Physics

LORENZO ROVIGATTI

GENERAL OBJECTIVES:
This course is designed as an introduction to computational biology and biophysics. It aims to bridge the gap between institutional learning and active research. The course is structured around three main aspects: i) TOPICS (principles, ideas); ii) METHODS (algorithms and computational techniques); iii) PERSPECTIVES of contemporary computational biology. Extensive reference and critical introductions to literature and current texts will be provided as guides for individual study. Efforts will be made to provide a clear framework of bibliographic references for each topic discussed, aiding in preparation for the final exam. At the end of the course, special guests will present original research lines of interest to students in biosystems, materials physics, and theoretical courses. By successfully completing the course, students will be able to navigate the world of computational biophysics at various scales (from molecules to cells) and master the main computation and analysis algorithms used in the field.

SPECIFIC OBJECTIVES:
A - Knowledge and Understanding
SO 1) Gain a historical-critical perspective of modern computational biology/biophysics
SO 2) Understand the fundamentals of modern evolutionary theory
SO 3) Gain practical experience with data analysis models based on Bayesian inference
SO 4) Gain direct experience with major bioinformatics databases (SwissProt, pFam, PDB,…)

B - Applied Skills
SO 7) Translate at least the main computational biophysics simulation and analysis algorithms into pseudo-code
SO 8) Improve programming skills in scripting languages (Python) or compiled languages (C/C++)
SO 9) Execute a molecular dynamics simulation of a small protein on GROMACS

C - Judgment Autonomy
SO 10) Evaluate the quality of a scientific article

D - Communication Skills
SO 11) Report the results of a research project to the class participants
SO 12) Actively participate in classroom discussions (in Italian and/or English)

E - Learning Skills
SO 13) Acquire fluency in consulting specific databases (e.g., PubMed, Google Scholar) to support/refute a research hypothesis
SO 14) Actively participate in the organization of self-learning groups

Minimum prerequisites:

- Thermodynamics at the undergraduate level in Physics
- Statistical mechanics at the undergraduate level in Physics
- Basic knowledge of at least one programming language (C, C++ or Python)
- Basic knowledge of the Linux terminal

Recommended prerequisites:

- Basic notions of biology and/or biophysics (even at the high school level)
- Good knowledge of a programming language (C, C++ or Python)"

This course offers an interdisciplinary journey through the physical principles underlying biological macromolecules and the computational tools used to study them. Spanning molecular biology, physics, and computer science, the program introduces key concepts in biophysics, molecular structure, and simulation techniques, with an emphasis on proteins and nucleic acids.

1. Introduction to Biophysics

The course begins with a foundational overview of biophysics. We will explore the nature of biological macromolecules and introduce the central dogma of molecular biology—how genetic information flows from DNA to RNA to proteins—and the cellular machinery that supports these processes.

2. Introduction to Computational Physics

To prepare for the computational aspects of the course, we will offer a brief but intensive crash course in Python, the programming language that will be used throughout the course. This section also includes an illustrative example from dynamic programming, providing a first glimpse into algorithmic problem solving in a biological context.

3. Proteins: Structure and Interactions

This section provides a deep dive into proteins, beginning with the chemical properties of amino acids and the interactions that drive protein folding and stability—including van der Waals forces, hydrogen bonds, and electrostatic interactions. We will then examine the hierarchical organization of protein structures: primary, secondary, tertiary, and quaternary.

4. Nucleic Acids: DNA and RNA

We turn next to nucleic acids, focusing on the molecular building blocks—nucleotides—and how they assemble into DNA and RNA strands. We will discuss the principles of hybridization and explore both the secondary and more complex tertiary structures that nucleic acids can adopt.

5. Folding, Design, and Structure Prediction

This central module addresses how proteins and nucleic acids fold into their functional forms, and how we can predict or even design these structures. Topics include thermodynamic and kinetic aspects of folding and unfolding, models such as Zimm-Bragg and Hydrophobic-Polar, and computational techniques like sequence and structure alignment. The module concludes with methods for predicting secondary structures in DNA and RNA.

6. Introduction to Quantum Molecular Mechanics

This lesson introduces quantum-level modeling of molecules. We will cover the basics of density functional theory (DFT) and the Car-Parrinello method, highlighting their applications in understanding the electronic structure of biomolecules.

7. Molecular Dynamics Simulations

This section provides a comprehensive introduction to molecular dynamics (MD), one of the most powerful tools for studying biomolecular systems. We will cover the main simulation algorithms, practical implementation tips, and commonly used observables such as the radial distribution function and pressure. We will also look at the role of all-atom force fields in simulating realistic molecular interactions.

8. Coarse-Grained Models

For systems that are too large or complex for all-atom simulations, coarse-grained models offer a valuable alternative. This section introduces both bottom-up and top-down approaches to coarse-graining, explaining when and how each strategy is used.

9. Enhanced Sampling Techniques

The course concludes with a focus on enhanced sampling techniques, which help overcome the limitations of traditional simulations. We will explore umbrella sampling, thermodynamic and Hamiltonian integration, and metadynamics—methods that allow deeper exploration of energy landscapes and rare events.

- Lehninger et al. (2005): a bible of biochemistry. Very useful as a reference for the basic biochemistry reactions involved in all biological systems.
- Finkelstein & Ptitsyn (2016): protein physics in a nutshell. It is based on a series of lectures that the authors have been delivering for years (if not decades). It is very comprehensive, and uses a informal approach that I find very compelling.
- Leach (2001): principles of molecular modelling, both quantum and classical. Perhaps a bit outdated in some parts, but still a very useful resource for a general introduction to modelling molecular interactions.
- Schlick (2010): also on molecular modelling, but oriented towards nucleic acids and proteins. Very useful as a crash course to DNA, RNA, and proteins, as well as to the way the are modelled with a computer.
- Frenkel & Smit (2023): the bible of molecular dynamics and Monte Carlo simulations. I use it to introduce the Monte Carlo algorithm and the basic molecular dynamics techniques.
- Israelachvili (2011): an incredible (and comprehensive) book on intermolecular forces. For our class, it is especially useful to understand van der Walls and hydrophobic forces
- Giustino (2014) and Böttcher & Herrmann (2021): I did not read them front-to-back, but only used them as sources for the Molecular quantum mechanics chapter.
- Michele Cascella and Raffaello Potestio (2025): An excellent resource on the theoretical foundations of multiscale modelling, with ample discussions on coarse graining procedures.

The complete bibliography can be found in the lecture notes.

There will be 60 hours of frontal lessons

The grade will be assigned through an oral exam. Optionally, students may reduce the program to bring to the oral exam by submitting two exercises during the semester (-30%) and/or a final project (-40%).