227-0939-00L  Cell Biophysics

SemesterAutumn Semester 2020
LecturersT. Zambelli
Periodicityyearly recurring course
Language of instructionEnglish


AbstractA mathematical description is derived for a variety of biological phenomena at the molecular and cellular level applying the two fundamental principles of thermodynamics (entropy maximization and Gibbs energy minimization).
ObjectiveEngineering uses the laws of physics to predict the behavior of a system. Biological systems are so diverse and complex prompting the question whether we can apply unifying concepts of theoretical physics coping with the multiplicity of life’s mechanisms.

Objective of this course is to show that biological phenomena despite their variety can be analytically described using only two concepts from statistical mechanics: maximization of the entropy and minimization of the Gibbs free energy.

Starting point of the course is the probability theory, which enables to derive step-by-step the two pillars of statistical mechanics: the maximization of entropy according to the Boltzmann’s law as well as the minimization of the Gibbs free energy. Then, an assortment of biological phenomena at the molecular and cellular level (e.g. cytoskeletal polymerization, action potential, photosynthesis, gene regulation, morphogen patterning) will be examined at the light of these two principles with the aim to derive a quantitative expression describing their behavior according to experimental data.

By the end of the course, students will also learn to critically evaluate the concepts of making an assumption and making an approximation.
Content1. Basics of theory of probability

2. Boltzmann's law

3. Entropy maximization and Gibbs free energy minimization

4. Two-state systems and the MWC model

5. Random walks and macromolecular structures

6. Electrostatics for salty solutions

7. Elasticity: fibers and membranes

8. Diffusion and crowding: cell signaling

9. Molecular motors

10. Action potential: Hodgkin-Huxley model

11. Photosynthesis

12. Gene regulation

13. Development: Turing patterns

14. Sequences and evolution
Literature- Statistical Mechanics: K. Dill, S. Bromberg, Molecular Driving Forces, 2nd Edition, Garland Science, 2010.

- Biophysics: R. Phillips, J. Kondev, J. Theriot, H. Garcia, Physical Biology of the Cell, 2nd Edition, Garland Science, 2012.
Prerequisites / NoticeParticipants need a good command of differentiation and integration of a function with one or more variables (calculus) as well as of Newton's and Coulomb's laws (basics of mechanics and electrostatics). Notions of vectors in 2D and 3D are beneficial.

Theory and corresponding exercises are merged together during the classes.