biological membranes and principles of … material/fundamentals i test 3/xid...and define the...

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

• 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 glyco-

calyx • 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

• 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 driv-

ing 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 Goldman-

Hodgkin-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

• 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

• 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 move-ment of charge and the shape of the action potential.

• Explain the refractory period in excitable cells and the its molecular basis PART 4: REVIEW

• 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

Carmel M. McNicholas, Ph.D.Department of Physiology & Biophysics

Contact Information:MCLM 868934 1 785

cbevense@uab. edu

BIOLOGICAL MEMBRANES AND PRINCIPLES OF SOLUTE AND WATER

MOVEMENT

Sept. ‘11

Slide 2 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.

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.

Slide 4

[Na+] = 15 mM[K+] = 120 mM[Cl-] = 20 mM

[protein] = 4 mMOsmolality = 290

mOsm

EXTRACELLULAR (~40%) INTRACELLULAR (~60%)

[Na+] = 142 mM[K+] = 4.4 mM[Cl-] = 102 mM

[protein] = 1 mMOsmolality = 290 mOsm

Capillary endothelium

BLOODPLASMA

~3 LINTRACELLULAR

FLUID~25 L

TRANSCELLULAR FLUID~1 L

Composition: variable

[Na+] = 145 mM[K+] = 4.5 mM[Cl-] = 116 mM

[protein] = 0 mMOsmolality = 290 mOsm

INTERSTITIAL FLUID~13 L

Plasma membraneEpithelial cells

The fluid compartments of a 70kg adult human

TOTAL BODY WATER (~42 L)Modified from: Boron & Boulpaep, Medical Physiology, Saunders, 2003.

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 com-partments.

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 con-tained within the ECF, which is further divided into two compartments: the plasma and the interstitial fluid. Cell membranes separate the ICF and ECF com-partments. There is a further sub-compartment of the extracellular fluid called transcellular fluid (e.g. synovial fluid, CSF) which is approx. 1L. Water and so-lutes 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.

Solute composition of key fluid compartments

•Osmolality constant

•Cell proteins –10-20% of the cell mass

•Structural and functional

The composition of the various body fluid compartments are strikingly differ-ent. The most important ions inside the cell are potassium, magnesium, phos-phates, bicarbonate and in lesser amounts sodium, calcium and chloride. Typi-cally, 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.

Slide 6 Membranes are selectively permeable

Gas molecules are freely permeable

Large / charged molecules need ‘assistance’ to traverse the plasma membrane

Small uncharged molecules are freely permeable









The composition of cellular membranes determines the permeability to vari-ous solutes and water. We will discuss the mechanisms that have evolved to allow for the transport of molecules across cellular membranes, however spe-cializations within the cell have evolved to allow for movement of substances into and out of cells.

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, mem-brane proteins come in two forms: peripheral proteins, which are dissolved in the cytoplasm and relatively loosely associated with the surface of the mem-brane, 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: em-phasis 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, ori-ginate from within a microdomain structure, where lipid–lipid, protein–protein, and protein–lipid interactions, as well as sub- and supramembrane (cytoskelet-al, extracellular matrix, other cell) effectors play equally important roles.

The Extracellular Matrix

The extracellular matrix (ECM) of animal cells functions in support, adhesion, movement and regulation

Epithelial cell

Basement membrane

Capillary endothelium

Connective tissue and

ECM

Fibroblast

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 require-ments. 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 intersti-tial 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 epi-thelial 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 fac-tors, 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.

Slide 9 The Extracellular MatrixThe 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, elastinTwo 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

Proteins have two functional types - they can be either structural (e.g. colla-gen 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 polypep-tide backbone as an unfolded random coil that always allows it to stretch and recoil, for example in skin. Polysaccharides are found covalently linked to pro-tein in the form of proteoglycans.

Slide 10 The CytoskeletonIntracellular network of protein filaments

RoleSupports and stiffens the cellProvides anchorage for proteinsContributes to dynamic whole cell activities (e.g., dividing and crawling of cells and moving vesicles and chromosomes)

Three Types Of CytoskeletalFibers

Microtubules (tubulin - green)Microfilaments (actin-red)Intermediate filaments

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 (vari-ous 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 constant-ly being assembled and disassembled.

Microfilaments are unusual because they vary greatly according to their loca-tion 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 togeth-er. 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 con-tractions necessary for everything from your action on a sports field to the beat-ing of your heart.

Slide 11 Structural JunctionsTight

JunctionsAdhering Junctions

Desmosome Zonula Adherens (belt)

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 exam-ple a protein named Paracellin-1 is found in the kidney where it is involved in paracellular Mg2+ absorption. The “tightness” of tight junctions varies consider-ably 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 epi-thelial 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 ad-herens, are spot-like structures that serve to maintain strong cell-cell adhesion. Hemidesmosomes can anchor cells to the basement membrane.

Slide 12 Gap Junctions

ROLE: Passage of solutes (MW<1000) from cell to cell.• Cell- cell communication• Propagation of electrical signal

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 pro-tein 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 deter-mines their permeability and selectivity.

Slide 13

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.

The Membrane Glycocalyx - cell coat

Alberts et al., Molecular Biology of the Cell, 4th Ed. Garland Science, 2002)

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 carbo-hydrates 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 mechan-ical and chemical damage to the cell. The membrane glycocalyx is also impor-tant in specific cell-cell recognition and interactions between different cells.

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 sur-rounding fluids. Most substances pass through the cell membrane itself by ac-tive 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 macro-molecules, 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 selec-tively secreted. To control secretion, specific substances are stored in secretory vesicles, which are released when triggered by an extracellular signal. The sig-nal, hormones being an example, binds to its specific cell surface receptor. Then the concentration of free Ca2+ is increased in the cell. The increased concentra-tion 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, neuro-transmission, receptor downregulation, antigen presentation, cell polarity, mi-tosis, growth and differentiation, and drug delivery. Endocytosis pathways can be subdivided into four categories: namely, phagocytosis, pinocytosis, clathrin-mediated 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 extra-cellular fluid and molecules within it. The filling of the pocket occurs in a non-specific 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 mor-phologically characteristic crystalline coat made up of a complex of proteins that mainly associated with the cytosolic protein clathrin. Clathrin-coated ve-sicles are found in virtually all cells and from domains of the plasma membrane termed clathrin-coated pits. Coated pits can concentrate large extracellular mo-lecules that have different receptors responsible for the receptor-mediated en-docytosis of ligands, e.g. low density lipoproteins, antibodies, growth factors and many more.

Caveoli are the most common reported non-clathrin coated plasma mem-brane buds, which exist on the surface of many, but not all cell types. They con-sist of the cholesterol-binding protein caveolin with a bilayer enriched in choles-terol 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.

Principles of Solute and Water Movement

Slide 18

Diffusion and Osmosis

Slide 19 Membranes are selectively permeable












Because of the cell membrane’s hydrophobic interior, the lipid bilayer serves as a barrier to charged molecules. This is imperative in maintaining the compo-sition 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 translo-cation of these ions. These specialized proteins are known as membrane trans-port 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 ex-tremely important.

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.

Diffusion is simply the net movement of a substance from an area of high con-centration 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 con-stant 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.

Diffusion of molecules from the extracellular side to the intracellular space is demonstrated is this slide. Eventually when there is no net movement the con-centration is at equilibrium.

Slide 22 Kinetic characteristic of diffusion of an uncharged solute

Model: compartments separated by permeable glass

A = cross sectional area of the glass discCs = concentration of uncharged solute∆x = thickness

compartment 1 compartment 2

∆x

Cs1 Cs

2

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 permea-ble 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.

Slide 23

According to kinetics, the rate of movement can be described as follows:rate of diffusion from 1 → 2 = kCs

1

-{rate of diffusion from 2 → 1 = kCs2}

----------------------------------------------------------------------------net rate of diffusion across barrier

= k(Cs1-Cs

2) = k∆Cswhere k is a proportionality constant.


∆x

Cs1 Cs

2

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 dif-

fusion 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 mem-brane. Properties of both contribute to the movement of the solute.

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 Dsis the diffusion coefficient of the solute.

The concentration gradient across the membrane is the driving force for net

diffusion.

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 “bounc-ing 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.

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 dif-fusion. 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.

Diffusion of an uncharged soluteModel: compartments separated by a lipid

bilayer

Biological membranes are composed of a lipid bilayer of phospholipids interspersed with integral and peripheral

proteins (“Fluid Mosaic Model”).


∆x

Cs1 Cs

2

The problem with our last model is that a biological membrane’s true compo-sition makes things much more complicated. In particular, a biological mem-brane 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.

Slide 27 The partition coefficient, Ks will increase or decrease the

driving force of the solute S across the membrane:Js = KsDs∆Cs/∆x

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

Cs1

HydrophilicKs < 1 Cs

2

LipophilicKs > 1

Partitioning of an uncharged solute across a lipid bilayer

Ks lies between 0 and 1

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 hy-drophilic S.

Thus, our flux equation must take this into account. To do so, we add an addi-tional (unitless) term to the equation: the partition coefficient Ks. Ks can be em-pirically 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 volumeOsmosis 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 wa-ter 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.

1 2 1 2

The solute concentration difference causes water to move from compartment 2 → 1. The pressure

required to prevent this movement is the osmotic pressure.

Time

Osmosis. The flow of volume

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 chemi-cal potential of water is reduced. Free energy is generated by the random movement of the water molecules. Solute reduces this random motion.

Slide 31

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.

(The piston applies pressure to stop water flow)

H2O

Cs2Cs

1

Compartment 1 Compartment 2

Osmosis. The flow of volumeAN IDEAL MEMBRANE

Piston

(Compartment 2 is open to the atmosphere)

(Meniscus)

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

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

Osmosis. Importance of osmolarity

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 coeffi-cient. Here for example we can calculate the osmolarity of a 154 mM NaCl solu-tion. Values for Φ can be obtained from handbooks.

Osmosis. The flow of volumeA NONIDEAL MEMBRANE

Piston H2O

Cs2Cs

1S

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

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. Im-agine such a nonideal membrane in which the membrane was equally permea-ble 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 ref-lection coefficient is a dimensionless number ranging between 0 and 1 that de-scribes 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 deter-mined using the equation ∆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.

Water or volume flow (Jv) across the membrane can also be generated by ap-plying pressure to the piston and creating a hydrostatic pressure difference (∆P) across the membrane. Under such conditions, volume flow will equal the prod-uct 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 com-bination 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 Starl-ing 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.

Slide 36

Arteriole VenuleInterstitial

space

Starling Forces

Osmotic (oncotic) pressure

= fluidmovement

Filtration dominates Absorption dominates

Importance of plasma proteins!

Interstitial fluid pressure under

normal conditions ~0 mmHg

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) re-mains 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.

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 normal-ly.

Slide 38

Principles of Ion Movement

Slide 39

K+

Cs1=100mM

Ac-

Cs2=10mM

Diffusion of Electrolytes

V+–

For charged species, both electrical and chemical forces govern diffusion.

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 concentra-tion difference across the membrane, for a charged solute, we need to consider, in addition, electrical forces.

Slide 40

All solutions must obey the principle of bulkelectroneutrality: the number of positive charges in a solution must be the same as the number of negative

charges.

The Principle of Bulk Electroneutrality

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.

Cs

1=100mM Cs2=10mMK+

Ac-

V +–


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 = Cs

2 = 55mM

Ac- K+

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 ace-tate, 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 hav-ing 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.

Slide 42

Cs1=100mM Cs

2=10mMK+

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:

2

1

log3.2S

SionCC

zFRTE ×=

R = gas constant; T = absolute temp.; F = Faraday’s constant; z = charge on the ion (valence); 2.3RT/F = 60 mV at 37ºC

2

1

log60S

SionCC

zE ×=

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 elec-troneutrality.

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 move-ment of that ion. That is, at equilibrium.

Slide 43 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.

At the Nernst equilibrium potential for an ion, there is no net movement because the electrical and chemical driving forces are equal and opposite.

2

1

log60S

SionCC

zE ×=

• 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

Cs1 = 100mM Cs

2 = 10mMNa+

Ac-

V +–

Calculating a Nernst Equilibrium Potential

For the model above, the Nernst potential for Na+,

ENa = 60 log(100/10) = +60 mV

2

1

log60S

SionCC

zE ×=

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 po-tential 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 concen-tration of the cation between the two compartments.

Taking valence of the ion into account in calculating a Nernst potential

[Cl-]i = 10 mM [Cl-]o = 100 mMi

oClClClE log60×−=

mVECl 6010100log60 −=×−=

Here, z = -1

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 pre-vious example. Here the valence is –1. We plug in the numbers into the equa-tion and arrive at a Nernst potential of –60mV, the same magnitude as that de-termined in our previous example but of opposite polarity.

Slide 46

[K+]i = 100 mM

ION Extracellular Conc. (mM)

Intracellular Conc. (mM)

Equilibrium Potential (mV)

Na+ 145 12 +67 Cl- 116 4.2 -89 K+ 4.5 155 -95

Ca2+ 1 1x10-4 +123

[K+]o = 10 mMi

oKKKE

][][log60×=

Equilibrium potentials of various ions for a mammalian cell

mVEK 6010010log60 −=×=

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.

Slide 47 Remember:

Log 10/100 = log 0.1 = –1Log 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.

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 in-ternal environment. Two sets of observations led investigators to believe there were additional transport mechanisms. One observation was that most biologi-cal 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 ver-sus 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+] concen-tration 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 bilay-er, thus simple passive diffusion of these solutes is negligible. Integral mem-brane 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 pro-teins: 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 pro-teins transport solute against the electrochemical gradient, these require ener-gy input and require ATP hydrolysis.

Slide 52

from: Boron, W.F. & Boulpaep, E.L., eds., Medical Physiology, 2003.

Transport through poresA 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

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.

Transport Through ChannelsGeneral 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.

3) Selectivity filterdetermines which ions can access the pore.

4) The channel pore determines selectivity.Source: Boron, W.F. & Boulpaep, E.L., eds., Medical Physiology, 2003.

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. Spe-cialized structures within the protein form selectivity filters, that is, they allow passage of certain ions over others.

Slide 54 Why do we need to know how ion channels influence cells……..?

Na+ channel blocker

Macular degeneration

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 carriersCarriers 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.

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 “open-ing’ whereas for a transporter the transport event is a complete cycle of con-formational 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 sim-plest form of carrier protein that mediates facilitated diffusion.

Slide 57 Carrier mediated transport

Cotransporter ExchangerFacilitated diffusion: the carrier transports solute from a region of higher to lower concentration. No additional energy sources are required.

Such proteins are important for:

1) the transport of cell nutrients and multivalent ions2) 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

Carrier-mediated transport: Facilitated diffusion

Fick’s 1st law][][max

XKXJJ

m

x+⋅

=

Carrier mediated transporter systems are important for the translocation of solutes and multivalent ions either into or out of the cell, and secondly for gene-rating 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), carrier-mediated 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 concentra-tion often closely resembles the hyperbolic plots characteristic of Michelis-Menten enzyme kinetics, and under these conditions, the kinetics of the trans-port 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 trans-porter in question, each will compete for binding. They thus display competitive inhibition.

Slide 59 Carrier mediated transport:

Active Transport• Movement of an uncharged solute from a region of lowerconcentration to higher concentration (uphill)• Movement of a charged solute against combined chemical and electrical driving forces• Requires metabolic energy• Two classes: primary and secondary

There are two classes of carrier-mediated transporters, those that are in-volved 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 in-volves ATP hydrolysis, either directly or indirectly, and the transporter can move solute from an area of low to high concentration, that is against its concentra-tion gradient. Active transport can be further subdivided into primary or sec-ondary. Primary active transport directly involves ATP hydrolysis. Secondary active transport refers to processes that mediate the uphill movement of so-lutes 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.

Slide 60 Primary Active Transport – Na-K ATPase

• ATP-dependent• Electrogenic• Important for maintaining ionic gradients (conduction,

nutrient uptake)• Important for maintaining osmotic balance

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 per-form 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 move-ment of solute generates a high intracellular K+ concentration and low Na+ Con-centration 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.

Slide 61 An example of a secondary active transporter is the

electroneutral Na/Cl cotransporter.

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.

Secondary Active Transport-Symport

Na+ Cl- Na+

One example of a secondary active transport mechanism is the NaCl cotrans-porter. 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 co-transporter uses this gradient to translocate Cl- into the cell against its electro-chemical gradient. Note sometimes multiple ions are transported as is the case for the NaKCl cotransporter found in a variety of cells. Remember these are co-transporters 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.

Comparison of Pores, Channels, and Carriers

PORE CHANNEL CARRIER

Conduit through membrane Always open Intermittently

open Never open

Unitary eventNone

(Continuously open)

Open/closeCycle 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)

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.

Na+Na+

K+K+Cl–~

Pr–

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 hy-drolysis 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 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

Gibbs-Donnan 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.

1 2

Na+Na+

Cl–P–

Initially

Na+Na+

Cl–

P–

Equilibrium

Cl–

1 2

We have discussed the role of the Na-pump in generating the membrane po-tential 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 semi-permeable membrane. Here the membrane is freely permeable to Na+, Cl- and water but is impermeable to negatively charged proteins (P-). The macromole-cules themselves contribute very little to the osmolarity of the cell because de-spite 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 num-bers 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 pro-tein 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 con-centration will be higher outside the cell than inside. The difference in the water concentration across the plasma membrane will cause water to move conti-nuously into the cell by osmosis causing it to rupture.

Slide 66

At equilibrium, the increase in osmotically active particles leads to the flow of water into compartment 2.

In animal cells, the presence of large impermeantintracellular anions tends to lead to cell swelling due to

Donnan forces. However, the Na+ pump actively extrudes osmotic solutes and counteracts the cell swelling.

Gibbs-Donnan equilibrium(the tendency for cells to swell)

Na+Na+

Cl–

P–

Equil.:Cl–

H2O

1 2

As we now know, the cell membrane is also permeable to water, thus at equi-librium 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 distensi-ble, it would bulge into compartment 1. In mammalian cells, the presence of large impermeant anions inside the cell would lead to cell swelling and ultimate-ly 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.

P-

[Na+][K+][Cl-]

~

Na+

2K+

3Na+

Cl-H2O

K+

Equal number of +ve and –ve charges move: Equilibrium

P-

↑[Na+]↓[K+]↑[Cl-]

Na+

Cl-

H2O

K+

Inhibition of the Na-pump (ouabain) → cell swelling

The Na-pump (Na-K pump) is essential for maintaining cell volume

~

Because plasma membranes are not rigid, the cell cannot generate a hydros-tatic 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 ma-cromolecules 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 concentra-tion of solutes, including numerous negatively charged organic molecules that are confined to the inside of the cell (fixed anions) and their accompanying ca-tions are required for charge balance. This tends to create a large osmotic gra-dient 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 Epithelia

Basal Lamina

Microvilli

Tight junction

• 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

Apical

Basolateral

An epithelium is an uninterrupted sheet of cells joined together by a conti-nuous 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 epitheli-al cells. There are a variety of types of epithelial cell, but they all have a com-mon 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.

Models of Ion Transport in Mammalian Cellse.g. Cl- secretory cell

Na+

K+Cl-K+Na+

K+

Cl-

Na+

H2O

TranscellularParacellular

Transepithelial potential difference

APICAL/MUCOSAL

SIDE

BASOLATERAL/SEROSAL/

BLOOD SIDE

NEGATIVE POSITIVE

Here is a typical cell model. Let’s consider some of the key points to remem-ber. 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 in-troduce how membrane transporters and channels functionally interact to ena-ble NaCl secretion. 1. Active transport –Na pump. Na gradient – Na moves down its concentration gradient via the NaKCl cotransporter. A basolateral K conduc-tance 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 com-bined with osmotic movement of water. The net result: NaCl secretion.

Slide 71 Absorptive Epithelia - e.g. Villus cell of the small intestine

(Modified from: Alberts et al., Molecular Biology of the Cell, 4th Ed. Garland Science, 2002)

Na+-driven glucose symport

Lateral domain

Basal domain

Carrier protein mediating passive transport of glucose

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 basola-teral energy utilizing Na pump setting up a concentration gradient. The Na con-centration gradient set up by the pump enables the influx of glucose via a sec-ondary 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 pa-racellular pathway and the fibers of the tight junctions that make up the junc-tions are not simply a random mesh, rather they contain specialized proteins. One such example is paracellin 1, a kidney tight junction protein that is impor-tant for renal Mg absorption.

Slide 72 Common Gating Modes of Ion Channels

(Source: Alberts et al., Molecular Biology of the Cell, 4th Ed. Garland Science, 2002)

Voltage-gating is only one way in which channels are opened. Other methods include ligand gating and mechanical gating.

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)

3) Selectivity. The channel pore allows only certain ions to pass through.

I

V

The slope of the line is used to determine the conductance of an electrophysi-ological 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 combina-tion 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 re-versal 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 charac-teristics 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.

Slide 74 Electrophysiological Technique: Patch Clamp

Slide 75 Terminology and Electrophysiological Conventions

-100 mV

+100 mV

0 mV

Membrane potential (Vm)

Depolarize

Hyperpolarize

V

IOUTWARD CURRENT

INWARD CURRENT

(Positive)

(Negative)

+100 mV-100 mV

Reversal Potential (I=0)

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 current-voltage relationship. Much can be learned about the electrophysiological prop-erties 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.

Slide 76 How the behavior of an ion channels can be modified to permit an increased ion flux:

Closed stateOpen state

Control/ Wild-type:

An increase in conductance (more current flows/opening) but the open probability stays the same:

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

Closed stateOpen state

Here pink is used to represent the closed state of the channel, downward def-lections are channel openings. Thus blue represents the open state. Modifica-tion of the channel protein, for example by phosphorylation can alter the chan-nel 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.

Ionic currents through a single channel sum to make macroscopic currents

Na+ Channel K+ Channel

VOLTAGE-GATED CHANNELS

VOLTAGE-dependent closure

TIME-dependent closure

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 chan-nels 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 pan-el shows the activity of a single channel, where downward deflections represent inward current through the channel. Notice in this case, that the channels spon-taneously 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.

Slide 78

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.

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.

Slide 79

Dep

olar

izin

g ph

ase

Restingpotential

Threshold

After-hyperpolarization

Overshoot

RepolarizingPhase

The Nerve Action Potential

-5 0 5 10 15 20-80

-60

-40

-20

0

20

Mem

bran

e Po

tent

ial (m

V)

Time (ms)

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 en-sues 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.

Slide 80 Changes in the underlying conductance of Na+ and K+ underlie

the nerve action potential

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 responsi-ble 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.

Na+ K+

+

Chemical and electrical gradients prior to initiation of an action potential

•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.

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 elec-trogenic nature of the Na-pump contributes only about 10% to the membrane potential. The remaining 90% depends on the pump indirectly.

Slide 82

Na+

+

A stimulus raises the intracellular potential to a thresholdlevel and voltage-gated Na+ channels open instantaneously

Stimulus

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

+ ++

++

+

++

Na+

Na+

Na+

Na+

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.

Slide 83

0 5 10 15 20-80

-60

-40

-20

0

20

Mem

bran

e Po

tent

ial (

mV)

Time (ms)

-100 +1000 +150-50 +50Eion

K+ Na+Cl-

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 chemical and electrical driving forces. Vm does not reach ENa.

Thus, the inward movement of Na results in the upstroke of the action poten-tial. The cell membrane potential moves toward ENa because of the increase in permeability as Na channels open. The potential does not quite reach ENa how-ever because these channels exhibit time dependent closure, or inactivation, as we discussed earlier. A the same time the Na+ channels are beginning to inacti-vate, 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.

Slide 84 + +

++

+

+

++

Na+Na++ +

+

++

+

++ K+

K+

- - ---

-

--K+

K+

K+

5. Cell repolarizes

3. Outward K+ gradient

4. Outward K+ flux as voltage-dependent K+ channels open →hyperpolarization

2. Na+ channels begin to close:

So here at stage 2 the Na+ channels are inactivating. The cell is now depola-rized, 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 be-come 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 voltage-gated 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.

100 +1000 +150-50 +50Eion

K+ Na+ Ca2+Cl-

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 after-hyperpolarization before the cell returns to its resting membrane potential.

0 5 10 15 20-80

-60

-40

-20

0

20

Mem

bran

e Po

tent

ial (

mV)

Time (ms)

Thus the repolarization of the cell in response to increased K+ efflux and de-creased 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.

Slide 86

Activation gateInactivation gate

REST

ACTIVATED(UPSTROKE) INACTIVATED

REPOLARIZATION→HYPERPOLARIZATION

DEPOLARIZING Vm

Na+

out

in

Gates Regulating Ion Flow Through Voltage-gated Na+ Channels

During an action potential, sodium channels first activate, driving the up-stroke, 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 sen-sor/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.

Slide 87 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.

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