TrainingsMasterBio-informatiqueComputational and Mathematical Biology – CMB

Master Bio-informatiqueComputational and Mathematical Biology – CMB

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 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.

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).

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 Semestre 1 CMB mention Bio-informatique

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  • Fundamentals in biology 1 (3 ECTS)

    Code: S40BI1Z1

    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

    Hourly volume : 18 hours.

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  • Professional perspectives for biological systems modelling (3 ECTS)

    Code: S40BI1Z2

    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.

    Hourly volume : 18 hours.

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  • Genomics (3 ECTS)

    Code: S40BI1Z3

    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.

    Hourly volume : 18 hours.

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  • Discrete modelling of dynamical biological systems 1 (3 ECTS)

    Code: S51IN1Z1

    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.

    Hourly volume : 18 hours.

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  • Programming & Algorithms (6 ECTS)

    Code: S51IN1Z2

    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

    Hourly volume : 36 hours.

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  • Computational Biology (3 ECTS)

    Code: S51IN1Z4

    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

    Hourly volume : 30 hours.

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  • Mathematics for modelling (6 ECTS)
    • Probabilities and statistics for modelling 1

      Code: S53MA1Z1A

      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.

      Hourly volume : 18 hours.

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    • Continuous dynamical systems and modelling : examples

      Code: S54MA1Z1B

      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.

      Hourly volume : 18 hours.

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  • Basics in algebra and analysis (3 ECTS)

    Code: S54MA1Z5B

    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

    Hourly volume : 18 hours.

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Master 1 CMB mention Bio-informatique Semestre 2 CMB mention Bio-informatique

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  • Analysis of Omics Data (6 ECTS)
  • Fundamentals of biology 2 (4 ECTS)

    Code: S40BI2Z1

    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

    Hourly volume : 24 hours.

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  • Statistical and computational tools for biological modelling (6 ECTS)
    • Graph theory and algorithms 1

      Code: S51IN2Z2A

      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

      Hourly volume : 18 hours.

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    • Statistics for biology

      Code: S53MA2Z2B

      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,…)

      Hourly volume : 18 hours.

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  • Advanced statistics (3 ECTS)

    Code: S53MA2Z1

    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

    Hourly volume : 18 hours.

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  • Probability and statistics for modelling 2 (3 ECTS)

    Code: S53MA2Z2

    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

    Hourly volume : 18 hours.

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  • Research project and scientific communication (6 ECTS)

    Code: S99XX2Z1

    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.

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  • CenTuri Seminars (2 ECTS)

    Code: S99XX2Z2

    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.

    Hourly volume : 12 hours.

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Master 2 CMB mention Bio-informatique Semestre 3 CMB mention Bio-informatique

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  • Biological interaction networks (3 ECTS)

    Code: S40BI3D7

    Content : unavailable.

    Hourly volume : 30 hours.

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  • Advanced Biology : Developmental Biology (3 ECTS)

    Code: S40BI3Z2A

    Content : unavailable.

    Hourly volume : 18 hours.

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  • Advanced Biology : Immunology (3 ECTS)

    Code: S40BI3Z2B

    Content : unavailable.

    Hourly volume : 18 hours.

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  • Advanced biology : Neurobiology (3 ECTS)

    Code: S40BI3Z4

    Content : unavailable.

    Hourly volume : 18 hours.

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  • Biological databases (3 ECTS)

    Code: S51IN3Z1

    Content : unavailable.

    Hourly volume : 18 hours.

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  • Statistical inference and big data in biology (3 ECTS)

    Code: S53MA3Z1

    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

    Hourly volume : 18 hours.

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  • Applications of mathematical modelling (3 ECTS)

    Code: S54MA3Z1

    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.

    Hourly volume : 18 hours.

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  • Interdisciplinary project in modelling (6 ECTS)

    Code: S99XX3Z1

    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.

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  • CenTuri Seminars 3 (3 ECTS)

    Code: S99XX4Z1

    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.

    Hourly volume : 30 hours.

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Master 2 CMB mention Bio-informatique Semestre 4 CMB Computational and Mathematical Biology

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Further information

Secrétariat pédagogique :

  • Sonia KERBACHE (sonia.kerbache@univ-amu.fr), tél. : +33(0)4 13 94 19 99, Aix-Marseille Université, Campus Luminy, Bâtiment TPR1, 163 av. de Luminy, case 901, 13009 Marseille.