Error Analysis of Modified Langevin Dynamics

We consider Langevin dynamics associated with a modified kinetic energy vanishing for small momenta. This allows us to freeze slow particles, and hence avoid the re-computation of inter-particle forces, which leads to computational gains. On the other hand, the statistical error may increase since there are a priori more correlations in time. The aim of this work is first to prove the ergodicity of the modified Langevin dynamics (which fails to be hypoelliptic), and next to analyze how the asymptotic variance on ergodic averages depends on the parameters of the modified kinetic energy. Numerical results illustrate the approach, both for low-dimensional systems where we resort to a Galerkin approximation of the generator, and for more realistic systems using Monte Carlo simulations

Fast Continuous Collision Detection and Handling for Desktop Virtual Prototyping

International audienceThis paper presents an overview of our recent work on continuous collision detection methods and constraints handling for rigid polyhedral objects. We demonstrate that continuous collision detection algorithms are practical in interactive dynamics simulation of complex polyhedral rigid bodies and show how continuous collision detection and efficient constraint-based dynamics algorithms allow to perform various virtual prototyping tasks intuitively, precisely and robustly on commodity desktop computers. Especially, we present two applications of our system to actual industrial cases. We note that both tasks are performed with a simple 2d mouse on a high-end computer

Interactive Chemical Reactivity Exploration

Elucidating chemical reactivity in complex molecular assemblies of a few hundred atoms is, despite the remarkable progress in quantum chemistry, still a major challenge. Black-box search methods to find intermediates and transition-state structures might fail in such situations because of the high-dimensionality of the potential energy surface. Here, we propose the concept of interactive chemical reactivity exploration to effectively introduce the chemist's intuition into the search process. We employ a haptic pointer device with force-feedback to allow the operator the direct manipulation of structures in three dimensions along with simultaneous perception of the quantum mechanical response upon structure modification as forces. We elaborate on the details of how such an interactive exploration should proceed and which technical difficulties need to be overcome. All reactivity-exploration concepts developed for this purpose have been implemented in the Samson programming environment.Comment: 36 pages, 14 figure

Variable gain haptic coupling for molecular simulation

Molecularinteractionstypicallyhaveahighdynamicrange(HDR), combining short-range stiff repulsive effects with long-range, soft attractive and repulsive terms. As a result, faithful haptic renderingofsuchmolecularinteractionsisbothimportantanddifficult,in particularinapplicationswherethepreciseperceptionofmolecular forces is necessary (e.g. in molecular docking simulations). Traditionally,teleoperationcouplingusingconstantgaincontrolschemes have limited applications since they are unable to transmit to users low attractive forces without truncating repulsive ones. Furthermore, constant scaling displacement induces either instability or time-consuming experiments (displacements are slow), which deteriorates the ease of manipulation. In this paper, we describe a variable gain haptic coupling method specifically designed to render high dynamic range (molecular) forces. The proposed method is evaluated by user tests on an experiment involving two water molecules. We observe that variable force amplification is widely appreciated, whereas variable displacement scaling is appropriated only for users familiar with haptic manipulation. A complex experiment on a HIV molecule is carried out using this variable gain system. Advantages and limitations of thisapproach arediscussed.

View-dependent dynamics of articulated bodies

Special Issue: CASA'2008 Special IssueInternational audienceWe propose a method for view-dependent simplification of articulated-body dynamics, which enables an automatic trade-off between visual precision and computational efficiency. We begin by discussing the problem of simplifying the simulation based on visual criteria, and show that it raises a number of challenging questions. We then focus on articulated-body dynamics simulation, and propose a semi-predictive approach which relies on a combination of exact, a priori error metrics computations, and visibility estimations. We suggest several variants of semi-predictive metrics based on hierarchical data structures and the use of graphics hardware, and discuss their relative merits in terms of computational efficiency and precision. Finally, we present several benchmarks and demonstrate how our view-dependent articulated-body dynamics method allows an animator (or a physics engine) to finely tune the visual quality and obtain potentially significant speedups during interactive or off-line simulations

IM-UFF: extending the Universal Force Field for interactive molecular modeling

International audienceThe universal force field (UFF) is a broadly applicable classical force field that contains parameters for almost every atom type of the periodic table. This force field is non-reactive, i.e. the topology of the system under study is considered as fixed and no creation or breaking of covalent bonds is possible. This paper introduces interactive modeling-UFF (IM-UFF), an extension of UFF that combines the possibility to significantly modify molecular structures (as with reactive force fields) with a broad diversity of supported systems thanks to the universality of UFF. Such an extension lets the user easily build and edit molecular systems interactively while being guided by physics based inter-atomic forces. This approach introduces weighted atom types and weighted bonds, used to update topologies and atom parameterizations at every time step of a simulation. IM-UFF has been evaluated on a large set of benchmarks and is proposed as a self-contained implementation integrated in a new module for the SAMSON software platform for computational nanoscience available at http://www.samson-connect.net

Generating conformational transition paths with low potential-energy barriers for proteins

International audienceThe knowledge of conformational transition paths in proteins can be useful for understanding protein mechanisms. Recently, we have introduced the As-Rigid-As-Possible (ARAP) interpolation method, for generating interpolation paths between two protein conformations. The method was shown to preserve well the rigidity of the initial conformation along the path. However, because the method is totally geometry-based, the generated paths may be inconsistent because the atom interactions are ignored. Therefore, in this article, we would like to introduce a new method to generate conformational transition paths with low potential-energy barriers for proteins. The method is composed of three processing stages. First, ARAP interpolation is used for generating an initial path. Then, the path conformations are enhanced by a clash remover. Finally, Nudged Elastic Band, a path-optimization method, is used to produce a low-energy path. Large energy reductions are found in the paths obtained from the method than in those obtained from the ARAP interpolation method alone. The results also show that ARAP interpolation is a good candidate for generating an initial path because it leads to lower potential-energy paths than two other common methods for path interpolation

ART-RRT: As-Rigid-As-Possible exploration of ligand unbinding pathways

International audienceThis article proposes a method to efficiently generate approximate ligand unbind-ing pathways. It combines an efficient tree-based exploration method with a morphing technique from Computer Graphics for dimensionality reduction. This method is com-putationally cheap and, unlike many existing approaches, does not require a reaction coordinate to guide the search. It can be used for finding pathways with known or unknown directions beforehand. The approach is evaluated on several benchmarks and the obtained solutions are compared with the results from other state-of-the-art approaches. We show that the method is time-efficient and produces pathways in good agreement with other state-of-the-art solutions. These paths can serve as first approximations that can be used, analyzed or improved with more specialized methods