# Randomness and information in biological data

## Summary

Biology is becoming more and more a data science, as illustrated by the explosion of available genome sequences. This course aims to show how we can make sense of such data and harness it in order to understand biological processes in a quantitative way.

## Content

Recently, biology has become more and more a data science. For instance, progress in sequencing has caused an explosion of available genome sequences. How can we make sense of such data and harness it in order to understand biological processes in a quantitative way? In many cases, biological data can be understood as being sampled from distributions of random variables. This course will first show the importance of randomness in biology. Then it will introduce some ways of extracting information from biological data, of assessing models and of approximately inferring the probability distributions underlying biological data. Some notions of statistics, information theory and statistical physics will be introduced, always with concrete applications to biological data in mind. Problems and numerical projects will allow students to apply the methods to real biological data. The course will be organized as follows:

**Part I: Randomness in biological processes and biological data **

- Randomness and random variables - Medical testing. Luria-Delbrück experiment.
- Importance of thermal fluctuations at the cellular scale - Chemical bonds, biopolymers, biomembranes.
- Random walks - Protein abundances in single cells. Population genetics. Other examples.

**Part II: Extracting information from biological data**

- Quantifying randomness in data - Entropy and its interpretation. Entropy in neuroscience data.
- Quantifying statistical dependence - Correlation. Mutual information. Coevolution in sequences of interacting proteins.
- Inferring probability distributions from data - Maximum likelihood, model selection and parameter estimation. Introduction to maximum entropy inference. Prediction of protein structure from multiple sequence alignments.
- Finding relevant dimensions in data: dimension reduction - Principal component analysis. Introduction to nonlinear methods.

## Keywords

Biological data, data science, sequencing data, neuroscience, population genetics, random variable, random walk, information theory, statistical physics, entropy, mutual information, inference, dimensionality reduction.

## Learning Prerequisites

## Required courses

Analysis; probability and statistics; linear algebra; general physics; programming.

## Recommended courses

Introductory machine learning.

## Learning Outcomes

By the end of the course, the student must be able to:

- Manipulate notions of statistics, information theory and statistical physics.
- Apply these notions to biological data.
- Analyze biological data in a quantitative way.
- Perform data analysis in Python.

## Teaching methods

Lectures, exercises, programming labs.

## Assessment methods

Written final exam during the exam session, graded numerical mini-project.

## Resources

## Bibliography

**Reference textbooks:**

- P. Nelson, Physical Modeling of Living Systems, WH Freeman, 2014
- D. MacKay, Information Theory, Inference, and Learning Algorithms, Cambridge University Press, 2003

**More advanced textbooks:**

- W. Bialek, Biophysics: Searching for Principles, Princeton University Press, 2012
- T. Cover and J. Thomas, Elements of Information Theory, 2nd ed, Wiley Interscience, 2006
- S. Cocco, R. Monasson and F. Zamponi, From statistical physics to data-driven modelling, Oxford University Press, 2022

## Ressources en bibliothèque

- P. Nelson, Physical Modeling of Living Systems, WH Freeman
- T. Cover and J. Thomas, Elements of Information Theory, 2nd ed, Wiley Interscience, 2006
- D. MacKay, Information Theory, Inference, and Learning Algorithms, Cambridge University Press, 2003

## Moodle Link

## In the programs

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Randomness and information in biological data**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Randomness and information in biological data**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Randomness and information in biological data**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Randomness and information in biological data**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Randomness and information in biological data**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Randomness and information in biological data**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks