Simulation of surface waves in porous media

We present a novel numerical algorithm for the simulation of seismic wave propagation in porous media, which is particularly suitable for the accurate modelling of surface wave-type phenomena. The differential equations of motion are based on Biot's theory of poro-elasticity and solved with a pseudospectral approach using Fourier and Chebyshev methods to compute the spatial derivatives along the horizontal and vertical directions, respectively. The time solver is a splitting algorithm that accounts for the stiffness of the differential equations. Due to the Chebyshev operator the grid spacing in the vertical direction is non-uniform and characterized by a denser spatial sampling in the vicinity of interfaces, which allows for a numerically stable and accurate evaluation of higher order surface wave modes. We stretch the grid in the vertical direction to increase the minimum grid spacing and reduce the computational cost. The free-surface boundary conditions are implemented with a characteristics approach, where the characteristic variables are evaluated at zero viscosity. The same procedure is used to model seismic wave propagation at the interface between a fluid and porous medium. In this case, each medium is represented by a different grid and the two grids are combined through a domain-decomposition method. This wavefield decomposition method accounts for the discontinuity of variables and is crucial for an accurate interface treatment. We simulate seismic wave propagation with open-pore and sealed-pore boundary conditions and verify the validity and accuracy of the algorithm by comparing the numerical simulations to analytical solutions based on zero viscosity obtained with the Cagniard-de Hoop method. Finally, we illustrate the suitability of our algorithm for more complex models of porous media involving viscous pore fluids and strongly heterogeneous distributions of the elastic and hydraulic material properties.

β1- and β3- voltage-gated sodium channel subunits modulate cell surface expression and glycosylation of Nav1.7 in HEK293 cells.

Voltage-gated sodium channels (Navs) are glycoproteins composed of a pore-forming α-subunit and associated β-subunits that regulate Nav α-subunit plasma membrane density and biophysical properties. Glycosylation of the Nav α-subunit also directly affects Navs gating. β-subunits and glycosylation thus comodulate Nav α-subunit gating. We hypothesized that β-subunits could directly influence α-subunit glycosylation. Whole-cell patch clamp of HEK293 cells revealed that both β1- and β3-subunits coexpression shifted V ½ of steady-state activation and inactivation and increased Nav1.7-mediated I Na density. Biotinylation of cell surface proteins, combined with the use of deglycosydases, confirmed that Nav1.7 α-subunits exist in multiple glycosylated states. The α-subunit intracellular fraction was found in a core-glycosylated state, migrating at ~250 kDa. At the plasma membrane, in addition to the core-glycosylated form, a fully glycosylated form of Nav1.7 (~280 kDa) was observed. This higher band shifted to an intermediate band (~260 kDa) when β1-subunits were coexpressed, suggesting that the β1-subunit promotes an alternative glycosylated form of Nav1.7. Furthermore, the β1-subunit increased the expression of this alternative glycosylated form and the β3-subunit increased the expression of the core-glycosylated form of Nav1.7. This study describes a novel role for β1- and β3-subunits in the modulation of Nav1.7 α-subunit glycosylation and cell surface expression.