NCERT Grounding
Section 13.1 of NCERT Biology Class XI opens with the declaration that growth is "one of the most fundamental and conspicuous characteristics of a living being." The chapter then defines growth, identifies where it occurs in a plant body, characterises its phases, and quantifies it through two mathematical models. This subtopic covers all of Section 13.1 (13.1.1 through 13.1.5).
"Growth can be defined as an irreversible permanent increase in size of an organ or its parts or even of an individual cell."
NCERT Biology, Class XI — Chapter 13, Section 13.1
Definition of Growth
Growth is defined as an irreversible permanent increase in size of an organ, its parts, or an individual cell. Three qualifiers in this definition are individually NEET-testable:
Irreversible
Once growth occurs, the increase in size cannot be reversed under normal conditions. This distinguishes true growth from temporary swelling — a piece of wood absorbing water swells but that swelling is reversible, so it is not growth.
Permanent
The change in size is sustained — not a transient osmotic response. Growth involves synthesis of new protoplasm, deposition of new cell wall material, and increases in organic dry mass.
Increase in Size
Measurable via multiple parameters: fresh weight, dry weight (most reliable), length, area, volume, or cell number. Dry weight is preferred because fresh weight fluctuates with the plant's hydration status.
Growth is accompanied by metabolic processes — both anabolic (synthesis) and catabolic (breakdown) — at the expense of energy. The example NCERT uses to contrast: expansion of a leaf is growth; swelling of wood in water is not, because the swelling reverses when water is removed.
Indeterminate Growth and Meristems
Plants retain the capacity for unlimited (indeterminate) growth throughout their life — a fundamental distinction from animals, which show determinate growth (reaching a fixed adult size). This capacity exists because plants maintain permanently embryonic zones called meristems.
| Meristem Type | Location | Growth Produced |
|---|---|---|
| Root Apical Meristem (RAM) | Root tip | Primary — elongation of root axis |
| Shoot Apical Meristem (SAM) | Shoot tip | Primary — elongation of shoot axis |
| Intercalary Meristem | Base of internodes (grasses) | Primary — internode elongation |
| Vascular Cambium | Between xylem and phloem (dicots, gymnosperms) | Secondary — increase in girth |
| Cork Cambium (Phellogen) | Cortex region (dicots, gymnosperms) | Secondary — bark formation, girth increase |
Meristematic cells divide and self-perpetuate. Daughter cells produced by the meristem eventually lose the capacity to divide, differentiate, and constitute the permanent plant body. This pattern — meristem producing cells that mature — is the open form of growth.
Three Phases of Growth
Regardless of the organ studied, the period of growth passes through three sequential phases that can be visualised along the length of a root tip from apex to mature zone.
Sequential Phases of Plant Growth (Root Tip Model)
-
Phase 1
Meristematic (Formative)
Cells actively divide by mitosis. Thin primary cellulosic walls. Dense cytoplasm. Large, conspicuous nuclei. Abundant plasmodesmatal connections. Located at root apex and shoot apex.
Dividing zone -
Phase 2
Elongation
Cells enlarge — increased vacuolation (small vacuoles coalesce into a central vacuole). New cell wall material is deposited. Wall loosening allows uptake of water and turgor-driven expansion. Located proximal to meristematic zone.
Expansion zone -
Phase 3
Maturation
Cells attain maximal size. Secondary wall thickening. Protoplasmic modifications (e.g., loss of protoplasm in tracheary elements). Cells differentiate into specialised tissues and cell types. Most permanent plant tissues originate here.
Differentiation zone
Figure 1. Longitudinal organisation of a root tip into three growth zones. The meristematic zone at the apex supplies new cells. The elongation zone immediately behind it accounts for the majority of length increase. The maturation zone furthest from the apex contains differentiated permanent tissues.
Growth Rate Types
The growth rate is the increase in growth per unit time. NCERT distinguishes two patterns — arithmetic and geometric — and two ways of expressing rate — absolute and relative.
Arithmetic Growth
Lt = L₀ + rt
Linear increase over time
- After mitosis, one daughter cell continues dividing; the other differentiates
- Growth increment is constant per unit time
- Plot of length vs. time → straight line
- Example: root elongation after removal of lateral buds; elongation zone of root
- r = growth rate / elongation per unit time
Geometric Growth
W = W₀eʳᵗ
Exponential increase over time
- After mitosis, both daughter cells continue dividing
- Growth accelerates rapidly — doubling with each cycle
- Plot of size vs. time → exponential curve (part of sigmoid)
- Example: early seedling growth; initial embryo development
- r = relative growth rate (efficiency index); reflects ability to produce new plant material
| Term | Symbol / Formula | What it measures |
|---|---|---|
| Absolute Growth Rate | Total growth per unit time | Total size increase in a given period — does not account for initial size |
| Relative Growth Rate | Growth per unit time per unit initial parameter | Growth expressed on a common basis (e.g., per unit initial area); allows comparison between organs of different sizes |
| r (arithmetic) | Lt = L₀ + rt | Constant elongation per unit time |
| r (geometric) | W = W₀eʳᵗ | Relative growth rate; also called efficiency index |
New cells per hour
A single maize root apical meristem can produce more than 17,500 new cells per hour. By contrast, watermelon cells can increase in size by up to 3,50,000 times. These extremes illustrate that growth can manifest as an increase in cell number or cell size.
Sigmoid (S-shaped) Growth Curve
When the parameter of growth is plotted against time for a cell, tissue, organ, or whole organism growing in a natural environment, a characteristic sigmoid (S-shaped) curve is obtained. This curve integrates both arithmetic and geometric phases and is universal across plant systems.
Figure 2. Idealised sigmoid growth curve typical of cells in culture and plant organs. The log phase represents the period of maximum growth rate — directly tested in NEET 2020. The stationary phase results from nutrient limitation or accumulation of inhibitory metabolites.
| Phase | Growth Rate | Cause | NEET relevance |
|---|---|---|---|
| Lag Phase | Very slow | Cells preparing metabolic machinery; initially small population | Trap: confuse with "maximum growth" |
| Log (Exponential) Phase | Maximum / Rapid | Both daughters dividing geometrically; nutrient abundant | Correct answer NEET 2020 Q.19 |
| Stationary Phase | Zero (plateau) | Nutrient depletion; inhibitor accumulation; space limitation | Confused with dormancy — not the same |
Conditions for Growth
All growth requires a baseline set of external conditions. Any deviation from optimal ranges arrests growth even if the plant's internal machinery is functional.
Water
Cell enlargement requires water for turgor-driven expansion. Water also provides the medium for enzymatic activities needed for growth.
Oxygen
Required for aerobic respiration to release metabolic energy essential for all growth activities including cell division and wall synthesis.
Nutrients
Macro and micro essential elements are required for synthesis of protoplasm and serve as energy sources. Deficiency arrests growth at multiple levels.
Temperature
Every plant has an optimum temperature range. Both extremes (too low or too high) are detrimental; temperature modulates enzyme kinetics underlying all growth processes.
Environmental signals — light and gravity — also modulate specific phases and directions of growth, acting via plant growth regulators such as auxins. These are covered in detail under the PGR subtopics.
Worked Examples
A root has a length of 2 cm at time zero. It elongates at a constant rate of 0.5 cm per hour. What is its length after 6 hours? Which type of growth does this represent?
Solution: Using the arithmetic growth formula: L₁ = L₀ + rt = 2 + (0.5 × 6) = 2 + 3 = 5 cm. This is arithmetic growth — the root elongates by a constant amount (0.5 cm) each hour, regardless of its current length. One daughter cell from each division differentiates; only one continues dividing.
A seedling weighs 1 g at the start of the exponential growth phase. Given r = 0.2 per day, what will be its weight after 5 days? What name is given to r in this context?
Solution: Using the geometric (exponential) growth formula: W = W₀eʳᵗ = 1 × e^(0.2 × 5) = e^1 ≈ 2.718 g. In this context, r is called the relative growth rate or efficiency index — it measures the plant's ability to produce new plant material per unit of existing material per unit time.
Two leaves A and B have areas of 10 cm² and 50 cm² respectively. Both increase in area by 5 cm² in the same time interval. Which leaf has a higher relative growth rate? Which has a higher absolute growth rate?
Solution: Both leaves have the same absolute growth rate (5 cm² per time interval). However, leaf A started smaller (10 cm²), so its relative growth rate = 5/10 = 0.5 per unit time. Leaf B's relative growth rate = 5/50 = 0.1 per unit time. Leaf A has a higher relative growth rate. This is the classic NCERT Figure 13.7 comparison — a common exam question.
Common Confusion & NEET Traps
Plants — Indeterminate
Open growth
- Retain meristems throughout life
- No fixed adult size — can grow indefinitely
- Leaves and flowers: determinate growth (limited dimensions)
- Roots and shoots: indeterminate via meristems
- Trees increase in height and girth over decades
Animals — Determinate
Closed growth
- Meristematic regions absent in adults
- Reach a fixed adult body size
- Growth ceases at maturity
- Cell renewal occurs but no net increase in body size
- Exception: tumours show uncontrolled division