2.1.5(d)(i)-(ii) - Transport across membranes and model cells

Choosing a transport route

A membrane transport question is usually solved by asking four linked questions.

1. Is the substance moving down a concentration gradient or against it?
2. Can it pass through the phospholipid bilayer directly, or does it need a membrane protein?
3. Is ATP required as an immediate source of energy?
4. Is the substance moving as individual molecules/ions, or is membrane vesicle movement involved?

[DIAGRAM: membrane_transport_routes: Lesson 043: Movement of molecules across membranes and model cells - diagram 01; asset_slug: 043_m02_1_5_movement_of_molecules_across_membranes_and_model_cells__diagram_01; recommended_method: drawn_biology; description: 16:9 deterministic drawn comparison of simple diffusion, facilitated diffusion, active transport, endocytosis and exocytosis with Biological labels for gradient, protein use and ATP.]

The main divide is passive versus ATP-requiring movement. Passive movement does not require ATP from the cell as an immediate energy source. Diffusion and facilitated diffusion are passive because the net movement is down a concentration gradient. Active transport, endocytosis and exocytosis require ATP.

The wording "net movement" matters. Molecules are always moving randomly, but if there are more molecules on one side of a membrane, more will move from that side to the other side per second. The overall result is movement from higher concentration to lower concentration until there is no concentration gradient. At that point, molecules still move in both directions, but there is no net movement.

A gradient is specific to one substance. A glucose gradient does not automatically tell you the direction of movement for ions, water or a different solute.

Diffusion and facilitated diffusion

Diffusion is the net movement of particles from a region where they are at a higher concentration to a region where they are at a lower concentration. In membranes, simple diffusion works best for small non-polar or lipid-soluble molecules because they can pass through the hydrophobic core of the phospholipid bilayer. Oxygen and carbon dioxide are standard examples.

Charged ions and many polar molecules cannot pass easily through the hydrophobic interior of the bilayer. They can still move passively if the membrane contains the correct transport protein. This is facilitated diffusion: the protein provides a route, but the concentration gradient still supplies the direction of net movement.

Channel proteins form hydrophilic pores through the membrane. They are useful for ions and other small polar substances. Carrier proteins bind a particular molecule, change shape, and release the molecule on the other side. Both routes are selective, so a membrane can be permeable to one solute but not another.

Carrier-mediated facilitated diffusion can reach a maximum rate because the number and turnover of carriers are limited. Once carriers are occupied and working at capacity, further increases in concentration can have little effect. Channel-mediated diffusion does not necessarily show the same carrier-saturation curve. That plateau is not because ATP has run out; ATP was not required in the first place.

Do not write that facilitated diffusion is active transport just because a protein is involved. The key mark-scheme distinction is ATP use and movement relative to the concentration gradient.

Osmosis is water movement across a partially permeable membrane and has its own lesson next. For this lesson, treat it only as a boundary reminder: do not use "osmosis" as a general word for all membrane transport.

A steeper concentration gradient produces a greater difference between the numbers crossing in opposite directions each second. More membrane surface provides more crossing sites, while a thinner barrier shortens the path. Increasing temperature generally increases random molecular motion. These explain rate changes without claiming that diffusion molecules choose a direction. For ions, electrical potential also affects movement; the simple concentration-only examples assume no opposing electrical gradient.

ATP-requiring movement

Active transport uses ATP as an immediate source of energy to move substances across membranes. It is usually taught as movement against a concentration gradient, from a lower concentration to a higher concentration. This cannot be explained by random movement alone, so a membrane carrier or pump protein changes shape using energy from ATP.

The word "immediate" is important. Respiration makes ATP elsewhere in the cell, but the primary active-transport pump described here uses ATP directly at the membrane protein. A low ATP supply can therefore reduce active transport, even if the concentration gradient still favours the opposite passive movement.

Endocytosis and exocytosis also require ATP, but they are not the same as a pump moving one ion at a time. They move material using vesicles made from or fused with membranes.

Both processes use membrane remodelling, so they can move substances that are too large for channels or carriers. They still need ATP because forming, moving and fusing vesicles requires energy.

[DIAGRAM: 043_vesicle_transport: Membrane invagination and vesicle fusion move material.; asset_slug: 043_vesicle_transport; recommended_method: drawn_biology; description: Membrane invagination and vesicle fusion move material.]

Model cells for diffusion

A model cell is not a living cell. It is a practical system that represents one important feature of a cell so that the feature can be investigated under controlled conditions. For this lesson, the useful features are selective permeability, diffusion distance, concentration gradient, surface area and volume.

Visking tubing, also called dialysis tubing, is a common artificial membrane. It can be tied into a small bag, filled with a mixture such as glucose and starch solution, rinsed on the outside, and placed in water. Check that the bag is sealed without leaks, rinse its outside and establish that the outside water initially tests negative for the solutes. After a set time, test the outside water again.

If glucose is detected outside but starch is not, the conclusion is not simply "diffusion happened". The stronger conclusion is that the membrane was permeable to the smaller glucose molecules but not to the larger starch molecules. The Visking tubing is a model for selective permeability, not a model for a complete plasma membrane.

Agar cubes are another model. A cube containing indicator can be placed in acid, alkali or another diffusing solution. A colour change shows how far the solution has diffused into the cube after a fixed time, or how long it takes to reach the centre. Smaller cubes have a larger surface area to volume ratio, giving more exchange surface per unit volume, and a shorter distance to the centre. They can therefore become completely penetrated sooner without individual molecules moving faster.

[DIAGRAM: model_cells: Selective dialysis tubing and agar-cube geometry; asset_slug: 043_m02_1_5_movement_of_molecules_across_membranes_and_model_cells__diagram_02; recommended_method: drawn_biology; description: Glucose can cross dialysis tubing whereas starch is retained, and cube size changes both surface area to volume ratio and distance to the centre.]

Rates, graphs and surface area

Diffusion investigations need a measured rate, not just a statement that a colour changed. The rate may be measured as:

• distance diffused per unit time
• mass or volume change per unit time
• concentration change per unit time
• $1/\text{time}$ when the endpoint is the time taken for a fixed change

For a cube, surface area and volume can be calculated from its side length. This is useful because diffusion across the outside depends on surface area, while the amount of material supplied by diffusion depends on volume.

When data are plotted, put the independent variable on the x-axis and the dependent variable on the y-axis. For example, surface area to volume ratio belongs on the x-axis if it is the factor being changed, and mean diffusion rate belongs on the y-axis if it is the measured outcome.

If the graph is a straight line, rate of change can be found from the gradient:

If the graph is curved and you need the rate at one point, use the gradient of a tangent at that point. For a distance-time graph, the tangent gives penetration distance per unit time. As a diffusion front moves deeper into agar, the diffusion path becomes longer and the effective concentration gradient can flatten; the front may advance more slowly. A gradient against SA:V has different units and is not itself a diffusion rate.

Uncertainty should shape the conclusion. A stopwatch result may include reaction-time uncertainty. A ruler measurement may include uncertainty from the smallest division. Repeats and a mean improve reliability, but they do not fix an invalid method where two variables were changed at the same time.

A section through a cube also allows a penetrated-volume calculation. If acid has travelled 0.20 cm inward from every face of a 1.0 cm cube, the unpenetrated core has side $1.0-2(0.20)=0.60\,\mathrm{cm}$. Its volume is $0.60^3=0.216\,\mathrm{cm^3}$, so $(1-0.216)\times100=78.4\%$ of the cube has changed colour. Subtract the penetration depth twice because acid enters from opposite faces.

In symbols, for comparable conditions, increasing area gives rate ∝ area; a thicker barrier gives a smaller rate. “>” means greater than, “<” less than, “≫” much greater, “≪” much less, “=” equal and “~” approximately. These compare quantities; they do not replace a statement of what was actually measured.

A straight penetration-distance graph can be described by $y=mx+c$. If distance increases from 1.0 mm at 20 s to 2.0 mm at 40 s, the gradient is $0.050\,\mathrm{mm\,s^{-1}}=5.0\times10^{-5}\,\mathrm{m\,s^{-1}}$; the intercept is zero for that line. Use this slope only over the interval where a straight line represents the data. For repeated penetration distances, calculate a mean and record their spread: 1.8, 2.0 and 2.2 mm have mean 2.0 mm and sample SD 0.2 mm. SD describes variation, not accuracy.

For ordered penetration measurements 1.8, 2.0, 2.0, 2.1 and 2.6 mm, the mean is 2.1 mm, the median is 2.0 mm and the mode is 2.0 mm. The high reading affects the mean more than the median; keep the observation record and investigate any possible cause before excluding it.

Designing and evaluating model-cell investigations

A valid PAG8-style model-cell diffusion investigation changes one independent variable and controls the others. Depending on the method, the independent variable could be concentration gradient, cube size, diffusion distance, surface area to volume ratio, temperature, or molecule size. The dependent variable must be measurable, such as time for colour change, distance diffused, concentration of glucose outside the tubing, mass change, or absorbance.

Controlled variables should match the factor being tested. In a Visking tubing investigation, useful controls include tubing length, volume inside the tubing, outside volume, starting concentration, time, temperature and how thoroughly the outside of the tubing is rinsed. In an agar cube investigation, useful controls include agar composition, indicator concentration, solution concentration, solution volume, temperature and time in solution.

Reliability comes from repeats, means and checking anomalies. Validity comes from whether the method really tests the intended factor. For example, comparing agar cubes of different size can investigate size-related exchange if agar composition and external solution are controlled. Cube size changes SA:V and distance to the centre together, so the experiment alone cannot separate those two effects.

Model limitations should be stated precisely.

When evaluating a model, do not just say "it is not a real cell". State the exact feature it models well and the exact feature it cannot model.

Use the final self-explanation to judge the practical evidence: a fair comparison, a measurable outcome and a precise model limitation.

For a penetration-depth investigation, immerse equal cubes of alkaline indicator agar in a large, stirred acid reservoir. Remove replicate cubes at planned times, rinse briefly to stop further surface reaction, cut through the centre and measure the changed layer with a ruler. Standardise the delay between removal and measurement. The colour boundary records indicator neutralisation, which is a proxy for acid penetration; it does not track a single molecule. Use eye protection for the acid and a tile and safe cutting technique for the blade.