This course will cover concepts of theoretical biophysics and introduce mathematical and numerical methods to solve problems in quantitative biology. In particular, we will focus on polymer physics, membranes, diffusion, electrostatic interactions, and self-organization within cells.

During the course, the students will learn techniques of quantitative reasoning such as dimensional analysis and methods for approximate analytic solutions of difficult mathematical problems (dominant balance, saddle point approximations, integral transforms, iteration techniques, etc). Problems will be tackled both analytically to understand the qualitative behavior of a system and numerical to obtain quantitative predictions.

### Syllabus

- The relevant scales and dimensions of biophysics
- Diffusion and Stokes-Einstein relation
- Elements of polymer physics
- Membranes
- Reaction rates
- Pattern formation and reaction diffusion systems
- Liquid-liquid phase transitions in cell biology

#### Literature

- The physical biology of the Cell by Rob Phillips et al
- Cell biology by the numbers by Rob Phillips and Ron Milo
- Physical Mathematics by Michael Brenner

### Lectures

- 2018-09-20 -- The relevant scales: sizes, energies, concentrations
- 2018-09-27 -- Brownian motion, diffusion, and Fick's law
- 2018-10-04 -- Diffusion coefficients and the Stokes-Einstein relation
- 2018-10-11 -- Elements of polymer physics
- 2018-10-18 -- Transcription factor search problems and polymers under force
- 2018-10-25 -- Bacterial gene regulation and signaling
- 2018-11-01 -- Elements of dynamical systems
- 2018-11-08 -- no lecture
- 2018-11-12 -- Tutorial session. Biozentrum room 612. 13-15h. Hand-written notes
- 2018-11-15 -- Linear stability analysis and oscillations
- 2018-11-22 -- Reaction rates
- 2018-11-29 -- Kinetic proofreading and percolation transitions
- 2018-12-06 -- Phase transitions in cell biology
- 2018-12-13 -- Chromosome organization and nucleosome positioning
- 2018-12-20 -- Bethedging and proportional betting