Blackboard & Practicals
Details on the hands-on and practical sessions will be given later.
Didier Gonze, Deterministic and stochastic modeling of circadian clocks
Circadian rhythms are generated at the cellular level by a gene regulatory network (GRN) involving interlocked feedback loops. This GRN can produce self-sustained oscillations with a period close to 24h, that can be entrained by light-dark cycles and are robust to molecular noise. In these practicals we will see (1) how to build and parameterize a mathematical model for this GRN, (2) how to simulate the model (numerical integration) and to predict the effect of mutations on the oscillatory dynamics (bifurcation analyses), (3) how to simulate the effect of light and to study entrainment under light-dark cycle or the response to jet lags, and (4) how to study the robustness of the oscillations with respect to molecular noise (stochastic simulations).
Hidde de Jong, Dynamical models integrating metabolism and gene expression.
We will step-by-step build quantitative ODE models of a metabolic network integrating regulation on both the metabolic and gene expression level, and investigate the effect of these layers of regulation on the networks dynamics. The course will be structured around the case of carbon catabolite repression in bacteria, using simple kinetic models. All simulations will be carried out by means of Matlab (no toolboxes needed) or Octave the free version of Matlab. The hand-out and the models and simulation code will be available from the instructor.
Ref: Kremling A, Geiselmann J, Ropers D, de Jong H (2015). Understanding carbon catabolite repression in Escherichia coli using quantitative models. Trends Microbiol., 23:99-109
Wolfram Liebermeister & Hugo Dourado, Optimal allocation of enzyme resources in cells & Introduction to Growth Balance Analysis
In this blackboard course, in a first session, students will learn about an economic aspect of microbial metabolism: the protein cost associated with metabolic fluxes. By considering a partitioning of protein resources between ribosomes and metabolic enzymes, enzyme demands in metabolism can be translated into predicted cell growth rates. We will discuss how the demand for metabolic enzymes can be computed from metabolic models based on resource allocation principles, and we’ll use this approach to estimate growth rates and proteomic fractions of ribosomes and metabolic enzymes in cells. We will finally discuss a direct connection between optimal enzyme levels and the flux control that these enzymes exert in the cell, which directly links the material cost and the functional benefit of an enzyme.
In a second session, we will introduce Growth Balance Analysis (GBA) as a simplified mathematical framework to model and analyze nonlinear models of entire self-replicating systems built on first physical principles. We show how a reformulation of the mathematical problem on independent variables allows us to derive fundamental analytical principles for all growing cells at balanced growth, capturing the global trade-offs in the cell resource allocation that extend previous results on the optimal microbial metabolism. This session requires only basic understanding of partial derivatives, and it is mainly focused on the general ideas behind its few mathematical derivations.
François Nedelec, Cytoskeleton simulations
During the practical session, participants will simulate a simple system with filaments and molecular motors using Cytosim. After a brief introduction to the topic and the underlying methods used to solve stochastic bio-mechanics, participants will install Cytosim on their laptops. Several simple systems will be provided, each designed to run quickly on a laptop, and one system will be selected for further investigation. Participants will learn to use Python scripts to easily modify model parameters and generate graphs, enabling them to characterize the system’s collective behavior across a range of parameters.
Anna Niarakis, Large scale biochemical networks and Boolean dynamics for modelling disease
During the session, the students will learn about network representations, basic concepts of graph theory, network topology, and relevant analyses, boolean dynamics, in silico simulations and perturbation analyses. Basics in Python or R are required. More precisely the two sessions will cover: (1) Static Disease Networks (molecular maps, pathway assembly, structural analysis etc.) with an overview of databases/ resources, of the different network representations using systems biology graphical notation (SBGN) languages (Process Description, Activity Flow) and of interactive network visualization and topological analysis ; (2) Dynamic Disease Networks (Logical (Boolean)/ Discrete Models) with an overview of network & model curation, of disease Boolean networks and of the logical/discrete modeling and simulation of disease networks and analysis of their dynamical properties.
Magali Richard & Franck Picard, Statistical analysis of single cell data
Single-cell sequencing technologies now enable the creation of high-dimensional molecular portraits of cell populations based on gene expression, chromatin states, and genomic variations. These advances have led to the generation of complex, high-dimensional data and have revolutionized our understanding of the complexity of living tissues in both normal and pathological states. Consequently, the field of single-cell data science has emerged, bringing with it new methodological challenges to fully harness the potential of single-cell data. In this session, we will focus on perturbation single-cell experiments, which enable comparisons between perturbed and non-perturbed tissues at the cellular level, allowing for the assessment of population heterogeneities at different scales. In particular, we will explore the methodological challenges of perturbation analysis and present alternative perspectives for analyzing such data, drawing on both machine learning and statistical approaches. We will illustrate this framework using scRNASeq data, with applications ranging from cancer biology to vaccine trials.
Cédric Vaillant & Daniel Jost, Multi-scale modeling of chromatin
All cells of an organism contain the same genetic information encoded in DNA but may have very different shapes or functions depending on their cell-types or on the environments. These differences reflect variations in gene expression between cell types. At the gene level, DNA is wrapped around proteins called histones and the macromolecular complex formed by DNA and histones is called chromatin. The control of gene expression is partly encoded by biochemical modifications of histones, the so-called epigenomic marks, or of DNA itself ; and how these marks organize in the 3D space of the nucleus. In this session, we will develop step-by-step how to build and simulate a mathematical stochastic model of chromatin regulation. In particular, we will cover how the 3D spatial organization of chromatin may impact chromatin and gene regulation.
All simulations will be carried out with Python. The hand-out and the models and simulation code will be available from the instructor.
Andrea Weisse, Modeling adaptative cellular growth
The first of the two sessions will cover basics of reaction kinetics and then build on those to see how one can build more complex models of cellular growth and their applications. The second session will be more hands-on. Students will build and simulate their own model of cellular growth. They will think about what modification might make the simulated cell ‘fitter’ than others. We aim to end the session running in silico competitions between the different student cells.
