BIO 332 · Plant Physiology · CSUMB
Three scales of the same problem. One cell losing water. One leaf across one day. One plant across a week without irrigation. Everything here runs on the same four numbers, and every published number has a source, and the model's own constants are listed as illustrative at the end. Syrah and Merlot are cultivars of one species, Vitis vinifera; the herbaceous option is a stand-in, for the reason given at the end.
−1.5 is lower than −0.5. That is the one piece of arithmetic that trips everybody up in this topic. A leaf at −1.5 MPa is holding its water more tightly, and is in more trouble, than a leaf at −0.5.
A cell that has just divided is tiny. It gets big by taking in water, pressing on its wall, and making the wall yield. So turgor is not a side effect of having water, it is the thing that does the growing. This is the Höfler diagram: what happens to Ψs, Ψp and Ψw as you take water back out of that cell.
Both cells get the same solutes. The only difference is the wall. That is the controlled comparison, and it is the only way to see what wall stiffness actually does.
Pressure has no direction of its own. What it produces is a force on every patch of wall, always at right angles to that patch, which is why the arrows point every way at once. The dark stubs outside the wall are the wall pushing back just as hard. Nothing here is moving, and the arrows are not water. Both cells are at the water content you set above, so they are drawn the same size.
At the same water content the stiff-walled cell has already spent most of its turgor while the soft-walled cell is still pushing hard. Both are drawn the same size, because they hold the same water. Keep going and the wall buckles inward along with the protoplast: that is cytorrhysis, and it is what happens to a leaf drying in air. It is not plasmolysis. Plasmolysis is the protoplast peeling off an intact wall, and it needs an outside solution to flow into the gap, which is why you see it on a microscope slide in salt water and never in a field.
Lockhart wrote it in one line in 1965. Growth rate = φ (Ψp − Y). The cell only expands while turgor is above a yield threshold Y, and φ is how readily the wall gives. Take water out, turgor drops, and expansion stops long before anything looks wilted. A lettuce that stopped expanding at two in the afternoon is a smaller head at harvest, and nobody saw it happen.
No reliable value of Y has been published for a leaf, so this page does not put a number on it.
Inside a living cell, Ψp is positive. The protoplast presses out, the wall presses back, and that pressure is turgor.
Outside, in the dead xylem conduit next door, Ψp is negative. The water there is under tension, being pulled from above. Same symbol, same equation, opposite sign, two cell diameters apart. That is why a conduit needs a lignified wall to stop it imploding while its neighbour needs a wall to stop it bursting.
Now connect that cell to the sky. Stomata open for carbon, water evaporates, tension builds, and the leaf's water potential falls. The cell from Part 1 is sitting inside this, losing turgor as the day goes on. Two leaves here, identical except that vine B has adjusted osmotically.
RWCsym is symplastic relative water content, the water inside the living cells. Total leaf RWC is always higher, because the apoplast holds water too, about 21 per cent of it in a crop leaf.
Read each block downward: solutes drag the potential below zero, the wall pushes it back up, and the bottom bar is where it lands. Both land in the same place. Only the green part keeps a leaf open for business.
Stop irrigating and run the same model for a week. The soil dries slowly and smoothly. The leaf does not: it swings every day, recovers every night, and each morning starts from a lower place than the last. Wilting is what happens when the bottom of one of those swings finally crosses the turgor loss point. Change the plant material or the weather above and watch the day it happens move. This figure runs its own drying curve and shows plant A only: the soil slider and the osmotic adjustment slider do not reach it.
Redrawn for BIO 332 from this model, after the classic figure in McElrone, Choat, Gambetta and Brodersen (2013), Nature Education Knowledge 4(5): 6. Soil dries smoothly, root tracks it with a lag, leaf oscillates hardest. Night bands are unshaded in the original; here they are shaded.
The stiff-walled vine cell is at or past turgor loss. The soft-walled crop cell still has most of its turgor. Same solutes, same water lost, completely different state, and the only difference is the wall. This is why a grapevine leaf feels leathery and a lettuce leaf feels crisp, and why the lettuce can lose far more water before it looks wrong.
Both move, together, a long way. That is the point Bartlett makes: solutes set the water potential at which you wilt, and the wall sets how much water you lose getting there. If you want a more drought tolerant variety, you are shopping for πo.
Mid afternoon, around 14:00, when turgor bottoms out. The low is not at solar noon, because air temperature and therefore evaporative demand lag the sun by a couple of hours. Cell expansion needs turgor above a yield threshold, so a shoot does most of its growing at night and at dawn. That is why you measure elongation before breakfast.
Nothing changed in the ground. The soil holds exactly the same water in both cases and the plant goes from coping to losing turgor. Denmead and Shaw showed this in 1962 with corn in containers sunk in an Iowa field: on an overcast humid day their plants held turgor down to about 24 per cent soil water content, and on a clear dry day they lost it at about 35 per cent, with field capacity for that soil at 36. Those three numbers are read off their Figure 2, and their corn was in containers sunk in the field, so rooting depth was restricted, which is the standing critique. Wilting is a race between supply and demand, and the sky sets the demand.
Nothing happens to it. That is the point. The chamber reads the water potential of the xylem sap, and at equilibrium that equals the leaf cells' Ψw. It cannot see Ψs and it cannot see turgor. Two plants at an identical reading can be one wilted and one fine. In a real field the adjusted plant would hold its stomata open longer and run slightly more negative; this model holds them equal to make the point clean.
It moves later, even though the crop herb has less negative solutes, because its soft wall drops the turgor loss point from −1.14 to −1.25 MPa. Be careful about that: this figure compares water potentials, so what you are seeing is a small ε effect, the one Part 1 tells you is minor. Now switch to Merlot and it moves three days, because its solutes are 0.43 MPa more concentrated. Small lever and big lever, side by side. The soft wall's real advantage only shows up in Part 1, where the axis is water content.
The cell follows a linear elastic pressure volume curve: Ψs = πo / R and Ψp = −πo − ε(1 − R) floored at zero, with R the symplastic relative water content. Setting Ψp to zero gives Bartlett's two equations exactly: πtlp = πoε / (πo + ε) and RWCtlp = (πo + ε) / ε. Parts 2 and 3 add the atmosphere: a diurnal VPD curve peaking about two hours after solar noon, transpiration E = gs × VPD / P solved together with hydraulic stomatal closure gs = gmax / (1 + (Ψ/Ψgs50)³), and Ψleaf = Ψsoil − E / K where K is the whole soil to leaf conductance, root and trunk and petiole in series, which falls as the soil dries.
Six honest limitations, and you should be able to name them. (1) ε is treated as a constant. It is not, it stiffens near full turgor, and published ε values are often computed on total rather than symplastic water content, which makes them about a fifth larger than the ones this model wants. (2) There is no capacitance, so the leaf re-equilibrates with the soil perfectly every night. A real leaf lags, and the water it lags with is stored partly in the pith you score in the microCT images. (3) Stomata here respond only to water potential; real stomata also respond directly to VPD. (4) Ψgs50 is one fixed number for every cultivar, so cultivars differ in their walls and solutes and in nothing else. (5) In Part 3 the soil dries on a fixed schedule whatever the plant does, so a plant cannot dry its own soil faster by holding its stomata open. (6) The per cultivar turgor loss points are derived, by combining πo from one study with ε from another. No paper published them. Treat the ranking as illustrative.
The constants, so you can check them. These are chosen to make the model behave realistically and they are not measurements: Kmax 7.4 mmol m⁻² s⁻¹ MPa⁻¹, halving at soil −0.95 MPa; gmax 0.36 and gnight 0.012 mol m⁻² s⁻¹; Ψgs50 −1.15 MPa; sunrise 05:36, sunset 18:42; night VPD 0.18 kPa; 45 per cent of the soil to leaf resistance placed below the petiole; and in Part 3 the soil follows −0.05 − 1.45(day/7)1.45 MPa. The herbaceous πo of −1.00 MPa is read off Bartlett's Figure 3a crop bar, not a table.
Units, because the field does not use these. California irrigation gear and irrigation talk run in bars, and sometimes psi. 1 MPa = 10 bars = 145 psi, so −1.2 MPa is −12 bars. If somebody tells you the block is at "minus fourteen", they mean −1.4 MPa.
Built for BIO 332 by Dr. Caetano Albuquerque, Department of Biology and Chemistry, CSUMB. Companion to the water potential lectures and to Teaching a Computer Leaf Anatomy.