Computational Biophysics & Quantitative Biology Skill

1. Recognize the Physical Process

The single most important step: identify what physical process the problem describes. In quantitative biology, almost every problem maps to one of these:

• Drug enters body → distributes → is eliminated: pharmacokinetics. Key quantities: dose, bioavailability, volume of distribution, clearance, half-life. The body is a compartment model.
• Radioactive tracer decays over time: nuclear medicine. Same math as drug elimination (exponential decay) but the rate constant is a physical property of the isotope, not a patient variable.
• Pathogen spreads through population: epidemiology. R₀ determines whether an epidemic grows or dies. Herd immunity threshold = 1 - 1/R₀. Every epidemic model starts here.
• Ligand binds receptor: binding equilibrium. At low [ligand], binding is linear. At saturation, all sites occupied. Kd = concentration at half-maximal binding. This same curve describes enzyme kinetics, drug-receptor occupancy, and surface adsorption.
• Contaminant enters environment: dilution + persistence. Two questions: what is the concentration after mixing (conservation of mass), and how long does it persist (exponential decay with environmental half-life)?
• Two populations differ genetically: population genetics. Fst measures differentiation. HWE tests if mating is random. Gene flow opposes drift.
• Neurons communicate in a network: computational neuroscience. Integrate-and-fire models, synaptic dynamics, balanced excitation/inhibition. Mean firing rate depends on input current relative to threshold.

Once you name the process, the mathematical structure follows. Solve algebraically first, substitute numbers second, and always check that units cancel correctly and the magnitude is physically reasonable.

2. Reasoning Patterns by Problem Type

These are not formulas. They are ways of thinking about what is happening physically.