Atomic-scale molecular dynamics and free energy calculations in explicit aqueous solvent are used to study the complex mechanism by which a molecule can intercalate between successive base pairs of the DNA double helix. We have analyzed the intercalation pathway for the anticancer drug daunomycin using two different methods: metadynamics and umbrella sampling. The resulting free energy pathways are found to be consistent with one another and point, within an equilibrium free energy context, to a three-step process. Daunomycin initially binds in the minor groove of DNA. An activated step then leads to rotation of the drug, coupled with DNA deformation that opens a wedge between the base pairs, bends DNA toward the major groove, and forms a metastable intermediate that resembles structures seen within the interfaces between DNA and minor-groove-binding proteins. Finally, crossing a small free energy barrier leads to further rotation of daunomycin and full intercalation of the drug, reestablishing stacking with the flanking base pairs and straightening the double helix.

The aim of this paper is twofold. First, three theoretical principles are formalized: randomization, overrepresentation and restriction. We develop these principles and give a rationale for their use in choosing the sampling design in a systematic way. In the model-assisted framework, knowledge of the population is formalized by modelling the population and the sampling design is chosen accordingly. We show how the principles of overrepresentation and of restriction naturally arise from the modelling of the population. The balanced sampling then appears as a consequence of the modelling. Second, a review of probability balanced sampling is presented through the model-assisted framework. For some basic models, balanced sampling can be shown to be an optimal sampling design. Emphasis is placed on new spatial sampling methods and their related models. An illustrative example shows the advantages of the different methods. Throughout the paper, various examples illustrate how the three principles can be applied in order to improve inference.

We propose a novel approach for smoothing on surfaces, namely estimating a function starting from noisy and discrete measurements. More precisely, we aim at estimating functions lying on a surface represented by NURBS, which are geometrical representations commonly used in industrial applications. The estimation is based on the minimization of a penalized least-square functional. The latter is equivalent to solve a 4th-order Partial Differential Equation (PDE). In this context, we use Isogeometric Analysis (IGA) for the numerical approximation of such surface PDE, leading to an IsoGeometric Smoothing (IGS) method for fitting data spatially distributed on a surface. Indeed, IGA facilitates encapsulating the exact geometrical representation of the surface in the analysis and also allows the use of at least globally C 1 −continuous NURBS basis functions for which the 4th-order PDE can be solved using the standard Galerkin method. We show the performance of the proposed IGS method by means of numerical simulations and we apply it to the estimation of the pressure coefficient, and associated aerodynamic force on a winglet of the SOAR space shuttle.