Cells

THE UNIT, TOPIC BY TOPIC — WHERE EACH ONE LIVES IN THIS GUIDE

The exam’s own words for what this unit is for: “explain the relationships between structure and function of organelles and cellular components on the subcellular and cellular levels,” and “select the data necessary to solve a problem and use them to perform the appropriate calculations with correct units.” The cards below are those two sentences with the nouns filled in.

THE PARTS, ONE SCORED SENTENCE EACH: STRUCTURE, THEN THE FUNCTION IT ALLOWS

The right-hand column is the one the exam scores. Read a row aloud as one sentence — “the inner membrane is folded, which multiplies the surface holding the ATP-making machinery, so more ATP is made per organelle” — and you have the shape of every organelle answer in this unit. The next card puts the parts on their route.

ORGANELLES AS A SYSTEM, NOT A LIST

The exam does not ask what an organelle is. It asks what the organelle’s structure lets it do, and it asks the organelles together: a protein made on a ribosome, folded in the ER, modified in the Golgi, and shipped in a vesicle is one story with five characters. The card above is the parts; this is the route.

Two sentences to keep. Compartments let incompatible reactions run in one cell: the lysosome’s enzymes work in an acidic interior the cytosol never sees. Folding multiplies surface without adding volume: cristae, and the ER’s sheets, are the same idea as the small cell in the next card.

SURFACE AREA AND VOLUME: THE CONSTRAINT EVERY CELL LIVES UNDER

The formulas (given on the reference sheet): cube $\mathrm{SA}=6s^2$, $V=s^3$; sphere $\mathrm{SA}=4\pi r^2$, $V=\frac{4}{3}\pi r^3$; rectangular solid $\mathrm{SA}=2\mathrm{lh}+2\mathrm{lw}+2\mathrm{wh}$, $V=\mathrm{lwh}$; cylinder $\mathrm{SA}=2\mathrm{\pi rh}+2\pi r^2$, $V=\pi r^{2}h$. Divide and the variables mostly cancel: a cube gives $\mathrm{SA}:V=6s^2∕s^3=6∕s$ and a sphere gives $4\pi r^2∕\frac{4}{3}\pi r^3=3∕r$. Notice that the units do not fully cancel — $\mu {\mathrm{\text{m}}}^2∕\mu {\mathrm{\text{m}}}^3=\mu {\mathrm{\text{m}}}^{-1}$ — so the ratio carries units of reciprocal length. It is not a pure number, and it is meaningless unless the area and the volume were measured in the same length unit to begin with.

Why it is a constraint. Everything a cell takes in or gives out crosses the membrane, so supply scales with surface area. Everything a cell consumes or produces happens in the interior, so demand scales with volume. Grow a cell by a factor of two in every direction and its surface grows four times, its volume eight: each unit of interior now has half the membrane serving it. That is why cells are small, why a large cell is folded or flattened or long, and why the CED’s illustrative examples — root hairs, gut epithelial cells, cilia, guard cells, stomata — are all surface-area answers to a volume problem.

The same rule, applied to whole organisms. As an organism gets bigger its surface-area-to-volume ratio falls, so it exchanges heat with its surroundings proportionally more slowly: a small mass loses heat fast, a large mass slowly. The CED’s consequence is in its own words: “typically, the smaller the organism, the higher the metabolic rate per unit body mass” — a mouse burns far more per gram than a horse because it is losing heat far faster per gram. Problem 3 puts numbers on it.

THE MEMBRANE, DRAWN HONESTLY

Every drawing of a membrane on the exam is scored on the same handful of facts, and they all follow from Unit 1’s phospholipid: a polar, phosphate-bearing head and two nonpolar tails.

The five facts the drawing carries (2.3.A, 2.3.B):

• Orientation. The polar, hydrophilic phosphate regions face the aqueous exterior and interior; the nonpolar, hydrophobic fatty-acid regions face each other in the membrane’s interior. That is the whole reason it is a bilayer and not a sheet.
• Proteins sit where their chemistry sits. An embedded protein’s hydrophilic regions are either inside the protein or exposed to the cytosol; its hydrophobic regions form the surface that touches the fatty-acid tails. A protein does not float in the membrane by accident — its own polar and nonpolar side chains (Unit 1, Topic 1.7) place it.
• Fluid mosaic. The framework is phospholipid; embedded in it are proteins, steroids (cholesterol, in vertebrate animals), glycoproteins, and glycolipids — and all of them can move around within the membrane. Fluid is the movement; mosaic is the mix.
• Selective permeability is the interior. The hydrophobic core is what stops ions and large polar molecules (2.4.A). The next card is the sorting rule.
• The cell wall is a different structure with a different job (2.4.B): in bacteria, archaea, fungi, and plants it is a boundary outside the membrane that gives structure, is a permeability barrier to some substances, and protects against osmotic lysis — the walled cell in pure water swells and stops; the animal cell bursts.

WHAT CROSSES, AND HOW: THE SORTING RULE FOR EVERY TRANSPORT QUESTION

Two questions sort every molecule: how big is it, and is it polar or charged? Then one more decides the energy: which way is it going relative to its gradient?

The definitions in the CED’s words (2.5.A): passive transport is the net movement of molecules from regions of high concentration to regions of low concentration without the direct input of metabolic energy; active transport requires the direct input of energy, and in some cases moves molecules from low concentration to high. Facilitated diffusion is passive — the protein provides a route, not a push. The selective permeability of the membrane is what allows gradients to exist in the first place (2.5.A.1); transport is what the cell does with them.

Ions carry charge, so their movement makes a voltage (2.6.A.1, 2.8.A.1). Charged ions such as Na${}^{+}$ and K${}^{+}$ need channel proteins to cross, and when they cross, the membrane becomes polarized. The Na${}^{+}$/K${}^{+}$ pump uses ATP to push 3 Na${}^{+}$ out and pull 2 K${}^{+}$ in per cycle — against both gradients — and that unequal exchange, plus the gradients it maintains, is what keeps the membrane potential. Membrane proteins are necessary for every active transport event; there is no pump without a protein.

The one-line test, and the exception that breaks it. For an uncharged solute the test is short: find the concentration gradient, then ask only whether it needs a protein — and answer that from size and polarity. For an ion it is not enough. Concentration is one half of an ion’s driving force; the voltage across the membrane is the other, and the two together are the electrochemical gradient. So an ion can move from low concentration to high without any energy being spent, through a channel, when the electrical pull is the stronger half. “Low to high, therefore a pump” is true of glucose and false of potassium, and the exam knows the difference. Active transport is the case where metabolic energy moves cargo against its relevant gradient — the sodium–potassium pump spends ATP directly.

TONICITY AND WATER POTENTIAL: THE DIRECTION, THEN THE NUMBER

Tonicity is a comparison, not a property. An external solution is hypotonic to a cell if it has fewer dissolved particles than the cell’s interior, hypertonic if more, isotonic if the same. Water moves by osmosis from hypotonic toward hypertonic — from the side with more water per particle to the side with less. In the CED’s other phrasing (2.7.B.2): water moves from regions of low osmolarity or solute concentration to regions of high osmolarity or solute concentration.

Water potential is the same statement with a number on it (given on the reference sheet): $\mathrm{\Psi }={\mathrm{\Psi }}_p+{\mathrm{\Psi }}_s$ and ${\mathrm{\Psi }}_s=-\mathrm{iCRT}$. Water potential compares water’s tendency to move. Water runs downhill in $\mathrm{\Psi }$ the way a ball runs downhill in height, and net movement stops when connected regions reach equal potential. Pure water in an open, unpressurized container is defined as zero. Dissolved solute lowers the solute term below zero, while positive pressure can raise total $\mathrm{\Psi }$ above zero. Negative values are therefore common, not automatic errors.

• $\mathrm{\Psi }$ — water potential, in bars. Pure water in an open, unpressurized container is $\mathrm{\Psi }=0$.
• ${\mathrm{\Psi }}_p$ — pressure potential. Zero in an open container (the sheet says so in print); positive in a turgid walled cell.
• ${\mathrm{\Psi }}_s$ — solute potential. Always $\le 0$: adding solute only ever lowers water potential.
• $i$ — ionization constant: $1$ for sucrose and glucose, $2$ for NaCl, $3$ for $\mathrm{CaC}{l}_2$. Count the ions.
• $C$ — mol/L. $R=0.0831$ L$\cdot$bar/(mol$\cdot$K). $T$ — kelvin ${=}^{\circ }$C $+273$.

Units check: $\left(\mathrm{\text{mol∕L}}\right)\left(L\cdot \mathrm{bar}\cdot \mathrm{mo}{l}^{-1}{K}^{-1}\right)\left(\mathrm{\text{K}}\right)=\mathrm{\text{bar}}$. The direction rule: water moves from higher $\mathrm{\Psi }$ to lower $\mathrm{\Psi }$. Compare signed values, never magnitudes; when pressure potential is positive, the lower value need not be negative.

Molarity and dilution (not on the sheet — memorize):

Osmoregulation is the organism keeping this under control (2.7.B): growth and homeostasis depend on the constant movement of water across membranes, and osmoregulation keeps water balance and internal solute composition where the organism needs them. The CED’s two illustrations are worth having ready: the contractile vacuole of a freshwater protist, pumping out the water that constantly enters a hypotonic pond; and the central vacuole of a plant cell, whose stored water and solutes hold the pressure potential that keeps the plant upright.

COMPARTMENTS, AND WHERE THEY CAME FROM

Why internal membranes (2.9): membranes and membrane-bound organelles compartmentalize the cell’s metabolic processes and specific enzymatic reactions. Two gains, both scored: internal membranes let processes run without competing — an acidic lysosome next to a neutral cytosol, an oxidizing reaction next to a reducing one — and they increase the surface area on which reactions can occur, which is the cristae argument again. A prokaryote typically lacks membrane-bound organelles but is not disorganized: it has internal regions with specialized structures and functions (2.10.A.2). A eukaryote keeps internal membranes that partition the cell into specialized regions (2.10.A.3).

Where two of them came from (2.10.A.1): membrane-bound organelles such as mitochondria and chloroplasts evolved from once free-living prokaryotic cells by endosymbiosis — an ancestral cell engulfed a prokaryote and kept it. When a prompt asks you to support that claim with evidence (skill 6.B), the evidence is structural and it is the same list for both organelles:

• Two membranes — the inner one the prokaryote’s own, the outer one the host’s, from the engulfing.
• Their own DNA, circular, like a bacterial chromosome and unlike the nucleus’s linear chromosomes.
• Their own ribosomes, closer in size and structure to bacterial ribosomes than to the cell’s cytosolic ones.
• They divide by fission, on their own schedule, the way bacteria do — a cell cannot make a new mitochondrion from scratch.

Write the evidence, then the claim it supports; a claim with no evidence attached is a statement, and statements do not score on a 6.B prompt.

THE GRAPHING KIT — SIX CHECKS FOR A CONSTRUCTED GRAPH

The CED lists them (skill 4.A). Check the representation against all six; which of them a particular question pays for is decided by its own rubric:

1.

Type of graph appropriate for the data. Continuous independent variable (concentration, time, mass) $\to$ a line or scatter graph. Categorical independent variable (species, treatment group) $\to$ a bar graph. Data spanning several orders of magnitude $\to$ a log scale on that axis, and say so on the axis.

2.

Axis labels with units, the independent variable on $x$, the dependent on $y$, and a legend if there is more than one series.

3.

Scaling — even intervals that use the space; the origin need not be zero, but the scale must be honest.

4.

Accurately plotted points, each one where the table puts it.

5.

Error bars when the data supply them. The exam’s own complaint: students “draw error bars incorrectly and fail to use them to draw conclusions about the significance of the data.” A bar of $\pm 2$ SEM approximates a 95% confidence interval; when two groups’ bars do not overlap, the difference is likely real; when they overlap substantially, you cannot claim it is.

6.

A trend line only when the data warrant one.

Percent change is not on the reference sheet, and the exam asks for it (skill 5.A): ${\displaystyle \frac{\text{final}-\text{initial}}{\text{initial}}}\times 100$. Keep the sign; it is the direction.