Below is a summary of my current research in the field of Biophysics and Non-equilibrium statistical Physics.
I. Stochastic thermodynamics
Fluctuation relations for molecular motors
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 about a decade ago. 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.
For molecular motors, fluctuation relations lead to specific thermodynamic constraints on their operation, which we have illustrated using simple stochastic models of molecular motors.
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.
II. 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.
III. 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.