Learning Outcomes
By the end of the semester, students will be able to:
1. Formulate deterministic and stochastic models of biological systems.
2. Implement simulations in Python/Mathematica with reproducible workflows.
3. Analyze stability, oscillations, and noise in complex systems.
4. Quantify information processing and robustness in biophysics.
5. Apply computational models to physiological or molecular case studies.
6. Critically evaluate model assumptions and identifiability.
Course Content (Syllabus)
Week 1 – Introduction & Foundations
- What is computational biophysics?
- Physics of living systems: order parameters, noise, function.
- Case study: photon counting in vision.
Week 2 – Probability, Thermodynamics & Statistical Mechanics Refresher
- Ensembles, free energy, fluctuations.
- Noise and robustness in biology.
- Lab: Monte Carlo simulation of the Ising model applied to biological systems.
Week 3 – Deterministic & Stochastic Models
- ODEs, PDEs, stochastic simulation (Gillespie).
- Stability, bifurcations, oscillations.
- Lab: Python simulation of stochastic gene expression.
Week 4 – Biological Circuits I: Feedback & Homeostasis
- Negative/positive feedback, network motifs.
- Case study: glucose–insulin regulation.
- Lab: Phase portraits & nullclines.
Week 5 – Biological Circuits II: Noise and Fragility
- Poisson noise, molecule counting, proofreading.
- Physiological fragility and disease onset.
- Lab: Simulating stochastic bistability.
Week 6 – Spatial & Reaction–Diffusion Models
- Turing patterns, chemotaxis, morphogenesis.
- PDE approaches and lattice models.
- Lab: Reaction–diffusion simulation in Python.
Week 7 – Simulation Methodologies
- Numerical integration of ODEs/PDEs.
- Stiff systems, multiscale modeling.
- Lab: Solver benchmarking & error analysis.
Week 8 – Parameter Estimation & Identifiability
- Structural vs. practical identifiability.
- Bayesian inference and fitting models to data.
- Lab: Parameter fitting for enzyme kinetics.
Week 9 – Monte Carlo & Molecular Dynamics
- Metropolis algorithm, Langevin dynamics.
- Applications: protein folding, ion channels.
- Lab: Simple MD simulation of Lennard-Jones particles.
Week 10 – Information Theory in Biology
- Entropy, mutual information, efficient representation.
- Case study: neural coding.
- Lab: Mutual information from simulated spike trains.
Week 11 – Modeling Aging & Disease
- Saturated repair model of aging.
- Periodic table of diseases.
- Lab: Hazard curves & survival analysis.
Week 12 – Frontiers & Student Presentations
- Machine learning in biophysics.
- Integrating data-driven vs. mechanistic models.
- Final project presentations.