Bioprocess Engineering & Formula Sheet
1000+ words of pure industrial biotechnology. Master Microbial Kinetics, Bioreactor Design, Oxygen Mass Transfer, and Downstream Processing to easily crack numerical questions in DBT BET 2026.
1. Microbial Growth Kinetics
Bioprocessing relies heavily on understanding how microbes grow over time. The growth curve has four main phases: Lag, Log (Exponential), Stationary, and Death phase. Numericals exclusively come from the Exponential (Log) phase.
The Monod Equation
The Monod equation is the fundamental law of bioprocessing. It links the specific growth rate (μ) of the cells to the concentration of the limiting substrate (S).
- μ = Specific growth rate (h⁻¹)
- μmax = Maximum specific growth rate (h⁻¹)
- S = Substrate concentration (g/L)
- Ks = Saturation constant. It is the substrate concentration at which μ = μmax / 2. (A lower Ks means the microbe has a high affinity for the substrate).
Doubling Time (td): The time required for the biomass to double. td = ln(2) / μ = 0.693 / μ.
2. Bioreactor Operation Modes
Bioreactors can be operated in three main modes. Understanding the mathematics behind the Continuous Culture (Chemostat) is mandatory for DBT JRF.
1. Batch Culture
A closed system. You add media and inoculum at time zero and harvest at the end. Nutrients deplete, and toxins accumulate over time.
2. Fed-Batch Culture
You continuously or semi-continuously add concentrated nutrients, but you do NOT remove any culture fluid until the end. Volume keeps increasing. It is used to avoid Substrate Inhibition and is the preferred method for producing Penicillin and recombinant proteins.
3. Continuous Culture (Chemostat)
Fresh media is pumped in at a constant flow rate (F), and culture fluid is removed at the exact same rate. Volume (V) remains constant.
The Golden Rule of Chemostats: At steady state, the specific growth rate of the cells perfectly matches the dilution rate. μ = D.
If you increase the flow rate too much so that D > μmax, the cells cannot divide fast enough and are flushed out. This is called Washout.
3. Oxygen Mass Transfer & Sterilization Kinetics
Oxygen Transfer Rate (OTR)
Because oxygen is highly insoluble in water/media, supplying enough oxygen is the biggest bottleneck in aerobic bioprocessing.
- KLa = Volumetric mass transfer coefficient (The most critical parameter for scaling up a bioreactor).
- C* = Saturation concentration of oxygen in the broth.
- CL = Actual dissolved oxygen concentration in the broth.
Thermal Sterilization (The Del Factor)
Sterilization follows first-order kinetics. The destruction of bacterial spores (usually Geobacillus stearothermophilus) is calculated using the Del factor (∇).
Where N0 is initial spore count, Nt is final spore count, kd is the specific death rate, and t is time. The D-value is the time required to reduce the microbial population by 90% (1 log reduction) at a specific temperature.
4. DBT BET Ultimate Formula Cheat-Sheet
Direct numericals will be framed using these exact formulas. Memorize the units carefully.
| Parameter | Formula | Meaning / Exam Logic |
|---|---|---|
| Cell Yield (YX/S) | YX/S = ΔX / ΔS | Grams of biomass produced per gram of substrate consumed. Always a positive fraction. |
| Product Yield (YP/S) | YP/S = ΔP / ΔS | Amount of product formed per unit of substrate consumed. |
| Critical Dilution Rate (Dcrit) | Dcrit = (μmax × S0) / (Ks + S0) | The exact dilution rate at which Washout begins. If D > Dcrit, cell mass drops to zero. |
| Reynolds Number (Re) | Re = (ρ × N × Di²) / μ | Determines flow type. Re > 10,000 means turbulent flow (good mixing). N=Impeller speed, Di=Impeller diameter, μ=viscosity. |
| Stokes' Law (Centrifugation) | v = [d²(pp - pl) × g] / 18μ | Settling velocity (v). Doubling the particle diameter (d) increases the settling velocity by 4 times. |
5. Fluid Rheology (Newtonian vs Non-Newtonian)
As cells grow and secrete products (like EPS or proteins), the culture broth changes its viscosity. DBT papers always have a matching question on fluid types.
- Newtonian Fluids: Viscosity remains constant regardless of shear rate (e.g., Water, simple sugar media).
- Pseudoplastic (Shear-thinning): Viscosity decreases as you stir faster. Most common in bioprocessing (e.g., fungal mycelial broths like Penicillium, Paper pulp).
- Dilatant (Shear-thickening): Viscosity increases as you stir faster (e.g., Corn starch in water, wet sand).
- Bingham Plastic: Requires a minimum initial force (Yield stress) to start flowing. Once flowing, it acts Newtonian (e.g., Tomato ketchup, Toothpaste).
Guaranteed Exam Hits
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Primary vs Secondary Metabolites: Primary metabolites (e.g., Amino acids, Ethanol) are produced during the Trophophase (Log phase) as they are essential for growth. Secondary metabolites (e.g., Antibiotics like Penicillin) are produced during the Idiophase (Stationary phase).
Impeller Types: Rushton Turbine is used for standard gas-liquid dispersion (breaks bubbles). Marine Impeller provides axial flow and is used for shear-sensitive animal cell cultures to prevent cell rupture.
Downstream Processing (Chromatography): Gel Filtration (Size Exclusion) separates by size; large molecules come out FIRST. Ion Exchange separates by charge. Affinity Chromatography separates by highly specific biological interactions (e.g., Antigen-Antibody, His-tag with Nickel).
Scale-up Criterion: The most common rule for scaling up a bioreactor from a 1-Liter lab flask to a 10,000-Liter industrial fermenter is keeping the Constant KLa (Oxygen transfer rate) or Constant Power per unit Volume (P/V).
LAL Test: The Limulus Amebocyte Lysate (LAL) test is used in quality control downstream to detect the presence of Endotoxins (Pyrogens) from Gram-negative bacterial cell walls in the final biopharmaceutical product.
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