Key Formulas & Equations
Core Concepts
PCR (Polymerase Chain Reaction)
A technique to amplify specific DNA segments exponentially. Three steps per cycle: Denaturation (95°C — strands separate), Annealing (55-65°C — primers bind), Extension (72°C — Taq polymerase synthesizes). After 30 cycles, ~1 billion copies from a single molecule.
Genetic Engineering
Direct manipulation of an organism's genes using biotechnology. Restriction enzymes cut DNA at specific sequences; ligases join fragments. Vectors (plasmids) carry foreign DNA into host cells. Applications: insulin production, gene therapy, GMO crops.
CRISPR-Cas9 Gene Editing
A revolutionary genome-editing tool derived from bacterial immune defense. A guide RNA directs the Cas9 nuclease to a target DNA sequence, where it creates double-strand breaks. Cellular repair (NHEJ or HDR) disrupts or edits the gene. Applications: disease treatment, agriculture, research.
Bioprocessing & Fermentation
Large-scale cultivation of microorganisms or cells to produce desired products (antibiotics, enzymes, biofuels). Key parameters: temperature, pH, dissolved oxygen, nutrient feed. Batch, fed-batch, and continuous modes. Downstream processing separates and purifies the product.
Gel Electrophoresis
A method to separate DNA, RNA, or proteins by size. Samples loaded into agarose gel wells. Electric field drives migration (DNA moves to positive electrode). Smaller fragments move faster. Stained with ethidium bromide or SYBR Safe for visualization under UV light.
Cell Culture & Aseptic Technique
Growing cells in controlled laboratory conditions (incubators, CO₂, sterile media). Primary cultures come directly from tissue; cell lines are immortalized. Aseptic technique prevents contamination: flame sterilization, laminar flow hoods, antibiotics. Applications: drug testing, vaccine production, research.
Worked Examples
Example 1: PCR Amplification
Problem: Starting with 10 copies of DNA, how many copies after 25 PCR cycles?
Step 1: DNA_final = DNA_initial × 2ⁿ
Step 2: DNA_final = 10 × 2²⁵ = 10 × 33,554,432
Step 3: DNA_final = 335,544,320 copies
Answer: Approximately 336 million copies are produced.
Example 2: Bacterial Growth
Problem: E. coli doubles every 20 minutes. Starting with 100 cells, how many after 2 hours?
Step 1: Generations: 120/20 = 6 generations
Step 2: N = 100 × 2⁶ = 100 × 64
Step 3: N = 6,400 cells
Answer: There are 6,400 cells after 2 hours.
Example 3: Beer-Lambert Law
Problem: A protein sample has absorbance 0.5, ε = 43,200 M⁻¹cm⁻¹, path length 1 cm. Find concentration.
Step 1: A = ε × c × l → c = A/(ε × l)
Step 2: c = 0.5/(43,200 × 1) = 1.157 × 10⁻⁵ M
Step 3: c ≈ 11.57 μM
Answer: The protein concentration is approximately 11.6 μM.
Example 4: Transformation Efficiency
Problem: You used 0.05 μg of plasmid DNA and got 200 colonies on a plate (dilution 1:100). Calculate transformation efficiency.
Step 1: TE = (colonies × dilution factor) / DNA (μg)
Step 2: TE = (200 × 100) / 0.05
Step 3: TE = 20,000 / 0.05 = 400,000 CFU/μg
Answer: Transformation efficiency = 4 × 10⁵ CFU/μg.
Practice Problems
Problem 1
What is the doubling time of a culture with μ = 0.5 hr⁻¹?
Answer: t_d = ln(2)/μ = 0.693/0.5 = 1.39 hours
Problem 2
In the Monod equation, what is μ when [S] = K_s?
Answer: μ = μ_max × K_s/(K_s + K_s) = μ_max/2 (half-maximal)
Problem 3
If 500 μg of substrate produces 200 μg biomass, what is Y_X/S?
Answer: Y_X/S = 200/500 = 0.4 g biomass / g substrate
Problem 4
What size DNA fragment (bp) has a mass of 1 μg? (Avg. 660 g/mol per bp)
Answer: Moles = 1×10⁻⁶/660 = 1.515×10⁻⁹ mol. bp = 6.022×10²³ × 1.515×10⁻⁹ = 9.13×10¹⁴ bp
Problem 5
A restriction enzyme cuts at 5'-GAATTC-3'. What is this enzyme called?
Answer: EcoRI (recognizes GAATTC, cuts between G and A)
Problem 6
In a fed-batch reactor, if X₀ = 2 g/L, Y_X/S = 0.5, and ΔS = 10 g/L, what is final biomass?
Answer: X_t = 2 + 0.5(10) = 2 + 5 = 7 g/L