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Lecture notes. Taken in part from: Adley, D. J. (1991) The Physiology of Excitable Cells , Cambridge,3ed. Calabrese, R. C., Gordon, J., Hawkins, R., & Qian, Ning. (1995) Essentials of neural Science and Behavior. Study guide and practice problems . Appleton & Lange

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Lecture notes

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Lecture notes l.jpg

Lecture notes

  • Taken in part from:

  • Adley, D. J. (1991) The Physiology of Excitable Cells, Cambridge,3ed.

  • Calabrese, R. C., Gordon, J., Hawkins, R., & Qian, Ning. (1995) Essentials of neural Science and Behavior. Study guide and practice problems. Appleton & Lange

  • Davson, H. (1970) A Textbook of General Physiology, 4th Ed., Williams and Wilkins

  • Hille, B. (1992) Ionic Channels of Excitable Membranes, 2ed., Sinauer.

  • Levitan, I. B. & Kaczmarek, L. K. (1991) The Neuron: Cell and Molecular biology, Oxford.

  • Mathews, G. G. (1998) Cellular Physiology of Nerve and Muscle, Blackwell Science


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CELLMEMBRANE

  • 1) KEEPS THE CELL INTACKT (IN PART)

  • 2) PERMEABLE TO SMALL MOLECULES

  • 3) IMPERMEABLE TO LARGE MOLECULES.


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DIFFUSION

PHYSICAL PROCESS THAT EQUILIBRATES FREELY MOVING SUBSTANCES


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CELLULAR COMPARTMENTS

  • INTRACELLULAR SPACE – The fluid space surrounded by the plasma membrane or cell wall.

  • EXTRACELLULAR SPACE – The fluid space surrounding the outside of a plasma membrane of a cell or cell wall.


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COMPOSITIONS OF PARTICLAS WITHIN AND OUTSIDE PLASMA MEBRANES


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PLASMA MEMBRANE


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FREEZE FRACTURE TECHNIQUE


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FRACTURE IS NOT ALONG CRYSTAL PLANES


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OSMOLARITY

  • CONCENTRATION OF WATER IN SOLUTIONS CONTAINING DIFFERENT DISSOLVED SUBSTANCES.


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Osmolarity (cont.)

  • THE HIGHER THE OSMOLARITY OF A SOLUTION THE LOWER THE CONCENTRATION OF WATER IN THAT SOLUTION.


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MOLARITY

  • THE MOLECULAR WEIGHT, IN GRAMS, OF A SUBSTANCE DISOLVED IN 1 LITER OF SOLUTION. (1 M)


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Molarity (cont.)

  • 1 MOLE OF DISOLVED PARTICLES PER LITER IS SAID TO HAVE 1 OSMAL


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MOLALITY

  • MOLES OF SOLUTION PER KILOGRAM OF SOLVENT

  • Takes into account that large dissolved molecules (protein of high molecular weight) displace a greater volume of water than small molecules


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Example

  • Glucose, sucrose do not greatly dissolve in water. Number of water molecules does not change.


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Osmolarity

  • Osmolarity takes into account how many dissolved particles result from each molecule of the dissolved substance.

  • 0.1 M glucose solution is 0.1 Osm solution.


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  • Glucose, sucrose and urea molecules do not dissociate when dissolved in water.

  • 0.1M glucose is a 0.1 Osm solution


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Osmolarity for dissociated substances

0.1 M NaCl = 0.1 M Na + 0.1M Cl = 0.2 Osm


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300 Osm

  • 300 mM glucose

  • 150 mM NaCl

  • 100 mM NaCl + 100 mM Sucrose

  • 75 mM NaCl + 75 mM KCl


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Mixing

  • The mixing is caused by the random independent motion of individual molecules (temperature dependent).


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Two separate actions

  • Random movement of the solute (glucose)

  • Random movement of the solvent (water).


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Osmosis

  • WHEN SOLUTIONS OF DIFFERENT OSMOLARITY ARE PLACED IN CONTACT WITH A BARRIER THROUGH WHICH WATER WILL MOVE ACROSS THE BARRIER, WATER WILL MOVE FROM THAT SIDE WITH THE GREATER NUMBER OF WATER MOLECULES PER UNIT VOLUME (Higher Osmolarity) TO THAT SIDE WITH THE LESSER WATER MOLECULES PER UNIT VOLUME (Lower Osmolarity).


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Home experiment

  • Mason or Kerr quart jar.

  • Dark Molasses

  • Large Carrot

  • Glass Tube


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Observable change

  • Mechanism is the same, diffusion. The results of the process is observable because the water moving into the carrot displaces the molasses forcing the molasses up the tube which can be seen.


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Work done by osmosis moves piston from left to right compartment


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Osmotic Pressure

  • Suppose that one could measure the force necessary to just keep the water from moving into compartment A.

  • That force divided by the cross sectional area of the piston would be the osmotic pressure of the system.


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Aqua pores

  • Pores have now been found that transfer only water and not ions.


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OSMOTIC CHANGE IN VOL.


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OSMOTIC BALALANCE VS CELL VOLUME

  • [S]in = [S]out

  • [S]in + [P]in = [S]out


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NO NET CHANGE WHEN IN BALANCE

  • IF A SUBSTANCE IS AT DIFFUSION EQUILIBRIUM ACROSS THE CELL MEMBARANE, THERE IS NO NET MOVEMENT OF THAT SUBSTANCE ACROSS THAT MEMBRANE.


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Osm vs. cell volume (cont.)

  • REQUIRES THAT:

  • [S]in = [S]out

  • and

  • [S]in + [P]in = [S]out

  • BE SIMULATENEOUSLY TRUE AT EQUILIBRIUM.


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  • How do cells in nature solve the simultaneous condition?


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Solution 1

  • MAKE THE CELL IMPERMEANT TO WATER

  • Certain epithelial cells (skin) are impermanent to water


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Solution 2

  • PUT THE CONTENTS OF THE CELL WITHIN AN INELASTIC WALL

  • Plant cell’s solution


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Solution 3

  • MAKE THE CELL MEMBRANE IMPERMEANT TO SELECTED EXTRACELLULAR SOLUTES


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Impermeant sucrose & protein


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ECF Osm. Lower than ICF


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ECF has permeant solute, ECF & ICF initially equal


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ECF contains a mixture of permeant and impermeant solutes


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  • [UREA]in + [P]in = [UREA]out +

    [SUCROSE]out


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IONS IN SOLUTION (WATER)

  • Ions in solution behave much like particles in solution.


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Na+, K+, Cl-, Ca2+

  • When they move they carry their charge with them.


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  • Some channels are non selective as to the type of cation.


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  • The movement of ions down their concentration gradient can do work.


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Size of ion depends on it ability to hold a water “cloud”


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Most channels only allow one species of ion to pass, a uniport


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Na+ channel. Water cloud must be stripped away


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Current through channels follows Ohm’s law


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CATION & ANIONS

  • Positively charged particles in solution tend to congregate near the negative pole of a battery.

  • Negatively charged particles tend to congregate near the positive poles.


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DIFFUSION POTENTIAL

  • DIFFERENTIAL DISTRIBUTION OF IONS IN SOLUTION BETWEEN TWO DIFFERENT COMAPARTMENTS, WITH A COMUNICATING CHANNEL, GIVE RISE TO A VOLTAGE GRADIANT IN THE SOLUTION.


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Concentration Cell

  • Different concentration of electrolyte XY in solution.

  • Membrane permeable to only X+


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Diffusion

  • Concentration in 1 is greater than 2 by twice as much


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Diffusion

  • If the barrier is moved, twice as many X+ moves down its gradient from compartment 1 to compartment 2, carrying a positive charge.


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Charge separation

  • Movement of charges from 1 to 2 sets up a potential difference between the two compartments.

  • This charge separation is in the direction of 2 to 1, opposite to the diffusion gradient.


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  • As the potential difference grows it will become increasing harder to move X+ from 1 to 2.

  • More and more X+ will move from 2 to 1


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Equilibrium Potential

  • An equilibrium position is reached at which the electrical (tending to move X+ from 2 to 1) just balances the chemical or concentration gradient (tending to move X+ from 1 to 2).


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Voltage

  • The potential difference that builds up in the above system is expressed as voltage (in mVolts).

  • That is, when charges are separated, a potential energy condition is constructed.

  • Volt is and expression that describes this potential difference in electrical terms.


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Voltage (cont.)

Voltage should be thought of as a gradient. A gradient implies looking at two places or states with respect to one another.


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Electrical conventions 1

If Compartment 1 is the reference chamber, Compartment 2 is said to be positive with respect to compartment 1. (A volt meter will point toward the positive pole).


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Electrical conventions 2

If the compartment 2 is the reference chamber, compartment 2 is negative with respect to compartment 1. (The voltmeter will point to the left chamber).


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Voltage (cont.)

2) This can be thought of as an electromotive force.

Charge separation gives rise to a difference of electrical potential (volts).

The voltage across the membrane (Vm) is called: membrane potential.

Vm = Vin - Vout


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Voltage (cont.)

3) Think of this voltage as a driving force for the movement of charges in space.

We will use the convention that the direction of current flow is the direction of the net movement of the positive charges (Franklin’s convention)

That is, in ionic solutions cations (+ charges) move in the direction of the electrical current


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  • When current flows in a cell (either cations or anions) the potential across the cell is disturbed, its degree of polarization is changed.

  • Depolarization is a reduction in the degree of negativity (reduced charge separation) across the membrane.

  • An increase in charge separation leads to more negativity called hyperpolarization.


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Ohm’s Law

  • Voltage is proportional to current.

  • V ∞ I

  • If the two are related you must have a proportionality constant.

    V = RI

    Where V is in volts, R is resistance, in ohms and I is in amperes. R is the slope of the line relating volts to current


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Equilibrium Potential

  • A potential can be calculated for each species of ions which represents the balance between the electromotive force (separation of charge) and diffusion (differential concentration gradient) for a given species of ion across a selectively permeable membrane.


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Temperature effect

  • There is a temperature coefficient that is implied in the Nernst equation. Increasing the temperature increases the random motion of the molecules in solution. This increase will increase the probability of a given ion to go through the channel.


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Nernst Equation

  • If one wants to know the dynamic value of the diffusion flow one would have to do work to stop the flow.

  • Assume an increment of work is done to just stop the flow of K down its gradient but no greater work.


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Sources of energy driving the Nernst equation

  • Diffusion gradient.

  • The generated electrical field (Separation of Charge).

  • These two forces work in opposite directions.


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  • The differential concentrations (Diffusion)


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Diffusion gradient of K


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Work opposing diffusion

  • δWc = δn(R)(T) ln([x]out/[x]in)

    Where

    δW =increment of work

    δn = increment of number of moles moved.

    R =gas constant (8.314 J deg-1 mole-1)

    T =absolute temperature

    X =molar concentrations of solute in

    compartment 1 an 2


Work of opposing electromotive force l.jpg

Work of opposing electromotive force

  • Work of electromotive force opposing diffusion

    δWe = δn (zFE)

    δWe = increment of work.

    δn = moles moved against an electrical

    gradient.

    Z = valence of the ion moved.

    F = Faraday’s constant(96,500).

    E = the potential difference between the

    two compartments.


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At Equilibrium, no net movement of X

  • δWe = δWc

    or

  • δn (z) (FE) = δn (R)(T)ln([X]1/[X]2)

  • Solving for E


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Nernst Equation

  • E = (RT/zF)ln([X]1/[X]2)

  • or

  • E = (25/z)ln([X]1/[X]2)

  • or

  • enumerating the constants

  • E = (58/z)log10([X1/X]2)

  • at 18o C

  • E is in millivolts.


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CRITICAL PROPERTIES OF THE NERNST EQUATION

  • Applies to only one ion at a time. Each ion will have its own equilibrium potential.


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Property 1

  • Applies only to those ions that can cross the membrane.


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Property 2

  • At equilibrium ions move across the membrane, but there is no net change in the number of ions that move per unit time.


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Nernst equation (cont)

  • If you exceed the equilibrium potential in excitable cells, the direction of current flow will be reversed and ions will flow in the opposite direction up hill (more on this later).


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Implications

  • If the concentration in one of the two chambers is changed, the voltage E must change.

  • If the voltage changes, the ratio of the two compartments change and the concentrations must change with respect to each other.


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The Effect External Δ Potassium Ion Concentrations on Membrane Potentials


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The Resting Membrane Potential

  • There is a resting membrane potential for all cells.

  • Requires: Selectively permeable membrane, diffusion gradient, separation of charge


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