A Second-Order Crank-Nicolson Leap-Frog Scheme for the Modified Phase Field Crystal Model with Long-Range Interaction.

In this paper, we construct a fully discrete and decoupled Crank-Nicolson Leap-Frog (CNLF) scheme for solving the modified phase field crystal model (MPFC) with long-range interaction. The idea of CNLF is to treat stiff terms implicity with Crank-Nicolson and to treat non-stiff terms explicitly with Leap-Frog. In addition, the scalar auxiliary variable (SAV) method is used to allow explicit treatment of the nonlinear potential, then, these technique combines with CNLF can lead to the highly efficient, fully decoupled and linear numerical scheme with constant coefficients at each time step. Furthermore, the Fourier spectral method is used for the spatial discretization. Finally, we show that the CNLF scheme is fully discrete, second-order decoupled and unconditionally stable. Ample numerical experiments in 2D and 3D are provided to demonstrate the accuracy, efficiency, and stability of the proposed method.

The Neuron-Specific Protein TMEM59L Mediates Oxidative Stress-Induced Cell Death.

TMEM59L is a newly identified brain-specific membrane-anchored protein with unknown functions. Herein we found that both TMEM59L and its homolog, TMEM59, are localized in Golgi and endosomes. However, in contrast to a ubiquitous and relatively stable temporal expression of TMEM59, TMEM59L expression was limited in neurons and increased during development. We also found that both TMEM59L and TMEM59 interacted with ATG5 and ATG16L1, and that overexpression of them triggered cell autophagy. However, overexpression of TMEM59L induced intrinsic caspase-dependent apoptosis more dramatically than TMEM59. In addition, downregulation of TMEM59L prevented neuronal cell death and caspase-3 activation caused by hydrogen peroxide insults and reduced the lipidation of LC3B. Finally, we found that AAV-mediated knockdown of TMEM59L in mice significantly ameliorated caspase-3 activation, increased mouse duration in the open arm during elevated plus maze test, reduced mouse immobility time during forced swim test, and enhanced mouse memory during Y-maze and Morris water maze tests. Together, our study indicates that TMEM59L is a pro-apoptotic neuronal protein involved in animal behaviors such as anxiety, depression, and memory, and that TMEM59L downregulation protects neurons against oxidative stress.