61 Based on equal probability of any base occurrence in a genome, what should be the minimum length of a
probe to bind specifically on a single locus on a bacterial genome of 1 Mbp?
(1) 6 bases
(2) 15 bases
(3) 10 bases
(4) 4 bases

🔍 Introduction

In molecular biology, DNA probes are short, single-stranded sequences used to detect specific DNA regions. When designing probes, specificity is crucial—especially if you want it to bind only one site in an entire genome. This article walks through the logic of calculating the minimum length of such a probe, assuming equal probability of the four nucleotides (A, T, G, C) and a bacterial genome size of 1 million base pairs (1 Mbp).

🔬 Understanding the Problem

• Bacterial genome size: 1 Mbp = 1,000,000 base pairs

• There are 4 possible bases at each position (A, T, G, C).

• A probe of length n has 4ⁿ possible combinations.

• We want the probe to be unique, i.e., it should match only one specific site in the genome.

🧠 The Key Question:

What is the minimum n such that a randomly chosen probe of that length occurs only once (or very rarely) in a 1 Mbp genome?

🔢 Step-by-Step Calculation

To ensure specific binding, the number of unique sequences (4ⁿ) should be at least equal to the genome size.

We solve:

4ⁿ ≥ 1,000,000

Let’s try values:

• 4⁶ = 4,096

• 4¹⁰ = 1,048,576 ✅

• 4¹⁵ = 1.07 × 10⁹ (too much)

So, n = 10 is the smallest length where the number of unique combinations is slightly more than 1 million.

✅ Correct Answer:

(3) 10 bases

🧬 Why This Matters

Using a 10-base probe ensures:

• High specificity: It binds to only one location in the genome.

• Minimal cross-reactivity: No accidental binding to similar regions.

• Effective diagnostics and gene detection in bacterial studies.

❌ Why Other Options Are Incorrect

• (1) 6 bases: 4⁶ = 4,096 → would bind to ~244 sites in 1 Mbp genome.

• (4) 4 bases: 4⁴ = 256 → extremely non-specific.

• (2) 15 bases: 4¹⁵ = 1.07 billion → overly specific; unnecessary for a small genome.

🔑 Summary

📌 Final Thoughts

The minimum length of a DNA probe for unique binding on a 1 Mbp bacterial genome is 10 bases, assuming random distribution and equal base probability. This is a critical concept in probe design for DNA hybridization, microarrays, and molecular diagnostics.

🏷 Tags & Keywords:

• DNA probe design

• bacterial genome analysis

• hybridization specificity

• unique probe binding

• minimum probe length calculation

📍 Final Answer: (3) 10 bases — the minimum length required for specific binding on a 1 Mbp bacterial genome.