Cell Size and Surface Area to Volume Ratio

Cell Size and Surface Area to Volume Ratio

Introduction

  • Cells are typically small due to the need for efficient nutrient and waste exchange with the environment.

Size Examples

  • Atoms: 0.1 nanometers
  • Small molecules: 0.3 - 0.9 nanometers
  • Lipids: ~1 nanometer
  • Proteins: Up to 10 nanometers
  • Viruses: Up to 70 nanometers
  • Chloroplast: ~1.5 micrometers (0.0015 mm)
  • Bacteria: 1 - 10 micrometers
  • Cells: 10 - 100 micrometers
  • Fish/frog eggs: ~ Millimeter Size
  • Hummingbirds: ~ 5 Centimeters
  • Humans: Upwards of 2 meters
  • Great blue whale: 20 - 30 meters (~90 feet)
  • Giant redwoods: ~ 100 meters (~330 feet)

Cell Membrane and Exchange

  • Cells must exchange nutrients and waste with their environment.
  • The cell membrane is the sole interface for this exchange.
  • The cell membrane has a limited surface area (SA).
  • The cytoplasm has a volume (V) that needs to be supported by this exchange.

Surface Area to Volume Ratio

  • The cell membrane's surface area must be sufficient to support the cytoplasm's volume.

Cube Example: 1x1x1

  • Surface area (SA) = length x width x number of sides = 1 \cdot 1 \cdot 6 = 6 units squared
  • Volume (V) = length x width x height = 1 \cdot 1 \cdot 1 = 1 unit cubed
  • SA:V ratio = 6:1

Cube Example: 2x2x2

  • Surface area (SA) = 2 \cdot 2 \cdot 6 = 24 units squared
  • Volume (V) = 2 \cdot 2 \cdot 2 = 8 units cubed
  • SA:V ratio = 24:8 = 3:1

Cube Example: 3x3x3

  • Surface area (SA) = 3 \cdot 3 \cdot 6 = 54 units squared
  • Volume (V) = 3 \cdot 3 \cdot 3 = 27 units cubed
  • SA:V ratio = 54:27 = 2:1

Importance of SA:V Ratio

  • A larger SA:V ratio is desirable for efficient exchange rates.
    • More surface area available to support the cell volume.
  • As cell size increases, the rate of diffusion/exchange slows down.
  • A cell may not be able to get rid of wastes or obtain nutrients fast enough.
  • As cell size increases, the SA:V ratio decreases.
  • Cells divide when they become too large to maintain an efficient SA:V ratio.

Surface Area and Volume in Relation to Cell Diameter

  • Surface area increases as the square of cell diameter.
  • Cell volume increases as the cube of cell diameter.
  • Maintaining a higher surface area compared to volume is critical for nutrient intake.

Nutrient and Waste Flow

  • Small cells are easier to maintain nutrient and waste flow than large cells.
  • Larger cells have less membrane per unit of volume.
  • Larger cells have a harder time obtaining nutrients, getting rid of wastes and regulating their internal environments.

Conclusion

  • Cells are typically small because they are more efficient due to their greater surface area to volume ratio.
  • We don't see cells the size of a desk or even a fingertip because these would not have sufficient surface area to support their volume.