# Theoretical Biophysics

## Venue:

Lectures will be given online. Link to the online lectures will be published on my homepage.

## Prerequisits:

As always, some assumptions need to be made. Here it is assumed that there is:

- a basic knowledge of statistical physics and
- some programming experience to understand the methods and algorithms.

## Abstract:

The emergence of new cross-disciplinary fields is one of the major driving forces in science and technology. Among the most important of these emerging fields are those which connect the life sciences with physics. Due to the vast amount of data that is now available there is the possibility to understand living organisms as complex dynamic systems. Biological processes occur on a wide range of spatial and temporal scales. The time scales of biological function range from very fast femtosecond molecular motions, to multi-second protein folding pathways, to cell cycle and development processes that take place over the order of minutes, hours and days. Similarly, the dimensions of biological interest range from small organic molecules to multi-protein complexes, to cellular processes, to tissues, to the interaction of human populations with the environment. Thus one needs to understand how on the smallest scale conformational changes of molecules plus their interaction give rise to collective phenomena.

## Learning Outcomes

- Have an understanding of the basic mathematical concepts that describe the probabilities of biophysical observables.
- Ability to apply numerical methods to complex biophysical problems.
- Construct, solve (either analytically or numerically), and interpret the results of a stochastic, dynamical models.
- Understand the role entropy in the functioning of biological systems.

## Literature

The lectures do not lean heavily on a specific textbook. Resources from the literature
will be introduced as needed in the downloadable material. Howwever, A small part of the lectures is based on

Theoretical Molecular
Biophysics Series: Biological and MedicalPhysics, Biomedical Engineering

Scherer, Philipp, Fischer, Sighart F.

1st Edition., 2010, XIII, 371 p. 250 illus., 3 in color., Hardcover ISBN: 978-3-540-85609-2

## Problem Sets

Collaboration on the sets is encouraged.

## Grading

- The course grade will be determined by an oral exam.
- Solutions to the problem sets are not required.

## Lecture notes:

- Introduction
- Methods
- Diffusion and Transport
- Reaction-diffusion
- Phase Transitions (updated)
- Growth, Aggregation and Deposition
- Pattern and Structure Formation
- Static and Temporal Networks
- RNA, Protein and DNA
- Membranes
- Learning

## Additional Literature

- Deep Learning: Ian Goodfellow, Yoshua Bengio and Aaron Courville
- Deep Learning Methods and Applications: Li Deng and Dong Yu
- A Brief Introduction to Neural Networks: David Kriesel
- Neural Networks and Deep Learning: Michael Nielsen
- Neural Networks & Learning Machines: Simon Haykin
- Machine Learning, Neural, & Statistical Classification: D. Michie, D.J. Spiegelhalter, C.C. Taylor
- An introduction to the Ginzburg-Landau theory of phase transitions and nonequilibrium patterns
- Fractals and Cancer
- Lung cancerâ€”a fractal viewpoint
- Fatalness of virus depends upon its cell fractal geometry
- The fractal time growth of COVID-19 pandemic: an accurate self-similar model, and urgent conclusions
- Fractal coastline
- Deep Learning Super-Diffusion in Multiplex Networks

## Side Remarks

- Newton vs the machine: solving the chaotic three-body problem using deep neural networks
- Equivalence of Cellular Automata to Ising Models and Directed Percolation
- C. M. Fortuin and P. W. Kasteleyn, Physica 57, 536 13 (1972)

## Provisional Schedule:

- Week 1
- General Introduction
- Methods
- Molecular Dynamics

- Week 2
- Methods (cont'd)
- Monte Carlo Methods

- Methods (cont'd)
- Week 3
- Diffusion
- Transport

- Week 4
- Reaction-Diffusion
- Cellular Automata

- Week 5
- Phase Transitions
- (public holiday)

- Week 6
- Phase Transitions (cont'd)
- Growth Models

- Week 7
- Growth Models (cont'd)
- Recap

- Week 8
- Pattern and Structure Formation
- (public holiday)

- Week 9
- Pattern and Structure Formation (cont'd)

- Week 10
- Static Networks
- Temporal Networks

- Week 11
- RNA, Proteins and DNA

- Week 12
- Membranes

- Week 13
- Learning

- Week 14
- Learning (cont'd)