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Master Bio-informatique | Computational and Mathematical Biology – CMB

RESPONSABLES

AIM

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CMB is an international Master of science dedicated to the analysis and the modelling of complex biological systems, created as a part of the graduate school of the Turing Center of living systems (CENTURI). It is shared by the departments of computer science, mathematics and biology, and aims at gathering students with a high potential coming from different backgrounds and at benefiting from the interdisciplinary synergies between training experts in that scientific area on the rise.

CMB offers a program by and for scientific research, with many opportunities for pursuing studies towards a PhD or obtaining a job in numerous companies having a research department.

The bioinformatics option of the CMB master will focus on the analysis of interaction networks involved in different types of biological processes (embryonic developmental, nervous system, immune response) in order to understand the relationship between network structure and the behaviour of complex biological systems.

LINKS WITH RESEARCH

This Master of science relies on the activities and skills of the laboratories that compose the Turing center of living systems (CENTURI).

RECOMMENDED PREREQUISITES

As this Master is a research-focused study path, a BSc in Life sciences (or related domains) obtained with Honors is required.

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PLAQUETTE DE LA FORMATION

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PROFESSIONAL SKILLS

  • Elaborate mathematical models enabling to simulate the dynamical behaviour of biological networks, to predict the impact of perturbations, and to identify key elements enabling to modify the properties of such systems
  • Apply the classical mathematical modeling approaches (differential equations, Boolean and related, stochastic) to elaborate mathematical models of a biological system.
  • Master the concepts of biology, mathematics and computer sciences required to achieve such models.
  • Estimate the parameters from experimental data, as well as from variable fitting methods.
  • Evaluate the impact of parametric choices on the modelling results.
  • Dispose of a practical experience of collaborative research between laboratories of experimental biology and theoretical biology (bioinformatics, computer sciences, mathematics).

INTERNSHIPS AND SUPERVISED PROJECTS

Group projects and internships in research laboratories will lead students to apply interdisciplinary approaches and interact directly with researchers from the institutes of the Turing Center for Living Systems (CENTURI).

PLAQUETTE DE LA FORMATION

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SPECIFIC TEACHING CONDITIONS

The Master Computational and Mathematical Biology, entirely taught in English, combines theoretical and practical courses of mathematics, computer sciences and biology. It provides an interdisciplinary training oriented towards modelling of complex biological systems.

Master 1 CMB mention Bio-informatique (60 ECTS)

Semestre 1 CMB mention Bio-informatique (30 ECTS)

Fundamentals in biology 1 (3 ECTS)

CONTENT

This course Fundamentals in biology is divided in 2 parts taught during the 1st and 2nd semester of CMB. In the first semester, we will give a presentation of the evolutionary theories that have founded modern biology (from Lamarck to Darwin), and a synthesis of the discoveries that have led to current concepts of molecular and cellular biology : the role of macromolecules in cell function (information transfer between DNA, RNA, proteins, regulation, etc.), heredity and cellular adaptation.

Below are some topics covered during the lectures :

  • Information, evolution causes for living organisms
  • Cellular information
  • Epigenetics – phenomenons, information, adaptation, mechanisms

PDF brochure.

VOLUME OF TEACHINGS

  • Lectures: 18 hours

Professional perspectives for biological systems modelling (3 ECTS)

CONTENT

The teaching unit consists of a presentation of the main professions involved in biological modelling. It will be carried out in two ways. First of all, some seminars will be offered with speakers from outside Aix-Marseille University in the academic and industrial field. Secondly, students will benefit from an immersion in Centuri laboratories where they will discover multidisciplinary research topics. To conclude this unit, students will be asked to present a specific problem related to data processing and modelling. The scientific aspect will also have to be integrated into a reflection on the underlying professional issues, whether in the academic or private sector.

PDF brochure.

VOLUME OF TEACHINGS

  • Tutorials: 18 hours

Genomics (3 ECTS)

CONTENT

Genomics is an interdisciplinary field of modern biology studying the full genetic complement (the genome) of an organism. With nearly 3,500 genomes now sequenced, the post-genomic era has considerably improved our knowledge of the origin of diversity and evolution of genomes, cellular pathways, organismal phenotypes and human diseases. The course will be split into three main topics of a teaching course followed by a practical informatics-oriented course designed to cover the methods of genome analysis, the evolution of eukaryotic genomes, the power of comparative genomics to understand gene regulation and will finish by exploring how genomics gives rise to epigenomics and how both allow our understanding of gene regulation and its dysfunction in the development of human diseases.

PDF brochure.

VOLUME OF TEACHINGS

  • Lectures: 9 hours
  • Pratical works: 9 hours

Discrete modelling of dynamical biological systems 1 (3 ECTS)

CONTENT

This course is an introduction to the basics of finite dynamic systems and PLC networks (definitions of local functions, global function/relationship, automata, interaction graph, transition graph) as well as the main static and dynamic properties. A part of the lecture will also focus on the parallel update mode.

The lectures should provide students the skills to implement modelling approaches (differential, logical, stochastic or deterministic equations) to develop mathematical models of a biological system, analyze mathematical models and biological data to understand complex systems, evaluate the adequacy between a biological question, available data, and mathematical formalisms and interpret and validate a study.

PDF brochure.

VOLUME OF TEACHINGS

  • Lectures: 6 hours
  • Tutorials: 6 hours
  • Pratical works: 6 hours

Programming & Algorithms (6 ECTS)

CONTENT

3 parts : 1) Unix : - file system and basic shell commands - text utilities - redirections, pipe 2) Programming language (Python) : - basic principles of imperative programming : variable, type, assignment, operators - control flow (conditional, iterations, loops) - basic data structures : tuple, list, dict - files (text, input/output) - local and external modules : math, random, numpy, scipy, matplotlib, pandas - functions 3) Algorithms : arrays, sorting, lists, stacks, queues

PDF brochure.

VOLUME OF TEACHINGS

  • Lectures: 12 hours
  • Tutorials: 12 hours
  • Pratical works: 12 hours

Computational Biology (3 ECTS)

CONTENT

Computational biology will introduce the biological concepts necessary to model complex systems, implement modelling approaches (differential, logical, stochastic or deterministic equations) to develop mathematical models of a biological system, analyze mathematical models and biological data to understand complex systems and assess the adequacy between a biological question.

The course is divided in 2 sections :

  • computational neuroscience : dynamic models of neuron function : dynamic behavioural simulation, biological aspects, computer complexity, analytical aspects
  • bioinformatics : alignment, molecular phylogeny, prediction and modelling of structural aspects of proteins, cis-regulation

PDF brochure.

VOLUME OF TEACHINGS

  • Lectures: 14 hours
  • Pratical works: 16 hours

Mathematics for modelling (6 ECTS)

Probabilities and statistics for modelling 1

CONTENT

This course is a quick revision of the basics of probability and statistics. The concepts will be taught in relation to concrete biology exemples (genome analysis, complex systems). The following concepts will be taught :

  • Combinatorial analysis
  • Probabilities concepts
  • Discrete distributions (Bernouilli, binomial, geometric, hypergeometric, Poisson)
  • Quick review of the basic continuous laws (normal and Student’s distribution)
  • Estimation and sampling
  • Statistical hypothesis tests

Some biological examples of applications could concern the probability of patterns in genomic sequences, the detection of differentially expressed genes.

PDF brochure.

VOLUME OF TEACHINGS

  • Lectures: 6 hours
  • Tutorials: 6 hours
  • Pratical works: 6 hours

Continuous dynamical systems and modelling : examples

CONTENT

The purpose of this course is to introduce some of the simplest differential equations and systems of differential equations which underlie the main continuous models used in biology (dynamics of populations or cells, biochemical processes, etc.). We will address both qualitative (long-time behavior) and quantitative (positivity, parameter dependency) properties of the considered models. In parallel to this theoretical study, numerical simulations will be performed during the computer sessions. Practicals will consist in using Python specialised libraries as scipy.integrate in order to visualise trajectories and systems behaviours.

PDF brochure.

VOLUME OF TEACHINGS

  • Lectures: 6 hours
  • Tutorials: 6 hours
  • Pratical works: 6 hours

Basics in algebra and analysis (3 ECTS)

CONTENT

This course will give a review of some basic notions of algebra and analysis. Illustrations in Python will be given. We will focus on the matrix tools necessary for regression :

  • Matrix calculation : matrix multiplication, matrix transposition
  • Determinant calculation with Python, matrix inverse with Python, linear system with Python
  • Calculation of eigenvalues/eigenvectors with Python
  • Function representation
  • Linear regression

PDF brochure.

VOLUME OF TEACHINGS

  • Lectures: 6 hours
  • Tutorials: 6 hours
  • Pratical works: 6 hours

Semestre 2 CMB mention Bio-informatique (30 ECTS)

Analysis of Omics Data (6 ECTS)

Bioinformatics Analysis of Omics Data

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VOLUME OF TEACHINGS

  • Tutorials: 15 hours
  • Pratical works: 15 hours

Statistical Analysis of Omics Data

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VOLUME OF TEACHINGS

  • Lectures: 10 hours
  • Pratical works: 20 hours

Fundamentals of biology 2 (4 ECTS)

CONTENT

The course is in conitnuity with the course Fundamentals of biology 1. This module will show how these molecular mechanisms underlie the development and functioning of tissues and organisms. It will be structured around four areas :

  • intergenerational transmission of traits ;
  • Organism development ;
  • immune system ;
  • Nervous system

Some examples topics covered during the lectures :

  • Information and organization : intergenerational transmission (cells, organisms Information, evolution causes for living organisms)
  • Organisms’ development
  • Information and organization of the immune system
  • Information and organization of the nervous system

PDF brochure.

VOLUME OF TEACHINGS

  • Lectures: 12 hours
  • Tutorials: 12 hours

Statistical and computational tools for biological modelling (6 ECTS)

Graph theory and algorithms 1

CONTENT

This introductory course focuses on graphs as mathematical objects and some of its uses to solve applications to biological networks. After intruducing different classes of graphs and their properties, the following points will be developped :

  • Planar graphs, graphs on a surface, Euler characteristic
  • Interval graphs, perfect graphs

PDF brochure.

VOLUME OF TEACHINGS

  • Lectures: 6 hours
  • Tutorials: 6 hours
  • Pratical works: 6 hours

Statistics for biology

CONTENT

This course aims at providing students with a practical approach of the analysis of biological data with R, based on the concepts acquired in the course “Probabilities and statistics for modelling 1”. The associated mathematical foundations will be developed in the course “Advanced statistics”. The following notions will be investigated :

  • Sampling and estimation (moments, robust estimators, confidence intervals)
  • Fitting
  • Additional distributions
  • Hypothesis testing (mean comparison, goodness of fit, …)

PDF brochure.

VOLUME OF TEACHINGS

  • Lectures: 6 hours
  • Tutorials: 6 hours
  • Pratical works: 6 hours

Advanced statistics (3 ECTS)

CONTENT

This course will tackle advanced notions in statistics such as :

  • Statistical inference (fundamental concepts, estimators, intervals and tests, quadratic error, bias and variance)confidence
  • Likelihood (Fisher information, likelihood ratio test)
  • Exponential family
  • Convergence
  • Multivariate Gaussian distributions

PDF brochure.

VOLUME OF TEACHINGS

  • Lectures: 6 hours
  • Tutorials: 6 hours
  • Pratical works: 6 hours

Probability and statistics for modelling 2 (3 ECTS)

CONTENT

This course is addressed to students with a background in biology, and aims at enforcing the theoretical grounds in order to allow them to apprehend advanced statistics. The following concepts will be investigated :

  • Numerical sequences and series (limits, convergence)
  • Continuous laws of probabilities (normal, Student, chi2, Snedecor distribution).
  • Introduction to the different notions of convergences in probabilities and Relationships between the different laws (convergence between laws).
  • Law of large number and Central limit theorem

PDF brochure.

VOLUME OF TEACHINGS

  • Lectures: 6 hours
  • Tutorials: 6 hours
  • Pratical works: 6 hours

Research project and scientific communication (6 ECTS)

CONTENT

At the end of the courses Professional perspectives for biological systems modelling , and Fundamentals of biology 1,, students will choose a scientific article at the interface of several disciplines on which they will work in groups. They will have to present in a memory and an oral presentation, to explain the biological context and the related basic concepts, to explain the methods used to interpret the biological data, to synthesize the results obtained in the article.

PDF brochure.

CenTuri Seminars (2 ECTS)

CONTENT

Scientific seminars constitute a good way to broaden your scientific horizon. In this regard, MSc students will frequently attend CENTURI seminars. At the end of the semester, students will be asked to write a summary of two seminars they have attended.

PDF brochure.

VOLUME OF TEACHINGS

  • Lectures: 12 hours

Master 2 CMB mention Bio-informatique (60 ECTS)

Semestre 3 CMB mention Bio-informatique (30 ECTS)

Biological interaction networks (3 ECTS)

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VOLUME OF TEACHINGS

  • Lectures: 10 hours
  • Tutorials: 8 hours
  • Pratical works: 12 hours

Advanced Biology : Developmental Biology (3 ECTS)

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VOLUME OF TEACHINGS

  • Lectures: 6 hours
  • Tutorials: 6 hours
  • Pratical works: 6 hours

Advanced Biology : Immunology (3 ECTS)

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VOLUME OF TEACHINGS

  • Lectures: 6 hours
  • Tutorials: 6 hours
  • Pratical works: 6 hours

Advanced biology : Neurobiology (3 ECTS)

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VOLUME OF TEACHINGS

  • Lectures: 6 hours
  • Tutorials: 6 hours
  • Pratical works: 6 hours

Biological databases (3 ECTS)

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VOLUME OF TEACHINGS

  • Lectures: 6 hours
  • Tutorials: 6 hours
  • Pratical works: 6 hours

Statistical inference and big data in biology (3 ECTS)

CONTENT

This course is an introduction to inferential statistics. It will be illustrated with biogical examples. The course will be composed by three parts

  • Multiple tests
  • Classification
  • Time series analysis

PDF brochure.

VOLUME OF TEACHINGS

  • Lectures: 6 hours
  • Tutorials: 6 hours
  • Pratical works: 6 hours

Applications of mathematical modelling (3 ECTS)

CONTENT

This course will propose some illustrations of the concepts and results of mathematical modelling to biological systems, with a specific focus on the domains of interest to CenTuri (immunology, developmental biology, neurology).

Practicals will consist in a personal project that may consist in extending one of the examples seen in the courses.

PDF brochure.

VOLUME OF TEACHINGS

  • Lectures: 6 hours
  • Tutorials: 6 hours
  • Pratical works: 6 hours

Interdisciplinary project in modelling (6 ECTS)

CONTENT

Following the module Research project and scientific communication, the students will do a short internship in laboratory. They will have to propose a modelling or data processing problem at the math-info-bio interface. They will be asked to synthesize their results in a dissertation and an oral presentation.

PDF brochure.

CenTuri Seminars 3 (3 ECTS)

CONTENT

Following the module Centuri seminars 2, the students will attend all the Centuri seminars of this semester. For two of them, they will be asked to broaden their knowledges on the subject and present an oral and written synthese. The work will be done in collaboration.

PDF brochure.

VOLUME OF TEACHINGS

  • Lectures: 10 hours
  • Tutorials: 10 hours
  • Pratical works: 10 hours

Semestre 4 CMB Computational and Mathematical Biology (30 ECTS)

Master thesis (30 ECTS)

CONTENT

Internship in research laboratories or in companies.

PDF brochure.

FURTHER INFORMATION

Secretariat :

  • Sonia KERBACHE (sonia.kerbache@univ-amu.fr), tél. : 04 91 82 90 80, Aix-Marseille Université, Campus Luminy. Bâtiment TPR2 ET GRAND H. 163 av. de Luminy. case 901. 13009 Marseille.

HOW TO APPLY AND REGISTER

https://formations.univ-amu.fr/xml/PRSBI5AA-en.xml