Phases and rates of growth

Along a growing root or shoot tip, you can see three phases of growth one after another:

• Meristematic phase (at the tip): cells keep dividing. They have dense protoplasm, large nuclei and thin primary walls.
• Elongation phase (just behind): cells grow bigger, mainly by taking in water into vacuoles (increased vacuolation), and lay down new wall material.
• Maturation phase (further back): cells reach their full size and take on their final shape and job.

Growth can follow two patterns:

• Arithmetic growth: after each division, only one daughter cell keeps dividing; the other differentiates and matures. Length goes up by the same amount each time, giving a straight line: Lt = L₀ + rt (final length = starting length + rate × time).
• Geometric growth: both daughter cells keep dividing. After a slow start (lag phase), growth becomes very fast (exponential or log phase): W₁ = W₀e^(rt), where r is the relative growth rate, also called the efficiency index. Then, as nutrients run short, growth slows and stops (stationary phase). Plotted, this makes an S-shaped (sigmoid) curve.

Growth rate can be compared in two ways. Absolute growth rate is the total growth per unit time. Relative growth rate is growth per unit time per unit of starting size. If two leaves each grow by 5 cm², but one started at 5 cm² and the other at 50 cm², their absolute growth is the same, but the smaller leaf has the much higher relative growth rate.

Growth needs water (cells swell with water, and enzymes work in it), oxygen (to release energy), nutrients (raw materials), and a suitable temperature. Light and gravity also affect some stages.