Polymerase Chain Reaction (PCR) Sep 17

Chi-Square Analysis in Genetics

Introduction to Chi-Square Analysis

The chi-square (χ²) test is a statistical method used in genetics to determine whether observed data fit expected ratios, such as those predicted by Mendelian inheritance. It helps evaluate the likelihood that deviations between observed and expected results are due to chance.

• Null Hypothesis (H0): Assumes no significant difference between observed and expected values.

• p-value: The probability that the observed deviation is due to random chance. A standard cutoff for significance is p = 0.05.

Chi-Square Test Procedure

1. Calculate expected values based on genetic hypothesis (e.g., Mendelian ratios).

2. Compute the chi-square statistic: $\chi^2 = \sum \frac{(O - E)^2}{E}$ where O = observed value, E = expected value.

3. Determine degrees of freedom (df): $\text{df} = \text{number of categories} - 1$

4. Compare the calculated χ² value to the critical value from the χ² distribution table at the chosen p-value (commonly 0.05).

Interpreting Results

• If p ≥ 0.05: Fail to reject the null hypothesis (differences are likely due to chance).

• If p < 0.05: Reject the null hypothesis (differences are statistically significant).

Example Table: Chi-Square Critical Values

Degrees of Freedom (df)	p = 0.05	p = 0.01
1	3.84	6.63
2	5.99	9.21
3	7.82	11.34
4	9.49	13.28

Example: If χ²exp = 6.4, df = 1, then 3.84 < 6.4 < 6.63, so 0.05 > p > 0.01.

Polymerase Chain Reaction (PCR)

Introduction to PCR

Polymerase Chain Reaction (PCR) is a molecular biology technique used to amplify specific DNA sequences exponentially. Invented by Kary Mullis in 1983, PCR revolutionized genetic research, diagnostics, and forensics.

• Taq DNA polymerase: A heat-stable enzyme from Thermus aquaticus that synthesizes DNA at high temperatures.

PCR Process and Phases

PCR consists of repeated cycles, each with three main steps:

1. Denaturation (94–96°C): Double-stranded DNA is separated into single strands by breaking hydrogen bonds.

2. Annealing (~55–60°C): Short DNA primers bind (anneal) to complementary sequences on the single-stranded template.

3. Extension (72°C): Taq polymerase extends the primers, synthesizing new DNA strands.

Each cycle doubles the amount of target DNA, leading to exponential amplification:

• After n cycles, the number of DNA copies is $2^n$ (assuming 100% efficiency).

PCR Components

• Template DNA: The DNA sequence to be amplified (often genomic DNA).

• Primers: Short, single-stranded DNA sequences that define the region to be amplified.

• dNTPs: Deoxynucleotide triphosphates (building blocks for new DNA synthesis).

• Taq polymerase: Heat-stable DNA polymerase enzyme.

• Buffer: Maintains optimal conditions for the reaction.

Primer Design and Target Selection

• Primers must flank the region of interest (e.g., an exon or a repeat region).

• Correct primer orientation and sequence are essential for specific amplification.

Example: To amplify exon 2 of a gene, select primers that bind to sequences on either side of exon 2.

Applications of PCR

• Molecular biology research (gene cloning, sequencing)

• Forensics (DNA fingerprinting, crime scene analysis)

• Genetic testing (detection of mutations, repeat expansions)

PCR in Genetic Testing: CAG Repeat Detection

PCR is used to detect the number of trinucleotide (CAG) repeats in genes such as HTT (Huntington's disease gene). The number of repeats can be determined by the size of the PCR product.

• Normal allele: Fewer than 35 CAG repeats

• Mutant allele: More than 35 CAG repeats (associated with Huntington's disease)

By comparing the PCR product size to a control sample with a known number of repeats, the repeat number in a patient's allele can be calculated:

• Total PCR product length = constant region + (number of CAG repeats × 3 bp)

Example Table: Genetic Diseases Detectable by PCR

Disease	Gene Mutation	Description
Huntington disease	HTT gene, CAG repeat expansion	Middle age onset, neurodegeneration
Fragile X syndrome	FMR1 gene, CGG repeat expansion	Intellectual disability, macroorchidism
Cystic fibrosis	CFTR gene, point mutations, deletions	Chronic lung disease, pancreatic insufficiency
Hemophilia A	F8 gene, point mutations, deletions	Factor VIII deficiency, bleeding disorder
Additional info: Many other single-gene disorders can be detected by PCR-based assays.

Summary Table: PCR Steps and Temperatures

Step	Temperature (°C)	Description
Denaturation	94–96	DNA strands separate
Annealing	55–60	Primers bind to template
Extension	72	Taq polymerase synthesizes new DNA

Key Points and Practice Questions

• Why is 95°C used in PCR? To denature (separate) the DNA strands by breaking hydrogen bonds.

• How do primers determine the PCR product? Primers define the start and end points of the amplified region.

• How is the number of CAG repeats determined? By comparing the PCR product size to a control with a known repeat number.

Additional info:

• PCR is foundational for many modern genetic and genomic techniques, including DNA sequencing, cloning, and diagnostics.

• Chi-square analysis is essential for interpreting genetic cross data and validating Mendelian ratios.