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We derive a Godunov-type numerical flux for the class of strictly convex, homogeneous Hamiltonians that includes H(p, q) = ap 2 + bq 2 − 2cpq, c 2 < ab. We combine our Godunov numerical fluxes with simple GaussSeidel type iterations for solving the corresponding Hamilton-Jacobi Equations. The resulting algorithm is fast since it does not require a sorting strategy as found, e.g., in the fast marching method. In addition, it provides a way to compute solutions to a class of HJ equations for which the conventional fast marching method is not applicable. Our experiments indicate convergence after a few iterations, even in rather difficult cases.

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Avian influenza virus subtype H5N1 is a potential pandemic threat with human-adapted strains resistant to antiviral drugs. Although virtual screening (VS) against a crystal or relaxed receptor structure is an established method to identify potential inhibitors, the more dynamic changes within binding sites are neglected. To accommodate full receptor flexibility, we use AutoDock4 to screen the NCI diversity set against representative receptor ensembles extracted from explicitly solvated molecular dynamics simulations of the neuraminidase system. The top hits are redocked to the entire nonredundant receptor ensemble and rescored using the relaxed complex scheme (RCS). Of the 27 top hits reported, half ranked very poorly if only crystal structures are used. These compounds target the catalytic cavity as well as the newly identified 150- and 430-cavities, which exhibit dynamic properties in electrostatic surface and geometric shape. This ensemble-based VS and RCS approach may offer improvement over existing strategies for structure-based drug discovery.

The emergence and continuing global spread of the highly virulent avian influenza H5N1 has raised concerns of a possible human pandemic. 1 Several approved anti-influenza drugs effectively target the neuraminidase (NA), a surface glycoprotein that cleaves terminal sialic acid residues and facilitates the release of viral progeny from infected cells. 2 The first crystal structures of group-1 NAs in apo form and in complex with currently available drugs 3 revealed that although the binding pose of oseltamivir (Tamiflu) was similar to that seen in previous crystallographic complexes, 4,5 the 150-loop adopted a distinct conformation, opening a new cavity adjacent to the active site. This open form of the 150-loop was proposed as a new opportunity for drug design. 3 However, under certain crystallization conditions, the 150-loop was found to adopt the same closed conformation as previously seen in group-2 structures, suggesting a slow conformational change may occur upon inhibitor binding. 3 The possible transience of the 150-loop cavity and its proximity to the inhibitor-binding site underscores the importance of dynamic biophysical studies to complement static crystal structures in NA drug discovery efforts. Through explicitly solvated molecular dynamics (MD) simulations of the apo and oseltamivir-bound forms of tetrameric N1, here we show that the 150-loop is able to open into significantly wider conformations than seen in the crystal structures. We find this motion in the 150-loop is coupled to motion in the neighboring 430-loop, which expands the active site cavity even further. In addition, we see that the 150-loop approaches the closed conformation in simulations of the oseltamivir-bound system, suggesting that the loop switching motion may be more rapid than previously proposed.Two separate MD simulations were carried out using apo and oseltamivir-bound crystal structures. 3 The tetramer structures are exceptionally stable over the course of the 40 ns simulations (Supporting Information Figure S1). A principal components analysis over all the chains for both systems reveals that the monomer subunits within each tetramer sample different regions of configurational space, establishing that their motion can be considered independent of one another ( Figure S2). On average, the apo N1 exhibits slightly higher overall per residue C R rootmean-square fluctuation (rmsf) values than the oseltamivir-bound system ( Figure S3). Further analysis reveals that the residues exhibiting the largest rmsf differences between the two systems are located at least 5.0 Å distal to the catalytic pocket, suggesting that the largest conformational changes are due to motions of surface-exposed loops rather than local changes directly within the active site pocket.Most notably, the MD trajectories suggest that the 150-loop is even more flexible than observed in the crystal structures. Although we do not sample the completely closed conformation, salt bridge and hydrogen bond interactions between oseltamivir and residues Asp151 and Arg15...