GEOMETRY OF INTERCALATION OF PSORALENS IN DNA APPROACHED BY MOLECULAR MECHANICS*

The results of molecular mechanical calculations on intercalation complexes of 3-carbethoxypsoralen, 5-methoxypsoralen, 8-methoxypsoralen, 7-methylpyrido[3,4-c]psoralen (MepyPs) and 7-methylpyrido[4,3-c]psoralen (2N-MePyPs) with the double stranded duodecanucleotide d(CGCGATATCGCG)2 are presented. In the energy-minimized structures, the psoralens are intercalated with their plane orthogonal to the helix axis. Stacking interactions between the furan ring of the psoralen and the adjacent bases are maximized in most derivatives studied, whereas the effect of the various substituents of the psoralen ring is to specifically push part of the molecule towards either the minor or the major groove, preventing a symmetrical intercalation (with respect to the two strands of the DNA). The relative position of the psoralen ring and of the adjacent thymine foreshadows the formation of furan-side monoadducts in 3-CPs, MePyPs and 2N-MePyPs, whereas the formation of a pyrone-side monoadduct appears as geometrically more favourable in 5-MOP and both furan- and pyrone-side monoadducts can be geometrically envisaged in 8-MOP. A good correlation therefore exists between the more or less favourable equilibrium geometries and the experimentally observed photoreactions. The present study is the first attempt to characterize the geometrical parameters as part of a complex set of geometrical, dynamical and excited state parameters governing the overall DNA-psoralen photoreaction.     

Computer Assisted Proof of Transverse Saddle-to-Saddle Connecting Orbits for First Order Vector Fields

In this paper we introduce a computational method for proving the existence of generic saddle-to-saddle connections between equilibria of first order vector fields. The first step consists of rigorously computing high order parametrizations of the local stable and unstable manifolds. If the local manifolds intersect, the Newton–Kantorovich theorem is applied to validate the existence of a so-called short connecting orbit. If the local manifolds do not intersect, a boundary value problem with boundary values in the local manifolds is rigorously solved by a contraction mapping argument on a ball centered at the numerical solution, yielding the existence of a so-called long connecting orbit. In both cases our argument yields transversality of the corresponding intersection of the manifolds. The method is applied to the Lorenz equations, where a study of a pitchfork bifurcation with saddle-to-saddle stability is done and where several proofs of existence of short and long connections are obtained.     

Relaxation of variational problems in two-dimensional nonlinear elasticity

Consider a plate occupying in a reference configuration a bounded open set Ω ⊂ ℝ ² , and let be its stored-energy function. In this paper we are concerned with relaxation of variational problems of type:

Homogenization of unbounded singular integrals in W 1,∞

We study homogenization by ??-convergence, with respect to the L ¹-strong convergence, of periodic multiple integrals in W ^1,?? when the integrand can take infinite values outside of a convex bounded open set of matrices.     

An oracle based method to compute a coupled equilibrium in a model of international climate policy

This paper proposes a computational game-theoretic model for the international negotiations that should take place at the end of the period covered by the Kyoto protocol. These negotiations could lead to a self-enforcing agreement on a burden sharing scheme given the necessary global emissions limit that will be imposed when the real extent of climate change is known. The model assumes a non-cooperative behavior of the parties except for the fact that they will be collectively committed to reach a target on total cumulative emissions by the year 2050. The concept of normalized equilibrium, introduced by J.B. Rosen for concave games with coupled constraints, is used to characterize a family of dynamic equilibrium solutions in an m-player game where the agents are (groups of) countries and the payoffs are the welfare gains obtained from a Computable General Equilibrium (CGE) model. The model deals with the uncertainty about climate sensitivity by computing an S-adapted equilibrium. These equilibria are computed using an oracle-based method permitting an implicit definition of the payoffs to the different players, obtained through simulations performed with the global CGE model GEMINI-E3. Partly supported by GICC (French Ministry of Ecology), TOCSIN (EU-044287) and the Swiss-NSF NCCR-Climate program of the Swiss NSF. For helpful comments and discussions, we thank A. Bernard, P. Thalmann, and the anonymous referee.     

Convex Sobolev inequalities and spectral gap

This Note is devoted to the proof of convex Sobolev (or generalized Poincaré) inequalities which interpolate between spectral gap (or Poincaré) inequalities and logarithmic Sobolev inequalities. We extend to the whole family of convex Sobolev inequalities results which have recently been obtained by Cattiaux, and Carlen and Loss for logarithmic Sobolev inequalities. Under local conditions on the density of the measure with respect to a reference measure, we prove that spectral gap inequalities imply all convex Sobolev inequalities including in the limit case corresponding to the logarithmic Sobolev inequalities. To cite this article: J.-P. Bartier, J. Dolbeault, C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Optimal control of a production-inventory system with customer impatience

We consider the control of a production-inventory system with impatient customers. We show that the optimal policy can be described using two thresholds: a production base-stock level that determines when production takes place and an admission threshold that determines when orders should be accepted. We describe an algorithm for computing the performance of the system for any choice of base-stock level and admission threshold. In a numerical study, we compare the performance of the optimal policy against several other policies.     

Gradient estimates for a degenerate parabolic equation with gradient absorption and applications

Qualitative properties of non-negative solutions to a quasilinear degenerate parabolic equation with an absorption term depending solely on the gradient are shown, providing information on the competition between the nonlinear diffusion and the nonlinear absorption. In particular, the limit as t→∞ of the L¹-norm of integrable solutions is identified, together with the rate of expansion of the support for compactly supported initial data. The persistence of dead cores is also shown. The proof of these results strongly relies on gradient estimates which are first established.