In 1992, Peter Agre's team injected frog eggs with RNA coding for a red blood cell membrane protein. When they moved the eggs into a dilute solution, the eggs carrying the protein swelled quickly, while ordinary eggs barely changed. They had found a water channel, later named an aquaporin, and in 2003 Agre shared the Nobel Prize in Chemistry for it. Let's look closer at what pulled the water in, and how you calculate it (unit 2, topics 2.5 to 2.8).
Water potential
Water moves by osmosis from higher water potential to lower water potential. You calculate water potential (Ψ, "psi") with:
Ψ = Ψp + Ψs
- Ψs, solute potential: pure water is 0. Every solute you add lowers it, so it's negative in any solution.
- Ψp, pressure potential: physical pressure. In an open beaker it's 0, so a solution's Ψ is just its Ψs. Inside a plant cell pushing on its wall, Ψp is positive.
Water potential is usually given in bars or megapascals. Less negative means higher.
Solute potential: Ψs = −iCRT
- i is the ionization constant: 1 for sucrose, about 2 for NaCl, because it splits into Na⁺ and Cl⁻.
- C is the molar concentration.
- R is the pressure constant, 0.0831 L·bar/(mol·K).
- T is temperature in kelvins: °C + 273.
Worked example: 0.2 M sucrose at 25 °C. Ψs = −(1)(0.2)(0.0831)(298) ≈ −4.95 bars. The same molarity of NaCl would be about twice as negative.
Tonicity, plants and protists
Tonicity compares a solution with a cell. Water moves from the hypotonic side to the hypertonic side.
- Plant cells in pure water fill their central vacuole and press on the cell wall. Ψp rises until the cell's Ψ matches the water outside, so the cell becomes turgid rather than bursting. That's why limp celery firms up in a glass of cold water. In a hypertonic solution the membrane pulls away from the wall: plasmolysis.
- Animal cells have no wall, so in a hypotonic solution they can burst, and in a hypertonic one they shrivel.
- Freshwater protists live in a hypotonic world. A contractile vacuole keeps collecting the water and expelling it.
Proteins that move things across
- Facilitated diffusion is passive: channel proteins (such as aquaporins and ion channels for Na⁺ and K⁺) or carrier proteins move substances down their gradient with no energy input.
- Active transport uses energy. The sodium-potassium pump uses ATP to move 3 Na⁺ out and 2 K⁺ in, building the electrochemical gradient behind the membrane potential.
- Cotransport uses that stored gradient: as Na⁺ or H⁺ flows back down it, a carrier drags another molecule against its own gradient.
- Endocytosis and exocytosis move large molecules in vesicles, and both need energy.
Common mistakes students make
- Forgetting Ψp. A plant cell's Ψ is Ψp + Ψs. Using Ψs alone often flips the direction of water movement.
- Reading "more negative" as "higher". −6 bars is lower than −2 bars, so water moves toward −6.
- Using °C in −iCRT. T must be in kelvins.
- Saying aquaporins pump water. They're channels; water still moves passively, down its water potential gradient.
- Using i = 1 for salt. NaCl dissociates, so i is about 2.
Frequently asked questions
What is water potential in AP Biology?
It's a measure of water's tendency to move, Ψ = Ψp + Ψs. Water moves from higher to lower water potential.
Why is solute potential always negative?
Pure water is set at 0, and adding solute lowers the water's tendency to move, so any solution has a negative Ψs.
How do you find the water potential of potato cells?
Put potato cores in a range of sucrose solutions and graph percent change in mass against molarity. Where the line crosses zero, there's no net movement, so that solution's Ψ matches the cells'.
Is facilitated diffusion active or passive?
Passive. Proteins help the molecules cross, but they still move down their gradient with no energy input.
Try it
Say each answer before you flip the card. Then predict: what would you expect to see if you put one slice of fresh potato in pure water and another in a strong salt solution for an hour, then pressed each one?
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