Membrane Transport Systems in Living CellsMembrane Transport

Systems in Living Cells

Prof. Ramkrishna Sen

rksen@iitkgp.ernet.in

Department of Biotechnology

Prof. Ramkrishna Sen

rksen@iitkgp.ernet.in

Department of Biotechnology

►Passive transport, facilitated passive transport (neutral molecules)►Osmosis (water transport)►Passive Ion channels for transporting Na+, K+, Cl-, Ca+2 ions►Active transport ( primary active and secondary active) transport for ions,

charged molecules

►Nernst equation for the equilibrium of ion transport (electrical gradient = chemical gradient) for individual ion►Donnan equilibrium (ion transport in presence impermeable ion in cellular compartment)►Goldman equation ( modified form of Nernst equation) for membrane potential considering all the transporting ions

►Electrical properties of Ion transporters and electrical equivalent (R-C)

circuit [ resistor-capacitor]

►Bulk transport

Membrane Transport System

The cell membrane contains many proteins including ion channels

How the cells exchange nurtrients and excretory products between inside and outside of the cell ?

Ultrastructure of a typical animal cell:

• Particles forced through a filter or a membrane by hydrostatic pressure.

– Hydrostatic pressure( mechanical potential energy)

• Fluid pressure of the blood generated by the left ventricle

• Opposed by osmotically (chemical potential energy) active particles in the blood (plasma proteins).

• Examples

– Blood pressure generated by the heart and blood vessels forces tissue fluid out of tiny openings in the capillary wall and leaving larger particles of blood cells and protein molecules inside the capillary.

– Coffee filters work by the pressure from weight of the water above the coffee grounds forcing the flavored water through the filter and leaving the large particles of coffee grounds on the filter paper.

• Filtration and osmosis are the major processes in the capillaries of tissues and the kidney.

These are passive transport process in capillaries of tissue to provide the nutrients in tissue level

Hydrostatic and osmotic pressure (tissue level):

Interstitial fluid (or tissue fluid) is a solution that bathes and surrounds the cells of multicellular animals. It is the main component of the extracellular fluid, which also includes plasma and trnascellular fluid. The interstitial fluid is found in the interstitial spaces, also known as the tissue spaces.

Blood flows from the heart to arteries, which branch and narrow into arterioles, and then narrow further still into capillaries. After the tissue has been perfused, capillaries branch and widen to become venules and then widen more and connect to become veins, which return blood to the heart.

The forces across a semi permeable membrane and allows calculation of the net flux:

Pc : Capillary hydrostatic pressure Pi :Interstitial hydrostatic pressure πc :Capillary oncotic pressure( colloid pressure )πi : Interstitial oncotic pressure Kf Filtration coefficient σ :Reflection coefficient

•Kf is the proportionality constant, and •Jv is the net fluid movement between compartments• ([Pc − Pi] − σ[πc − πi]) Net driving force

How tissue fluid (interstatial fluid) movement occurs

All cells acquire the molecules and ions they need from their surrounding extracellular fluid (ECF). There is an unceasing traffic of molecules and ions •In and out of the cell through its plasma membrane Examples: glucose, Na+,K+, Ca2+

•In eukarytoic cells, there is also transport in and out of membrane-bounded intracellular compartments such as the nucleus, endoplasmic reticulum,

and mitochondria. Examples: proteins,mRNA, Ca2+, ATP

How cells acquire molecules, ions from tissue fluid (interstatial fluid)

εr of surrounding ~ 80

electrical permittivity εr ( dielectric constant) about 2

Lipid Bilayer -- primary barrier selective based upon size and polarity of molecules a) Nonpolar molecules (O2, hydrocarbons, fatty acids)-- pass freely b) Small uncharged polar molecules (H2O, CO2 ) pass freely but more slowly than nonpolar

molecules c) Large polar molecules and ions -- don't pass freely d) Macromolecules (proteins, nucleic acids, polysaccharides) cannot pass unless a special

mechanism exists (signal hypothesis).

Cells solve the problem of transporting ions and small molecules across their membranes: Facilitaed diffusion :Transmembrane proteins create a water-filled pore through which ions and some small hydrophilic molecules can pass by diffusion. The channels can be opened (or closed) according to the needs of the cell.

Active transport : Transmembrane proteins, called transporters, use the energy of ATP to force ions or small molecules through the membrane against their concentration gradient.

Protein mediated diffusion differs from non-mediated diffusion of O2 and CO2 in four distinct ways: 1. the speed and specificity of the transport 2. the transport capacity is finite, i.e., exhibits saturation kinetics 3. transport can be competitively inhibited (antagonists) 4. transport can be chemically inactivated (heat, high salt concentration)

Solving the problems of transporting polar and ionic molecules

Comparison of properties of carriers, pores and channels

Membrane Carriers: How do they function?

• Chemical driving force

– Difference in energy due to a concentration gradient that causes a molecule to move from high to low concentration

• Electrical driving force

– Difference in energy due to a separation of charge that acts to move ions from high energy to low energy

• Electrochemical driving force

– Sum of the chemical and electrical driving forces

►Both hydrostatic force (P, mechanical potential energy) and osmotic force (Osm, chemical potential energy) regulate fluid flow through membrane pores.

►These force are interconvertible and net driving force for water between cell and extra cellular solution = RT (Osmcell - Osmext ) + (Pcell – Pext )

►Experimental measurements made in cells that show no net transmembrane hydrostatic or osmotic pressure difference, but a net difference in transmembrane electrical potential?

Driving force responsible for membrane transport

Plasma Membrane : Environmental Boundary (Barrier)

Ionic imbalance (particularly, Na+ and K+) between inside and outside created by membrane ionic pumps, ion exchangers and channels, establishes resting menbrane potential. This is used to drive other process (such as molecule import), as well as for information processing (e.g. nerve cells).

Activities of plasma membrane ionic pumps are energized by hydrolysis of ATP.

N.B: All the ‘live’ cells establish and maintain the membrane potential.

Types of Transport Processes

There are 4 basic mechanisms

1. DIFFUSION : Movement of molecules through the membrane in which

-no energy is required

-molecules move in response to a concentration gradient, Passive transport

2. OSMOSIS: Movement of water from an area of high to low concentration of water

-movement of water toward an area of high solute concentration

3. FACILITATED DIFFUSION: Movement of a molecule from high to low concentration with the help of a carrier protein.

-is specific

-is passive

-saturates when all carriers are occupied

4. ACTIVE TRANSPORT: Requires energy for transport molecules against concentration gradient , energy expanded in the form of ATP

5. BULK TRANSPORT: Bulk transport of substances through endocytosis and exocytosis

Net movement of particles from area of high concentration to area of low concentration– Due to their constant, random motion– Difference between the high and low concentrations is a concentration gradient– Diffusion tends to eliminate the gradient– Also known as movement “down the concentration gradient”

Simple diffusion -Nonpolar and lipid-soluble substances

- Diffuse directly through the lipid bilayer

-Diffuse through channel proteins

Factors influence diffusion process:• Distance

– The shorter the distance, the more quickly gradients are eliminated

– Few cells are situated greater than 125 µm from a blood vessel

• Molecular Size– Ions and small molecules diffuse more rapidly

• Temperature temp., motion of particles

• Steepness of concentrated gradient – The larger the gradient, the faster diffusion proceeds

• Membrane surface area – The larger the area, the faster diffusion proceed

Diffusion Transport Process

Diffusion Across Membranes• Simple Diffusion

– Lipophilic substances can enter cells easily because they diffuse through the lipid portion of the membrane

• Examples are fatty acids, steroids, alcohol, oxygen, carbon dioxide, and urea,

• Channel-Mediated Diffusion– Membrane channels are transmembrane proteins

• Only 0.8 nm (8Å) in diameter

– Used by ions, very small water-soluble compounds

– Much more complex than simple diffusion

• Are there enough channels available?

• Size and charge of the ion affects which channels it can pass through

But, A is the same molecule whether it’s inside or

outside, so..

Passive Transport: Permeability of a membrane for a nonelectrolyte solute (glucose)

Steps of membrane diffusion (any can be rate limiting):

•enter the membrane (potential barrier) (1)• diffusion through the bilayer core (2)•exit the membrane (potential barrier) (3)

Flux= mol solute/(Sec.cm2)

J = P ( C1 – C2 ) P = permeability coefficient( cm/sec) =d

Kp Dm

Kp - partition coefficient ( C membrane / C aqueous ); Dm – Diffusion coefficient of molecule in the

membrane; d – thickness of membrane

n - number of molecules inside cell (mol)

t - time (seconds)

P - permeability constant for a particular molecule (cm/sec)

Diffusion coefficient (D,cm2/sec)/thickness of membrane (x,cm)

A - surface area of the cell membrane (cm2)

C - concentration of diffusing molecule (mol/cm3)

X - width of cell membrane (cm)

Variables in Simple Diffusion

►The concentration gradient, dC/dx, equivalent to (Cout - Cin)/dx where Cout and Cin are the substrate concentrations inside and outside the cell, and dx is the width of the cell membrane.

► When the concentration outside the cell (Cout) is larger than inside the cell (Cin), the concentration gradient (dC/dx) will be positive, and net movement will be into the cell (positive value of dn/dt).

D

P ( Δc )

n - number of molecules inside cell

t - time (seconds)

Vmax- saturation constant (mol/cm3/sec)

K - constant determining speed of saturation (mol/cm3)

C - concentration of diffusing molecule (mol/cm3)

X - width of cell membrane (cm)

Facilitated diffusion variables

•Facilitated diffusion involves a limited number of carrier proteins.

•At low concentrations, molecules pass through the carrier proteins in a way similar to that of simple diffusion.

•At high solute concentrations, all the proteins are occupied with the diffusing molecules. Increasing the solute concentration further will not change the rate of diffusion.

•There is some maximum rate of diffusion (Vmax) when all the carrier proteins are saturated.

•The rate of diffusion will increase with increasing solute concentration, but must asymptotically approach the saturation rate, Vmax.

•How quickly the carrier proteins become saturated can be described by the variable K, the concentration gradient at which the rate of diffusion is 1/2 Vmax.

•K and Vmax depend on properties of the diffusing molecule, such as its permeability (P), as well as the surface area (A) of the cell, but for simplification we give the above equation.

• Large polar molecules such as glucose and amino acids, cannot diffuse across the phospholipid bilayer. Also ions such as Na+ or Cl- cannot pass.

• These molecules pass through protein channels instead. Diffusion through these channels is called FACILITATED DIFFUSION.

• Movement of molecules is still PASSIVE just like ordinary diffusion, the only difference is, the molecules go through a protein channel instead of passing between the phospholipids.

Carrier Mediated Transport: Facilitated Diffusion

The sugar is bound by the protein, a flip-flop mechanism reverses the membrane direction of the sugar-protein complex, the sugar is released and the protein flips around once more to initiate a new cycle.   Transport activity is dependent upon the sugar concentrations and the number of transport proteins in the outer cell membrane.  In principle the GLUT family can transport glucose both into and out of cells.   In most tissues the internal glucose concentration is quite low; transport can only proceed from the extracellular area into the cell. 

Turnover rate (s-1 ) of glucose transporter: 0.1-1.3x104

• Glucose and amino acids are insoluble in lipids and too large to fit through membrane channels

• Passive process, i.e. no ATP used

• Solute binds to receptor on carrier protein

– Latter changes shape then releases solute on other side of membrane

– Substance moved down its concentration gradient

A well studied example is the glucose transport across red blood cell membranes (erythrocyte membrane). Comparing the diffusion coefficient D for glucose across synthetic phospholipid membranes (vesicle membrane; bilayer) with that of erythrocyte cell membranes shows a 10+6 fold increase of glucose diffusion across the cell membranes. [ D(bilayer) 2.4x10-10cm2/s ; D(erythrocyte)=2x10-4cm2 /s ]

Carrier Mediated Transport: Facilitated Diffusion

1. You graphed dn/dt as a function of dC/dx. What is the slope of this line? What do increases or decreases in the slope mean biologically?

2. Now assume the concentration gradient is a constant. How does the rate of diffusion (dn/dt) change with the surface area (A) of the cell and the permeability (P) of the diffusing molecule? Graph dn/dt as a function of A or P and describe the function.

3. Look at the equation for facilitated diffusion and find the horizontal asymptote. What happens to dn/dt as dC/dx approaches infinity?

4. Try graphing this equation with different values for K. How does this change the concentration at which the carrier proteins are saturated?

5. Compare simple and facilitated diffusion of glucose into erythrocytes by graphing rate of diffusion (micromoles per hour) as a function of external glucose concentration (mmol/cm3). For facilitated diffusion, Vmax= 500 micromoles per hour and K=1.5 mmol/cm3. For simple diffusion, A x P is 3 cm3/hour.

6. How do rates of simple and facilitated diffusion differ in response to a concentration gradient?

7. How is the permeability of a molecule across the lipoprotein membrane related to the molecule's solubility in lipids and size?

Questions on diffusion and facilated diffusion

It is passive transport of water through a semi-permeable membrane

• Why does water move in that particular direction?

• The flow of water across a selectively permeable membrane

– Always from an area of high water concentration to an area of low water concentration.

– A special case of diffusion of water across a selectively permeable membrane, such as the plasma membrane.

• A semi-permeable membrane is freely permeable to water but not to solutes

• Osmosis moves water through aquaporins toward the hypertonic solution.

• It is a very important process because water is found throughout cells and extra-cellular areas of the body.

Osmosis ( a special case of diffusion)

= MRTM-molarity of solute( moles/litre)

- Osmotic pressure of solution ( atm or torr)

• Osmolarity = the total solute concentration in an aqueous solution

– Osmolarity = molarity (mol/L) of particles in solutions• A 1 M Glucose solution = 1 Osmolar (Osm)• But a 1 M NaCl soln = 2 Osmolar because NaCl dissociates into 2 particles (Na and Cl)

whereas Glucose does not• Physiological solutions are expressed in milliosmoles per liter (mOsm/L)

– blood plasma = 300 mOsm/L or 0.3 Osm/L

Tonicity - property of a solution to affect fluid volume and pressure within a particular cell (depends on concentration and permeability of solute,)

• Isotonic solution– solution with the same solute concentration as that of the cytosol; normal saline[0.15M

NaCl]• Hypotonic solution

– lower concentration of nonpermeating solutes than that of the cytosol (high water concentration)

– cells absorb water, swell and may burst (lyse)• Hypertonic solution

– has higher concentration of nonpermeating solutes than that of the cytosol (low water concentration)

– cells lose water + shrivel (crenate)

Osmolarity and Tonicity

cell = out solutesolute

solutesolute

Water is in thermodynamic equilibrium across cell membranes

Hypotonic Isotonic Hypertonic

Transport of water can be induced either by osmotic pressure differences, giving rise to the osmotic permeability (Pf), or by a difference in tracer concentrations, giving rise to the diffusion permeability (Pd).

►The diffusion permeability accounts for water molecules transported through the entire channel,

►Osmotic permeability accounts for water entering and leaving the channel at its exits such that Pf/Pd is greater than one.

The ratio Pf/Pd measures the number of essential steps that water molecules need to pass the channel.

For aquaporin with an osmotic permeability (Pf) of 6 x 10-20 m3s-1 per channel subunit, an equivalent hydraulic conductivity of 4.4 x 10-22 m3s-1MPa-1 per channel subunit can be calculated.

►For a gradient of 0.1 MPa (1 bar) in osmotic pressure, which is physiologically realistic, 1.5 x 106 water molecules will flow through each channel subunit per second.

This is similar to the flux through an ion channel for a typical driving force.

Schematic depiction of water movement through the narrow selectivity filter of the aquaporin channel

Aquaporin (the water channel): The HIGHWAY for water transport

Transport of ions through membrane

Ion Channels referred the ion it permeate

Three basic properties of ion channels:

• To conduct ions rapidly ( high turn over number)

• Exhibit high selectivity: only certain ion species flow while others are excluded

• Conduction be regulated by processes known as gating, i.e. ion conduction is turned on and off in response to specific environmental stimuli

• The flux of ions through the ion channels : passive

Ion channels do not bind the ions that pass through them.They are selective in determining which ion can pass.Types of gated ion channels: voltage-gated, stretch-gated, phosphorylation-gated and ligand-gated channels.

Ion channels are with oligomeric arrangement with Intrinsic symmetry and the pore Size Correlates with the number of Subunits

•Voltage-Dependent (Na+, K+, Ca++)

•Ligand-Gated•Mechanosensitive

•Connexins(Gap Junctions)

Ion Channels

Turnover rate (s-1 ) of Na-K ATPase pump: 5x102

Turnover rate (s-1 ) of Ca - ATPase pump: 2x102

Compartmentation of Ionic Pools and Electrochemical Driving Forces

Ion Channels: Uniporter(passive), antiporter( primary active/seconadary active) ,symporter (seconadry active, cotransporter)

Compartmentation of Ionic Pools and Electrochemical Driving Forces

Ion Channels: Uniporter(passive), antiporter( primary active/seconadary active) ,symporter (seconadry active, cotransporter)

Categories of Ion Permeability Pathways

Lodish et al. (2000) Molecular Cell Biology4th Edition [W.H. Freeman & Co.]

Primary Active Transport

• Solute pumping– Pump or protein carrier

• An enzyme-like protein carrier that pumps or carries solutes such as ions of sodium, potassium, and calcium, into or out of the cell against their concentration gradients.

– ATPase• The enzyme on the protein carrier or pump that catalyzes the breakdown or

phosphorylation of ATP producing energy that drives the pump.– This action may require up to 40% of a cell’s supply of ATP

– Sodium-potassium pump (Na+/K+ ATPase Pump)

• Maintains the resting membrane potential of nerve and muscle cells• Sodium

– Primary extra-cellular ion that is constantly “leaking” into cells. • Potassium

– Primary intracellular ion that is constantly “leaking” out of cells.• The sodium/potassium pump constantly pumps 3 sodium ions out and 2

potassium ions into the cell, maintaining the relative negativity inside the cell.

• All cells have a negative charge inside because of this mechanism.

3Na+

ATP

3Na+

2K+

2K+

Secondary Active Transport

• Movement of a molecule that is coupled to the active transport of another molecule

– One substance moves down its electrochemical gradient and releases energy in the process

– This energy is then used to drive the movement of another substance against its electrochemical gradient

Cotransport (Symport) - Movement of 2 substances in the same direction -Example Sodium-linked glucose transport Couples the inward flow of sodium with the inward flow of glucose Sodium movement with its electrochemical gradient releases energy that drives the movement of glucose against its concentration gradient

Countertransport (Antiport exchange)– Movement of 2 substances in opposite directions– Example

– Sodium proton exchange» Couples the inward flow of sodium with the outward flow

of protons (H+)» Energy released from the inward flow of sodium along its

electrochemical gradient is used to drive the outward flow of protons against its electrochemical gradient

PASSIVE SOLUTE TRANSPORT - SUMMARY

• Passive transport moves towards the electrochemical equilibrium.

• Simple diffusion depends on the concentration gradient for an unchargedsolute. In case of a charged solute, conc. gradients and electrical effectscontribute to diffusion.

• Polar organic solutes (glucose, amino acids) move across membranes withthe help of transporter proteins in the direction of the electrochemicalequilibrium (facilitated diffusion).

• The permeability of a membrane for a lipid solute depends on how readily thethe solute enters into and moves across the membrane lipid bilayer – simplediffusion.

For inorganic ions, the permeability depends on the number of ion channels.

■ Solute transport is active if it can move solutes away from electrochemical equilibrium.

• Active transport is primary if the transporter is an ATPase (energy comesdirectly from ATP), example: • Na+ -K+ -ATPase is a primary active transport mechanism • Other important ATPases: Ca2+ -ATPase in the sarcoplasmic reticulum of muscle cells. H+-K+ -ATPase is the proton-pump that acidifies stomach content. vesicular or v-type H+ -ATPase in gills and kidneys.

• Active transport is Secondary if the energy comes from a solute electrochemical gradient (indirectly from ATP). Organic solutes are pumped by secondary-active transport mechanism. • The transport of ions can create voltage differences (electrogenic) or not (electroneutral).

Summary of Active Transport

Nernst Equation: It describes the flux of the ion under combine influence of concentration gradient and the electric gradient field

Passive transport of ions across the membrane driven by two factors:

a) Concentration gradient b) electrical gradient

The direction of diffusional and electrical fluxes is opposing

Jtotal = Jconc.grad + Jelec.grad

Z F Dion

RTC

dΔФ

dXJelec..grad = -

D - diffusion coefficent of ion

C - conc. of ion

Ф - electrical gradient(membrane potential)

X- thickness of membrane

Z-valency of ion

F-Faraday constant

R-gas constant

T-temp.

At equilibrium Jtotal = 0

Jconc.grad = Jelec.grad

RT

ZFln

Cin

Cout

ΔФ(volt) = Фin - Фout = -

Effect of the passive transport of ions across the semi permeable membrane

- Dion

dC

dX─Jconc.grad =

Z F Dion

RTC

dΔФ

dX -Jtotal = - Dion

dC

dX─

Nernst Equation : Equilibrium ionic potential of individual ion( Eion), when ion concentration gradient is equivalent to electrical gradient

• ENa = 61.54mV log [Na]o/[Na]I = 62 mV

• EK = 61.54mV log [K]o/[K]I = -80 mV

• ECa = 30.77mV log [Ca]o/[Ca]I = 123 mV

• CCl = -61.54mV log [Cl]o/[Cl]I = - 65 mV

Ion Inside Outside

(mM) (mM)

K+ 125 5

Na+ 12 120

Cl- 5 125

H2O 55,000 55,000

Anion- 108 0

• Eion = 2.303 RT/zF log [ion]o/[ion]in

• Eion = ionic equilibrium potential

• Z= charge of ion• F= Faraday’s constant• T= absolute temperature (0Kelvin/-273°C) • R= gas constant

Goldman equation

►The membrane potential experimentally measured is often different than the Nernst potential for any given cell, due to the existence of other ions. ►The Goldman equation (also called the Goldman-Hodgkin-Katz equation)which quantitatively describes the relationship between membrane potential and permeable ions. ►According to the Goldman equation, the membrane potential is a compromise between various equilibrium potentials, each dependent on the membrane permeability and absolute ion concentration.

For multiple ions, the ion flux through the membrane at the resting state is zero, consider the three major ions involved in the nerve cell stimulation, Na+, K+, and Cl− ions.

where PNa, PK, and PCl are the relative membrane permeabilities (D/L) of Na+, K+, and Cl- ions, respectively. [D-diffusion coefficient of ion, L-thickness of ion channel]

Goldman prediction of membrane potential = – 84 mV (almost equivalent to equilibrium ionic potential of K+ )

PNa, PK, and PCl = 1:0.1:1

oCliNaiK

iClONaOKm ClPNaPKP

ClPNaPKP

F

RTV

][][][

][][][ln

Valid when the total membrane current equals zero;

Im=IK+INa+ICl=0

Goldman-Hodgkin-Katz equation.

ii

OOm NaK

NaK

F

RTV

][][

][][ln

Dependence of the resting membrane potential on [K+]o and on the PNa/Pk ratio, a. The blue line describes an instance in which there is no Na+ permeability (i.e., PNa/Pk = 0). The three orange curves describe the Vm predicted by the GHK Equation for a values greater than zero. The deviation of these orange curves from linearity is greater at low values of [K+]o, where the [K+]o is relatively larger.

Ignoring the contribution Cl- for membrane potential development, the Goldman equation becomes:

Goldman and Nernst equation for membrane potential

Osmotic swelling is an unavoidable problem for all cells

• The swelling arises from the presence of negatively-charged proteins( Y- ) trapped in the cytoplasm

• First, imagine that a water-permeable membrane separates two rigid compartments. – One compartment has a 150 mmolal concentration of NaCl. – The other one has 150 mEq/liter of Na+ and an equal quantity of anionic charge as protein –

however, the protein concentration is only 1 mmolal. – Is there an osmotic gradient? – Is there a solute gradient?

Intermediate conditions: Cl- diffused down its gradient; why did Na+ move against its gradient? Notice that there is now a gradient of electrical charge – this is a Donnan potential.

Now imagine water trying to move osmotically – is there a gradient of hydrostatic pressure? The system has come into Gibbs-Donnan equilibrium – all forces are balanced.

Initial conditions

P=RTOsm

RT F

lnCCl,in

CCl,out

RT F

lnCNa,in

CNa,out

- =

Gibbs-Donnan equilibrium: A semipermeable membrane separates two compartments that have rigid walls and equal volumes. The membrane is permeable to Na+, Cl , and water, but not to the macromolecule Y, which carries 150 negative charges.

+ CNa,out= CNa,inCNa,total

CCl,in

CCl,out

CNa,out

CNa,in

=

+ CCl,out= CCl,inCCl,total

+ CY-= CCl,inCCl,out

= CNa,outCNa,in

Animal cells could never attain Gibbs-Donnan Equilibrium

• Why not? The plasma membrane cannot sustain a hydrostatic pressure gradient.

• Without the evolution of some means of avoiding Gibbs-Donnan equilibrium, there would be no protein-containing cells.

The Na+/K+ Pump counteracts G-D equilibration

The Na+/K+ pump undergoes cycles in which it spends an ATP to eject 3 Na+ from the cell and at the same time to take 2 K+ into the cell.

On the average, this counteracts leakage of Na+ and K+ across the membrane down their electrochemical gradients.

The bottom-line effect of this is to make the cell effectively impermeable to NaCl.

Gibbs-Donnan equilibrium is not approached and the cell does not swell, in spite of the presence of protein anion (X-).

When Na/K pump stop working?

The effect of Gibbs – Donnan in the living cell

►Cells contain impermeable anions( e,g, proteins, nucleic acids etc.)

►If these anions are at equilibrium with out side and inside salt concentration, the ratio of all monovalent cations ( CNa,out / Can,in ) would be the same

►There will be osmotic pressure difference causing the cells to swell

►Active transport maintains a homeosttaic steady state in which there is osmotic balance regulating the cell volume

1. What is the resting ΔΦ for Na+ ions, if the outside concentration is 140 mM and the inside concentration is 50 mM?

2. A cell contains 100 mM of KCl and 500 mM of protein chloride. The outside of the cell medium has 400 mM KCl. Assuming that the cell membrane is permeable to Cl− and K+ ions and impermeable to the protein, determine the equilibrium concentrations and the membrane potential. Also assume that these compounds can completely dissociate.

Problems: Nernst, Donnan

Ohm’s law

An open ion channel follows Ohm’s law!

Electrical circuit model of ion-channel

Reduced circuit obtained by combining the ion-specific pathways using the Goldman equation

Electrophysiologists model the effects of ionic concentration differences, ion channels, and membrane capacitance in terms of an equivalent circuit, which is intended to represent the electrical properties of a small patch of membrane. The equivalent circuit consists of a capacitor in parallel with four pathways each consisting of a battery in series with a variable conductance. The capacitance is determined by the properties of the lipid bilayer, and is taken to be fixed. The voltage of each ionic pathway is determined by the concentrations of the ion on each side of the membrane. The conductance of each ionic pathway at any point in time is determined by the states of all the ion channels that are potentially permeable to that

ion, including leakage channels, ligand-gated channels, and voltage-dependent channels.

Equivalent circuit

Electrical equivalent circuit model of membrane: Sodium (Na+) and potassium (K+) channels, which are the primary contributors to the nerve action potential, are

represented by their equivalent channel resistance (RNa , RK), Nernst potentials (ENa, EK),

and channel currents (INa, IK). The leak current (IL ) represents current due to chloride

ions, calcium, and magnesium to simplify the model and also because these channels are passive and not voltage-dependent like the Na+ and K+ channels.

K+

(150mM)

K+

(4mM)

Na+

(145mM)

Na+

(20mM)

Na/K-ATPase 1

Ca++

(0.1µM)

Ca++

(2.5mM)

Na

2- Na/Ca- Exchanger

3 - Ca - ATPase

Electrogenic pumps contribute several mv (negative) to resting membrane potential

Na/K – ATP ase( 3Na/2K)

Ca- ATPase

Na/Ca-Exchanger(3Na/1Ca)

Electrogenic pump contribution to membrane potential

1. Concentration gradient of Na+, K+, Ca+2 across the membrane

2. The relative permebility( electrical conductance ) of each of the ions ( regulated by ion channels)

3. Electrogenic pumps (Na/K - ATPase[3Na in 2K out of the cell], Ca -ATPase, Na/Ca -exchangers[3Na exchange for 1Ca)

Therefore, to determine Em , the individual ion equilibrium potential are multiplied by relative membrane permeabilities( conductance) and summed up

What determines transmembrane potential( Em )?

Bulk Transport

Endocytosis occurs when the plasma membrane envelops food particles and liquids.

1. phagocytosis – the cell takes in particulate matter

2. pinocytosis – the cell takes in only fluid

3. Receptor-mediated endocytosis – specific molecules are taken in after they bind to a receptor

Exocytosis – movement of materials out of the cell

Endocytosis

Exocytosis occurs when material is discharged from the cell.

-vesicles in the cytoplasm fuse with the cell membrane and release their contents to the exterior of the cell

-used in plants to export cell wall material

-used in animals to secrete hormones, neurotransmitters, digestive enzymes

Exocytosis

• Equilibrium is the state of a system without input of energy or matterfrom outside.

• Passive transport moves towards, active transport can move against the

electrochemical equilibrium of a system.

• Uncharged molecules equalize concentrations by simple diffusion, charged

molecules are also moved by electrical forces.

• The permeability of a membrane for a solute depends how readily it

dissolves into the membrane and the number of channels (inorganic ions).

• Active transport uses metabolic energy (ATP) to transport a solute against

the electochemical gradient.

• Organic solutes can be moved across membranes by transporters, but only

towards the electrochemical equilibrium (facilitated diffusion).

• Active transport is primary when it directly uses ATP (ATPases), secondary

if the energy for transport comes from a concentration gradient.

MEMBRANE TRANSPORT – SUMMARY

Questions

a. Draw a situation where a molecule of NaCl will enter the cell. Assume

that a transport protein is needed

• Is the extracellular environment hypo-, hyper-, or isotonic?

• Direction of water?

b. What is membrane potential? How it is generated? How this help for transport of ions?

c. How Carrier mediated transport help transport of Glucose. Is it active or passive transport process.

d. Describe primary and secondary active transport mechanism with example.

Problem: Facilitated Diffusion of Glucose

Assume: a concentration of glucose inside the cell of 0.5 millimolar and a concentration of glucose outside the cell of 5 millimolar (mM) at body temperature of 37°C, so an absolute temperature of 37 + 273 = 310°K, and the plasma membrane is permeable to glucose.

Calculate the amount of free energy released.

ΔG = (2)(273+37) x ln (0.5/5)= (2)(310) x ln (0.1)= (620)(−2.3) = −1426 cal/mole= −1.4 kcal/mole

(If you prefer to work with log10, multiply the log10 by 2.303, thus log10 (0.1) = −1; −1 x 2.303 = −2.3)

Because the process proceeds with the release of free energy, it can proceed spontaneously.

In this case, facilitated diffusion would be required because glucose is not permeamble to membrane and needs transport channels to allow it to pass through the lipid bilayer of the plasma membrane.

Problem: Active Transport of Glucose

Filtration of the blood in the glomeruli of the kidneys produces a nephric filtrate with a concentration of glucose the same as that of the blood (~ 5 mM). All of this glucose is normally reclaimed by active transport.

Problem: What is the free energy needed to move glucose

back from the tubular fluid to the blood when the

concentration in the tubular fluid has dropped to 0.005 mM?

The problem is to pump glucose into the cell (where it is about

0.5 mM) and then across the plasma membrane at the

basolateral surface of the cell into the interstitial fluid, where

the glucose concentration is 5 mM (the same as in the blood).

So the total gradient through which the glucose must be

pumped is 0.005 mM -> 5 mM.

ΔG = (2)(310) x ln (5/.005)

= 620 ln (1000) = (620)(6.91) = + 4284 cal/mole

= + 4.3 kcal/mole

Where is the needed energy to come from?

The Na+/glucose Cotransporter

The active transport of glucose is mediated by the Na+/glucose cotransporter. This is a symporter; that is, both the sodium ion and the glucose molecule are passing through the membrane in the same direction:► sodium DOWN its gradient of about

•140 mM outside to •10 mM inside

while glucose is going UP its gradient (0.005 mM -> 5 mM).

A mole of sodium ions (Na+) moving down this concentration gradient releases −1.6 kcal of free energy. ΔG = (2)(310) ln (10/140)= (620) ln (0.07) = (620)(− 2.64) = −1637 cal/mole= −1.6 kcal/mole Is this enough to move a mole of glucose? No, but there is another force we must consider. Sodium ions carry a single positive charge and the interior of the cell is negatively charged . So the attraction between opposite charges provides a second force for bringing Na+ into the cell. This, too, can be quantified by ΔG = (z)(F)(Vm) where z = the charge on the ion (+1 in this case) F = 23,062 = the calories released as one mole of charge moves down a voltage gradient of 1 volt (1000 mV) Vm = the membrane potential, about − 70 mV in mammalian cells.Still not enough to move a mole of glucose, so at least two sodium ion are needed to bring one molecule of glucose into the cell. So the driving force for the active transport of glucose (and other small organic molecules, e.g., amino acids) is the force provided by the movement of sodium ions following their electrochemical gradient. the sodium gradient across the two sides of the plasma membrane is created by the active transport of Na+ OUT of the cell by the Na+/K+ ATPase; the single most profligate user of energy in the our body.

Solution

Problem: Active transport of amino acidsHow many sodium ions are needed to provide the free energy to transport a molecule of glutamic acid from a concentration of 0.1 mM outside the cell to 20 mM inside the cell? Again, assume a temperature of 37°C (310°K) at pH 7.0.

SolutionAt pH of ~7, glutamic acid molecules carry a net charge of minus 1. So, once again, we have a problem of determining the movement of a molecule against an electrochemical gradient; that is, against both a concentration gradient (20/0.1 = 200) and a electrostatic gradient (moving a negative charge against a voltage of − 70 mV).ΔG = (R)(T) x ln(20/0.1) + (z)(F)(Vm)= [(2)(310) x ln(200)] + [(−1)(23,062)(− 0.070)= (620) x (5.3) + 1614= 3286 + 1614= 4900 or 4.9 kcal/mole Because sodium ions release only 3.3 kcal/mole, at least 2 Na+ are needed to cotransport one molecule of glutamic acid.