Randomness and information in biological data

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

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

Part II: Extracting information from biological data

1. Quantifying randomness in data - Entropy and its interpretation.  Entropy in neuroscience data.
2. Quantifying statistical dependence - Correlation. Mutual information. Coevolution in sequences of interacting proteins.
3. 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.
4. Finding relevant dimensions in data: dimension reduction - Principal component analysis. Introduction to nonlinear methods.