---
title: "Plant Water and Mineral Nutrition"
book: "University Biology — Year 1"
subject: biology
language: en
chapter: 23
exercises: 12
source: https://one-course.com/books/biology/3/en/chapter/23-plant-water-and-mineral-nutrition
---

# Chapter 23 — Plant Water and Mineral Nutrition

A maize plant in July draws a litre of water a day out of soil that feels dry to the hand, and with it the thirty milligrams of nitrogen, as nitrate, that it needs to build a day’s growth. It has no pump. The water enters because the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) is drier than the soil, in the precise sense of [Chapter 7](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#ch-b1-membranes-transport); the nitrate enters because the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) spend [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) to make it; and both must pass a single layer of [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) whose walls are sealed with [wax](https://one-course.com/books/biology/3/en/chapter/9-lipids#def-b1-lipids-wax) before they reach the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues). This chapter describes the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) as an absorbing [organ](https://one-course.com/books/biology/3/en/chapter/2-functional-organization-of-a-mammal#def-b1-mammal-organization-organ), the [water potentials](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) that drive water from soil to [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues), the mineral elements a plant needs and how it takes them up, the special case of nitrogen, and the fungi and bacteria that most [roots](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) employ to do part of the work.

## 23.1 The root as an absorbing organ

**Definition 23.1 (Apoplast, symplast, endodermis).**

Water and solutes cross the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) cortex by two routes: the *apoplast*, the continuous system of [cell walls](https://one-course.com/books/biology/3/en/chapter/10-carbohydrates#prop-b1-carbohydrates-wall) and intercellular spaces, through which they move without crossing any membrane; and the *symplast*, the continuous [cytoplasm](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) of the [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) connected by [plasmodesmata](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) ([Chapter 6](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#ch-b1-eukaryotic-cell)), entered by crossing one plasma membrane. At the inner boundary of the cortex the *[endodermis](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#prop-b1-flowering-plant-organization-stemroot)* ([Chapter 3](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#ch-b1-flowering-plant-organization)) blocks the apoplast: a band of suberin and lignin, the *Casparian strip*, impregnates its radial walls, so that everything entering the vascular cylinder must pass through an endodermal [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell)’s membrane. The membrane’s transporters thus decide what reaches the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues), and prevent what has been loaded into the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) from leaking back.

![The two paths across the root cortex. The apoplastic path runs through the walls until the Casparian strip stops it; the symplastic path crosses one membrane at the epidermis and then runs from cell to cell. Both converge on the membranes of the endodermis.](https://one-course.com/images/onecourse/chapters/biology-3/b1-plant-water-minerals/fig-a8560fe75eb3.svg)

*The two paths across the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) cortex. The apoplastic path runs through the walls until the [Casparian strip](#def-b1-plant-water-minerals-pathways) stops it; the symplastic path crosses one membrane at the epidermis and then runs from [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) to [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell). Both converge on the membranes of the [endodermis](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#prop-b1-flowering-plant-organization-stemroot).*

**Proposition 23.2 (Root pressure).**

The [endodermis](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#prop-b1-flowering-plant-organization-stemroot) and the [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) within it pump ions into the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues), which lowers the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues)’s [water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) and draws water in osmotically from the cortex; when the shoot transpires little (at night, in humid air), the water accumulates and the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) sap is pushed upward under a positive *[root pressure](#prop-b1-plant-water-minerals-rootpressure)* of a few tenths of a megapascal — enough to force droplets out of the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) tips of small plants (*guttation*) and to refill air-blocked vessels, but not enough to lift sap to the top of a tree. By day the pull of transpiration ([Chapter 24](https://one-course.com/books/biology/3/en/chapter/24-plant-gas-exchange-and-sap-transport#ch-b1-plant-transport)) takes over and the [root pressure](#prop-b1-plant-water-minerals-rootpressure) vanishes.

**Evidence.** A stem cut near the ground exudes sap for hours from its stump, and a manometer attached to the stump registers a pressure of $0.1\text{ to }0.3\,\mathrm{MPa}$; the exudate is richer in ions than the soil solution, and its flow stops when the [roots](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) are cooled or poisoned with an [inhibitor](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-inhibitors) of respiration: the flow is driven by active ion loading, not by any pumping of water. ∎

## 23.2 Water: from soil to xylem

**Proposition 23.3 (The water-potential ladder).**

Water moves from soil to [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) because the [water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) ([Chapter 7](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#ch-b1-membranes-transport)) falls at each step:

| compartment | $\Psi$ ($\mathrm{MPa}$) |
| --- | --- |
| moist soil | $-0.03$ to $-0.3$ |
| soil at the wilting point | $-1.5$ |
| [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) cortex [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) | $-0.3$ to $-0.6$ |
| [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) | $-0.5$ to $-0.8$ |
| [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) | $-1.0$ to $-2.0$ |
| air at $50\,\%$ relative humidity | $-95$ |

The soil’s potential is set mostly by the tension with which its pores hold water (capillarity); the [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell)’ by their solutes and their [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell); the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues)’s by the tension of the transpiring column; the air’s by its humidity, $\Psi = (RT/V_w)\ln(\text{RH})$, which is enormous even in humid air. The steepest step by far is the last, from [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) to air: that is where nearly all the driving force is spent, and why plants control it with [stomata](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues).

![Water potential along the path through a transpiring maize plant on a summer day. Each step is lower than the last; the drop to the outside air, a hundred times larger than all the others together, is not drawn.](https://one-course.com/images/onecourse/chapters/biology-3/b1-plant-water-minerals/fig-71b358815860.svg)

*[Water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) along the path through a transpiring maize plant on a summer day. Each step is lower than the last; the drop to the outside air, a hundred times larger than all the others together, is not drawn.*

**Method 23.4 (Reading a water-potential profile).**

1. List the compartments in order and their $\Psi$ ; water flows only from higher to lower, so the sequence must decrease along the path or the flow reverses.
2. Split each [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) ’s $\Psi$ into $\Psi_s$ (solutes, negative) and $\Psi_p$ ( [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) , positive); a [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) at $\Psi = -0.4$ with $\Psi_s = -0.9$ has $\Psi_p = +0.5$ . [Xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) water has $\Psi_s \approx 0$ and negative $\Psi_p$ : it is under tension.
3. The flow across a step is the difference of $\Psi$ times the hydraulic conductance of the barrier; the [endodermis](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#prop-b1-flowering-plant-organization-stemroot) and the [stomata](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) are the two steps of low conductance where the plant regulates.
4. Dry the soil and its $\Psi$ falls; when it reaches the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) ’s, flow stops and the plant wilts; when the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) ’ $\Psi_p$ reaches zero the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) hangs. Recovery needs the soil, not the plant, to change.

**Example 23.5 (A litre a day).**

A maize plant’s fine [roots](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) offer some $0.2\,\mathrm{m}^{2}$ of surface with a hydraulic conductance of about $2 \times 10^{-7}\,\mathrm{m}\,\mathrm{s}^{-1}\,\mathrm{MPa}^{-1}$; between soil at $-0.2\,\mathrm{MPa}$ and [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) at $-0.6\,\mathrm{MPa}$ the flux is $2\times 10^{-7}\times 0.4\times 0.2 = 1.6 \times 10^{-8}\,\mathrm{m}^{3}/\mathrm{s}$ — a litre and a half a day, all of it lost from the [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs). The [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) does no work to move it: the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs)’s transpiration sets the tension, and the soil supplies the water as long as its potential stays above the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs)’s.

## 23.3 Mineral nutrition

**Definition 23.6 (Essential elements).**

An element is *essential* to a plant if the plant cannot complete its life cycle without it and no other element can replace it. Seventeen are: carbon, hydrogen and oxygen from air and water; the *macronutrients* taken from the soil in grams per kilogram of dry mass — nitrogen (as nitrate or ammonium), phosphorus (phosphate), potassium, calcium, magnesium, sulfur (sulfate); and the *micronutrients* needed in milligrams or less — iron, manganese, zinc, copper, boron, molybdenum, chlorine, nickel. Nitrogen builds [proteins](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) and nucleic acids; phosphorus, [nucleotides](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-nucleotide) and membranes; potassium is the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell)’s main cation and the osmotic agent of [stomata](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues); magnesium sits in [chlorophyll](https://one-course.com/books/biology/3/en/chapter/14-photosynthesis-and-autotrophy#def-b1-photosynthesis-pigments); iron in the cytochromes and ferredoxin; molybdenum in [nitrate reductase](#prop-b1-plant-water-minerals-nitrate) and nitrogenase.

**Proposition 23.7 (How the list was made).**

The [essential elements](#def-b1-plant-water-minerals-elements) were identified by growing plants in water containing known salts only.

**Evidence.** Sachs and Knop (1860s) grew plants to maturity in solutions of a few mineral salts, with no soil at all, proving that soil supplies nothing but minerals and support; leaving out one salt at a time gave a characteristic sickness for each element, and adding it back cured it. The [micronutrients](#def-b1-plant-water-minerals-elements) were found later, as chemists learned to purify the salts: a plant deprived of molybdenum, needed at one part in ten million, fails to reduce nitrate. The technique, hydroponics, now feeds greenhouses. ∎

![Three tomato plants in nutrient solutions: complete (left), without nitrogen (centre: stunted, the older leaves yellow as their nitrogen is moved to the young ones), without phosphorus (right: dark leaves tinged purple). Each missing element has its signature.](https://one-course.com/images/onecourse/chapters/biology-3/b1-plant-water-minerals/img-753188d25885.jpg)

*Three tomato plants in nutrient solutions: complete (left), without nitrogen (centre: stunted, the older [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) yellow as their nitrogen is moved to the young ones), without phosphorus (right: dark [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) tinged purple). Each missing element has its signature.*

**Method 23.8 (Reading a deficiency).**

1. Ask where the symptom appears. Elements the plant can move in the phloem (N, P, K, Mg) are withdrawn from old [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) to feed young ones: the old [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) show the deficiency first. Elements it cannot move (Ca, Fe, B) are stranded where they were laid down: the young [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) and growing tips show it.
2. Ask what the element does: no nitrogen, little [chlorophyll](https://one-course.com/books/biology/3/en/chapter/14-photosynthesis-and-autotrophy#def-b1-photosynthesis-pigments) and [protein](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide) — pale, stunted; no magnesium or iron, [chlorophyll](https://one-course.com/books/biology/3/en/chapter/14-photosynthesis-and-autotrophy#def-b1-photosynthesis-pigments) fails — yellow [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) with green veins; no potassium, the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) margins scorch; no calcium, the growing tips die.
3. Confirm by supplying the suspected element alone and watching the new growth.

**Proposition 23.9 (Active uptake of ions).**

The soil solution holds ions at micromoles to a few millimoles per litre; the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) hold potassium at $100\,\mathrm{mmol}/\mathrm{L}$, phosphate at $10\,$, nitrate at several. Uptake is therefore mostly uphill and paid for with [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp), but indirectly: a *[proton pump](#prop-b1-plant-water-minerals-uptake)* in the plasma membrane ([Chapter 7](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#ch-b1-membranes-transport)) exports $\mathrm{H^+}$, making the outside acid and the inside negative by $-120\text{ to }-200\,\mathrm{mV}$; cations such as $\mathrm{K^+}$ then enter through [channels](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-transporters) down the electrical gradient, and anions ($\mathrm{NO_3^-}$, $\mathrm{H_2PO_4^-}$, $\mathrm{SO_4^{2-}}$) by [symporters](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#prop-b1-membranes-transport-secondary) that ride protons back in. Transporters are selective: potassium is taken up a hundred times more readily than sodium of the same charge and nearly the same size, and the plant holds sodium out even in salty soil. [Roots](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) use a third of the plant’s respiration on this transport.

## 23.4 Nitrogen

**Proposition 23.10 (Nitrate to amino acid).**

Most plants take nitrogen as nitrate. In the [cytosol](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-organelle) *[nitrate reductase](#prop-b1-plant-water-minerals-nitrate)*, a molybdenum [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme), reduces it to nitrite with electrons from NADH; in the [plastid](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plastid) *nitrite reductase* reduces nitrite to ammonium with electrons from ferredoxin; and ammonium is fixed at once into glutamine and [glutamate](https://one-course.com/books/biology/3/en/chapter/16-biosyntheses-and-the-integrated-cell#def-b1-biosyntheses-integration-nitrogen) ([Chapter 16](https://one-course.com/books/biology/3/en/chapter/16-biosyntheses-and-the-integrated-cell#ch-b1-biosyntheses-integration)) — ammonium itself is toxic and never accumulates. The whole reduction costs eight electrons per nitrogen, a tenth of a [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs)’s photosynthetic electron flow on a nitrate-rich soil, and a [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) does much of it in the light, straight from the chloroplast’s ferredoxin. Ammonium, where the soil offers it, is taken up directly and skips the cost.

**Definition 23.11 (Nitrogen fixation and nodules).**

No eukaryote can use the $\mathrm{N_2}$ of the air. Some bacteria can: *nitrogenase* breaks the triple bond of $\mathrm{N_2}$ and reduces it to two ammonia, at a cost of sixteen [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) and eight electrons per molecule, and only where oxygen is excluded. Legumes (peas, beans, clover) house such bacteria (*Rhizobium*) in *[root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) nodules*: the plant builds a chamber, feeds the bacteria sugar, and keeps the oxygen low with a red [protein](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide), leghaemoglobin, that delivers it to the bacteria’s respiration at a concentration too low to harm the [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme); the bacteria give back ammonium, which the plant turns into [amino acids](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-aminoacid). A field of clover fixes a hundred kilograms of nitrogen per hectare a year, for which the plant pays a tenth of its photosynthesis. The nitrogen cycle as a whole belongs to the Year 2 volume.

![Nodules on the roots of a legume: each is a chamber of plant tissue filled with bacteria, pink with leghaemoglobin, where atmospheric nitrogen is fixed.](https://one-course.com/images/onecourse/chapters/biology-3/b1-plant-water-minerals/img-392649e0f5d3.jpg)

*Nodules on the [roots](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) of a legume: each is a chamber of plant [tissue](https://one-course.com/books/biology/3/en/chapter/4-animal-body-plans-and-tissues#def-b1-body-plans-tissues-tissue) filled with bacteria, pink with leghaemoglobin, where atmospheric nitrogen is fixed.*

**Example 23.12 (The price of nitrogen).**

A maize plant needs about $30\,\mathrm{mg}$ of nitrogen a day; from nitrate at $2\,\mathrm{mmol}/\mathrm{L}$ it gets that in the litre of water it transpires, and spends a few hundred millimoles of electrons reducing it. A clover plant fixing the same amount pays $16\,$ [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) per $\mathrm{N_2}$ plus the reductant — roughly $6\,\mathrm{g}$ of sugar per gram of nitrogen, some $0.2\,\mathrm{g}$ a day, a tenth of its production — and can grow on soil with no nitrate at all. Farmers have rotated legumes with cereals for two thousand years to move that nitrogen from one field to the next.

## 23.5 Partners in the soil

**Definition 23.13 (Mycorrhiza).**

A *mycorrhiza* is an association between a [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) and a fungus, found in nine plants out of ten. In the commonest form the fungal hyphae grow into the cortex [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) and branch inside them into *arbuscules*, the [exchange surface](https://one-course.com/books/biology/3/en/chapter/1-the-organism-a-system-in-interaction-with-its-environment#prop-b1-organism-environment-surfaces), while outside the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) a network of hyphae a few micrometres across explores the soil for metres. The fungus delivers phosphate and other poorly mobile ions, and water, that the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs)’s own hairs could not reach; the plant delivers sugar, a tenth or more of its photosynthesis. Trees of temperate forests carry a second form, in which the fungus sheathes the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) tips and threads between the [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell); its fruiting bodies are the mushrooms of the forest floor.

**Evidence.** Seedlings grown in sterilised soil grow poorly and take up little phosphate; inoculated with spores of the fungus, they grow several times larger. Radioactive phosphate placed in soil beyond the reach of the [roots](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) appears in the plant only if hyphae connect the two, and labelled carbon fed to the [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) appears in the hyphae within a day. Cutting the hyphae with a fine mesh that lets solutes but not fungi pass abolishes the gain. ∎

![A root stained to show its mycorrhizal fungus: hyphae running between the cells and branching into arbuscules inside them — a second absorbing surface, supplied by the plant with sugar.](https://one-course.com/images/onecourse/chapters/biology-3/b1-plant-water-minerals/img-ed3ca5dba0df.jpg)

*A [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) stained to show its mycorrhizal fungus: hyphae running between the [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) and branching into arbuscules inside them — a second absorbing surface, supplied by the plant with sugar.*

**Example 23.14 (Why phosphate needs a fungus).**

Phosphate binds to soil particles and diffuses a millimetre in a day; a [root hair](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) takes up all the phosphate within reach in hours and then waits. Hyphae a tenth as thick as a [root hair](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) reach ten times farther per gram of [tissue](https://one-course.com/books/biology/3/en/chapter/4-animal-body-plans-and-tissues#def-b1-body-plans-tissues-tissue), and a metre of hypha costs the plant a thousandth of what a metre of [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) does. For nitrate, which moves freely with the soil water, the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs)’s own hairs suffice, and plants on nitrate-rich soils reduce their fungus; for phosphate, the fungus is the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs)’s extension.

## 23.6 Exercises

**Exercise 23.1 ★.**

Define [apoplast](#def-b1-plant-water-minerals-pathways) and [symplast](#def-b1-plant-water-minerals-pathways), and say what the [Casparian strip](#def-b1-plant-water-minerals-pathways) does.

**Solution of Exercise 23.1.**

[Apoplast](#def-b1-plant-water-minerals-pathways): the continuous walls and spaces, crossed without passing a membrane. [Symplast](#def-b1-plant-water-minerals-pathways): the connected [cytoplasm](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) of the [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell), entered through one membrane and continued through [plasmodesmata](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell). The [Casparian strip](#def-b1-plant-water-minerals-pathways) blocks the [apoplast](#def-b1-plant-water-minerals-pathways) at the [endodermis](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#prop-b1-flowering-plant-organization-stemroot), forcing everything through a membrane and preventing back-leakage from the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues).

**Exercise 23.2 ★.**

List the six [macronutrients](#def-b1-plant-water-minerals-elements) a plant takes from the soil and one role of each.

**Solution of Exercise 23.2.**

N ([proteins](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide), nucleic acids), P ([nucleotides](https://one-course.com/books/biology/3/en/chapter/11-nucleotides-and-nucleic-acids#def-b1-nucleic-acids-nucleotide), membranes), K (osmotic agent, [stomata](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues)), Ca (walls, signalling), Mg ([chlorophyll](https://one-course.com/books/biology/3/en/chapter/14-photosynthesis-and-autotrophy#def-b1-photosynthesis-pigments)), S ([amino acids](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-aminoacid) cysteine and methionine).

**Exercise 23.3 ★.**

From the water-potential figure, read $\Psi$ in the soil, the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) and the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell), and state the direction of flow at each step.

**Solution of Exercise 23.3.**

Soil $-0.2\,$, [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) $-0.6\,$, [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) $-1.3\,\mathrm{MPa}$: from soil into the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs), from [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) up to the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) — always toward the more negative value.

**Exercise 23.4 ★.**

Why do nitrogen deficiency and iron deficiency show on different [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs)?

**Solution of Exercise 23.4.**

Nitrogen is mobile in the phloem: the plant withdraws it from old [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) to feed the young, so old [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) yellow first. Iron is not remobilised: the young [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs), built without it, are the ones that yellow.

**Exercise 23.5 ★★.**

A [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) cortex [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) has $\Psi_s = -0.9\,\mathrm{MPa}$ and $\Psi_p =
0.5\,\mathrm{MPa}$; the soil is at $-0.2\,\mathrm{MPa}$, the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) at $-0.6\,\mathrm{MPa}$. Show that water flows from soil to [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) to [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues), and compute the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell)’s $\Psi_p$ at which it would stop taking up water from this soil.

**Solution of Exercise 23.5.**

[Cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) $\Psi = -0.9 + 0.5 = -0.4\,\mathrm{MPa}$: soil ($-0.2$) $>$ [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) ($-0.4$) $>$ [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) ($-0.6$), so water flows soil $\to$ [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) $\to$ [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues). Uptake stops when the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) reaches $-0.2\,\mathrm{MPa}$, i.e. $\Psi_p = -0.2 + 0.9 = 0.7\,\mathrm{MPa}$.

**Exercise 23.6 ★★.**

Compute the [water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) of air at $90\,\%$, $50\,\%$ and $10\,\%$ relative humidity at $25\,{}^{\circ}\mathrm{C}$ ($RT/V_w =
137\,\mathrm{MPa}$). Compare with the soil at the wilting point and comment.

**Solution of Exercise 23.6.**

$\Psi = 137\ln(\text{RH})$: $-14\,\mathrm{MPa}$, $-95\,\mathrm{MPa}$, $-315\,\mathrm{MPa}$. Even humid air is ten times drier, in this sense, than soil at the wilting point: a [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) always loses water to air; the only question is how fast.

**Exercise 23.7 ★★.**

A [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) at $-150\,\mathrm{mV}$ takes up $\mathrm{K^+}$ from $0.1\,\mathrm{mmol}/\mathrm{L}$ to $100\,\mathrm{mmol}/\mathrm{L}$. Compute the Nernst potential for this ratio at $25\,{}^{\circ}\mathrm{C}$ and say whether [channels](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-transporters) alone can do it. Repeat for nitrate at $0.5\,$ outside and $5\,\mathrm{mmol}/\mathrm{L}$ inside.

**Solution of Exercise 23.7.**

$E_K = 25.7\ln(0.1/100) = -178\,\mathrm{mV}$: at $-150\,\mathrm{mV}$ the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) is slightly less negative than needed, so a thousandfold accumulation needs a little more than [channels](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-transporters) — but a ratio of 100 would be at equilibrium: [channels](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-transporters) do nearly all of it. Nitrate: $E = -25.7\ln(0.5/5)
= +59\,\mathrm{mV}$; the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) is at $-150\,$, $209\,\mathrm{mV}$ away and in the wrong direction: an anion must be pumped in, by proton symport.

**Exercise 23.8 ★★.**

Explain why guttation is seen at dawn on grass but never on a tall tree, and what happens to [root pressure](#prop-b1-plant-water-minerals-rootpressure) when transpiration begins.

**Solution of Exercise 23.8.**

At night, with no transpiration, ion loading into the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) draws water in and a [root pressure](#prop-b1-plant-water-minerals-rootpressure) of a few tenths of a megapascal pushes sap up a few metres at most — enough to reach the tips of grass blades and force droplets out, not to reach the top of a tree. When the [stomata](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) open, transpiration puts the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) under tension and [root pressure](#prop-b1-plant-water-minerals-rootpressure) disappears.

**Exercise 23.9 ★★.**

A plant is transferred to a solution lacking molybdenum. Predict its growth on nitrate and on ammonium, and explain the difference.

**Solution of Exercise 23.9.**

Without molybdenum [nitrate reductase](#prop-b1-plant-water-minerals-nitrate) does not work: on nitrate the plant cannot make [amino acids](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-aminoacid) and shows nitrogen deficiency though nitrate is abundant. On ammonium it grows normally, since ammonium enters the [amino acids](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-aminoacid) without reduction. The difference locates the element in one [enzyme](https://one-course.com/books/biology/3/en/chapter/13-enzymes-and-biochemical-catalysis#def-b1-enzymes-enzyme).

**Exercise 23.10 ★★★.**

Compute the electrons needed to reduce $30\,\mathrm{mg}$ of nitrate nitrogen to ammonium per day, and the NADPH-equivalents; compare with the electrons a maize [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) of $500\,\mathrm{cm}^{2}$ moves through its [photosystems](https://one-course.com/books/biology/3/en/chapter/14-photosynthesis-and-autotrophy#def-b1-photosynthesis-zscheme) in a day at $4\,\text{µ}\mathrm{mol}$ $\mathrm{CO_2}$ per square metre per second (4 electrons per $\mathrm{CO_2}$, $12\,\mathrm{h}$).

**Solution of Exercise 23.10.**

$30\,\mathrm{mg}$ of N $= 2.14\,\mathrm{mmol}$; $\times 8 = 17\,\mathrm{mmol}$ of electrons, $8.6\,\mathrm{mmol}$ of NADPH-equivalents. [Leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs): $0.05\times
4\times 10^{-6}\times 43\,200 = 8.6\,\mathrm{mmol}$ of $\mathrm{CO_2}$, $35\,\mathrm{mmol}$ of electrons: nitrate reduction takes half as many electrons as carbon fixation on this reckoning — a large fraction, which is why plants do it in the light and why fast-growing [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) are heavy consumers of reductant.

**Exercise 23.11 ★★★.**

A clover fixes $30\,\mathrm{mg}$ of nitrogen a day at $16\,$ [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) and $8\,$ electrons per $\mathrm{N_2}$, and $6\,\mathrm{g}$ of sugar per gram of nitrogen overall. Compute the [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) spent by nitrogenase alone, the sugar it would cost (30 [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) per glucose), and the fraction of the $6\,\mathrm{g}$ that this represents. Where does the rest go?

**Solution of Exercise 23.11.**

$2.14\,\mathrm{mmol}$ of N $= 1.07\,\mathrm{mmol}$ of $\mathrm{N_2}$: [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) $16\times 1.07 = 17\,\mathrm{mmol}$, i.e. $0.57\,\mathrm{mmol}$ of glucose, $0.10\,\mathrm{g}$; plus 8 electrons per $\mathrm{N_2}$ (another $0.05\,\mathrm{g}$ of glucose). The $6\,\mathrm{g}/\mathrm{g}$ rule gives $0.18\,\mathrm{g}$ a day: nitrogenase itself is most of it, and the rest is building and maintaining the nodules, their leghaemoglobin, and the bacteria’s own respiration to keep oxygen low.

**Exercise 23.12 ★★★.**

“A [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) is a mining operation that hires contractors.” Discuss in a paragraph: what the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) does itself (water, mobile ions), what it contracts out (phosphate, fixed nitrogen), what it pays, and when it stops paying.

**Solution of Exercise 23.12.**

The [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) itself takes water and the mobile ions (nitrate, potassium) that the soil water brings to its hairs, spending [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) only on the [proton pump](#prop-b1-plant-water-minerals-uptake). For phosphate, which will not come to it, it pays a fungus in sugar to extend its reach; for nitrogen in a soil without nitrate it pays bacteria in sugar to fix it. The fee is a tenth or more of its photosynthesis, and the plant stops paying when the service is not needed: on phosphate-rich soil mycorrhizae are reduced, on nitrate-rich soil legumes make fewer nodules — contractors are kept only while they are cheaper than doing the job alone.

## 23.7 Problem: The Water-Potential Ladder of a Maize Root

**Problem 23.1.**

Weekend problem — water and nitrate from a July soil into a maize plant: potentials at each step, the flux through the roots, the nitrogen it carries and the cost of reducing it, ending on the daily water flux into the root

A maize plant in July: [fine-root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) surface $0.2\,\mathrm{m}^{2}$, hydraulic conductance of the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) $2 \times 10^{-7}\,\mathrm{m}\,\mathrm{s}^{-1}\,\mathrm{MPa}^{-1}$; [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) area $0.5\,\mathrm{m}^{2}$. Soil [water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) $-0.2\,\mathrm{MPa}$; [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) cortex [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) with $\Psi_s = -0.9\,\mathrm{MPa}$ and $\Psi_p = 0.5\,\mathrm{MPa}$; [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) $-0.6\,\mathrm{MPa}$; [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) $-1.3\,\mathrm{MPa}$; air at $50\,\%$ relative humidity ($RT/V_w = 137\,\mathrm{MPa}$). Soil nitrate $2\,\mathrm{mmol}/\mathrm{L}$; the plant needs $30\,\mathrm{mg}$ of nitrogen a day. Nitrate reduction to ammonium uses 8 electrons per nitrogen; photosynthesis moves 4 electrons per $\mathrm{CO_2}$ and the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) fixes $4\,\text{µ}\mathrm{mol}$ of $\mathrm{CO_2}$ per square metre per second for $12\,\mathrm{h}$.

**Part I — The ladder.**

1. Compute the [water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) of the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) cortex [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) .
2. Write the sequence soil, cortex, [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) , [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) , and verify that water flows inward and upward at each step.
3. Compute the [water potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-osmosis) of the air.
4. Compute the drop from soil to [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) and the drop from [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) to air; what fraction of the total is the last step?
5. The soil dries to $-0.9\,\mathrm{MPa}$ . What happens to the flow into the cortex [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) , and to their [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) ?
6. The soil dries to $-1.5\,\mathrm{MPa}$ . What happens to the [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) , and why does watering restore them?

**Part II — The flux.**

7. Compute the water flux into the [roots](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) (conductance $\times$ surface $\times$ the difference between soil and [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) ).
8. Convert it to litres per day.
9. All of it is lost by transpiration. Compute the transpiration per square metre of [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) per hour, in grams.
10. Express the transpiration per square metre of [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) per second in millimoles of water ( $18\,\mathrm{g}/\mathrm{mol}$ ).
11. The [stomata](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) close at midday and the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) ’s $\Psi$ rises to $-0.9\,\mathrm{MPa}$ while the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) ’s rises to $-0.4\,\mathrm{MPa}$ . Recompute the flux. What has the plant done, and why?
12. Why does the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) take up water without spending energy, while it must spend energy to take up nitrate?

**Part III — Nitrogen.**

13. Compute the nitrate carried into the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) by the water flux of question 8, in millimoles and in milligrams of nitrogen.
14. Does it cover the plant’s need? What happens to the balance?
15. The [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) accumulates nitrate to $5\,\mathrm{mmol}/\mathrm{L}$ in its [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) . Compute the [free energy](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#prop-b1-water-small-molecules-gibbs) of moving one mole from $2\,\mathrm{mmol}/\mathrm{L}$ outside to $5\,\mathrm{mmol}/\mathrm{L}$ inside against a [membrane potential](https://one-course.com/books/biology/3/en/chapter/7-membranes-and-membrane-transport#def-b1-membranes-transport-potential) of $-150\,\mathrm{mV}$ ( $RT = 2.48\,\mathrm{kJ}/\mathrm{mol}$ ; an anion entering a negative [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) ).
16. The uptake is a symport with two protons. Compute the [free energy](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#prop-b1-water-small-molecules-gibbs) two protons release entering a [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) at $-150\,\mathrm{mV}$ from pH 5.5 to pH 7.5, and check it suffices.
17. Compute the electrons needed per day to reduce the $30\,\mathrm{mg}$ of nitrogen to ammonium.
18. Compute the electrons the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) moves through its [photosystems](https://one-course.com/books/biology/3/en/chapter/14-photosynthesis-and-autotrophy#def-b1-photosynthesis-zscheme) per day, and the fraction diverted to nitrate.

**Part IV — Alternatives.**

19. If the soil offered ammonium instead of nitrate, what would the plant save, and what problem would ammonium uptake create for its pH balance?
20. A clover fixes the same $30\,\mathrm{mg}$ of nitrogen a day. With $16\,$ [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) and $8\,$ electrons per $\mathrm{N_2}$ , compute the [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp) spent by nitrogenase per day.
21. At $6\,\mathrm{g}$ of sugar per gram of nitrogen fixed overall, compute the clover’s daily cost in sugar and compare it with a production of $3\,\mathrm{g}$ of sugar per day. Is the bargain worth it in a soil of $2\,\mathrm{mmol}/\mathrm{L}$ nitrate? In a soil with none?
22. Phosphate is at $2\,\text{µ}\mathrm{mol}/\mathrm{L}$ in the soil solution. Compute the phosphate the water flux of question 8 brings in, and compare with a need of $4\,\mathrm{mg}$ of phosphorus a day ( $31\,\mathrm{g}/\mathrm{mol}$ ). What must the plant rely on?
23. Explain in two sentences how the [Casparian strip](#def-b1-plant-water-minerals-pathways) lets the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) keep nitrate at $5\,\mathrm{mmol}/\mathrm{L}$ in its [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) while the soil is at $2\,$ .
24. A mutant lacks the [Casparian strip](#def-b1-plant-water-minerals-pathways) . Predict the composition of its [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) sap and its behaviour in salty soil.
25. State the result: the water flux into the maize [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) per day, the nitrogen it delivers, and the fraction of the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) ’s electrons spent reducing it.

**Solution of Problem 23.1.**

**1.** $-0.9 + 0.5 = -0.4\,\mathrm{MPa}$. **2.** $-0.2 > -0.4 > -0.6 > -1.3$: each step lower, water moves soil $\to$ cortex $\to$ [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) $\to$ [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs). **3.** $137\ln 0.5 = -95\,\mathrm{MPa}$. **4.** Soil to [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) $1.1\,\mathrm{MPa}$; [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) to air $94\,\mathrm{MPa}$: $99\,\%$ of the total is the last step. **5.** Soil at $-0.9$ is below the cortex [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell)’ $-0.4$: water [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) the [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) until they fall to $-0.9$, i.e. their [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) drops to zero; uptake stops until the [cells](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) lower their $\Psi_s$ by accumulating solutes. **6.** The soil is now below the [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs)’ $-1.3$: water flows out of the plant; the [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) lose [turgor](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) and wilt. Watering raises the soil’s $\Psi$ above the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs)’s and the flow resumes; the [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs), whose walls were intact, refill. **7.** $2\times 10^{-7}\times 0.2\times(-0.2 - (-0.6)) =
1.6 \times 10^{-8}\,\mathrm{m}^{3}/\mathrm{s}$. **8.** $1.6\times 10^{-8}\times 86\,400 = 1.4 \times 10^{-3}\,\mathrm{m}^{3} =
1.4\,\mathrm{L}$ per day. **9.** $1400\,\mathrm{g}$ over $0.5\,\mathrm{m}^{2}$ and $12\,\mathrm{h}$ of daylight (most of it): about $230\,\mathrm{g}$ per square metre per hour. **10.** $230/18 = 12.8\,\mathrm{mol}$ per square metre per hour, $3.5\,\mathrm{mmol}$ per square metre per second — a thousand water molecules for every $\mathrm{CO_2}$ fixed at $4\,\text{µ}\mathrm{mol}$. **11.** Difference $-0.2 - (-0.4) = 0.2$: flux halved, $0.7\,\mathrm{L}$ a day. Closing the [stomata](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) has cut the loss, the tension has relaxed, and the whole ladder has risen: the plant trades carbon gain for water when the air is driest. **12.** Water moves down its own potential gradient, created by the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs)’s evaporation, so the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) is passive; nitrate must be concentrated against both a concentration and an electrical gradient, which only coupling to the [proton pump](#prop-b1-plant-water-minerals-uptake) can pay for. **13.** $1.4\,\mathrm{L}\times2\,\mathrm{mmol}/\mathrm{L} = 2.8\,\mathrm{mmol}$, $39\,\mathrm{mg}$ of nitrogen. **14.** Yes, with a third to spare; the surplus is stored in the [vacuoles](https://one-course.com/books/biology/3/en/chapter/6-functional-organization-of-the-eukaryotic-cell#def-b1-eukaryotic-cell-plantcell) as nitrate or excluded at the [endodermis](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#prop-b1-flowering-plant-organization-stemroot). **15.** $\Delta G = RT\ln(5/2) + zFV = 2.48\times 0.92 + (-1)(96.5)(-0.15)
= 2.3 + 14.5 = 16.8\,\mathrm{kJ}/\mathrm{mol}$. **16.** Per proton: $RT\ln(10^{-7.5}/10^{-5.5}) + F(-0.15) =
-11.4 - 14.5 = -25.9\,\mathrm{kJ}$; two protons: $-52\,\mathrm{kJ}$, three times what is needed. **17.** $2.14\,\mathrm{mmol}\times 8 = 17\,\mathrm{mmol}$ of electrons. **18.** $0.5\times 4\times 10^{-6}\times 43\,200 = 86\,\mathrm{mmol}$ of $\mathrm{CO_2}$, $346\,\mathrm{mmol}$ of electrons: $5\,\%$ to nitrate. **19.** It would save the 8 electrons per nitrogen; but taking up a cation and releasing a proton for each acidifies the soil around the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) and the [cell](https://one-course.com/books/biology/3/en/chapter/5-the-cell-unit-of-life#def-b1-cell-unit-of-life-cell) must export acid, and ammonium is toxic if it accumulates, so it must be assimilated at once in the [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs). **20.** $1.07\,\mathrm{mmol}$ of $\mathrm{N_2}$ $\times 16 =
17\,\mathrm{mmol}$ of [ATP](https://one-course.com/books/biology/3/en/chapter/8-water-and-small-biomolecules#def-b1-water-small-molecules-atp). **21.** $6\times 0.03 = 0.18\,\mathrm{g}$ of sugar, $6\,\%$ of $3\,\mathrm{g}$. With $2\,\mathrm{mmol}/\mathrm{L}$ of nitrate available for the cost of its reduction ($5\,\%$ of the electrons), fixation is a poor bargain and a legume makes few nodules; with no nitrate it is the only way, and $6\,\%$ of production is cheap for the whole of the plant’s [protein](https://one-course.com/books/biology/3/en/chapter/12-amino-acids-and-proteins#def-b1-proteins-peptide). **22.** $1.4\times 2\times 10^{-6} = 2.8\,\text{µ}\mathrm{mol}$, $0.09\,\mathrm{mg}$ of phosphorus — a fortieth of the need; the plant must rely on diffusion to its [root hairs](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs), which soon exhaust their surroundings, and above all on its mycorrhizal fungus. **23.** The strip blocks the [apoplast](#def-b1-plant-water-minerals-pathways), so nitrate can enter the [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) only through endodermal membranes that pump it inward; and it prevents the concentrated [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) sap from leaking back out along the walls, so the gradient is held. **24.** Its [xylem](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-tissues) sap would resemble the soil solution — dilute, unselected, with sodium and other unwanted ions — and could not be kept concentrated; in salty soil sodium would reach the [leaves](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs) freely and the plant would be poisoned, where a normal plant excludes it at the [endodermis](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#prop-b1-flowering-plant-organization-stemroot). **25.** About $1.4\,\mathrm{L}$ of water a day through $0.2\,\mathrm{m}^{2}$ of [root](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs), carrying $39\,\mathrm{mg}$ of nitrogen against a need of $30\,$, whose reduction takes about $5\,\%$ of the [leaf](https://one-course.com/books/biology/3/en/chapter/3-functional-organization-of-a-flowering-plant#def-b1-flowering-plant-organization-organs)’s photosynthetic electrons.