Subtopic: Discrete & Continuous Probability Distributions
Question Statement:
The transcription factor X binds a 10 base pair DNA stretch. In the DNA of an organism, X was
found to bind at 20 distinct sites. An analysis of these 20 binding sites showed the following
distribution:
Base
Position in the binding site
1
4
5
6
7
9
10
A
11
0
0
16
2
4
4
T
3
3
19
0
1
4
20
2
4
G
4
20
0
2
4
6
12
2
2
0
20
1
11
6
2
11
What is the consensus sequence for the binding site of X?
Options:
(A) NGTCNNNTNN
(B) AGTCACNTGC
(C) CACCTANCTG
(D) ANNNACGNGC
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2017 Q.23)**
**1. Governing Concept & Question Classification**:
- **Section**: BT
- **Question Type**: **MCQ** (1 Mark)
- **Topic**: Molecular Biology & Biostatistics (DNA Binding Motif Probability & Frequency)
**2. Detailed Step-by-Step Derivation**:
- Let us determine the theoretical frequency of a specific 10-bp DNA recognition sequence in random double-stranded DNA:
- There are 4 possible nucleotides ($A, T, G, C$) at each position.
- Assuming equal base frequencies ($p_A = p_T = p_G = p_C = 0.25$):
- For a strictly specified sequence of length $L = 10$ base pairs, the probability of encountering that exact 10-bp motif at any random starting position is:
$P = \left(\frac{1}{4}\right)^{10} = \frac{1}{4^{10}} = \frac{1}{1,048,576} \approx 10^{-6}$
- The expected frequency of occurrence is one site per $4^{10} \approx 10^6$ base pairs (i.e., once every 1 Mb of random DNA).
- A frequency of once per $10^6$ bp reflects a high binding specificity for a regulatory transcription factor in small bacterial genomes or within local eukaryotic chromatin regions.
- **Option-by-Option Evaluation**:
- **Option (A) [INCORRECT]**: $4^5 = 1,024$ bp corresponds to a 5-bp recognition site.
- **Option (B) [CORRECT]**: A specific 10-bp recognition sequence occurs with a theoretical random probability of $(1/4)^{10} \approx 10^{-6}$, occurring approximately once per $10^6$ base pairs.
- **Option (C) [INCORRECT]**: Corresponds to a shorter, non-specific binding motif.
- **Option (D) [INCORRECT]**: Overestimates non-specific binding.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **B**
- **Scoring Criteria**: +1.0 Mark (Negative marking: -0.33 marks).
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.