Thermodynamics of nanocluster phases: a unifying theory.

We propose a unifying, analytical theory accounting for the self-organization of colloidal systems in nanocluster or microcluster phases. We predict the distribution of cluster sizes with respect to interaction parameters and colloid concentration. In particular, we anticipate a proportionality regime where the mean cluster size grows proportionally to the concentration, as observed in several experiments. We emphasize the interest in a predictive theory in soft matter, nanotechnologies, and biophysics.

Thermal denaturation of fluctuating DNA driven by bending entropy.

A statistical model of homopolymer DNA, coupling internal base-pair states (unbroken or broken) and external thermal chain fluctuations, is exactly solved using transfer kernel techniques. The dependence on temperature and DNA length of the fraction of denaturation bubbles and their correlation length is deduced. The thermal denaturation transition emerges naturally when the chain fluctuations are integrated out and is driven by the difference in bending (entropy dominated) free energy between broken and unbroken segments. Conformational properties of DNA, such as persistence length and mean-square-radius, are also explicitly calculated, leading, e.g., to a coherent explanation for the experimentally observed thermal viscosity transition.

IS911 transpososome assembly as analysed by tethered particle motion.

Initiation of transposition requires formation of a synaptic complex between both transposon ends and the transposase (Tpase), the enzyme which catalyses DNA cleavage and strand transfer and which ensures transposon mobility. We have used a single-molecule approach, tethered particle motion (TPM), to observe binding of a Tpase derivative, OrfAB[149], amputated for its C-terminal catalytic domain, to DNA molecules carrying one or two IS911 ends. Binding of OrfAB[149] to a single IS911 end provoked a small shortening of the DNA. This is consistent with a DNA bend introduced by protein binding to a single end. This was confirmed using a classic gel retardation assay with circularly permuted DNA substrates. When two ends were present on the tethered DNA in their natural, inverted, configuration, Tpase not only provoked the short reduction in length but also generated species with greatly reduce effective length consistent with DNA looping between the ends. Once formed, this 'looped' species was very stable. Kinetic analysis in real-time suggested that passage from the bound unlooped to the looped state could involve another species of intermediate length in which both transposon ends are bound. DNA carrying directly repeated ends also gave rise to the looped species but the level of the intermediate species was significantly enhanced. Its accumulation could reflect a less favourable synapse formation from this configuration than for the inverted ends. This is compatible with a model in which Tpase binds separately to and bends each end (the intermediate species) and protein-protein interactions then lead to synapsis (the looped species).

Detection of confinement and jumps in single-molecule membrane trajectories.

We propose a variant of the algorithm by [R. Simson, E. D. Sheets, and K. Jacobson, Biophys. 69, 989 (1995)]. Their algorithm was developed to detect transient confinement zones in experimental single-particle tracking trajectories of diffusing membrane proteins or lipids. We show that our algorithm is able to detect confinement in a wider class of confining potential shapes than that of Simson et al. Furthermore, it enables to detect not only temporary confinement but also jumps between confinement zones. Jumps are predicted by membrane skeleton fence and picket models. In the case of experimental trajectories of mu-opioid receptors, which belong to the family of G-protein-coupled receptors involved in a signal transduction pathway, this algorithm confirms that confinement cannot be explained solely by rigid fences.

Interprotein interactions are responsible for the confined diffusion of a G-protein-coupled receptor at the cell surface.

The monitoring of the movements of membrane proteins (or lipids) by single-particle tracking enables one to obtain reliable insights into the complex dynamic organization of the plasma membrane constituents. Using this technique, we investigated the diffusional behaviour of a G-protein-coupled receptor. The trajectories of the receptors revealed a diffusion mode combining a short-term rapid confined diffusion with a long-term slow diffusion. A detailed statistical analysis shows that the receptors have a diffusion confined to a domain which itself diffuses, the confinement being due to long-range attractive inter-protein interactions. The existing models of the dynamic organization of the cell membrane cannot explain our results. We propose a theoretical Brownian model of interacting proteins that is consistent with the experimental observations and accounts for the variations found as a function of the domain size of the short-term and long-term diffusion coefficients.

Flip dynamics in octagonal rhombus tiling sets.

We investigate the properties of classical single flip dynamics in sets of two-dimensional random rhombus tilings. Single flips are local moves involving three tiles which sample the tiling sets via Monte Carlo Markov chains. We determine the ergodic times of these dynamical systems (at infinite temperature): they grow with the system size N(T) like const.xN(2)(T)lnN(T); these dynamics are rapidly mixing. We use an inherent symmetry of tiling sets and a powerful tool from probability theory, the coupling technique. We also point out the interesting occurrence of Gumbel distributions.