biological membranes and principles of solute … year/fall a 2008/fundamentals i/cmb...enclosed...

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

Contact Information:MCLM 868934 1785

[email protected]

BIOLOGICAL MEMBRANES BIOLOGICAL MEMBRANES AND PRINCIPLES OF AND PRINCIPLES OF SOLUTE AND WATER SOLUTE AND WATER

MOVEMENTMOVEMENT

Slide 2

OUTLINEOUTLINE

••Biological Membranes and Principles of Solute Biological Membranes and Principles of Solute and Water Movementand Water Movement

••Diffusion and OsmosisDiffusion and Osmosis

••Principles of Ion MovementPrinciples of Ion Movement

••Membrane TransportMembrane Transport

••Nerve Action PotentialNerve Action Potential

••HANDOUT AND PROBLEM SETHANDOUT 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. This figure shows the basic structure of a cell.

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Enclosed within the plasma membrane of eukaryotic cells are membranes of the endoplasmic reticulum (a site of protein production), golgi apparatus (a protein sorter), mitochondiria (energy producers) and other membrane enclosed organelles that maintain the characteristic differences between the contents of each organelle and the cytosol.

Slide 5

TranscellularTranscellularFluidFluid

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

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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 6

Solute composition of key fluid compartmentsSolute composition of key fluid compartments

•Osmolalityconstant

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

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 consttuted by proteins. There are two types of proteins, structural and functional.

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Cellular Membranes: Cellular Membranes: •• Separate the cell from the outside world. Separate the cell from the outside world. •• Separate compartments (e.g., organelles) inside the cell.Separate compartments (e.g., organelles) inside the cell.•• Provide a scaffold for membrane proteinsProvide a scaffold for membrane proteins

There are:There are:•• General functions (e.g., regulation of solute movement) General functions (e.g., regulation of solute movement) common to all cellular membranes.common to all cellular membranes.•• Diverse functions in the different regions and organellesDiverse functions in the different regions and organellesor specialized functions that depend on the cell type. or specialized functions that depend on the cell type.

Source: Source: Boron & Boron & BoulpaepBoulpaep, , Medical Medical Physiology, Physiology, Saunders, Saunders, 2003. 2003.

Two adjacent cellsTwo adjacent cellsPM = Plasma PM = Plasma membranemembraneEach PM has Each PM has ‘‘railroad railroad tracktrack’’ appearance: 2 appearance: 2 dense lines separated dense lines separated by a clear spaceby a clear space

PMPM

PMPM

Single Single bilayerbilayer

Membranes are vital because they separate the cell from the outside world. They also separate compartments inside the cell to protect important processes and events. There are general functions common to all cellular membranes such as control of permeability, but they also have diverse functions in the different regions and organelles of a cell and then there are specialized functions that depend on the cell type. However, at the electron microscopic level, they share a common structure. The figure shows the typical "Unit" membrane which resembles a railroad track with two dense lines separated by a clear space. Despite their diverse functions, all biological membranes have a common structure: each is a very thin (~5nm) film of lipids and protein molecules held together mainly by noncovalent interactions.

Slide 8

Dr. Whikehart has covered in detail the components of the cellular membrane. My goal is to build on this knowledge and also to incorporate information from Dr. Cotlin’s lectures. We know the cell membrane is composed of lipids and proteins – the predominant lipid type are phospholipids. Covalently attached to some of the lipids and proteins that form the plasma membrane are carbohydrates.

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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 The Membrane GlycocalyxGlycocalyx -- cell coatcell coat

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

First lets consider the glycocalyx which is also known as the cell coat. These are both terms that are used to describe the 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 as shown a couple of slides ago. A chain composed of several sugar molecules is an oligosaccharide. There are also polysacchride 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 via a GPI anchor. 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 10

Membranes are selectively permeableMembranes are selectively permeable

Gas molecules are freely permeableSmall uncharged molecules are freely permeable, water channels also exist

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

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

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.

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Slide 12

The CytoskeletonThe CytoskeletonIntracellular network of protein filaments

RoleRole

Supports 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 Three Types Of CytoskeletalCytoskeletal FibresFibres

Microtubules (tubulin)Microfilaments (actin)Intermediate filaments

The cytoskeleton is an important, complex, and dynamic cell component. The cytoskeleton maintains the cell's 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.

Slide 13

Microtubule assembly/disassembly

Microtubules in fibroblasts

Microtubules are made of tubulin subunits and are often used by cells to hold their shape. Microtubules are also the major component of cilia and flagella. 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 made of actin subunits and polymerized and depolymerized in vivo. Microfilaments are approximately a third of the diameter of a microtubule, and are often

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used by cells to change their shapes as well as hold structures.

Slide 14

Figure 4:(a) The eukaryotic cytoskeleton. Microfilaments are shown in red, microtubules in green, and the nuclei are in blue. By linking regions of the cell together, the cytoskeleton helps support the shape of the cell. Figure 4:(b) Microscopy of keratin filaments (intermediate filaments) inside cells. Figure 4:(c) Microtubules in a methanol-fixated cell, visualized with anti-beta-tubuline antibodies. (License: Public domain). (Source:http://en.wikipedia.org/wiki/Image:KeratinF9.png, JWSchmidt; License:GFDL). (Source:http://en.wikipedia.org/wiki/Image:Microtutubules_gel_fixated.jpg; License: GFDL)

Slide 15

MembraneMembrane--cytoskeleton Attachments in cytoskeleton Attachments in

the Red Blood Cellthe Red Blood Cell

Proteins associated with the cytoskeleton control cell structure by directing bundling and alignment of filaments, as well as by moving the filaments around.

e.g. An interesting group of cytoskeletally-associated proteins are cellular motors, such as myosin (an motor that moves along actin filaments) and kinesin (a microtubule motor).

There are a great number of proteins associated with the cytoskeleton, controlling its structure by directing bundling and alignment of filaments, as well as by moving the filaments around. A particularly interesting group of cytoskeletally-associated proteins are cellular motors, such as myosin (an motor that moves along actin filaments) and kinesin (a microtubule motor).

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Structural JunctionsStructural 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 junctional proteins can 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. In addition, microvilli are found in certain cell types where they serve to increase the surface area of the cell. In this case the plasma membrane encloses specialized proteins. Tight junctions often allow some kinds of small molecules and ions to pass, paracellularly. Tight

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junctions also restrict the diffusion of membrane components — proteins and lipids — between the apical and basolateral membranes

Slide 17

Gap JunctionsGap Junctions

ROLEROLE: 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 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.

Slide 18

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The Extracellular MatrixThe Extracellular MatrixThe ECM is an organized meshwork of polysaccharides

and proteins secreted by fibroblasts. Commonly referred to as connective tissue.

COMPOSITION:ProteinsProteins: Collagen (major protein comprising the ECM),

fibronectin, laminin, elastinTwo functions: structural or adhesive

PolysaccharidesPolysaccharides: 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

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. 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.

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Membrane Transport: Membrane Transport: EndocytosisEndocytosis and and ExocytosisExocytosis: : transport across but not through transport across but not through

membranesmembranes

EXOCYTOSISEXOCYTOSIS: : Transport molecules migrate to the Transport molecules migrate to the plasma membrane, fuse with it, and release their plasma membrane, fuse with it, and release their contents.contents.

ENDOCYTOSISENDOCYTOSIS: 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. Requires energy.

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. In addition to proteins found in the membrane that allow movement of substances across the membrane, there are also specialized mechanisms to allow substances to move into and out of the cell. These mechanisms are known as exocytosis and endocytosis. Exocytotic mechanisms have evolved to remove substances and endocytotic mechanisms to allow substances to enter the cell.

Slide 21

Exocytosis involves the movement of intracellular vesicles to the plasma membrane. The vesicle fuses with the plasma membrane and the contents are extruded to the extracellular milieu.

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Endocytosis involves the cell membrane indenting, and allowing incorporation of extracellular substances into the cells interior. There are three types of endocytosis listed here. During phagocytosis, large particles are engulfed. An example of a cell type that utlizes this mechanism is macrophages and some white blood cells. These do not involve carrier mediated transport, but can involve membrane proteins as is the case for receptor mediated endocytosis. One example of receptor-mediated endocytosis is the uptake of cholesterol into cells. Most cells cannot synthesize cholelestrol which is carried in the blood predominantly in low density lipoproteins (LDLs). Many cells have LDL receptors on their plasma membrane. When LDL binds to these receptors, the receptor-LDL complexes migrate to coated pits, where they aggregate and are taken up into the cell by receptor-mediated endocytosis. Individuals who lack LDL or have defective LDL receptors are prone to atherosclerosis because they have high concentrations of cholesterol laden LDL in their blood

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Slide 23

ReceptorReceptor--mediated mediated EndocytosisEndocytosis

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Slide 24

Principles of Solute Principles of Solute and Water Movementand Water Movement

Diffusion and OsmosisDiffusion and Osmosis

Slide 26

Membranes are selectively permeableMembranes are selectively permeable

Gas molecules are freely permeableSmall uncharged molecules are freely permeable, water channels also exist

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

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

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.

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DiffusionDiffusion

Diffusion is the net movement of a substance (liquid Diffusion is the net movement of a substance (liquid or gas) from an area of higher conc. to one of lower or gas) from an area of higher conc. to one of lower

conc. due to random thermal motion.conc. due to random thermal motion.

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, 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, 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 28

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. We are going to consider the factors that influence the movement of solute. In the next slide we will begin with a simple system.

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Kinetic characteristic of diffusion Kinetic characteristic of diffusion of an uncharged soluteof an uncharged solute

Model: compartments separated by permeable glass

A = cross sectional area of the glass discCs = concentration of uncharged soluteΔx = thickness

compartment 1 compartment 2

Δx

Cs1 Cs

2

Now lets 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.

Slide 30

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 diffusionnet rate of diffusion = k(Cs

1-Cs2) = kkΔΔCCss, where k is a

proportionality constant.


Δx

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 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.

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Diffusion is proportional to the surface area of the barrier (A) and inversely proportional

to its thickness (Δx).

kk can thus be expressed as ADADs//ΔΔxx, where Dsis the diffusion coefficient of the solute.

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

diffusion.

One 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 an S 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. Note: the diffusion coefficient of a solute is a measure of the rate at which a solute (S) can move across a barrier having a cross sectional area of 1cm2 and a thickness of 1cm when the concentration difference across the barrier is 1mol/L.

Slide 32

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 = ADsΔCs/Δx. Dividing both

sides by A (to obtain flux), we obtain:

FickFick’’ss first law of diffusion:first law of diffusion:

Flux = Flux = JJss = D= DssΔΔCCss//ΔΔxx“The rate of flow of an uncharged solute due to The rate of flow of an uncharged solute due to

diffusion is directly proportional to the rate of change diffusion is directly proportional to the rate of change of concentration with distance in direction of flowof 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 zerozero.

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.

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Diffusion of an uncharged soluteDiffusion of an uncharged soluteModel: compartments separated by a Model: compartments separated by a lipid lipid

bilayerbilayer

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

proteins (“fluid mosaic model”).


Δx

Cs1 Cs

2

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.

Slide 34

The partition coefficient, Ks will increase or decrease the driving force of the solute S across the membrane:

JJss = = KKssDDssΔΔCCss//ΔΔxx

Because it is difficult to measure Ks, Ds and Δx, these terms are often combined into a permeability coefficient,

Ps = KsDs/Δx. It follows that:JJss = = PPssΔΔCCss

CCss11

HydrophilicHydrophilicKKss < 1< 1 CCss

22

LipophilicLipophilicKKss > 1> 1

Partitioning of an uncharged solute Partitioning of an uncharged solute across a lipid across a lipid bilayerbilayer

Ks = 1 if all ‘s’goes into liquid and 0 if ‘s’ stays in water

This is a representation of the lipid bilayer. Again, recall that the concentration on side 1 is greater than side 2 and the solute will be moving 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

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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 35

Molecules that move rapidly through a membrane have a high permeability coefficient (Ppermeability coefficient (Pss))

Slide 36

PERMEABILITY COEFFICIENT, Ps:Influenced by differences in lipid solubility rather than

molecular size of an uncharged solute.

PARTITION COEFFICIENT, Ks:Js is directly proportional to a solute’s lipid solubility

(Overton’s law).

DIFFUSION COEFFICIENT, Ds:Depends on the size of the solute molecule and the

viscosity of the medium. Values are inversely proportionalto the radius of the solute (Stokes-Einstein Equation).

Thus smaller molecules are more permeable and have the largest diffusion coefficients and diffuse most readily.

Within the membrane, the link between solute flux and driving force is the partition and diffusion coefficients. Let’s evaluate these two coefficients in more detail. First of all, independent of a solute’s diffusion coefficient, flux is directly proportional to the solute’s lipid solubility. This is known as Overton’s law and has been repeatedly verified. In fact, Overton used his observation that lipid-soluble molecules transverse membranes more readily that water-soluble molecules of the same size to hypothesize the lipophilic nature of the membrane. Flux is also proportional to the diffusion coefficient. And at the turn of the

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century Einstein contributed to our understanding of this variable by showing that the resistance experience by a diffusing particle is caused by frictional interaction between the particle and the medium. Furthermore, based on Stoke’s law, he determined that diffusion is inversely proportional to the molecule’s radius as well as the medium’s viscosity.

Slide 37

They noticed that small, water soluble molecules entered cells faster than predicted based on the assumption that the membrane acted like a simple hydrophobic barrier – this assumption is known as Overton's Law.

Collander et al., postulated that membranes contained features that enabled them to act as molecular sieves.

These turn out to be protein pores, channels and pumps.

Aqueous pores in membranes: In the late 1940's Collanderand colleagues studied the movement of molecules into cells.

Slide 38

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Solute movement across a lipid bilayer through entry into the lipid phase occurs by simple diffusion.

This movement occurs downhilldownhill and is passivepassive.

Slide 40

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.

Selectively permeable membrane

Hypotonicsolution

Hypertonicsolution

H2O

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.

C. M. Bevensee, 9/14/2008 8:54:33 AM 21

Slide 42

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

C. M. Bevensee, 9/14/2008 8:54:33 AM 22

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, 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. In the next slide, we’ll consider the more realistic case where the membrane exhibits some permeability to the solute S. 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 (��) that must be applied to prevent the diffusion of water can be determined using the van’t Hoff equation: ��=RT(� Cs). At 37C (=310K), the product RT is ~25 atm.

C. M. Bevensee, 9/14/2008 8:54:33 AM 23

The osmotic pressure (Δπ ) required is determined from the van’t Hoff

equation:

ΔπΔπ = RT= RTΔΔCCSS = (25.4)= (25.4)ΔΔCCSS at 37at 37°°C.C.

Where, R = the gas constant, T = absolute temperature and ΔCS is the

concentration difference of the uncharged solute

Slide 45

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) 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.

C. M. Bevensee, 9/14/2008 8:54:33 AM 24

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 Δπ = 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 nonidealmembranes is:

ΔπΔπeffeff = = σσSSRTRTΔΔCCSS

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 d(pi) (��) 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 � (sigma) equals zero, the membrane is freely permeable to the solute and the solute will diffuse down it’s 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 � 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 ��eff = �SRT�CS.

C. M. Bevensee, 9/14/2008 8:54:33 AM 25

Osmotic and hydrostatic pressure differences in volume flow

Volume flow across a membrane is described by:JJVV = = KKffΔΔPP

where Kf is the membrane’s hydraulic conductivity and ΔP is the sum of pressure differences.

These pressure differences can be hydrostatic (ΔPH), osmotic (Δπeff) 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, JJVV = = KKff((ΔπΔπeffeff –– ΔΔPPHH)) and (Δπeff – ΔPH) is the driving force for volume flow (Starling Hypothesis).

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.

C. M. Bevensee, 9/14/2008 8:54:33 AM 26

Arteriole VenuleInterstitial

space

Starling ForcesStarling Forces

Hydrostatic pressure

Osmotic (oncotic) pressure

= fluidmovement

Filtration dominates Absorption dominates

Importance of plasma proteins!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 �= 1) 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. Thus, as fluid moves from the arterial to the venous end, the hydrostatic pressure decreases and the colloid osmotic pressure increases such that filtration dominates at the arterial end and absorption dominates at the venous end.

Slide 49

TonicityTonicity

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.

C. M. Bevensee, 9/14/2008 8:54:33 AM 27

Principles of Ion MovementPrinciples of Ion Movement

Slide 51

Na+

Cs1=100mM

Ac-

Cs2=10mM

Diffusion of ElectrolytesDiffusion of Electrolytes

V+–

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

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 Na (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.

C. M. Bevensee, 9/14/2008 8:54:33 AM 28

Cs1=100mM Cs

2=10mMNa+

Ac-

V +–


Law of electroneutrality (for a bulk solution) must be maintained. In the above model in which the membrane

becomes permeable to sodium (Na+) and acetate (Ac–), both ions will move from side 1 → 2.

The concentration gradient between compartment 1 and 2 is the driving force.

Na+ (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

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, sodium is smaller than acetate and will therefore want to move faster across the membrane. [Diffusion is inversely proportional to the sqrt(molecular weight).] As sodium 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.

C. M. Bevensee, 9/14/2008 8:54:33 AM 29

Cs

1=100mM Cs2=10mM

Na+

Ac-

V +–


When the membrane is permeable to only one of the ions (e.g., Na+) 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 results occurs when the membrane is made permeable to only one of the ions-- sodium 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 can not 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.

Slide 54

The Nernst EquationNernst Equationequilibriumequilibrium

no net movementno net movement

is satisfied for ions at 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 because

the electrical and chemical driving electrical and chemical driving forces are equal and oppositeforces are equal and opposite..

C. M. Bevensee, 9/14/2008 8:54:33 AM 30

All solutions must obey the principle of bulk

few charges adjacent to the

electroneutrality: the number of positive charges in a solution must be the same as the number of negative

charges.

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

membrane.

The Principle of Bulk The Principle of Bulk ElectroneutralityElectroneutrality

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. When a potential difference exists across a cell membrane, charges line up against the membrane but there are equal and opposite charges within the bulk solution.

Slide 56

Cs1 = 100mM Cs

2 = 10mMNa+

Ac-

V +–

Calculating a Nernst Equilibrium PotentialCalculating 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 ×=

So lets 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 57

Taking valence of the ion into account Taking valence of the ion into account

in calculating a Nernst potentialin calculating a Nernst potential

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

oClClClE log60 ×−=

mVE Cl 6010

100log60 −=×−=

Here, z = -1

Lets 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.

C. M. Bevensee, 9/14/2008 8:54:33 AM 31

[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

mVE K 6010010log60 −=×=

As a final example, lets use K+ as our monovalent cation. As you probably know, and we will discuss the reason why in the next lecture, the K+ concentration inside the cell is higher than the outside. I have given a table outlining the relative concentrations of the various ions in your handout. Now 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 Ca 2+ the valence we would use to calculate the potential is +2. Over this course in physiology, you will be learning the significance of these potentials.

Slide 59

RememberRemember:

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.

C. M. Bevensee, 9/14/2008 8:54:33 AM 32

GoldmanGoldman--HodgkinHodgkin--Katz Katz (GHK) (GHK) equationequation

Determining membrane potentialThe constant field equation allows us to compute the

voltage across a membrane permeable to more than one ion. For the classical membrane permeable to Na+, K+ and

Cl–, the equation is:

where PNa, PK and PCl are membrane permeabilities for the associated ions. The greater the membrane permeability

to an ion, the more that ion’s Nernst potential will contribute to Vm.

oCliNaiK

iCloNaoKm ClPNaPKP

ClPNaPKPF

RTV][][][][][][ln −++

−++

++++

=

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 (Vm). This is the point at which there is no net flow of current because the electrical and chemical driving forces for an ion are equal and there is no net ionic movement. For the case where the cell is permeable to more than one ion, for example Na+, K+ and Cl-, we use the Goldman-Hodgkin-Katz equation to calculate Vm. THE GHK equation is also known as the constant field equation. In this equation we take the membrane permeability into account. Note that the intracellular and extracellular concentrations for Cl- are flipped compared to those for Na and K. This is because in the GHK equation we cannot take into account valence. In calculating the log values if we reverse the numbers we arrive at opposite polarity. For example as I have given to remind you in the handout, log 100/10 = 1 and the log 10/100 is –1. Same value different sign. If the permeability to Na+ and Cl- are zero, the equation reduces to the Nernst potential for K+. If Na+ and Cl- permeabilities are low, the membrane potential is closer to the Nernst potential for K+, but not exactly at EK. You may also see the GHK equation given as shown here where we consider relative permeabililities rather than absolute permeabilities to calculate Vm.

C. M. Bevensee, 9/14/2008 8:54:33 AM 33

Membrane Transport Membrane Transport Mechanisms IMechanisms I

Slide 62

Slide 63

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 Thus, mechanisms other than simple diffusion across the lipid across the lipid bilayerbilayer are required for the are required for the passage of solutes across the membrane.passage of solutes across the membrane.

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

C. M. Bevensee, 9/14/2008 8:54:33 AM 34

assymetry is essential for many processes including nerve conduction and muscle contraction. Thus, diffusion processes alone cannot account for the assymetries.

Slide 64

Slide 65

Transport across membranes: Transport across membranes: Passive DiffusionPassive Diffusion

Conc

entr

ation

grad

ient

Conc

entr

ation

grad

ient

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

C. M. Bevensee, 9/14/2008 8:54:33 AM 35

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. We will discuss each of these in turn.

Slide 66

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

Transport through poresTransport through poresA general characteristic of pores is that they are always open.Examples:

1) PorinsPorins are found in the outer membrane of gram-negative bacteria and mitochondria..2) Monomers of PerforinPerforin 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. by permeabilizing them to granzymes, ions, water, etc.

Slide 67

The English Channel!The English Channel!

C. M. Bevensee, 9/14/2008 8:54:33 AM 36

Transport Through ChannelsTransport 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. Specialized structures within the protein form selectivity filters, that is they allow passage of certain ions over others. Some examples are shown here…though as you can imagine there are many more. We will discuss voltage gated Na channels when we learn about the action potential in the next lecture. Other channel proteins are designed to reabsorb important solutes, others, especially K channels to generate cell membrane potentials.

Slide 69

Solute movement through pores and channels occurs via simple

diffusion, is passive and passive and downhill.downhill. Metabolic energy is not

required.

C. M. Bevensee, 9/14/2008 8:54:33 AM 37

Transport through carriersTransport 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 “opening’ whereas for a transporter the transport event is a complete cycle of conformational changes. Because the number of binding sites are 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 71

Types Of CarrierTypes Of Carrier--mediated Transportmediated TransportTwo classes of carrier-mediated transporters include those that engage in facilitated diffusion and active

transport.Facilitated diffusionFacilitated diffusion: the carrier transports solute

from a region of higher to lower concentration. No additional energy sources are required.

Active transportActive transport: the carrier performs work and transports solute against its chemical or electrochemical driving force. Such work can be performed with energy derived from:

–ATP hydrolysis (primary active transport)–another solute moving down its electrochemical gradient (secondary active transport)

There are two classes of carrier-mediated transporters, those that are involved in facilitated diffusion and those that are involved in active transport. During 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

C. M. Bevensee, 9/14/2008 8:54:33 AM 38

derives its energy by coupling the movement of one of the transported solutes to the downhill movement of another solute.

Slide 72

From: Purves et al., Life: The Science of Biology, 4th Edition, by Sinauer Associates

Carrier mediated transport: Active TransportCarrier mediated transport: Active TransportCotransporter Exchanger

Conc

entr

atio

n gr

adie

nt

Here we show diagramatically the process of active transport. Here on the left is a primary active transporter, directly utilizing ATP. Coupled transport can come in two ‘flavors’ where the transported molecules move in the same direction, as is the case for a symport molecule and in opposite directions, as is the case for antiporters.

Slide 73

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 often display competitive inhibition][][max

XKXJJ

m

x+⋅

=

CarrierCarrier--mediated transport: mediated transport: Facilitated diffusionFacilitated diffusion

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

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, 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

C. M. Bevensee, 9/14/2008 8:54:33 AM 39

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 Michelis-Menten 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.

Slide 74

Carrier mediated transport:Carrier mediated transport:Active TransportActive Transport

• Movement of an uncharged solute from a region of lower higher

uphilluphill

againstagainstcombined chemical and electrical driving forces

Requires metabolic energy

concentration to concentration ( )

• Movement of a charged solute

•

• Two classes: primary and secondary active transport

C. M. Bevensee, 9/14/2008 8:54:33 AM 40

Primary Active TransportPrimary Active Transport

Na-K-ATPase, the Na-pump:Found in all mammalian cells

• ATP-dependent• Electrogenic• Important for maintaining ionic gradients (conduction, nutrient uptake)• Important for maintaining osmotic balance

Here is an example of a primary active transporter, the Na-K ATPase or Na pump found in all mammalian cells. 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. The NaK-ATPase is also termed the Na+ pump is shown here. 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.

Slide 76

An example of a secondary active transporter is an electroneutral Na/Cl cotransporter.

Thus, 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 TransportSecondary Active Transport--SymportSymport

Na+ Cl- Na+ Cl-

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.

C. M. Bevensee, 9/14/2008 8:54:33 AM 41

Others that move one solute in one direction and another in the opposite direction are termed exchangers or antiporters.

Slide 77

Secondary Active TransportSecondary Active Transport--AntiportAntiport

Slide 78

Comparison of Pores, Channels, and CarriersComparison of Pores, Channels, and Carriers

200-50,0001-100 millionUp to 2 billion

Particles translocated per

second

1-560,000 *---

Particles translocated per

‘event’

Cycle of conformational

changesOpen/close

None (Continuously

open)Unitary event

Never openIntermittently openAlways openConduit through

membrane

CARRIERCHANNELPORE

* Assuming a 100 pS channel, a driving force of 100 mV and an open time of 1 ms

C. M. Bevensee, 9/14/2008 8:54:33 AM 42

Factors which contribute to a cell's membrane potential (net negative charge on the inside):

1. Negatively charged proteins in the cell's interior.

2. Plasma membrane's selective permeability to various ions.

3. The sodium-potassium pump. This electrogenicpump translocates 3 Na+ out for every 2 K+ in - a net loss of one positive charge per cycle.

Combined these represent the electrochemical gradient. Ions may not always move down their concentration gradients, but they will move down their electochemical gradients. At equilibrium, the distribution of ions on either side of the membrane may be different from the expected distribution when charge is not a factor. It is important to note that uncharged solutes always diffuse down their concentration gradients because they are unaffected by membrane potential. The factors that contribute to the cell’s membrane potential are given here, we will discuss each in the next few slides.

Slide 80

The The ““pumppump--leakleak”” modelmodel

(generating the membrane potential)(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, is essential in 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

C. M. Bevensee, 9/14/2008 8:54:33 AM 43

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 permeabilities and concentrations of the ions.

Slide 81

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

2

1

log60log60Cl

Cl

Na

Nam C

CCCV == 1

2

2

1

Cl

Cl

Na

Na

CC

CC

=

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 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 semi-permeable 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. Lets assume initially that the Na concentration initially on both

C. M. Bevensee, 9/14/2008 8:54:33 AM 44

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. Because Vm must be the same in the two cases, we combine the two equations. This ratio is known as the Donnan ratio. 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. Animal cells pump out Na, plant cells have rigid wall and many protozoa extrude water from special contractile vacuoles.

C. M. Bevensee, 9/14/2008 8:54:33 AM 45

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.

GibbsGibbs--DonnanDonnan equilibriumequilibrium(the tendency for cells to swell)(the tendency for cells to swell)

Na+Na+

Cl–

P–

Equil.:Cl–

H2O

1 2

As we said the 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.

C. M. Bevensee, 9/14/2008 8:54:33 AM 46

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 NaThe Na--pump (Napump (Na--K pump) is K pump) is essential for maintaining cell volumeessential for maintaining cell volume

~

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 equli. 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.

C. M. Bevensee, 9/14/2008 8:54:33 AM 47

biological membranes and principles of solute … year/fall a 2008/fundamentals i/cmb...enclosed...

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