This MCQ module is based on: Growth Rates Differentiation
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Growth Rates Differentiation
🎓 Class 11
Biology
CBSE
Theory
Ch 13 – Plant Growth and Development
⏱ ~14 min
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Growth Rates, Conditions for Growth and Differentiation
Part 1 established that growth can be measured. This part asks a sharper question: at what rate, and by what mathematical pattern? Two patterns exist, they arise from two different fates of daughter cells, and each has its own equation. We then turn to what a cell becomes once it stops dividing — and to the remarkable fact that in plants this decision can be reversed.
13.1.4 Growth Rates
The increased growth per unit time is termed the growth rate. The rate of growth can therefore be expressed mathematically, and an organism or a part of it can produce more cells in a variety of ways. The growth rate shows an increase that may be arithmetic or geometrical.
Arithmetic growth
In arithmetic growth, following mitotic cell division, only one daughter cell continues to divide while the other differentiates and matures.
The simplest expression of arithmetic growth is exemplified by a root elongating at a constant rate. On plotting the length of the organ against time, a linear curve is obtained. Mathematically:
Lt = L0 + rt
Lt = length at time ‘t’ • L0 = length at time ‘zero’ • r = growth rate / elongation per unit time
Lt = length at time ‘t’ • L0 = length at time ‘zero’ • r = growth rate / elongation per unit time
Geometric growth
In most systems, the initial growth is slow (lag phase), and it increases rapidly thereafter — at an exponential rate (log or exponential phase). The cellular reason is different from the arithmetic case: here, both the progeny cells following mitotic cell division retain the ability to divide and continue to do so.
But this cannot continue indefinitely. With limited nutrient supply, the growth slows down, leading to a stationary phase.
The sigmoid curve. If we plot the parameter of growth against time, we get a typical sigmoid or S-curve. A sigmoid curve is a characteristic of living organisms growing in a natural environment. It is typical for all cells, tissues and organs of a plant.
The exponential growth can be expressed as:
W1 = W0 ert
W1 = final size (weight, height, number etc.) • W0 = initial size at the beginning of the period
r = growth rate • t = time of growth • e = base of natural logarithms
W1 = final size (weight, height, number etc.) • W0 = initial size at the beginning of the period
r = growth rate • t = time of growth • e = base of natural logarithms
What r means. Here r is the relative growth rate and is also the measure of the ability of the plant to produce new plant material, referred to as efficiency index. Hence the final size W₁ depends on the initial size W₀ — two plants with the same r but different starting sizes will not end up the same.
In-text questions — more examples of sigmoid growth, and what curve a seasonal tree would show. More sigmoid examples: a population of yeast or bacteria in a fixed volume of broth; cells in a tissue culture; the growth of a single leaf, fruit or seed from initiation to maturity; the increase in dry weight of an annual crop over a season; the growth of a whole organism such as a maize plant. The chapter's own generalisation is the guide here — the curve is typical for all cells, tissues and organs of a plant, because every one of them starts slowly, accelerates and then levels off as some resource becomes limiting.
The seasonal tree: not a single S, but a stepped or intermittent curve — a series of sigmoid rises separated by flat stretches. Each favourable season produces a fresh burst of cambial and apical activity, while in the unfavourable season growth halts and the curve plateaus. Over many years the steps accumulate into an overall pattern that still rises, but the fine structure records the seasons. This is why annual rings can be counted in a temperate tree at all.
The seasonal tree: not a single S, but a stepped or intermittent curve — a series of sigmoid rises separated by flat stretches. Each favourable season produces a fresh burst of cambial and apical activity, while in the unfavourable season growth halts and the curve plateaus. Over many years the steps accumulate into an overall pattern that still rises, but the fine structure records the seasons. This is why annual rings can be counted in a temperate tree at all.
Absolute and relative growth rates
Quantitative comparisons between the growth of living systems can be made in two ways:
(i) Absolute growth rate. The measurement and comparison of total growth per unit time.
(ii) Relative growth rate. The growth of the given system per unit time expressed on a common basis, e.g., per unit initial parameter.
In-text question — two leaves A and B both increase in area by 5 cm², so which has the higher relative growth rate and why? The smaller leaf, A. Both leaves show the same absolute growth rate, since both added 5 cm² in the same time. But the relative rate is expressed per unit initial parameter, so it depends on where each started. If leaf A began at 5 cm² and leaf B at 50 cm², then A's relative growth is 5/5 = 1.0, a 100% increase, while B's is 5/50 = 0.1, a 10% increase. The smaller leaf has grown ten times as much in relative terms. This is exactly why the exponential equation makes W₁ depend on W₀, and why a single absolute figure can badly mislead when comparing systems of different sizes — the same 5 cm² means something very different to a seedling leaf than to a mature one.
13.1.5 Conditions for Growth
The essentials. Water, oxygen and nutrients are very essential elements for growth.
- Water. Plant cells grow in size by cell enlargement, which in turn requires water. Turgidity of cells helps in extension growth. Thus plant growth and further development is intimately linked to the water status of the plant. Water also provides the medium for enzymatic activities needed for growth.
- Oxygen. Oxygen helps in releasing metabolic energy essential for growth activities.
- Nutrients. Macro and micro essential elements are required by plants for the synthesis of protoplasm and act as a source of energy.
- Temperature. Every plant organism has an optimum temperature range best suited for its growth, and any deviation from this range could be detrimental to its survival.
- Environmental signals. Light and gravity also affect certain phases or stages of growth.
🎯 Interactive: Which condition is missing?
Effect on growth: Cell enlargement fails; extension growth stops
Plant cells grow in size by cell enlargement, which requires water, and turgidity of cells helps in extension growth. Water also provides the medium for the enzymatic activities needed for growth, so plant growth and development is intimately linked to the water status of the plant.
13.2 Differentiation, Dedifferentiation and Redifferentiation
Differentiation
The cells derived from root apical and shoot apical meristems and cambium differentiate and mature to perform specific functions.
Differentiation is the act leading to maturation. During differentiation, cells undergo few to major structural changes both in their cell walls and protoplasm.
The chapter's example is worth studying closely because it shows how extreme these changes can be. To form a tracheary element, the cells would lose their protoplasm — that is, the cell dies as part of becoming what it is for. They also develop a very strong, elastic, lignocellulosic secondary cell wall, to carry water to long distances even under extreme tension.
In-text prompt — correlate anatomical features to the functions they perform. Every anatomical detail from Chapter 6 is now readable as an answer to a functional demand. Sclerenchyma has thick lignified walls and no protoplasm at maturity, because its job is pure mechanical strength. Sieve tube elements keep their cytoplasm but lose their nucleus and have perforated end walls, because they must conduct a living stream of sap. Guard cells keep chloroplasts and unevenly thickened walls, because they must change shape reversibly. Root hair cells extend a long thin projection with a thin wall, to maximise absorbing surface. In each case the structure is not arbitrary — it is what the function costs.
Dedifferentiation
Plants show another interesting phenomenon. The living differentiated cells, that by now have lost the capacity to divide, can regain the capacity of division under certain conditions.
Dedifferentiation is that phenomenon. The chapter's example: the formation of meristems — interfascicular cambium and cork cambium — from fully differentiated parenchyma cells.
Redifferentiation
While doing so, such meristems or tissues are able to divide and produce cells that once again lose the capacity to divide but mature to perform specific functions — i.e., they get redifferentiated.
In-text question — list some tissues in a woody dicotyledonous plant that are products of redifferentiation. All the secondary tissues, since each is produced by a cambium that was itself formed by dedifferentiation:
• Secondary xylem and secondary phloem, from the vascular cambium (including its interfascicular part);
• Cork or phellem, secondary cortex or phelloderm — together the periderm — from the cork cambium (phellogen);
• Secondary medullary rays and lenticels.
All of these are cells that again lost the capacity to divide and matured for a specific function.
• Secondary xylem and secondary phloem, from the vascular cambium (including its interfascicular part);
• Cork or phellem, secondary cortex or phelloderm — together the periderm — from the cork cambium (phellogen);
• Secondary medullary rays and lenticels.
All of these are cells that again lost the capacity to divide and matured for a specific function.
In-text questions — how would you describe a tumour, and what would you call parenchyma cells made to divide in tissue culture? A tumour is best described as dedifferentiation that has gone out of control: differentiated cells regain the capacity to divide, but unlike a cambium they keep on dividing without organised redifferentiation, giving a disorganised mass rather than a functional tissue. The key contrast with normal dedifferentiation is the absence of regulation and of an orderly return to maturity. In plants this is seen in crown gall tumours.
For the tissue culture question, the parenchyma cells made to divide under controlled laboratory conditions form a callus — a mass of undifferentiated cells, in the chapter's own words from Section 13.4.2. Producing it is an act of dedifferentiation, and coaxing that callus to form shoots and roots afterwards is redifferentiation. The whole technique of plant tissue culture rests on the fact that plant cells can be made to reverse this decision, which animal cells cannot easily do.
For the tissue culture question, the parenchyma cells made to divide under controlled laboratory conditions form a callus — a mass of undifferentiated cells, in the chapter's own words from Section 13.4.2. Producing it is an act of dedifferentiation, and coaxing that callus to form shoots and roots afterwards is redifferentiation. The whole technique of plant tissue culture rests on the fact that plant cells can be made to reverse this decision, which animal cells cannot easily do.
Differentiation in plants is open too
Recall that growth in plants is open — it can be indeterminate or determinate. We may now say that even differentiation in plants is open, because cells or tissues arising out of the same meristem have different structures at maturity.
Position decides fate. The final structure at maturity of a cell or tissue is also determined by the location of the cell within. For example, cells positioned away from root apical meristems differentiate as root-cap cells, while those pushed to the periphery mature as epidermis.
In-text question — add more examples of open differentiation correlating a cell's fate to its position in an organ. Several, all from tissue you already know:
• In the root, cells of the same apical meristem become epidermis at the periphery, cortex beneath it, endodermis at the inner limit of the cortex, and pericycle and vascular tissue in the centre — purely according to radial position.
• From the vascular cambium, the same meristem produces secondary xylem on its inner face and secondary phloem on its outer face. Nothing but position distinguishes the two.
• In the leaf, mesophyll cells near the upper surface become palisade while those below become spongy; epidermal cells mostly become ordinary, but a pair beside a pore becomes guard cells.
• In the shoot apex, cells at the flanks become leaf primordia while those at the summit remain meristematic.
This positional control is precisely what makes plant differentiation “open”: identical starting cells, different destinies.
• In the root, cells of the same apical meristem become epidermis at the periphery, cortex beneath it, endodermis at the inner limit of the cortex, and pericycle and vascular tissue in the centre — purely according to radial position.
• From the vascular cambium, the same meristem produces secondary xylem on its inner face and secondary phloem on its outer face. Nothing but position distinguishes the two.
• In the leaf, mesophyll cells near the upper surface become palisade while those below become spongy; epidermal cells mostly become ordinary, but a pair beside a pore becomes guard cells.
• In the shoot apex, cells at the flanks become leaf primordia while those at the summit remain meristematic.
This positional control is precisely what makes plant differentiation “open”: identical starting cells, different destinies.
| Feature | Differentiation | Dedifferentiation | Redifferentiation |
|---|---|---|---|
| Direction of change | Meristematic → mature | Mature → meristematic | Meristematic (regained) → mature |
| Capacity to divide | Lost | Regained | Lost again |
| Definition | The act leading to maturation, with structural changes in wall and protoplasm | Living differentiated cells regaining the capacity of division under certain conditions | Products of such meristems again losing division capacity but maturing for specific functions |
| Example | Formation of a tracheary element — protoplasm lost, lignocellulosic secondary wall formed | Formation of interfascicular cambium and cork cambium from fully differentiated parenchyma | Secondary xylem, secondary phloem, cork |
📐 Activity 13.2 — Demonstrate dedifferentiation with a stem cutting
What to do. Take a healthy cutting of a soft-stemmed dicot — coleus, rose or sugarcane node — and stand its cut lower end in water or moist sand, out of direct sun. Take a second, identical cutting and seal its cut end with wax as a control. Keep both for ten to fourteen days, then examine the cut ends with a hand lens; if you can, cut a thin transverse section of the region just above the cut and look at it under the microscope.
Predict: what will appear at the cut end, from which pre-existing cells will it arise, and which of the three processes of Section 13.2 does its appearance demonstrate?
Observation. The open cutting develops a swollen mass of pale tissue at the cut surface, and from it adventitious roots emerge over the following days. The waxed control develops neither.
What it demonstrates. All three processes in sequence. The pale mass is a callus — a mass of undifferentiated cells — formed from fully differentiated parenchyma cells near the cut, which regained the capacity of division. That is dedifferentiation. Those dividing cells then produce daughters that once again lose the capacity to divide but mature to perform specific functions, organising themselves into a root apex with its own epidermis, cortex and vascular tissue — redifferentiation, and within the new root tip, ordinary differentiation.
Two further points worth noting. First, the new root arises where no root was pre-formed, which is why it is called adventitious — a direct illustration that differentiation in plants is open and that a cell's fate follows its position and circumstances, not a fixed programme. Second, this is exactly the process that Part 3 will show can be accelerated by a plant growth regulator: auxins help to initiate rooting in stem cuttings, an application widely used for plant propagation.
🎯 Competency-Based Questions
Scenario: Two cultures are set up. Culture X contains 100 bacterial cells in 10 mL of fresh broth, sealed. Culture Y is a root of a seedling whose elongation is measured hourly and found to increase by exactly 1.2 mm every hour for twelve hours. Separately, a piece of tobacco stem internode is placed on a nutrient medium and forms a pale mass of cells.
Q1. Identify the growth pattern in X and in Y, and give the equation for each. L3 Apply
X is geometric growth, since both progeny cells following mitotic division retain the ability to divide and continue to do so; plotted against time it gives a sigmoid or S-curve with a lag, an exponential and — because the broth is sealed and the nutrient supply limited — a stationary phase. Equation: W₁ = W₀ert. Y is arithmetic growth: a constant 1.2 mm per hour is exactly a root elongating at a constant rate, giving a linear curve, because only one daughter cell continues to divide while the other differentiates and matures. Equation: Lt = L₀ + rt, with r = 1.2 mm h⁻¹.
Q2. Name the pale mass formed on the tobacco internode and the two processes involved in producing it and then regenerating a plant from it. L2 Understand
The pale mass is a callus — a mass of undifferentiated cells. Its formation is dedifferentiation: living differentiated cells that had lost the capacity to divide regain the capacity of division under certain conditions. Regenerating shoots and roots from it is redifferentiation, in which those dividing cells produce daughters that once again lose the capacity to divide but mature to perform specific functions.
Q3. Fill in the blanks: In the exponential equation W₁ = W₀e^rt, the term r is the ______ growth rate and is also the measure of the ability of the plant to produce new plant material, called the ______ index. Hence the final size W₁ depends on the ______ size. L1 Remember
relative; efficiency; initial (W₀).
Q4. A nursery reports that its small saplings “grow faster” than its large ones, while a forester insists the large trees add far more wood each year. Can both be right? L4 Analyse
Yes — they are quoting the two different growth rates the chapter distinguishes. The forester is using the absolute growth rate, the measurement and comparison of total growth per unit time; a large tree with a big crown and a long cambial cylinder genuinely lays down more wood per year. The nursery is using the relative growth rate, the growth per unit time expressed on a common basis, e.g., per unit initial parameter; a sapling doubling its small size has a far higher relative rate. This is the same situation as leaves A and B, which both increase in area by 5 cm² yet differ greatly in relative growth rate. Neither is wrong; the dispute is about which basis of comparison is meant, and a careful answer always states which rate is being used.
Q5. “Since plant cells can dedifferentiate, plant differentiation is not a real commitment at all.” Evaluate. L5 Evaluate
The claim overreaches from a true premise. True: plants really do show that living differentiated cells, that by now have lost the capacity to divide, can regain the capacity of division under certain conditions, and the interfascicular cambium and cork cambium formed from fully differentiated parenchyma cells are everyday proof. Tissue culture exploits this on an industrial scale, and it is a genuine and profound difference from animals. But the claim ignores three limits. (i) Only living cells can do it. A cell that has completed differentiation into a tracheary element has lost its protoplasm altogether — it is dead, and no condition will bring it back. The same is true of mature sclerenchyma and cork. For such cells, differentiation is absolutely final. (ii) It requires particular conditions, not merely a wish — wounding, hormones, a nutrient medium. (iii) It is regulated. Dedifferentiation without regulated redifferentiation is not a useful flexibility but a tumour. A fair conclusion: differentiation in plants is remarkably reversible for living parenchymatous cells and irreversible for those whose maturation involved death, and the flexibility is valuable precisely because it is normally kept under control.
🧠 Assertion–Reason Questions
For each pair choose: (A) Both A and R are true and R is the correct explanation of A. (B) Both A and R are true but R is not the correct explanation of A. (C) A is true but R is false. (D) A is false but R is true.
Assertion (A): Geometric growth cannot continue indefinitely and ends in a stationary phase.
Reason (R): With limited nutrient supply the growth slows down, giving the sigmoid curve characteristic of living organisms growing in a natural environment.
Answer: A. Both are true and the reason is the correct explanation. The stationary phase is imposed by resource limitation, not by any loss of dividing ability in the cells.
Assertion (A): Cells arising from the same meristem always mature into the same kind of cell.
Reason (R): The final structure at maturity of a cell or tissue is determined by the location of the cell within the organ.
Answer: D. The assertion is false — differentiation in plants is open precisely because cells arising from the same meristem have different structures at maturity. The reason states the true principle: position decides fate, as when cells away from the root apical meristem become root-cap cells while those pushed to the periphery become epidermis.
Assertion (A): A mature tracheary element cannot dedifferentiate.
Reason (R): To form a tracheary element the cell loses its protoplasm, and only living differentiated cells can regain the capacity of division.
Answer: A. Both are true and the reason explains the assertion. Dedifferentiation is defined for living differentiated cells; a cell that shed its protoplasm during maturation is beyond recall.
Coming next. Part 3 takes up Sections 13.3 and the opening of 13.4 — development as the sum of growth and differentiation, plasticity and heterophylly, the characteristics of plant growth regulators, and the accidental discoveries behind all five of them, followed by the physiological effects of auxins and gibberellins.
Frequently Asked Questions - Growth Rates, Conditions and Differentiation
What is the difference between arithmetic and geometric growth?
In arithmetic growth, following mitotic division only one daughter cell continues to divide while the other differentiates and matures, giving a linear curve expressed as Lt = L0 + rt. In geometric growth both progeny cells retain the ability to divide, so growth is exponential, expressed as W1 = W0 e raised to rt.
What is a sigmoid growth curve?
It is the S-shaped curve obtained when a growth parameter is plotted against time in geometric growth: a slow lag phase, a rapid exponential or log phase, and a stationary phase caused by limited nutrient supply. A sigmoid curve is characteristic of living organisms growing in a natural environment and is typical for all cells, tissues and organs of a plant.
What do the terms in W1 = W0 e^rt mean?
W1 is the final size in weight, height or number; W0 is the initial size at the beginning of the period; r is the growth rate; t is the time of growth; and e is the base of natural logarithms. Here r is the relative growth rate and also the efficiency index, the measure of the plant's ability to produce new plant material.
What is the difference between absolute and relative growth rate?
Absolute growth rate is the measurement and comparison of total growth per unit time. Relative growth rate is the growth of the given system per unit time expressed on a common basis, for example per unit initial parameter. Two leaves may add the same 5 square centimetres, yet the smaller one has a far higher relative growth rate.
What conditions are necessary for plant growth?
Water, oxygen and nutrients are essential. Water is needed for cell enlargement and turgidity and provides the medium for enzymatic activity; oxygen helps release metabolic energy; nutrients are required for synthesis of protoplasm and as a source of energy. In addition every plant has an optimum temperature range, and light and gravity affect certain stages of growth.
What is differentiation in plants?
It is the act leading to maturation of cells derived from the root and shoot apical meristems and the cambium, so that they can perform specific functions. During differentiation cells undergo few to major structural changes in both cell walls and protoplasm, as when a cell loses its protoplasm and forms a strong lignocellulosic secondary wall to become a tracheary element.
What are dedifferentiation and redifferentiation?
Dedifferentiation is the phenomenon in which living differentiated cells that had lost the capacity to divide regain it under certain conditions, as in the formation of interfascicular cambium and cork cambium from fully differentiated parenchyma. Redifferentiation is when the cells produced by such meristems once again lose the capacity to divide but mature to perform specific functions.
Why is differentiation in plants described as open?
Because cells or tissues arising out of the same meristem have different structures at maturity, the final structure being determined by the location of the cell. For example, cells positioned away from the root apical meristem differentiate as root cap cells while those pushed to the periphery mature as epidermis.
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