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.