PhD Position F/M Campagne Doctorant: Impact of Qualitative Variations of the Dynamics of Boolean Networks

We propose a PhD in co-supervision

• the Antique INRIA team (INRIA Paris, located at ENS Paris); 
• the MaBioS CNRS research group (I2M, Marseille Institute of Mathematics).

The main goal  is to develop theoretical results on the impact on the dynamics of the Boolean networks when their regulatory functions are gradually replaced with other regulatory functions respecting the same regulatory graph (i.e. complying with the same variable signs). The achieved results should be integrated into an efficient publicly available software. 

The travel expenses of the PhD candidate between both research institutes are covered within the limits of the scale in force.

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CONTEXT

Boolean networks are widely used in the context of Biology to model the behavior of regulatory systems (e.g. gene regulation). A Boolean network is defined as a set of regulatory Boolean functions whose value determines the state of each corresponding variable. Boolean networks are usually abstracted as a regulatory graph, which summarizes the signs of the occurrences of each variable in the regulatory functions of the Boolean network. Fitted with an update policy, a Boolean network induces a transition system. The emergent behaviors of Boolean networks are defined as the terminal strongly connected components of this transition system. They can be either fixed points (when the strongly connected component is made of a single state) or exhibit a periodic behavior (otherwise). Inferring, understanding, and predicting these emergent behaviors is the most important challenge in the Boolean network community.  

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GOAL 

The goal of this PhD is to investigate how the emergent behaviors of a network may be transformed when the regulatory functions defining the network are gradually modified while keeping the same regulatory graph. We will focus on the asynchronous update policy, when the value of only one variable is update at each transition step. 

In the first year, we will set up the formal foundations of the notion of local neighborhood for regulatory functions. 
More precisely, the set of functions will be partially ordered according to the inclusion of their true set. We will study the number of adjacent functions of a given regulatory function and how they are distributed among the many possible sign distributions. 

In the second year, we will study the impact on the behaviors of the Boolean network when some regulatory functions are replaced with adjacent - or close by - functions, respecting the same regulatory graphs. We will study the impact both on the transition systems and on the emergent behaviors (that is to say the terminal strongly connected components). 

In the third year, we will firstly apply these results and produce some static analysis tools to assess common reachability properties over pairs of close Boolean networks, and secondly, we will address the case of a class of stochastic Boolean networks that cope with the intrinsic stochasticity that is observed in biological systems. 

Main activities: 

• Formalize the notion of local transformation of Boolean networks
• Design the formal foundations of the notion 
• Study the impact of local transformation on the emergent behavior of the models 
• Implement these results in a static analysis tool. 

Technical skills and level required :

• A2.2.1 Static Analysis
• A2.4. Formal method for verification, reliability, certification
• A2.4.2. Model-checking
• A6.1.3 Discrete modelling 

Languages :

• English or French 

Relational skills :

• Curious and eager to discover colleagues' research.  
• Generous and happy to explain their results inside and outside the team.

• Subsidized meals
• Partial reimbursement of public transport costs
• Leave: 7 weeks of annual leave + 10 extra days off due to RTT (statutory reduction in working hours) + possibility of exceptional leave (sick children, moving home, etc.)
• Possibility of teleworking
• Flexible organization of working hours (after 12 months of employment)
• Professional equipment available (videoconferencing, loan of computer equipment, etc.)
• Social, cultural and sports events and activities
• Access to vocational training
• Social security coverage

Monthly gross salary : 2100 € during the first and second years. 2190 € the last year.