Question 1 of 6: Cell Structure and Function

Question 1: Cell Structure and Function (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

(a) Lipid membranes are the physical boundary that makes a "cell" possible at all: the amphipathic phospholipid bilayer — hydrophilic phosphate head groups facing the aqueous cytosol and extracellular fluid, hydrophobic fatty-acyl tails buried in the interior — spontaneously self-assembles into a continuous, self-sealing sheet that is essentially impermeable to ions and large polar molecules. This lets the cell maintain an internal chemical environment (ion concentrations, pH, metabolite pools, macromolecular machinery) that is completely different from, and independent of, its surroundings, which is the precondition for every regulated biochemical process the cell carries out. The same bilayer chemistry, wrapped around organelles, subdivides the eukaryotic cytoplasm into compartments (nucleus, mitochondria, ER, Golgi, lysosomes) so that incompatible reactions — e.g. the low-pH hydrolytic environment of a lysosome and the neutral-pH cytosol — can run simultaneously a few nanometres apart without destroying each other. Because the bilayer is a two-dimensional fluid rather than a rigid wall, it also hosts and orients the huge population of integral membrane proteins (channels, carriers, pumps, receptors, enzymes) that carry out selective transport, signal transduction and energy transduction (e.g. the proton-motive-force-driven ATP synthase of the inner mitochondrial membrane depends on that membrane being an intact, low-permeability barrier to protons). Finally, membrane budding and fusion — possible only because the bilayer is a fluid, self-sealing sheet — underlie vesicular trafficking, endocytosis, exocytosis and cell division. In short, the lipid membrane is simultaneously the barrier that defines "inside" versus "outside," the scaffold that organizes compartments and proteins, and the dynamic structure that makes membrane traffic possible.

(b) The four most abundant elements in living cells, by mass, are oxygen, carbon, hydrogen and nitrogen (O > C > H > N), together accounting for roughly 96–99% of a typical cell's dry-plus-wet mass. The strongest single piece of evidence is water content: water is 65–70% of a cell's total mass and is built from only oxygen and hydrogen, immediately making O and H dominant by mass even before any organic chemistry is considered. The remaining ~30–35% is dominated by the four major classes of macromolecules — proteins (~15–18% of cell mass), nucleic acids (~5–7%), lipids (~5–7%) and polysaccharides (~2–3%) — and every one of these classes is built primarily from carbon backbones (long chains and rings of C–C and C–H bonds) decorated with oxygen (carbonyl, hydroxyl, carboxyl, phosphate-ester groups) and, for proteins and nucleic acids specifically, nitrogen (amide/peptide bonds and the amine groups of amino-acid side chains; the purine/pyrimidine rings and amino groups of nucleotide bases). Sulfur (cysteine/methionine, a few cofactors) and phosphorus (nucleic-acid backbone, ATP, phospholipids) are present but at far lower molecular abundance than C, H, O and N, which is why they do not make the top-four list even though they are essential. Taken together, the elemental composition of a cell simply reflects the elemental composition of water plus the C/H/O/N backbone chemistry shared by proteins, nucleic acids, lipids and carbohydrates.

(c) The governing relation is $$ \frac{dm}{dt} = -kA(C_i - C_o) $$ where $dm/dt$ (kg/s) is the net rate at which mass of the diffusing solute crosses the membrane; $k$ (m/s) is a permeability coefficient that lumps together the solute's diffusivity within the membrane, the membrane's thickness, and the solute's partition coefficient between the membrane and the surrounding aqueous phases — it is a property of the solute–membrane pair, not of the concentrations; $A$ (m²) is the membrane surface area available for exchange; and $(C_i - C_o)$ (kg/m³) is the concentration difference of the solute between the inside and outside of the membrane, i.e. the concentration gradient driving transport. The negative sign is a bookkeeping convention: it makes $dm/dt$ negative (mass leaving the "inside" compartment) whenever $C_i > C_o$, correctly describing net outward flow down the gradient, and positive (net inward flow) whenever $C_o > C_i$. The driving principle behind passive diffusion is purely thermodynamic and requires no cellular energy input: molecules undergo continuous random (Brownian) thermal motion, and because there are simply more molecules on the high-concentration side, the random motion produces a statistically greater net flux from high to low concentration until the gradient is dissipated and $C_i = C_o$ (dynamic equilibrium, net flux zero). The rate is directly proportional to both the available membrane area $A$ and the size of the gradient $(C_i-C_o)$, and it depends on the specific solute–membrane permeability $k$ — small, uncharged, lipophilic molecules (O₂, CO₂, ethanol) have a high $k$ and diffuse rapidly across the bare bilayer, while ions and large polar solutes have a vanishingly small $k$ through the lipid itself and require a protein-mediated pathway (part d).

(d) Both facilitated diffusion and active transport use an integral membrane protein to move a solute across the bilayer, but they differ in the direction of movement relative to the concentration gradient and in whether metabolic energy is consumed. Facilitated diffusion (panel a below) uses a channel or carrier protein purely as a passive conduit: the solute still moves down its concentration (or electrochemical) gradient, from high to low concentration, exactly as in Fick's-law diffusion above, and no ATP is hydrolyzed — the protein simply provides a faster or more selective pathway than the bare lipid bilayer allows (e.g. GLUT transporters for glucose, or ion channels). Active transport (panel b) moves a solute against its concentration/electrochemical gradient, from low to high concentration, which is thermodynamically unfavourable and therefore requires an external energy source, most commonly ATP hydrolysis (ATP → ADP + P_i) directly coupled to the pump protein (primary active transport, e.g. the Na⁺/K⁺-ATPase), or the energy stored in a previously-established gradient of a second solute (secondary active transport/co-transport).