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We investigate system-size effects on the rotational diffusion of membrane proteins and other membrane-embedded molecules in molecular dynamics simulations. We find that the rotational diffusion coefficient slows down relative to the infinite-system value by a factor of one minus the ratio of protein and box areas. This correction factor follows from the hydrodynamics of rotational flows under periodic boundary conditions and is rationalized in terms of Taylor-Couette flow. For membrane proteins like transporters, channels, or receptors in typical simulation setups, the protein-covered area tends to be relatively large, requiring a significant finite-size correction. Molecular dynamics simulations of the protein adenine nucleotide translocase (ANT1) and of a carbon nanotube porin in lipid membranes show that the hydrodynamic finite-size correction for rotational diffusion is accurate in standard-use cases. The dependence of the rotational diffusion on box size can be used to determine the membrane viscosity.
Autophagy is a highly conserved catabolic process through which defective or otherwise harmful cellular components are targeted for degradation via the lysosomal route. Regulatory pathways, involving post-translational modifications such as phosphorylation, play a critical role in controlling this tightly orchestrated process. Here, we demonstrate that TBK1 regulates autophagy by phosphorylating autophagy modifiers LC3C and GABARAP-L2 on surface-exposed serine residues (LC3C S93 and S96; GABARAP-L2 S87 and S88). This phosphorylation event impedes their binding to the processing enzyme ATG4 by destabilizing the complex. Phosphorylated LC3C/GABARAP-L2 cannot be removed from liposomes by ATG4 and are thus protected from ATG4-mediated premature removal from nascent autophagosomes. This ensures a steady coat of lipidated LC3C/GABARAP-L2 throughout the early steps in autophagosome formation and aids in maintaining a unidirectional flow of the autophagosome to the lysosome. Taken together, we present a new regulatory mechanism of autophagy, which influences the conjugation and de-conjugation of LC3C and GABARAP-L2 to autophagosomes by TBK1-mediated phosphorylation.