Movement of Materials Across Membranes

This single idea explains why cells are small, why they divide, and why big organisms are multicellular. It's really just geometry.

The problem

A cell absorbs nutrients and expels waste across its surface (the membrane), but it uses those materials throughout its volume. So what matters is the ratio of surface to volume.

For a cube of side $L$: $\text{SA} = 6L^2, \qquad \text{V} = L^3, \qquad \frac{\text{SA}}{\text{V}} = \frac{6}{L}$

What the maths tells us

The ratio is $6/L$ — as the cell grows ($L$ increases), the ratio shrinks. A large cell has too little surface to supply its large interior, so the centre starves. Watch it fall as the cell gets bigger: - side $L = 1$ → ratio $6:1$ - side $L = 2$ → ratio $3:1$ - side $L = 4$ → ratio $1.5:1$

Consequences

- Cells stay small so exchange keeps up with demand. - When a cell grows too big, it divides to restore a healthy ratio. - Structures that need lots of exchange (e.g. the small intestine, lungs) evolve folds and villi to increase surface area.

The cell must maintain its intracellular environment within a narrow range of conditions in order to function normally. Concentrations inside the cell are therefore kept different from concentrations outside, and the difference is maintained by the selectively permeable cell membrane. Cells constantly exchange gases, nutrients, ions and wastes across it — and what must cross depends on how the organism feeds.

CELL INPUTS AND OUTPUTS

Autotrophs build their own large, energy-rich organic compounds from small inorganic molecules: carbon dioxide and water for photosynthesis, plus nitrate and nitrite ions (nitrogen), phosphate ions (phosphorus) and sulfate ions (sulfur) absorbed from the soil, which combine with glucose to form amino acids, nucleotides, bases and lipids. Heterotrophs cannot do this, so they must ingest organic compounds ready-made.

FACTORS DETERMINING TRANSPORT

Four main factors determine how a molecule crosses the cell membrane:

1. Concentration gradient - when the concentration of a substance is higher on one side of the membrane, there is a driving force for it to move to the other side until the concentrations are equal (equilibrium).
2. Lipid solubility and charge - the membrane core is an uncharged lipid bilayer, so uncharged, lipid-soluble substances (such as gases) cross readily, while charged substances (such as ions) cross far less readily and may need transporters.
3. Size - the membrane is a dense structure; large molecules cannot slip through and may require endocytosis or exocytosis.
4. Transporters and carriers - proteins embedded in the membrane carry substances that could not otherwise cross; movement through them may or may not require energy (usually ATP).

Passive processes run "downhill" along a concentration gradient at no energy cost. The rate also depends on temperature, the steepness of the gradient, the size and charge of the molecules, and the distance to travel (set by the surface-area-to-volume ratio).

PASSIVE TRANSPORT

• Simple diffusion - small, generally uncharged molecules pass directly between the phospholipids, from high to low concentration, with no protein required. Examples: oxygen, carbon dioxide, ethanol, small uncharged lipids, steroid hormones.
• Facilitated diffusion - movement still runs down the gradient, but through a protein, for substances that are too large, charged or lipid-insoluble: carrier proteins transport glucose and amino acids; channel proteins pass ions such as Na⁺, K⁺ and Cl⁻. Channels may be gated, opening or closing depending on conditions.

Three facts about diffusion:

1. The greater the concentration difference, the faster the rate.
2. Smaller molecules diffuse faster than larger ones.
3. Gradients are maintained by blood flow or movement constantly carrying the arriving substance away.

MOLECULAR TRANSPORT (passive and active) — diffusion and facilitated diffusion run down the concentration gradient; active transport pumps against it, requiring a carrier and ATP.

OSMOSIS

Osmosis is the diffusion of water across a semi-permeable membrane. Water is freely permeable, and its movement is directly related to the solute concentration (ions, proteins) on either side: water moves from low solute concentration (much free water) towards high solute concentration. Osmosis is passive and requires no energy. The environment of a cell is described by three terms:

• Hypertonic - extracellular solute concentration is higher than intracellular; water is drawn out of the cell (too little water causes dehydration).
• Hypotonic - extracellular solute concentration is lower; water is drawn into the cell (too much water can cause it to burst).
• Isotonic - solute concentrations are equal; there is no net movement of water.

Water can slip between the phospholipids only very slowly, so cells that move large volumes use aquaporins — specialised water channels. In humans they are concentrated in the nephron of the kidney, where they respond to the hormone ADH to control how much water is excreted into urine.

ACTIVE TRANSPORT

Some substances cannot move passively: they are too large or charged, or the gradient points the wrong way. Active transport uses specific transport proteins (pumps), powered by ATP, to move substances (glucose, amino acids, ions) against the gradient, from low to high concentration. Active transport mechanisms such as the sodium-potassium counter-transporter (Na⁺/K⁺ ATPase) are especially important in maintaining concentration differences across the membrane. Cells use active transport when the amount of a substance must be regulated, or when a substance is needed where diffusion will not deliver it.

A worked example is glucose absorption in the intestine. Glucose first moves from the gut lumen into the villi cells and on into the blood by facilitated diffusion. Once blood glucose exceeds the concentration in the villi, the gradient reverses — so active transport takes over. Without it, glucose would simply be excreted as waste.

ENDOCYTOSIS AND EXOCYTOSIS

Vesicle-mediated transport is a separate category from protein-pump active transport. Large molecules with complex three-dimensional structures — enzymes, antibodies and others — cannot fit through any membrane protein, let alone between the phospholipids. The only way in is endocytosis; the only way out is exocytosis. Both enclose the cargo in a membrane vesicle, and both require ATP.

In endocytosis, the membrane invaginates (folds inward) around the substance and pinches off a vesicle inside the cell:

1. The particle approaches the membrane and binds to specific receptors — it must be recognised before it is allowed in.
2. The membrane engulfs the particle, forming a sac.
3. The sac pinches off, forming an intracellular vesicle that is then processed.

There are two types: phagocytosis ("eating" — large, solid material) and pinocytosis ("drinking" — small, dissolved material). Examples: iron, cholesterol — and bacteria, engulfed by white blood cells.

ENDOCYTOSIS — the particle approaches, the membrane engulfs it to form a sac, and the sac pinches off as an intracellular vesicle to be processed.

The reverse of endocytosis is exocytosis, used to expel wastes and to transport products such as hormones out of the cell. The vesicle is usually generated by the Golgi body once a molecule has been modified and packaged, travels to the membrane along the cytoskeleton, then fuses with the membrane, releasing its contents into the extracellular environment. Cargo includes integral proteins, enzymes, antibodies and hormones.

In summary:

Overall, the rate at which a cell exchanges materials depends on its surface-area-to-volume ratio, the concentration gradients it maintains, and the physical and chemical nature — polarity, lipid solubility, size and charge — of the substances being moved.