14. Consider a spherical bacterial cell which has a diameter 2 µm. The density of the cell is 1 g/mL,
the dry weight of the cell is roughly 30 percent of its total, and half of that mass is protein. Calculate
the protein mass in this cell.
a.62 pg
b.0.62 pg
c.6.2 pg
d.620 pg
Protein Mass in Bacterial Cell: Calculation for 2 µm Spherical Cell
The protein mass in this 2 µm diameter spherical bacterial cell is 0.62 pg, corresponding to option b .
Volume calculation yields 4.19 × 10⁻¹⁸ m³; at 1 g/mL density (1000 kg/m³), total wet mass is 4.19 × 10⁻¹² g. Dry weight (30%) is 1.26 × 10⁻¹² g, and protein (half of dry) is 6.28 × 10⁻¹³ g or 0.62 pg .
Step-by-Step Calculation
Start with sphere volume V = (4/3)πr³, where radius r = 1 µm = 10⁻⁶ m.
- Volume: (4/3)π(10⁻⁶)³ = 4.19 × 10⁻¹⁸ m³
- Total mass: V × 1 g/mL = 4.19 × 10⁻¹² g (since 1 mL = 10⁻⁶ m³, density matches)
- Dry mass: 0.3 × 4.19 × 10⁻¹² = 1.26 × 10⁻¹² g
- Protein mass: 0.5 × 1.26 × 10⁻¹² = 6.28 × 10⁻¹³ g = 0.62 pg (1 pg = 10⁻¹² g)
Option Analysis
Options test precision in unit handling and percentages.
- a. 62 pg: Overestimates by factor of 100, likely from pg to ng error or misplaced decimal
- b. 0.62 pg: Matches exact calculation of 6.28 × 10⁻¹³ g rounded appropriately
- c. 6.2 pg: Off by factor of 10, possibly ignoring one decimal in mass conversion
- d. 620 pg: Excessively high, from misconverting units like m³ to mL incorrectly
Key Parameters Table
| Parameter | Value | Unit |
|---|---|---|
| Diameter | 2 | µm |
| Radius | 1 | µm |
| Volume | 4.19 × 10⁻¹⁸ | m³ |
| Total Wet Mass | 4.19 × 10⁻¹² | g |
| Dry Weight (30%) | 1.26 × 10⁻¹² | g |
| Protein (50% dry) | 6.28 × 10⁻¹³ | g (0.62 pg) |
Final Answer: b. 0.62 pg
This calculation underscores typical bacterial cell composition for microbiology.
