My research in the last decade has focused on Non-equilibrium statistical Physics and on its applications to biophysics. I have made a number of contributions to the field of Stochastic Thermodynamics, a new branch of Thermodynamics, which blends together stochastic dynamics, information theory and thermodynamics. At the moment, I am mainly active in research on molecular systems and on the origin of life. Previously, I have been working in the field of soft-matter and biophysics, where I have been working on the dynamics of biofilaments and biological membranes driven out of equilibrium by active forces.

1. Stochastic thermodynamics

It is a general rule that as a system gets smaller its fluctuations increase. As a consequence, in small systems (like a colloidal particle or an enzyme), thermodynamic quantities like work or heat are only defined in a statistical sense. Exact relations between the statistical distributions of these thermodynamic quantities, known as fluctuations relations, have been obtained at the end of the nineties. Such ideas have lead to the emergence of a new field, concerned by the specificity of thermodynamics for small systems and which has been called stochastic thermodynamics.

• Fluctuation relations for molecular motors

  My first encounter with Stochastic Thermodynamics was through a study of stochastic models (such as ratchet models) for molecular motors, which lead us to find that thermodynamically consistent models of molecular motors should obey a symmetry relation called Fluctuation relations.

• Modified fluctuation-dissipation theorem off-equilibrium

  Within the linear regime, the fluctuations relations mentioned above lead to modified fluctuation-dissipation theorems off-equilibrium for systems obeying markovian dynamics. In sept. 2012, my former PhD student Gatien Verley defended his thesis on this topic.
  The thesis is entitled "Fluctuations and response in non-equilibrium systems". In this thesis, we have derived a modified fluctuation-dissipation theorem near general non-equilibrium states (which may be non-stationary)
  and new second-law like inequalities for transitions between non-stationary states.

• Thermodynamic inference

  The idea of this research is to develop methods of inference of thermodynamic quantities (free energies or entropy production) from an analysis of non-equilibrium fluctuations and imposing symmetry constraints in the form of fluctuation relations.

• Fluctuations and broken symmetries

  There we extended the use of fluctuation relations to the fluctuations of order parameters in equilibrium systems, which are much better understood than non-equilibrium ones. We recover old results but also new ones regarding constraints on the equilibrium fluctuations of order parameters.

• Kinetics and Thermodynamics of reversible polymerization

  There we develop a stochastic thermodynamics approach to treat polymerization models such as mass-exchange polymerization processes which are important in the metabolism of sugars. This work is part of a general effort to use Stochastic Thermodynamics to study Chemical Reaction Networks.

• Thermodynamic trade-offs and efficiency

  We investigate consequences of fluctuation relations known as uncertainty relations in a number of non-equilibrium systems. We develop a framework to understand power-efficiency trade-offs based on such a relation.

2. Evolution of molecular systems and the origin of life

• Transient compartmentalization dynamics

  In his thesis "Physical aspects of Origin of life scenarios" defended in nov 2019, my former PhD student A. Blokhuis developed a very comprehensive analysis of various scenarios of the emergence of life from the point of view of physical chemistry, thermodynamics and statistical physics. One important result in the thesis was the recognition of transient compartmentalization with pooling and selection as a key concept for the evolution of molecular systems. In particular, we proved that cell division considered in earlier models such as the stochastic corrector model was in comparison a less important ingredient. This therefore represents good news for the field on the Origin of life, because cell or proto-cell division requires a rather sophisticated machinery or mechanism, which may not have been available from the start. In contrast, transient compartmentalization is a simpler mechanism, which can result from natural fluctuations of the environment due to for instance day-night cycles.
  
  Various compartmentalization schemes
  considered in the evolution of molecular systems
  
  

• Control of growth and divisions in cells

  With A. Genthon, we built models to describe the control of growth and divisions in growing cell populations using stochastic models. We establish some links with this model and the field of Stochastic Thermodynamics.
  

3. Dynamics of biofilaments: actine and microtubules

• Coupling polymerization to force and to hydrolysis in single filaments of actin and microtubules

  Microtubules and actin filaments display unusual non-equilibrium dynamical behaviors, which are relevant for cell functioning. These behaviors, such as treadmilling and dynamic instability, result from an interplay between the polymerization and the ATP/GTP hydrolysis. We present a stochastic model (with two variants depending on the mechanism of hydrolysis), which accounts for this coupling and allows to characterize the dynamics of these polymers at the single filament level. In one particular extension of this model, we investigate the collective dynamics of an ensemble of parallel non-hydrolyzable filaments which push by polymerizing against a moving barrier. Such an approach is relevant to analyze for instance the process of force generation by actin filaments.

• Force exerted by an ensemble of parallel filaments pushing against a movable barrier.

  We have developed a model to describe the force generated by the polymerization of an array of parallel biofilaments. The filaments are assumed to be coupled only through mechanical contact with a movable barrier. We calculate the filament density distribution and the force–velocity relation with a mean-field approach combined with simulations. We identify two regimes: a non-condensed regime at low force in which filaments are spread out spatially and a condensed regime at high force in which filaments accumulate near the barrier. We confirm a result previously known from other related studies, namely that the stall force is equal to N times the stall force of a single filament. In the model studied here, the approach to stalling is very slow, and the velocity is practically zero at forces significantly lower than the stall force.

4. Biomimetic systems based on lipid membranes

• Lipid vesicle coupled to a cytoskeleton

  In 2004, I have worked together with J. B. Fournier and E. Raphael on a simple model of a membrane coupled to a cytoskeleton, described a lattice of entropic springs.

• Lipid vesicle coupled to light-activable ionic pumps

  Active membranes are artificial lipid membranes containing inclusions such as ionic channels or pumps. As a result of the conformation changes undergone by these channels or pumps (which can be triggered by light or by the application of an electric field), the fluctuations of the membrane can not be purely described as equilibrium fluctuations. Part of these fluctuations are non-equilibrium fluctuations, which must arise from an a priori unknown distribution of active forces associated with the conformations changes undergone by the ion channels or pumps.

• Ionic transport across planar lipid membrane containing ion channels

  The goal of this work started in 2007 is to construct a coherent model of an active membrane which would include a description of the ionic transport occurring across the ionic channels or pumps, which has been missing in some previous models of active membranes. In order to address this issue, we have constructed a framework based on an electrokinetic description of the ionic transport occurring through a membrane which is slightly conductive to ions.