5.
In bacteria, glucose absorbed via the cell surface is used to synthesize ATP. The ATP, in
turn, powers processes throughout the cell volume. Based on this alone, which of the
following types of cells would you expect to have the slowest growth rate?
a. Short rods (cylinder: length = 2μm, diameter = 1 μm)
b. Long rods (cylinder: length = 4μm, diameter = 1 μm)
c. Small cocci (sphere: diameter = 1μm)
d. Large cocci (sphere: diameter = 4μm)
Glucose uptake through bacterial cell surfaces limits ATP production for volume-wide processes, making surface-to-volume (SA/V) ratio critical for growth rate. Higher SA/V enables faster nutrient absorption and growth; lower SA/V slows it. Large cocci exhibit the lowest SA/V, predicting slowest growth.
SA/V Ratio Calculations
Exact dimensions yield these SA/V values (cylinders include ends; spheres standard formulas).
| Cell Type | Dimensions | Surface Area (μm²) | Volume (μm³) | SA/V Ratio (μm⁻¹) |
|---|---|---|---|---|
| Short rods | 2×1 μm cylinder | 7.854 | 1.571 | 5.000 |
| Long rods | 4×1 μm cylinder | 14.137 | 3.142 | 4.500 |
| Small cocci | 1 μm sphere | 3.142 | 0.524 | 6.000 |
| Large cocci | 4 μm sphere | 50.265 | 33.510 | 1.500 |
Small cocci top with 6.0, favoring rapid glucose influx and ATP synthesis. Short rods (5.0) follow closely due to balanced cylinder geometry.
Option Analysis
Short rods (a): Moderate-high SA/V (5.0) supports efficient nutrient uptake relative to volume, enabling solid growth rates typical of many bacilli.
Long rods (b): Elongation drops SA/V to 4.5 as volume doubles without proportional surface gain, moderately slowing growth versus shorter forms.
Small cocci (c): Highest SA/V (6.0) maximizes surface per volume, ideal for fast division in nutrient-rich environments like Staphylococcus.
Large cocci (d): Lowest SA/V (1.5) severely limits glucose absorption per cytoplasmic volume, bottlenecking ATP and yielding slowest growth—correct answer.
Growth Rate Implications
Bacteria maintain SA/V homeostasis for optimal growth, with rods scaling surface synthesis to match volume demands. Spheres minimize SA/V at larger sizes per geometric principles, explaining why cocci rarely exceed ~2 μm diameter in nature. This principle applies directly to CSIR NET questions on microbial physiology.
