Understanding how ligands bind to G-protein coupled receptors (GPCRs) provides insights into a myriad of cell processes and is crucial for drug development. Here we extend a hybrid molecular mechanics/coarse-grained (MM/CG) approach applied previously to enzymes to GPCR/ligand complexes. The accuracy of this method for structural predictions is established by comparison with recent atomistic molecular dynamics simulations on the human β2 adrenergic receptor, a member of the GPCRs superfamily. The results obtained with the MM/CG methodology show a good agreement with previous all-atom classical dynamics simulations, in particular in the structural description of the ligand binding site. This approach could be used for high-throughput predictions of ligand poses in a variety of GPCRs.

Context. Local helioseismology has so far relied on semi-analytical methods to compute the spatial sensitivity of wave travel times to perturbations in the solar interior. These methods are cumbersome and lack flexibility. Aims. Here we propose a convenient framework for numerically solving the forward problem of time-distance helioseismology in the frequency domain. The fundamental quantity to be computed is the cross-covariance of the seismic wavefield. Methods. We choose sources of wave excitation that enable us to relate the cross-covariance of the oscillations to the Green's function in a straightforward manner. We illustrate the method by considering the 3D acoustic wave equation in an axisymmetric reference solar model, ignoring the effects of gravity on the waves. The symmetry of the background model around the rotation axis implies that the Green's function can be written as a sum of longitudinal Fourier modes, leading to a set of independent 2D problems. We use a high-order finite-element method to solve the 2D wave equation in frequency space. The computation is 'embarrassingly parallel', with each frequency and each azimuthal order solved independently on a computer cluster. Results. We compute travel-time sensitivity kernels in spherical geometry for flows, sound speed, and density perturbations under the first Born approximation. Convergence tests show that travel times can be computed with a numerical precision better than one millisecond, as required by the most precise travel-time measurements. Conclusions. The method presented here is computationally efficient and will be used to interpret travel-time measurements in order to infer, e.g., the large-scale meridional flow in the solar convection zone. It allows the implementation of (full-waveform) iterative inversions, whereby the axisymmetric background model is updated at each iteration.

The aim of this paper is to present a new model of in vitro cell electropermeabilization, which describes separately the conducting state and the permeable state of the membrane submitted to high voltage pulses. We first derive the model based on the experimental observations and we present the numerical methods to solve the non-linear partial differential equations. We then present numerical simulations that corroborate qualitatively the experimental data dealing with the uptake of propidium iodide (PI) after millipulses. This tends to justify the validity of our modeling. Forthcoming work will be to calibrate the parameters of the model for quantitative description of the uptake.

The aim of this paper is to provide new models of cell electropermeabilization involving only a few parameters. A static and a dynamical model, which are based on the description of the electric potential in a biological cell, are derived. Existence and uniqueness results are provided for each differential system, and an accurate numerical method to compute the solution is described. We then present numerical simulations that corroborate the experimental observations, providing the consistency of the modeling. We emphasize that our new models involve very few parameters, compared with the most achieved models of Neu and Krassowska (Phys Rev E 53(3):3471-3482, 1999) and DeBruin and Krassowska (Biophys J 77:1225-1233, 1999), but they provide the same qualitative results. Thus, these models will facilitate drastically the forthcoming inverse problem solving, which will consist in fitting them with the experiments.

Abstract. This work offers some contributions to the numerical study of acoustic waves propagating in the Sun and its atmosphere. The main goal is to provide boundary conditions for outgoing waves in the solar atmosphere where it is assumed that the sound speed is constant and the density decays exponentially with radius. Outgoing waves are governed by a Dirichlet-to-Neumann map which is obtained from the factorization of the Helmholtz equation expressed in spherical coordinates. For the purpose of extending the outgoing wave equation to axisymmetric or 3D cases, different approximations are implemented by using the frequency and/or the angle of incidence as parameters of interest. This results in boundary conditions called Atmospheric Radiation Boundary Conditions (ARBC) which are tested in ideal and realistic configurations. These ARBCs deliver accurate results and reduce the computational burden by a factor of two in helioseismology applications.Résumé. Ce travail apporte quelques contributions à l'étude numérique des ondes acoustiques se propageant dans le Soleil et son atmosphère. Il se base sur la caractérisa-tion des ondes sortantes dans l'atmosphère représentée par une vitesse constante et une densité décroissant exponentiellement. Les ondes sortantes sont régies par un opérateur Dirichlet-to-Neumann qui est obtenu par la factorisation de l'équation de Helmholtz formulée dans les coordonnées sphériques. Afin d'étendre l'équation des ondes sortantes à des géométries axisymétriques ou 3D, différentes approximations sont menées en utilisant la fréquence et/ou l'angle d'incidence comme paramètres d'intérêt. Ceci mène à des conditions de frontière que nous appelons Conditions de Radiation Atmosphériques (ARBC) et qui sont testées en configuration idéalisées et réalistes. Ces conditions ARBC offrent des résultats précis et réduisent le coût de calcul d'un facteur deux pour le cas du Soleil.1991 Mathematics Subject Classification. 00A71, 35L05, 85A20, 33C55, 65M60.December 1, 2017.

The temporal covariance between seismic waves measured at two locations on the solar surface is the fundamental observable in time-distance helioseismology. Above the acoustic cut-off frequency (∼5.3 mHz), waves are not trapped in the solar interior and the covariance function can be used to probe the upper atmosphere. We wish to implement appropriate radiative boundary conditions for computing the propagation of high-frequency waves in the solar atmosphere. We consider the radiative boundary conditions recently developed by Barucq et al. (2017) for atmospheres in which sound-speed is constant and density decreases exponentially with radius. We compute the cross-covariance function using a finite element method in spherical geometry and in the frequency domain. The ratio between first-and second-skip amplitudes in the time-distance diagram is used as a diagnostic to compare boundary conditions and to compare with observations. We find that a boundary condition applied 500 km above the photosphere and derived under the approximation of small angles of incidence accurately reproduces the 'infinite atmosphere' solution for high-frequency waves. When the radiative boundary condition is applied 2 Mm above the photosphere, we find that the choice of atmospheric model affects the time-distance diagram. In particular, the time-distance diagram exhibits double-ridge structure when using a VAL atmospheric model.

We propose a non-linear steady-state model of irreversible electropermeabilization in a biological tissue. The non-linear problem is solved using a modified fixed point iteration. The unknown parameters are experimentally estimated from the observation of the necrosis on a potato tissue for different applied voltages. A variability study of the parameters involved in the model is performed.Index Terms-Electropermeabilization (EP), non-linear conductivity.

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