ("eyelashes"), which are extensions that look a little like
microvilli, but are longer and have a different structure and function. Within the
cytoplasm at the core of each cilium is a bundle of microtubules.
Slide 70
Models of Ion Transport in Mammalian Cells
e.g. Cl- secretory cell
Transepithelial potential difference
NEGATIVE
POSITIVE
Na+
APICAL/
MUCOSAL
SIDE
K+
ClNa+
Na+ BASOLATERAL/
K+
SEROSAL/
ClBLOOD SIDE
K+
H 2O
Paracellular
Transcellular
Slide 71
Absorptive Epithelia - e.g. Villus cell
of the small intestine
Na+-driven glucose
symport
Lateral domain
Carrier protein
mediating passive
transport of glucose
Basal domain
(Modified from: Alberts et al., Molecular Biology of the Cell, 4th Ed. Garland Science, 2002)
Slide 72
Common Gating Modes of Ion Channels
(Source: Alberts et al., Molecular Biology of the Cell, 4th Ed. Garland Science, 2002)
Here is a typical cell model. Let’s consider some of the key points to remember. First, the cell is polarized and can be separated into an apical, also called
the brush border or mucosal side and basolateral, or serosal side. The apical
membrane faces toward the lumen. So, for example, if you imagine your gut is a
tube the center of the tube is the lumen and the outside of the tube would face
the blood. Solutes and water can move either between the cells, this is termed
paracellular; or through the cells, termed transcellular. The tight junctions play
yet another role in polarizing the epithelium and prevent the lateral movement
of ions from the apical side to the basolateral side or vice versa. In addition to
membrane potentials, there can also be transepithelial potentials. That is the
lumenal side of the cell can have a different potential with respect to the blood
side. This potential can also play a role in the movement of charged molecules.
For example in the case where the lumen is negative, a positively charged ion
will move down its electrical gradient. Let’s use the example shown here to introduce how membrane transporters and channels functionally interact to enable NaCl secretion. 1. Active transport –Na pump. Na gradient – Na moves down
its concentration gradient via the NaKCl cotransporter. A basolateral K conductance sets the membrane potential of the basolateral membrane. Cl channels
on the apical membrane open and allow movement of Cl form the cell to the
lumen. Na moves paracellularly following the negatively charged Cl ion combined with osmotic movement of water. The net result: NaCl secretion.
So now let’s consider a cell that is capable of absorbing solute. Let’s use the
absorption of glucose in the GI tract as our example. Again we have the basolateral energy utilizing Na pump setting up a concentration gradient. The Na concentration gradient set up by the pump enables the influx of glucose via a secondary active transport mechanism the Na-glucose cotransporter/symporter
(SGLT1) we introduced yesterday. In this case the glucose concentration is high
inside the cell and so glucose is moving against its concentration gradient from
low to high. Now we have set up a concentration gradient for glucose across the
basolateral membrane and glucose now wants to move down its concentration
gradient via a facilitated diffusion mechanism mediated by glucose transporters
on the basolateral membrane. Note these transporters are different from the
apical glucose transporters. Note the tight junctions are impermeable to glucose
so once on the basolateral side it will stay there. It is worth noting that the paracellular pathway and the fibers of the tight junctions that make up the junctions are not simply a random mesh, rather they contain specialized proteins.
One such example is paracellin 1, a kidney tight junction protein that is important for renal Mg absorption.
Voltage-gating is only one way in which channels are opened. Other methods
include ligand gating and mechanical gating.
Slide 73
Diffusion of electrolytes through
membrane channels
The following are three important features of ion channels
that influence flux :
1) Open probability (Po). Opening and closing of channels are
random processes. The Po is the probability that the channel is
in an open state.
2) Conductance. 1/R to the movement of ions. Where V=IR
(Ohms law)
I
V
3) Selectivity. The channel pore allows only certain ions to
pass through.
Slide 74
Electrophysiological Technique: Patch Clamp
Slide 75
Terminology and Electrophysiological Conventions
Membrane
potential (Vm)
+100 mV
(Positive)
Depolarize
OUTWARD
CURRENT
I
V
0 mV
-100 mV
Slide 76
-100 mV
Hyperpolarize
+100 mV
Reversal
Potential
(I=0)
(Negative)
INWARD
CURRENT
How the behavior of an ion channels can be
modified to permit an increased ion flux:
Control/ Wild-type:
Closed state
Open state
An increase in conductance (more current flows/opening)
but the open probability stays the same:
Closed state
Open state
An increase in open probability (the channel spends more
time in the open state, or less time in the closed state)
but the conductance stays the same:
Closed state
Open state
The slope of the line is used to determine the conductance of an electrophysiological process. This can be for either macroscopic currents or single channel.
The slope of the line when studying macroscopic currents in a cell is a combination of all individual conductances in the cell. For a single channel, the slope of
the line is used to determine the conductance of an individual channel. The reversal potential in this case would be used to determine the selectivity of the
channel being studied. Another term you may come across is open probability.
This is the probability that a channel is in an open state. These three are characteristics that determine the overall flux - open probability, conductance and
selectivity. In the next slide we will see how if single channel behavior changes,
how this influences flux through a channel.
Here we introduce some of the terminology that you will encounter. As the
cell membrane becomes more positive it is said to depolarize. Conversely, as
the cell membrane potential becomes more negative, the membrane potential
is said to hyperpolarize. On the right hand side is a schematic of a currentvoltage relationship. Much can be learned about the electrophysiological properties of either whole cells, portions of a cell membrane or single ion channels
and transporters using the techniques we discussed in the previous slide. You
may come across these IV relationships. Much information is obtained from
such a graph. As the current goes from inward to outward the line traverses the
X axis - the point at which this occurs is called the reversal potential i.e. the
point at which the net current is zero.
Here pink is used to represent the closed state of the channel, downward deflections are channel openings. Thus blue represents the open state. Modification of the channel protein, for example by phosphorylation can alter the channel conductance. Thus the deflections would become larger. Another way that
ionic flux could be increased is to increase the channel open probability as
shown on the lower figure. Here the channel spends less time in the closed
state and more time in the open state, thus for a given period of time, more
ions would be permitted to flow.
Slide 7
Ionic currents through a single channel
sum to make macroscopic currents
TIMEdependent
closure
Na+ Channel
K+ Channel
VOLTAGE-GATED CHANNELS
VOLTAGEdependent
closure
Slide 78
Shown here are two examples of voltage-gated channels at the macroscopic
and single channel level. On the left is a recording of voltage-gated Na+ channel
activity. A stepwise change in the potential induces these voltage-gated channels to open and a sudden increase in macroscopic current is observed. If one
records these channels in the cell, many of these channels open together and a
macroscopic current is elicited in response to this voltage pulse. The lower panel shows the activity of a single channel, where downward deflections represent
inward current through the channel. Notice in this case, that the channels spontaneously begin to close in a time-dependent manner, illustrated clearly in the
macroscopic current trace. Later we will be discussing the generation of the
action potential and the importance of this channel behavior will become ap+
parent. On the right hand side is an example of a voltage-gated K channel.
Again a stepwise change in potential elicits a channel opening, but notice here
the channel only closes down when the potential is stepped back to its original
value. Here openings are upward, representing outward K+ movement. Thus
closure of this channel is voltage, not time dependent.
The resting membrane potential is when the cell is in a steady state condition
and there is now net charge flow. This potential depends upon the relative
permeability of the cell in question to any permeant ion.
The resting membrane potential (Vm) describes a
steady state condition with no flow of electrical
current across the membrane.
Vm depends at any time depends upon the
distribution of permeant ions and the permeability
of the membrane to these ions relative to the
Nernst equilibrium potential for each.
Slide 79
20
0
-20
-40
-60
-80
Resting
potential
Slide 80
Overshoot
Depolarizing phase
Membrane Potential (mV)
The Nerve Action Potential
Threshold
-5
0
Repolarizing
Phase
5
10 15 20
Time (ms)
After-hyperpolarization
Changes in the underlying
conductance of Na+ and K+ underlie
the nerve action potential
Certain types of cells are called excitable, that is if the membrane potential is
depolarized beyond a certain level, the threshold, a large potential change ensues and an action potential can be elicited. This is an action potential recorded
from a neuron illustrating several features. First, the resting potential of the cell
is negative. A slow depolarization raises the membrane potential to a threshold
level at which time an action potential is elicited in an all-or-none manner. The
membrane potential rapidly depolarizes and becomes more and more positive
reaching a crest known as the overshoot. The cell potential then repolarizes,
progressively becoming more negative. For a period of time the cell is even
more negative than at rest, this phase of the action potential is known as the
after-hyperpolarization.
Two types of conductance underly the nerve action potential. We will discuss
these in more detail shortly. First a Na+ conductance which is responsible for the
upstroke of the action potential and second a K+ conductance which is responsible for repolarization of the cell. We will consider each of these in due course
but first let’s consider the underlying forces on sodium and potassium.
Slide 81
Chemical and electrical gradients prior
to initiation of an action potential
K+
Na+
•At rest, the cell membrane
potential (Vm-rest) is generated
by ion gradients established by
the Na- pump.
•The K+ conductance
(permeability) is high, Na+
conductance is extremely low,
hence Vm-rest is strongly negative.
+
Slide 82
A stimulus raises the intracellular potential to a threshold
level and voltage-gated Na+ channels open instantaneously
Stimulus
Na+
+
Na+
Na+
+
+ +
+ +
+
Na+
+
Na+
Slide 83
Membrane Potential (mV)
+
The rapid upstroke, or
depolarizing phase, is due to
an increase in Na+ conductance
of the cell membrane due to
activation of voltage-gated
Na+ channels. An all-or-none
response. The cell potential
moves toward ENa due to
20 chemical and electrical driving
forces. Vm does not reach ENa.
0
-20
-40
-60
0
5
10
15
Time (ms)
Na+
K+ Cl-100
As the cell is stimulated, the cell membrane potential is depolarized and
reaches a threshold potential (approximately -50 - -20 mV) which leads to the
opening of voltage-gated Na channels. There is a large concentration gradient
for Na to flow into the cell and also a strong electrical influence for positive
charge movement into the cell given the negative resting membrane potential.
Thus under the influence of both strong concentration and electrical gradients
as soon as the Na channels open Na moves into the cell and the cell depolarizes.
1. The membrane becomes permeable to Na+ and
there is a rapid Na+ influx due to due to both
electrical and chemical gradients. The cell
membrane potential becomes progressively, but
rapidly, more positive - i.e. it depolarizes
20
-80
We learned how the Na+ pump generates an inwardly directed Na gradient
and an outwardly directed K+ gradient. It is important to remember that the Na+
pump only generates the gradients, it is the presence of ion channels that leads
to the generation of membrane potentials. So at rest, the neuron has a negative
potential - closer to the reversal potential of K+, which is approximately -90mV,
than Na+ which has a reversal potential of approximately +70mV. There is also a
Cl- conductance which contributes to the resting potential. Thus there are both
chemical and electrical forces that can influence ion movement. NOTE: the electrogenic nature of the Na-pump contributes only about 10% to the membrane
potential. The remaining 90% depends on the pump indirectly.
-50
Slide 84
2. Na+ channels Na+
begin to close:
0
+50
+
+
+
+
+
+
+100
Na+
+
+
+150
+
+
+
+
K+
++
+
+
Eion
3. Outward K+ gradient
4. Outward K+ flux
as voltagedependent K+
K+
channels open →
hyperpolarization
K+
- -
- -
-
K+
K+
Thus, the inward movement of Na results in the upstroke of the action potential. The cell membrane potential moves toward ENa because of the increase in
permeability as Na channels open. The potential does not quite reach ENa however because these channels exhibit time dependent closure, or inactivation, as
we discussed earlier. A the same time the Na+ channels are beginning to inactivate, voltage-gated K+ channels activate. The net result is that the membrane
potential never reaches ENa. The stronger the initializing stimulus, the more Na+
channels that open and the more positive the overshoot.
5. Cell repolarizes
So here at stage 2 the Na+ channels are inactivating. The cell is now depolarized, so let’s consider the forces on K+. Remember the Na+ pump sets up a large
concentration gradient for K+. In addition as the membrane potential has become positive due to the efflux of Na+, there is an additional electrical gradient
that favors the movement of positive charge out of the cell. Thus as the voltagegated K+ channels open, there are both concentration and electrical gradients
for K+ efflux. These channels open in response to depolarization and the net
result is repolarization of the cell.
Membrane Potential (mV)
Slide 85
20
0
-20
-40
-60
-80
0
5
10 15
Time (ms)
20
As the cell depolarizes, the
Na+ channels inactivate and
the permeability to Na+ is
reduced. Voltage-gated K+
channels open and the cell
membrane potential becomes
permeable to K+ thereby
driving Vm toward EK. The
continued opening of K+
channel causes a brief afterhyperpolarization before the
cell returns to its resting
membrane potential.
K+ Cl-100
Slide 86
-50
Na+
0
+50
Ca2+
+100
+150
Eion
Gates Regulating Ion Flow Through
Voltage-gated Na+ Channels
DEPOLARIZING Vm
REST
ACTIVATED
(UPSTROKE)
INACTIVATED
out
in
Na+
REPOLARIZATION
→HYPERPOLARIZATION
Slide 87
Activation gate
Inactivation gate
REFRACTORY PERIODS
During RP the cell is incapable of eliciting a normal
action potential
• Absolute RP: no matter how great the stimulus an
AP cannot be elicited. Na+ channel inactivation gate is
closed.
• Relative RP: Begins at the end of the absolute PR
and overlaps with the after-hyperpolarization. An
action potential can be elicited but a larger than
normal stimulus is required to bring the cell to
threshold.
Thus the repolarization of the cell in response to increased K+ efflux and decreased Na+ influx is shown here in purple. Now the cell is highly permeable to
K+ and the cell membrane potential moves toward EK. Unlike the Na+ channels
that closed in a time dependent manner, the K+ channels close in response to
membrane potential. As a result the cell moves very close to EK and becomes
strongly hyperpolarized. For a brief time there is a hyperpolarization of the cell
membrane potential beyond the resting membrane potential. This is known as
an afterhyperpolarization. Eventually, these voltage-gated K+ channels close and
the cell membrane potential returns to its resting state.
During an action potential, sodium channels first activate, driving the upstroke, and then inactivate, facilitating repolarization to the resting potential.
The channel's m gate (activation gate) is closed at rest and activates rapidly to
an open state after depolarization. The inactivation gate (h gate) is open at rest
and closes relatively slowly after depolarization. Hodgkin and Huxley's empirical
model attributed the behavior of what are now called gates to a voltage sensor/effector belonging to each gate, which sensed the voltage and opened or
closed the attached gate. Later work showed that only the m gate has a voltage
sensor/effector. The apparent voltage sensitivity of inactivation comes from the
fact that a receptor for an “inactivation particle” becomes available only when
the activation gate is partially or fully activated. A further conformational
change in response to the repolarizing Vm forces the h gate to swing into the
resting position.