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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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### DIFFUSION

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

CELLMEMBRANE

- 1) KEEPS THE CELL INTACKT (IN PART)
- 2) PERMEABLE TO SMALL MOLECULES
- 3) IMPERMEABLE TO LARGE MOLECULES.

PHYSICAL PROCESS THAT EQUILIBRATES FREELY MOVING SUBSTANCES

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.

OSMOLARITY

- CONCENTRATION OF WATER IN SOLUTIONS CONTAINING DIFFERENT DISSOLVED SUBSTANCES.

Osmolarity (cont.)

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

MOLARITY

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

Molarity (cont.)

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

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

Example

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

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.

- Glucose, sucrose and urea molecules do not dissociate when dissolved in water.
- 0.1M glucose is a 0.1 Osm solution

Osmolarity for dissociated substances dissolved in water.

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

300 Osm dissolved in water.

- 300 mM glucose
- 150 mM NaCl
- 100 mM NaCl + 100 mM Sucrose
- 75 mM NaCl + 75 mM KCl

Mixing dissolved in water.

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

Two separate actions dissolved in water.

- Random movement of the solute (glucose)
- Random movement of the solvent (water).

Osmosis dissolved in water.

- 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).

Home experiment dissolved in water.

- Mason or Kerr quart jar.
- Dark Molasses
- Large Carrot
- Glass Tube

Observable change dissolved in water.

- Mechanism is the same mechanism as diffusion, but observable with water for its causes observable changes in the volume of liquid of chamber into which the water moves.

Osmotic Pressure compartment

- Suppose that one could measure the force necessary to just keep the water from moving into compartment A.
- That force devided by the cross sectional area of the piston would be the osmotic pressure of the system.

Aquapores compartment

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

OSMOTIC CHANGE IN VOL. compartment

OSMOTIC BALALANCE VS CELL VOLUME compartment

- [S]in = [S]out
- [S]in + [P]in = [S]out

NO NET CHANGE WHEN IN BALANCE compartment

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

Osm vs. cell volume (cont.) compartment

- REQUIRES THAT:
- [S]in = [S]out
- and
- [S]in + [P]in = [S]out
- BE SIMULATENEOUSLY TRUE AT EQUILIBRIUM.

Solution 1 compartment

- MAKE THE CELL IMPERMEANT TO WATER
- Certain epithelial cells (skin) are impermanent to water

Solution 2 compartment

- PUT THE CONTENTS OF THE CELL WITHIN AN INELASTIC WALL
- Plant cell’s solution

Solution 3 compartment

- MAKE THE CELL MEMBRANE IMPERMEANT TO SELECTED EXTRACELLULAR SOLUTES

Impermeant sucrose & protein compartment

ECF Osm. Lower than ICF compartment

- [UREA] compartmentin + [P]in = [UREA]out +
[SUCROSE]out

IONS IN SOLUTION (WATER) compartment

- Ions in solution behave much like particles in solution.

Na compartment+, K+, Cl-, Ca2+

- When they move they carry their charge with them.

Na “cloud”+ channel. Water cloud must be stripped away

CATION & ANIONS “cloud”

- 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.

DIFFUSION POTENTIAL “cloud”

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

Concentration Cell “cloud”

- Different concentration of electrolyte XY in solution.
- Membrane permeable to only X+

Diffusion “cloud”

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

Diffusion “cloud”

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

Charge separation “cloud”

- 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.

- 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

Equilibrium Potential harder to move X

- 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).

Voltage harder to move X

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

Voltage (cont.) harder to move X

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

Electrical conventions 1 harder to move X

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).

Electrical conventions 2 harder to move X

- 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).

Voltage (cont.) harder to move X

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

Voltage (cont.) harder to move X

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

Equilibrium Potential harder to move X

- 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.

Temperature effect harder to move X

- 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.

Nernst Equation harder to move X

- 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.

Sources of energy driving the Nernst equation harder to move X

- Diffusion gradient.
- The generated electrical field (Separation of Charge)

- The differential concentrations (Diffusion) harder to move X

Diffusion gradient of K harder to move X

Work opposing diffusion harder to move X

- 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 harder to move X

- 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.

At Equilibrium, no net movement of X harder to move X

- δWe = δWc
or

- δn (z) (FE) = δn (R)(T)ln([X]1/[X]2)
- Solving for E

Nernst Equation harder to move X

- 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.

CRITICAL PROPERTIES OF THE NERNST EQUATION harder to move X

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

Property 1 harder to move X

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

Property 2 harder to move X

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

Nernst equation (cont) harder to move X

- 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).

Implications harder to move X

- 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.

The Effect External harder to move XΔ Potassium Ion Concentrations on Membrane Potentials

The Resting Membrane Potential harder to move X

- There is a resting membrane potential for all cells.
- Requires: Selectively permeable membrane, diffusion gradient, separation of charge

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