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tooluniverse-computational-biophysics

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Solve quantitative problems in biophysics — pharmacokinetics (PK volume of distribution, clearance, half-life), epidemiology (R0, attack rate), toxicology (LD50, NOAEL), population genetics (Hardy-Weinberg, Fst), enzyme kinetics (Michaelis-Menten), thermodynamics. Use for first-principles quantitative biology calculations, dose calculations, exposure assessment, and biophysical-property estimation.

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# 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.
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