Developmentally Regulated Sphingolipid Degradation in Leishmania major

Leishmania parasites alternate between extracellular promastigotes in sandflies and intracellular amastigotes in mammals. These protozoans acquire sphingolipids (SLs) through de novo synthesis (to produce inositol phosphorylceramide) and salvage (to obtain sphingomyelin from the host). A single ISCL (Inositol phosphoSphingolipid phospholipase C-Like) enzyme is responsible for the degradation of both inositol phosphorylceramide (the IPC hydrolase or IPCase activity) and sphingomyelin (the SMase activity). Recent studies of a L. major ISCL-null mutant (iscl−) indicate that SL degradation is required for promastigote survival in stationary phase, especially under acidic pH. ISCL is also essential for L. major proliferation in mammals. To further understand the role of ISCL in Leishmania growth and virulence, we introduced a sole IPCase or a sole SMase into the iscl− mutant. Results showed that restoration of IPCase only complemented the acid resistance defect in iscl− promastigotes and improved their survival in macrophages, but failed to recover virulence in mice. In contrast, a sole SMase fully restored parasite infectivity in mice but was unable to reverse the promastigote defects in iscl−. These findings suggest that SL degradation in Leishmania possesses separate roles in different stages: while the IPCase activity is important for promastigote survival and acid tolerance, the SMase activity is required for amastigote proliferation in mammals. Consistent with these findings, ISCL was preferentially expressed in stationary phase promastigotes and amastigotes. Together, our results indicate that SL degradation by Leishmania is critical for parasites to establish and sustain infection in the mammalian host

A posteriori error estimates for fully discrete schemes for the time dependent Stokes problem

The final publication is available at Springer via http://dx.doi.org/10.1007/s10092-018-0259-2This work is devoted to a posteriori error analysis of fully discrete finite element approximations to the time dependent Stokes system. The space discretization is based on popular stable spaces, including Crouzeix–Raviart and Taylor–Hood finite element methods. Implicit Euler is applied for the time discretization. The finite element spaces are allowed to change with time steps and the projection steps include alternatives that is hoped to cope with possible numerical artifices and the loss of the discrete incompressibility of the schemes. The final estimates are of optimal order in L∞(L2) for the velocity error

Solving the systems of equations arising in the discretization of some nonlinear PDE's by implicit Runge-Kutta methods

We construct and analyze iterative methods for the efficient solution of the nonlinear equations that result from the application of Implicit Runge-Kutta methods to the temporal integration of nonlinear evolution equations. Some of the schemes we consider have as starting point Newton’s method and can be applied to a large class of evolution equations

CONSERVATIVE, DISCONTINUOUS-GALERKIN METHODS FOR THE GENERALIZED KORTEWEG-DE VRIES EQUATION

Abstract. We construct, analyze and numerically validate a class of conservative, discontinuous Galerkin schemes for the Generalized Korteweg-de Vries equation. Up to round-off error, these schemes preserve discrete versions of the first two invariants (the integral of the solution, usually identified with the mass, and the L 2 –norm) of the continuous solution. Numerical evidence is provided indicating that these conservation properties impart the approximations with beneficial attributes, such as more faithful reproduction of the amplitude and phase of traveling-wave solutions. The numerical simulations also indicate that the discretization errors grow only linearly as a function of time. Key words. Conservative discontinuous Galerkin methods, Korteweg-de Vries, error estimate