Jacques Prost

Auditory sensitivity provided by self-tuned critical oscillations of hair cells

We introduce the concept of self-tuned criticality as a general mechanism for signal detection in sensory systems. In the case of hearing, we argue that active amplification of faint sounds is provided by a dynamical system that is maintained at the threshold of an oscillatory instability. This concept can account for the exquisite sensitivity of the auditory system and its wide dynamic range as well as its capacity to respond selectively to different frequencies. A specific model of sound detection by the hair cells of the inner ear is discussed. We show that a collection of motor proteins within a hair bundle can generate oscillations at a frequency that depends on the elastic properties of the bundle. Simple variation of bundle geometry gives rise to hair cells with characteristic frequencies that span the range of audibility. Tension-gated transduction channels, which primarily serve to detect the motion of a hair bundle, also tune each cell by admitting ions that regulate the motor protein activity. By controlling the bundles propensity to oscillate, this feedback automatically maintains the system in the operating regime where it is most sensitive to sinusoidal stimuli. The model explains how hair cells can detect sounds that carry less energy than the background noise.

Formation and interaction of membrane tubes.

We show that the formation of membrane tubes (or membrane tethers), which is a crucial step in many biological processes, is highly nontrivial and involves first-order shape transitions. The force exerted by an emerging tube is a nonmonotonic function of its length. We point out that tubes attract each other, which eventually leads to their coalescence. We also show that detached tubes behave like semiflexible filaments with a rather short persistence length. We suggest that these properties play an important role in the formation and structure of tubular organelles.

Curvature-driven lipid sorting needs proximity to a demixing point and is aided by proteins

Sorting of lipids and proteins is a key process allowing eukaryotic cells to execute efficient and accurate intracellular transport and to maintain membrane homeostasis. It occurs during the formation of highly curved transport intermediates that shuttle between cell compartments. Protein sorting is reasonably well described, but lipid sorting is much less understood. Lipid sorting has been proposed to be mediated by a physical mechanism based on the coupling between membrane composition and high curvature of the transport intermediates. To test this hypothesis, we have performed a combination of fluorescence and force measurements on membrane tubes of controlled diameters pulled from giant unilamellar vesicles. A model based on membrane elasticity and nonideal solution theory has also been developed to explain our results. We quantitatively show, using 2 independent approaches, that a difference in lipid composition can build up between a curved and a noncurved membrane. Importantly, and consistent with our theory, lipid sorting occurs only if the system is close to a demixing point. Remarkably, this process is amplified when even a low fraction of lipids is clustered upon cholera toxin binding. This can be explained by the reduction of the entropic penalty of lipid sorting when some lipids are bound together by the toxin. Our results show that curvature-induced lipid sorting results from the collective behavior of lipids and is even amplified in the presence of lipid-clustering proteins. In addition, they suggest a generic mechanism by which proteins can facilitate lipid segregation in vivo.

Generic theory of active polar gels: a paradigm for cytoskeletal dynamics

Abstract.We develop a general theory for active viscoelastic materials made of polar filaments. This theory is motivated by the dynamics of the cytoskeleton. The continuous consumption of a fuel leads to a non equilibrium state characterized by the generation of flows and stresses. Our theory can be applied to experiments in which cytoskeletal patterns are set in motion by active processes such as those which are at work in cells.

A minimal system allowing tubulation with molecular motors pulling on giant liposomes

The elucidation of physical and molecular mechanisms by which a membrane tube is generated from a membrane reservoir is central to the understanding of the structure and dynamics of intracellular organelles and of transport intermediates in eukaryotic cells. Compelling evidence exists that molecular motors of the dynein and kinesin families are involved in the tubulation of organelles. Here, we show that lipid giant unilamellar vesicles (GUVs), to which kinesin molecules have been attached by means of small polystyrene beads, give rise to membrane tubes and to complex tubular networks when incubated in vitro with microtubules and ATP. Similar tubes and networks are obtained with GUVs made of purified Golgi lipids, as well as with Golgi membranes. No tube formation was observed when kinesins were directly bound to the GUV membrane, suggesting that it is critical to distribute the load on both lipids and motors by means of beads. A kinetic analysis shows that network growth occurs in two phases: a phase in which membrane-bound beads move at the same velocity than free beads, followed by a phase in which the tube growth rate decreases and strongly fluctuates. Our work demonstrates that the action of motors bound to a lipid bilayer is sufficient to generate membrane tubes and opens the way to well controlled experiments aimed at the understanding of basic mechanisms in intracellular transport.

An Elastic Analysis of Listeria monocytogenes Propulsion

The bacterium Listeria monocytogenes uses the energy of the actin polymerization to propel itself through infected tissues. In steady state, it continuously adds new polymerized filaments to its surface, pushing on its tail, which is made from previously cross-linked actin filaments. In this paper we introduce an elastic model to describe how the addition of actin filaments to the tail results in the propulsive force on the bacterium. Filament growth on the bacterial surface produces stresses that are relieved at the back of the bacterium as it moves forward. The model leads to a natural competition between growth from the sides and growth from the back of the bacterium, with different velocities and strengths for each. This competition can lead to the periodic motion observed in a Listeria mutant.

Fluidization of tissues by cell division and apoptosis

During the formation of tissues, cells organize collectively by cell division and apoptosis. The multicellular dynamics of such systems is influenced by mechanical conditions and can give rise to cell rearrangements and movements. We develop a continuum description of tissue dynamics, which describes the stress distribution and the cell flow field on large scales. In the absence of division and apoptosis, we consider the tissue to behave as an elastic solid. Cell division and apoptosis introduce stress sources that, in general, are anisotropic. By combining cell number balance with dynamic equations for the stress source, we show that the tissue effectively behaves as a viscoelastic fluid with a relaxation time set by the rates of division and apoptosis. If the system is confined in a fixed volume, it reaches a homeostatic state in which division and apoptosis balance. In this state, cells undergo a diffusive random motion driven by the stochasticity of division and apoptosis. We calculate the expression for the effective diffusion coefficient as a function of the tissue parameters and compare our results concerning both diffusion and viscosity to simulations of multicellular systems using dissipative particle dynamics.

Nature of curvature coupling of amphiphysin with membranes depends on its bound density

Cells are populated by a vast array of membrane-binding proteins that execute critical functions. Functions, like signaling and intracellular transport, require the abilities to bind to highly curved membranes and to trigger membrane deformation. Among these proteins is amphiphysin 1, implicated in clathrin-mediated endocytosis. It contains a Bin-Amphiphysin-Rvs membrane-binding domain with an N-terminal amphipathic helix that senses and generates membrane curvature. However, an understanding of the parameters distinguishing these two functions is missing. By pulling a highly curved nanotube of controlled radius from a giant vesicle in a solution containing amphiphysin, we observed that the action of the protein depends directly on its density on the membrane. At low densities of protein on the nearly flat vesicle, the distribution of proteins and the mechanical effects induced are described by a model based on spontaneous curvature induction. The tube radius and force are modified by protein binding but still depend on membrane tension. In the dilute limit, when practically no proteins were present on the vesicle, no mechanical effects were detected, but strong protein enrichment proportional to curvature was seen on the tube. At high densities, the radius is independent of tension and vesicle protein density, resulting from the formation of a scaffold around the tube. As a consequence, the scaling of the force with tension is modified. For the entire density range, protein was enriched on the tube as compared to the vesicle. Our approach shows that the strength of curvature sensing and mechanical effects on the tube depends on the protein density.

Spontaneous Oscillations of Collective Molecular Motors

We present a physical mechanism which can lead to oscillatory motion of molecular motors cooperating in large groups when the system is elastically coupled to its environment. Analytical and numerical calculations reveal a characteristic type of oscillatory behavior with cusplike extrema. Typical oscillation frequencies are determined by the internal time scales of the motors. The physical mechanism we describe generates in a natural way many of the characteristic properties of spontaneous oscillations observed in some muscles and myofibrils.

Self-Organized Beating and Swimming of Internally Driven Filaments

We study a simple two-dimensional model for motion of an elastic filament subject to internally generated stresses and show that wave-like propagating shapes which can propel the filament can be induced by a self-organized mechanism via a dynamic instability. The resulting patterns of motion do not depend on the microscopic mechanism of the instability but only of the filament rigidity and hydrodynamic friction. Our results suggest that simplified systems, consisting only of molecular motors and filaments could be able to show beating motion and self-propulsion.