Growth, Differentiation, and Mathematics — Key Points

Plant Growth Definition:

• Irreversible + permanent increase in size
• Involves: Cell division + cell enlargement + cell differentiation
• NOT reversible changes (wilting/turgidity = not growth)

Three Phases of Growth:

1. Meristematic phase: Active cell division at apices; cells small, densely cytoplasmic
2. Elongation phase: Vacuoles enlarge; cells increase in size; most visible elongation
3. Maturation phase: Cells differentiate; acquire permanent shape and function

Growth Curves:

• Arithmetic growth: Linear (straight line graph)
  • Formula: Lt = $L_{0}$ + rt
  • Biology: One daughter divides, one differentiates
  • Example: Elongating root tip region
• Geometric growth: Exponential (J-shaped initially)
  • Formula: $W_{1}$ = $W_{0}$eʳᵗ
  • Biology: Both daughters continue dividing
  • Example: Early embryo development

Sigmoid Curve Phases:

1. Lag phase: Slow, cells preparing machinery; low AGR
2. Log phase: Exponential; maximum AGR at inflection point; follows geometric model
3. Stationary phase: Plateau; limiting factors; growth ≈ 0

Differentiation Types:

Totipotency:

• All plant cells retain full genetic potential (genome)
• Differentiation is epigenetically reversible
• Basis of tissue culture and clonal propagation
• Demonstrated by F.C. Steward (carrot phloem cell → whole plant, 1958)

Tissue Culture Hormone Ratios (Skoog-Miller):

• High auxin : low cytokinin → root formation
• Low auxin : high cytokinin → shoot formation
• Equal → callus (undifferentiated) maintenance

Key Meristem Types:

• Shoot Apical Meristem (SAM): Primary growth of shoot
• Root Apical Meristem (RAM): Primary growth of root
• Vascular Cambium: Secondary xylem and phloem
• Cork Cambium: Bark (periderm) formation
• Intercalary Meristem: Growth at nodes (grasses)