Overview
This lecture explains how the total surface area to volume ratio (TSA:V) affects diffusion rates in cells, with examples using jelly cubes to illustrate why most cells are microscopic.
Total Surface Area to Volume Ratio (TSA:V)
- TSA:V refers to the comparison between an object's surface area and its volume.
- Most cells are microscopic because a high TSA:V allows efficient diffusion.
- Larger objects or cells have a lower TSA:V, making diffusion less effective.
Jelly Cube Diffusion Example
- When equal-sized jelly cubes are placed in a solution, smaller cubes become fully colored faster.
- Although larger cubes have more surface area, they also have a much larger volume, which slows overall diffusion.
- The key factor is the minimum distance the solution must travel to reach the cube's center.
- As cube size increases, the volume increases faster than surface area, lowering the TSA:V ratio.
Calculating TSA:V Ratios
- Surface area of a cube: 6 × (side length)².
- Volume of a cube: (side length)³.
- Smaller cubes have a higher TSA:V, facilitating quicker diffusion throughout the cube.
- For example:
- 1mm cube TSA:V = 6:1
- 5mm cube TSA:V = 6:5 (or 1.2:1)
- 10mm cube TSA:V = 3:5 (or 0.6:1)
Biological Implications
- High TSA:V means substances like oxygen can diffuse quickly to all parts of the cell.
- Large cells struggle to get enough nutrients to their center, leading to inefficient ATP production and potential cell death.
- Evolution favors small cell size to maximize TSA:V for survival.
Special Cases and Minimum Diffusion Distance
- Two objects with the same minimum diffusion distance, even if different shapes or volumes, can fill up at the same rate.
- The minimum distance for diffusion is a crucial determinant in how fast the entire volume is filled.
Key Terms & Definitions
- Total Surface Area (TSA) — The sum of all outer surfaces of an object.
- Volume — The amount of space an object occupies.
- TSA:V Ratio — Surface area divided by volume, indicating diffusion efficiency.
- Diffusion — The passive movement of particles from high to low concentration.
Action Items / Next Steps
- Practice calculating TSA:V ratios for different shapes and sizes.
- Review how TSA:V impacts diffusion in cells for upcoming exam questions.