Laurent Michel

The ATP synthase (F0−F1) complex in oxidative phosphorylation

The transmembrane electrochemical proton gradient generated by the redox systems of the respiratory chain in mitochondria and aerobic bacteria is utilized by proton translocating ATP synthases to catalyze the synthesis of ATP from ADP and Pi. The bacterial and mitochondrial H+-ATP synthases both consist of a membranous sector, F0, which forms a H+-channel, and an extramembranous sector, F1, which is responsible for catalysis. When detached from the membrane, the purified F1 sector functions mainly as an ATPase. In chloroplasts, the synthesis of ATP is also driven by a proton motive force, and the enzyme complex responsible for this synthesis is similar to the mitochondrial and bacterial ATP synthases. The synthesis of ATP by H+-ATP synthases proceeds without the formation of a phosphorylated enzyme intermediate, and involves co-operative interactions between the catalytic subunits.

Semi-classical analysis of a random walk on a manifold

We prove a sharp rate of convergence to stationarity for a natural random walk on a compact Riemannian manifold (M, g). The proof includes a detailed study of the spectral theory of the associated operator.

Semi-Classical Behavior of the Scattering Amplitude for Trapping Perturbations at Fixed Energy

We study the semi-classical behavior as h → 0 of the scattering amplitude f(�,!,�, h) as- sociated to a Schr¨ odinger operator P(h) = − 1 h 2 � + V(x) with short-range trapping perturbations. First we realize a spatial localization in the general case and we deduce a bound of the scattering am- plitude on the real line. Under an additional assumption on the resonances, we show that if we modify the potential V(x) in a domain lying behind the barrier {x : V(x) > �}, the scattering amplitude f(�,!,�, h) changes by a term of order O(h 1 ). Under an escape assumption on the classical trajec- tories incoming with fixed direction !, we obtain an asymptotic development of f(�,!,�, h) similar to the one established in the non-trapping case.

Scattering theory for the Schrödinger equation with repulsive potential

Abstract We consider the scattering theory for the Schrodinger equation with − Δ − | x | α as a reference Hamiltonian, for 0 α ⩽ 2 , in any space dimension. We prove that, when this Hamiltonian is perturbed by a potential, the usual short range/long range condition is weakened: the limiting decay for the potential depends on the value of α, and is related to the growth of classical trajectories in the unperturbed case. The existence of wave operators and their asymptotic completeness are established thanks to Mourre estimates relying on new conjugate operators. We construct the asymptotic velocity and describe its spectrum. Some results are generalized to the case where − | x | α is replaced by a general second order polynomial.

Remarks on Non-Linear Schrödinger Equation with Magnetic Fields

We study the nonlinear Schrödinger equation with time-depending magnetic field without smallness assumption at infinity. We obtain some results on the Cauchy problem, WKB asymptotics and instability.

Mapping of the pyrophosphate binding sites of beef heart mitochondrial F1-ATPase by photolabelling with azidonitrophenyl [α-32P]pyrophosphate

4-Azido-2-nitrophenyl [alpha-32P]pyrophosphate (azido-[alpha-32P]PPi) mimics ADP and PPi by some of its binding properties when assayed in the absence of photoirradiation with mitochondrial F1-ATPase. Upon photoirradiation, both alpha- and beta-subunits of F1-ATPase were covalently labelled. Following chemical and enzymatic cleavages of each of the two photolabelled subunits, peptides containing the covalently bound radioactivity were separated by HPLC and identified by amino acid sequencing. Bound azido-[alpha-32P]PPi was found to be concentrated in two distant sequences of the alpha-subunit, namely Asp194-Thr221 and Lys386-Met437, and in a single sequence of the beta-subunit Glu294-Met358 with most of the photoprobe bound to beta-Tyr-311 and beta-Tyr-345. These results are discussed in terms of a model in which the pyrophosphate binding sites of F1 are located in regions of the alpha- and beta-subunits exposed at the interface between the two subunits and correspond to non-catalytic and catalytic adenine nucleotide binding sites, respectively.

Photolabeling of the phosphate binding site of chloroplast coupling factor 1 With [32P]azidonitrophenyl phosphate

Chloroplast F1‐AT Pase (CF1) was photolabeled by a radiolabeled photoactivatable derivative of Pi, 4‐azido‐2‐nitrophenyl [32P]phosphate (ANPP). The radioactivity was localized in the β subunit of CF1. Upon cleavage of the β subunit by cyanogen bromide, the predominantly labeled peptide was recovered, which was subsequently subjected to tryptic digestion. A tryptic peptide (spanning Ile312‐Arg354), was found to contain nearly all the covalently bound radioactivity. By Edman degradation, the labeled amino acid residues were identified as Tyr328, Val329 and Pro330. The labeled β‐Tyr328 of CF1 is the equivalent of β‐Tyr311 of F1 from beef heart mitochondria, which was previously found to be photolabeled by ANPP [J. Garin et al. (1989) Biochemistry 28, 1442–1448].

Semi-classical estimate of the residues of the scattering amplitude for long-range potentials

In this paper, we study the residue of the scattering amplitude for the Schrodinger operator with long-range perturbation of the Laplacian, in the case where there are resonances exponentially close to the real axis. If the resonances are simple and under a separation condition, one proves that the residue of the scattering amplitude associated with a resonance ξ is bounded by C(h)|Im ξ|. Here C(h) denotes an explicit constant depending polynomially on h−1 and the number of resonances in a fixed box. This generalizes a recent result of Stefanov concerning compactly supported perturbations and isolated resonances.

Scattering amplitude and scattering phase for the Schrödinger equation with strong magnetic field

In this paper we consider the Schrodinger equation with constant magnetic field of strength b>0 in all dimension. We study the behavior of the scattering amplitude and the scattering phase when the parameter b goes to infinity and the energy is far from the Landau levels.

SPECTRAL ANALYSIS OF HYPOELLIPTIC RANDOM WALKS

We study the spectral theory of a reversible Markov chain associated to a hypoelliptic random walk on a manifold M. This random walk depends on a parameter h which is roughly the size of each step of the walk. We prove uniform bounds with respect to h on the rate of convergence to equilibrium, and the convergence when h goes to zero to the associated hypoelliptic diffusion.