Diffusion and osmosis

Diffusion and the three factors affecting its rate

Molecules and ions in a liquid or gas are in constant random motion. Movement of any individual particle is undirected, but where the concentration is higher on one side than the other, more particles cross from the higher-concentration side than in the reverse direction. The net result is movement down the concentration gradient until the gradient is abolished. That is diffusion, and it requires no energy from the cell: the kinetic energy of the particles themselves drives it.

Diffusion

The net movement of particles from a region of higher concentration to a region of lower concentration, down a concentration gradient, as a result of their random motion.

Simple diffusion

Diffusion directly through the phospholipid bilayer, available to small non-polar molecules such as oxygen and carbon dioxide.

Passive

Requiring no energy from ATP; driven by the kinetic energy of the particles themselves.

Three quantities set the rate, combined in a single relationship that should be quoted and applied.

rate of diffusion ∝ (surface area × difference in concentration) ÷ thickness of the exchange surfaceOften called Fick's law. The first two multiply the rate; the third divides it.

Describe the drawing

The relationship written as a fraction across the top, with surface area multiplied by difference in concentration above the line and thickness of the exchange surface below it. Three sketches sit underneath. On the left a flat bar is compared with a folded zigzag of the same width, giving more surface. In the middle eight particles are packed above a barrier and one sits below it. On the right a thin bar is compared with a bar several times thicker.

Gas exchange surfaces are adapted for each of the three terms. Human lungs hold roughly 70 m² of alveolar surface, which addresses the first term. The barrier between alveolar air and blood is around 0.3 µm thick, being one flattened epithelial cell and one capillary endothelial cell, which addresses the third. Ventilation and continuous blood flow replace the air and the blood on either side, which maintains the second, since a gradient allowed to equalise no longer drives net movement.

Facilitated diffusion is still diffusion

Ions and larger polar molecules cannot cross the hydrophobic core on their own. They cross through proteins instead: through a channel protein, which is a hydrophilic pore, or on a carrier protein, which binds the molecule, changes shape and releases it on the other side. In both cases the substance moves down its gradient and the cell expends no ATP. For an uncharged molecule that gradient is the concentration gradient; for an ion, charge counts as well, and the ion moves down the combined electrochemical gradient, concentration and electrical attraction taken together.

Describe the drawing

One membrane drawn across the width of the figure with three routes through it side by side. In each column nine particles are scattered above the membrane and only three below, and a long arrow points from the crowded side to the empty one. The left route passes straight between the phospholipids, the middle route passes through the gap in a two-walled channel protein, and the right route passes through a carrier protein with a binding site cut into it.

Because the protein routes are finite in number, facilitated diffusion differs from simple diffusion at high concentration gradients. Raising the concentration gradient increases the rate of simple diffusion roughly in proportion. Facilitated diffusion also increases, but to a maximum. Carrier proteins show this clearly: each binding and conformational change takes time, so the rate levels off once all carriers are occupied, however steep the gradient becomes. Channels pass ions rapidly enough that over the ranges most experiments cover they behave almost like simple diffusion, although they too have a maximum throughput. A plateau in such a graph indicates that a protein, usually a carrier, is involved.

The presence of a channel or carrier protein does not make transport active. Facilitated diffusion uses a membrane protein but does not require ATP because the substance moves down its electrochemical gradient.

Osmosis and water potential

Water crosses membranes constantly, some of it through the bilayer and much of it through channel proteins called aquaporins. The direction it moves is set by water potential, given the symbol ψ (the Greek letter psi) and measured in kilopascals.

Water potential (ψ)

The tendency of water molecules to move out of a solution, measured in kPa. Pure water at atmospheric pressure has a water potential of 0 kPa; adding solute makes the solute potential negative.

Osmosis

The net movement of water molecules from a solution of higher water potential to a solution of lower water potential, through a partially permeable membrane.

Two consequences follow. Pure water at atmospheric pressure is the zero point, so a solution at atmospheric pressure has a negative water potential, because adding solute makes the solute potential negative. The condition 'at atmospheric pressure' is required, because positive pressure potential raises the total water potential: a solution under sufficient pressure can have a water potential above zero.

The word 'higher' means less negative. Water moves from −400 kPa to −1200 kPa, because −400 is the higher of the two. Handle the negative signs carefully when comparing values.

Adding solute lowers water potential because water molecules associate with the dissolved particles and are less free to leave. A 1.0 mol dm⁻³ sucrose solution has a water potential of about −3500 kPa; 0.2 mol dm⁻³ is around −540 kPa. Human blood plasma is roughly −800 kPa, and red blood cells remain intact at that value.

In a cell, two separate things affect water potential and they are added together.

ψ = ψ_s + ψ_pWater potential = solute potential + pressure potential. Pearson Edexcel Biology B writes it as ψ = P + π, turgor pressure plus osmotic potential. Solute potential is always negative; pressure potential in a living plant cell is zero or positive.

Solute potential (ψ_s, sometimes called osmotic potential) is the contribution from dissolved solutes, and it is negative in any real cell. Pressure potential (ψ_p) is the contribution from physical pressure. In a plant cell, water entering pushes the contents against the cellulose wall, the wall pushes back, and that push is a positive pressure potential that raises the cell's water potential back towards zero. An animal cell has no wall and therefore develops no significant pressure potential, which is why plant and animal cells respond differently to the same solution.

Plant cells and animal cells in solution

Describe the drawing

Three plant cells drawn side by side, each as a rigid rectangular wall with the living contents shaded inside it. The left cell is pressed hard against its wall and labelled turgid, the middle cell just fills the wall with no push left, and the right cell has shrunk into a rounded blob well clear of its wall. Under each cell three numbers in kilopascals give the solute potential, the pressure potential and their sum, which matches the bathing solution above.

Put a plant cell in pure water and water enters by osmosis. The contents swell against the wall, pressure potential climbs, and water keeps entering until the cell's water potential has risen to equal the water outside. The cell is now turgid. The wall is strong enough to prevent bursting, and the pressure generated is what supports a non-woody plant. Wilting occurs when cells lose that pressure potential.

Move that cell into a concentrated sucrose solution and the flow reverses. Water leaves, the contents shrink, and pressure potential falls. At the moment it reaches exactly zero the contents are just touching the wall but exerting no pressure on it. This is incipient plasmolysis, and at that point ψ_p = 0, so ψ = ψ_s. With further water loss the membrane pulls away from the wall altogether, leaving a gap the external solution fills. The cell is plasmolysed.

An animal cell has no wall, so neither outcome occurs. In a solution of higher water potential than its contents, distilled water for example, water enters, the membrane cannot resist the pressure, and the cell bursts. In a red blood cell this is haemolysis. In a solution of lower water potential, water leaves and the cell shrinks and puckers into a spiky shape: crenation. Blood plasma is maintained close to −800 kPa so that neither haemolysis nor crenation occurs in circulating red blood cells.

Plasmolysis, haemolysis and crenation can all be watched under a light microscope. Strips of red onion epidermis mounted in a series of sucrose solutions show plasmolysis, and the solution in which half the cells are plasmolysed is taken as the point of incipient plasmolysis, so its water potential estimates the solute potential of the cells. Animal blood from a supplier, diluted in a series of salt solutions, shows crenated cells in the strong solutions and fewer intact cells in the dilute ones as they burst.

Turgid

A plant cell whose contents press against the wall, giving a positive pressure potential.

Incipient plasmolysis

The point at which the pressure potential of a plant cell has just fallen to zero, so its water potential equals its solute potential.

Plasmolysis

The pulling away of the cell surface membrane from the cell wall as water leaves a plant cell.

Haemolysis

The bursting of a red blood cell when water enters it by osmosis.

Crenation

The shrinking and puckering of an animal cell when water leaves it by osmosis.

Finding the water potential of potato tissue

A cell's water potential cannot be measured directly. The investigation uses a dilution series to identify the external solution that produces no net movement of water, since that solution has the same water potential as the cells.

Make sucrose solutions from a 1.0 mol dm⁻³ stock. A standard set is 0.8, 0.6, 0.4, 0.2 and 0.0 mol dm⁻³, each made by mixing a measured volume of stock with a measured volume of distilled water. Cut cylinders of potato with a cork borer, trim them to the same length, blot them dry and record the mass of each. Leave one cylinder in each solution for a fixed time, then blot and reweigh.

Work in percentage change in mass, not raw change. The cylinders start at slightly different masses, and a percentage removes that difference: percentage change = (change in mass ÷ initial mass) × 100. Plot it against sucrose concentration and draw a line of best fit. Where the line crosses zero, the cylinder neither gained nor lost water, so that solution's water potential equals the potato's. Read the concentration off, then convert it to a water potential: 0.1 mol dm⁻³ sucrose is about −260 kPa, 0.2 is −540, 0.3 is −820, 0.4 is −1120, 0.5 is −1450, 0.6 is −1800, 0.7 is −2180, 0.8 is −2580, 0.9 is −3000 and 1.0 is −3500 kPa.

Non-living models: Visking tubing and agar

A membrane is 7 nm thick and a cell a few micrometres across, so neither can be observed directly on a bench. Two non-living models make the processes visible at flask scale. Because neither model is alive, any movement observed is diffusion or osmosis alone: no carrier proteins, no active transport and no metabolism contribute to the result.

Visking tubing, also sold as dialysis tubing, is a cellulose membrane with pores that let water and small solutes through and hold back large molecules. It makes a workable model gut: fill a length with a mixture of starch and glucose solutions, seal it, rinse the outside, and suspend it in a boiling tube of water. Test that outer water at intervals and Benedict's solution turns positive while iodine stays orange-brown: glucose has crossed the membrane and starch has not, which is the reason digestion has to hydrolyse polymers before anything can be absorbed. The same tubing models osmosis: fill it with concentrated sucrose solution, fit a capillary tube through the bung, and stand it in water. Water enters by osmosis, down the water potential gradient and through the partially permeable membrane, and the level climbs the capillary; the steeper the gradient, the faster the climb.

Agar makes diffusion itself visible. Set the jelly with dilute sodium hydroxide and a few drops of phenolphthalein and it sets pink; drop a cube of it into dilute hydrochloric acid and the pink fades from the outside inwards as the acid diffuses in and neutralises the alkali. Timing how long the last of the colour takes to vanish measures how long diffusion needs to reach the centre.

Cutting cubes of different sizes extends the experiment. A 5 mm cube loses its colour in a couple of minutes; a 20 mm cube retains a pink core for much longer. The acid and the jelly are unchanged, so the difference is geometric: the small cube has the larger surface area to volume ratio, and no point inside it is far from a face. A 5 mm cube has 6 × 25 = 150 mm² of surface serving 125 mm³ of volume, a ratio of 1.2 mm⁻¹, while a 20 mm cube has 2,400 mm² serving 8,000 mm³, a ratio of 0.3 mm⁻¹. Diffusion alone supplies a small object and cannot supply a large one, which is why large organisms require exchange surfaces and transport systems.

State the model's limits when a question asks for them. Visking tubing has pores but no proteins, so it models simple diffusion and osmosis and nothing else: no facilitated diffusion, no active transport, no selectivity beyond size. That limits it as a model of a membrane, but it also means that anything crossing it did so by diffusion or osmosis alone.

Visking tubing

A partially permeable cellulose membrane, with pores that pass water and small solutes but not large molecules, used as a non-living model of a membrane.