What is growth?
Growth is a lasting (irreversible) increase in size, mass or cell number. A dry seed that swells with water has not yet grown; a root that gets longer by new cells has. Growth uses energy, so it depends on respiration.
Plants grow all their life at special regions called meristems: at root and shoot tips (apical, for length) and at the sides (lateral cambium, for thickness). This is open growth.
Seed germination
Germination is when the embryo in a seed wakes up and grows into a seedling.
- Water is soaked up (imbibition). The seed swells and the coat softens.
- Enzymes wake up and break stored starch, fat and protein into food the embryo can use. Gibberellin helps in cereals.
- Respiration rises and uses O₂ to release energy.
- The radicle (baby root) comes out first, anchoring the seedling and taking in water. Then the plumule (baby shoot) grows up.
Needs: water, oxygen, a suitable temperature; some seeds also need light. Seeds that do not germinate even with all these are dormant, often because of ABA or a hard coat.
Phases of growth
Watch a root tip from bottom to top:
- Meristematic phase: at the very tip (behind the root cap). Cells are small, with thin walls, a big nucleus and dense cytoplasm. They keep dividing.
- Elongation phase: just above. Cells take in water, form a big vacuole and become long. Most of the length increase happens here.
- Maturation phase: further up. Cells reach final size, walls thicken and they become special cells. Root hairs are here.
Growth rate: arithmetic and geometric
Growth rate is the increase in growth per unit time.
Arithmetic growth
After each division only one daughter cell keeps dividing; the other matures. Length grows by the same amount each time: Lt = L₀ + rt. Graph: a straight line. Example: a root growing steadily.
Geometric growth
Both daughter cells keep dividing, so the number doubles. Growth is slow at first (lag phase), then very fast (log or exponential phase), then slows when food and space run short (stationary phase). The graph is an S-shaped (sigmoid) curve. In the fast phase: W₁ = W₀ e^(rt), where r is the relative growth rate (efficiency index) and e ≈ 2.718.
Absolute and relative growth rate
Absolute growth rate = total growth per unit time. Relative growth rate = growth per unit time ÷ starting size. Two leaves may both grow 5 cm² in a day, but a small leaf that started at 5 cm² has a much higher relative rate than one that started at 50 cm².
Conditions for growth
- Water: cells enlarge by taking in water (turgor), and enzymes work in water.
- Oxygen: for respiration, which gives energy to build cells.
- Nutrients: N, P, K and others are building blocks.
- Temperature: each plant has a best range; too cold or too hot slows enzymes.
- Light and gravity: affect some stages, such as germination of some seeds, flowering and the direction of growth.
Differentiation, dedifferentiation and redifferentiation
- Differentiation: cells from meristems become special in structure and job. Example: a cell that becomes a xylem vessel loses its protoplasm and forms a thick, strong wall to carry water.
- Dedifferentiation: a living mature cell gets back the power to divide. Example: parenchyma cells form interfascicular cambium and cork cambium; cells in tissue culture form a callus.
- Redifferentiation: cells made by these new meristems again lose the power to divide and become special. Example: cork cambium makes cork cells; cambium makes secondary xylem and phloem.
Development and plasticity
Development is the whole sequence from germination to death, including growth and differentiation. Plants can take different forms in different conditions: this is plasticity. In cotton, coriander and larkspur, young and old leaves have different shapes; in buttercup, leaves in water and in air differ. This is heterophylly.
Plant growth regulators (hormones)
Plant growth regulators (PGRs) are small chemicals that control growth in tiny amounts. Promoters: auxin, gibberellin, cytokinin. Inhibitors: ABA, and ethylene mostly (it also promotes some things).
Auxin (IAA, IBA; synthetic NAA, 2,4-D)
Made at stem tips. Starts roots on stem cuttings; causes apical dominance (the top bud stops side buds); prevents early fruit and leaf drop; makes seedless fruits (parthenocarpy) in tomato; 2,4-D kills broad-leaved weeds in cereal fields. First found from bending oat tips toward light (Darwins, Went).
Gibberellins (GA₁ … GA₁₀₀+; GA₃ is common)
Make stems long (bolting in cabbage), increase grape stalk length and apple size, increase sugarcane yield, speed up malting and break seed dormancy. Found from the "foolish seedling" disease of rice caused by a fungus, Gibberella.
Cytokinins (kinetin, zeatin)
Help cell division, make side buds grow (overcome apical dominance), form new leaves and shoots, and delay leaf ageing (senescence). Found in coconut milk and from DNA of herring sperm (kinetin).
Ethylene (a gas)
Ripens fruits (increases respiration: the climacteric), causes leaf and flower fall, breaks dormancy, makes rice stems grow fast in deep water, and promotes root hairs and female flowers in cucumber. Ethephon releases ethylene and is widely used.
Abscisic acid (ABA)
The stress hormone. Closes stomata in drought, keeps seeds and buds dormant, stops growth, and helps seeds mature and survive drying. It usually works against gibberellin.
Try it: see hormones and growth at home
- Growth diary: soak 6 moong seeds overnight, keep them on wet cotton. Measure the root length every day for 7 days. Plot length vs day. Is it a straight line or an S-curve?
- Dry vs wet: keep 3 seeds on dry cotton. Predict: will they germinate? Check after 2 days.
- Ethylene test: put a raw banana in a closed paper bag with a ripe apple, and another raw banana alone. Which ripens first?
- In the 3D free play, set water to 0 and guess the growth rate before looking.
Key formulas and definitions
- Arithmetic growth: Lt = L₀ + rt
- Geometric growth: W₁ = W₀ e^(rt)
- Absolute growth rate = increase in size ÷ time
- Relative growth rate = (increase ÷ time) ÷ starting size
- Sigmoid curve: lag → log (exponential) → stationary
- Promoters: auxin, gibberellin, cytokinin · Inhibitors: ABA, ethylene (mostly)
Worked examples
1. A root is 2 cm long and grows arithmetically at 0.5 cm per day. How long after 6 days?
Lt = L₀ + rt = 2 + 0.5 × 6 = 2 + 3 = 5 cm.
2. A stem grows from 10 cm to 34 cm in 8 days arithmetically. Find r.
r = (Lt − L₀) ÷ t = (34 − 10) ÷ 8 = 24 ÷ 8 = 3 cm per day.
3. A culture starts with 1 cell and each cell divides once a day, both daughters dividing. How many cells after 5 days?
Number doubles daily: 1 × 2⁵ = 32 cells. This is geometric growth.
4. Leaf A grows from 5 to 10 cm² and leaf B from 50 to 55 cm² in one day. Compare absolute and relative growth rates.
Absolute: both 5 cm² per day. Relative: A = 5 ÷ 5 = 1 (100%); B = 5 ÷ 50 = 0.1 (10%). A has 10 times the relative rate.
5. Using W₁ = W₀ e^(rt), a plant of 2 g has r = 0.1 per day. Find its mass after 10 days (e ≈ 2.718).
rt = 0.1 × 10 = 1. W₁ = 2 × e¹ = 2 × 2.718 ≈ 5.44 g.
6. For the same plant, how long until the mass doubles? (ln 2 ≈ 0.693)
W₁ = 2W₀ → e^(rt) = 2 → rt = 0.693 → t = 0.693 ÷ 0.1 ≈ 6.9 days.
7. A farmer removes the top bud of a tea bush. What happens, and which hormone explains it?
Side buds grow and the bush becomes dense. Auxin from the top bud had held them back (apical dominance); removing the tip removes that auxin.
Common mistakes
- Calling the swelling of a dry seed in water "growth". Growth must be irreversible; the first swelling is just water uptake.
- Mixing up arithmetic and geometric growth. Arithmetic = same amount each time (straight line); geometric = doubling, gives an S-curve.
- Saying ethylene is a liquid or only an inhibitor. It is a gas and also promotes ripening, root hairs and some growth.
- Thinking dedifferentiation happens in dead cells. Only living, mature cells like parenchyma can dedifferentiate.