**Modeling, fitting and controlling biological systems: the toggle switch example**

**Gregory Batt**

*INRIA, Paris*

In this course, our ambition is to demonstrate on a simple but realistic problem the model-based approach employed in quantitative biology. As a running example, we will use the toggle switch, a synthetic genetic network built in *E. coli*. It is one of the most extensively-studied system. Yet interesting quantitative questions are still open.

- In the first practical session, we will draft an ordinary differential equation model of the system, find realistic values for the parameters and analyze its behavior using numerical simulation.
- In the second practical session, we will consider (simulated) noisy experimental data and use optimization tools to fit the model to the data.
- In the last practical session, we will extend our model with inducers and solve
*in silico*simple control problems.

**Important note:** We will use **Matlab** for all computations. Therefore, it is expected that participants will come with the installed program. No toolboxes are needed. Student versions are available at 35€. If you encounter any issues with this matter, please contact me (gregory.batt@inria.fr) and we will find a solution.

**Modeling gene expression: stochasticity and spatial dynamics**

**Hugues Berry **&** François Nédelec**

*INRIA, Lyon & EMBL, Heidelberg*

This hands-on session is an introduction to the modeling of the dynamics of stochastic gene expression. As a toy model, the linear « central dogma » model will be considered (one gene->one mRNA->one protein). After a brief overview of the theoretical analysis of this system (mass action laws, methods of moments), we will simulate the stochastic dynamics of the system using Gillespie’s algorithm, that accounts for stochasticity due to low copy numbers. In a second stage, we will simulate spatially explicit dynamics using Individual-based modeling, that also accounts for diffusion-based stochasticity and is expected to converge to Gillespie’s simulations only for infinite diffusion coefficients (in three dimensions). All programming will be done in **Scilab**, but note that for time constraints reason, the organisers will provide most of the necessary code.

**Towards integrated models of cellular processes: metabolism, gene expression, signaling**

**Hidde de Jong**

*INRIA, Grenoble*

We will discuss what are integrated models of the cell and why they are necessary.

We will review three approaches that have been used to construct integrated models of the cell:

- flux balance models,
- kinetic models,
- resource allocation models.

We will finish with open questions and perspectives.

**Qualitative dynamical modeling of cellular networks**

**Denis Thieffry**

*Ecole Normale Supérieure, Paris*

This course will introduce the Boolean and multilevel logical formalism, along with different formal methods enabling the modeling of rather large signaling/regulatory networks.

- The first class will be devoted to an overview of the basics of the logical framework, along with a presentation of the main variations regarding model definition and updating policies.
- The second class will be devoted to handling the software
**GINsim**(version 2.9.3, to be downloaded from http://ginsim.org) to define and analyze a relatively simple model. Note that to run GINsim on your laptop, you need a recent version of the Java Virtual Machine (1.6 or 1.7). - The third and last class will be devoted to the handling of a more complex model, and to the use of advanced algorithms enabling the simulation of large networks (computation of stable states, model reduction, state transition graph compression).

Students should read the **GINsim tutorial** and at least one of the articles listed below before the class:

- Fauré A, Naldi A, Chaouiya C, Thieffry D (2006). Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle. Bioinformatics 22: e124-31.
- Bérenguier D, Chaouiya C, Monteiro PT, Naldi A, Remy E, Thieffry D, Tichit L (2013). Dynamical modeling and analysis of large cellular regulatory networks. Chaos 23: 025114.
- Grieco L, Calzone L, Bernard-Pierrot I, Radvanyi F, Kahn-Perlès B, Thieffry D (2013). Integrative modelling of the influence of MAPK network on cancer cell fate decision. PLoS Computational Biology 9: e1003286.
- Abou-Jaoudé W, Monteiro PT, Naldi A, Grandclaudon M, Soumelis V, Chaouiya C, Thieffry D (2015). Model checking to assess T-helper cell plasticity. Frontiers in Bioengineering and Biotechnology 2: 86.