Lipidation of the autophagy proteins LC3 and GABARAP is a membrane-curvature dependent process

The phagophore membrane is highly curved along the rim of the open cup, suggesting that the molecular mechanisms governing its formation and growth could rely on membrane curvature-dependent events. To this end, we recently reported that lipidation of the LC3 protein family is facilitated on highly curved membranes in vitro. We further showed that the conjugating enzyme ATG3 contains an amphipathic helix that is responsible for this membrane curvature dependency, and that the maintenance of this amphipathic structure is essential for ATG3 function in vivo.     

Mechanisms of membrane deformation by lipid-binding domains

Among an increasing number of lipid-binding domains, a group that not only binds to membrane lipids but also changes the shape of the membrane has been found. These domains are characterized by their strong ability to transform globular liposomes as well as flat plasma membranes into elongated membrane tubules both in vitro and in vivo. Biochemical studies on the structures of these proteins have revealed the importance of the amphipathic helix, which potentially intercalates into the lipid bilayer to induce and/or sense membrane curvature. Among such membrane-deforming domains, BAR and F-BAR/EFC domains form crescent-shaped dimers, suggesting a preference for a curved membrane, which is important for curvature sensing. Bioinformatics in combination with structural analyses has been identifying an increasing number of novel families of lipid-binding domains. This review attempts to summarize the evidence obtained by recent studies in order to gain general insights into the roles of membrane-deforming domains in a variety of biological events.     

Geometric and potential driving formation and evolution of biomolecular surfaces

This paper presents new geometrical flow equations for the theoretical modeling of biomolecular surfaces in the context of multiscale implicit solvent models. To account for the local variations near the biomolecular surfaces due to interactions between solvent molecules, and between solvent and solute molecules, we propose potential driven geometric flows, which balance the intrinsic geometric forces that would occur for a surface separating two homogeneous materials with the potential forces induced by the atomic interactions. Stochastic geometric flows are introduced to account for the random fluctuation and dissipation in density and pressure near the solvent–solute interface. Physical properties, such as free energy minimization (area decreasing) and incompressibility (volume preserving), are realized by some of our geometric flow equations. The proposed approach for geometric and potential forces driving the formation and evolution of biological surfaces is illustrated by extensive numerical experiments and compared with established minimal molecular surfaces and molecular surfaces. Local modification of biomolecular surfaces is demonstrated with potential driven geometric flows. High order geometric flows are also considered and tested in the present work for surface generation. Biomolecular surfaces generated by these approaches are typically free of geometric singularities. As the speed of surface generation is crucial to implicit solvent model based molecular dynamics, four numerical algorithms, a semi-implicit scheme, a Crank–Nicolson scheme, and two alternating direction implicit (ADI) schemes, are constructed and tested. Being either stable or conditionally stable but admitting a large critical time step size, these schemes overcome the stability constraint of the earlier forward Euler scheme. Aided with the Thomas algorithm, one of the ADI schemes is found to be very efficient as it balances the speed and accuracy.      

A differential geometry approach for biomedical image processing

We show in this paper how simple considerations about bio-arrays images lead to a peak segmentation allowing the genes activity analysis. Bio-arrays images have a particular structure and the aim of the paper is to present a mathematical method allowing their automatic processing. The differential geometry approach used here can be also employed for other types of images presenting grey level peaks corresponding to a functional activity or to a chemical concentration. The mathematical method is based on elementary techniques of differential geometry and dynamical systems theory and provides a simple efficient algorithm when the peaks to segment are isolated.     

The rate of fusion of phospholipid vesicles and the role of bilayer curvature

Kinetics of Ca²⁺-induced fusion of phosphatidylserine vesicles is studiied for lipid concentrations varying from 1 μM to 100 μM. Fusion is monitored by mixing of aqueous vesicle contents and by explicitly accounting for leakage. The analysis provides separately rates of aggregation and fusion. The rate of fusion per se decreases steeply with vesicle size.     

Effects of micropatterned curvature on the motility and mechanical properties of airway smooth muscle cells

Geometric features such as size and shape of the microenvironment are known to alter cell behaviors such as growth, differentiation, apoptosis, and migration. Little is known, however, about the effect of curvature on cell behaviors despite that many cells reside in curved space of tubular organs such as the bronchial airways. To address this question, we fabricated micropatterned strips that mimic airway walls with varying curvature. Then, we cultured airway smooth muscle cells (ASMCs) on these strips and investigated the cells’ motility and mechanical properties using time-lapse imaging microscopy and optical magnetic twisting cytometry (OMTC). We found that both motility and mechanical properties of the ASMCs were influenced by the curvature. In particular, when the curvature increased from 0 to 1/150 μm⁻¹, the velocity of cell migration first decreased (0–1/750 μm⁻¹), and then increased (1/750–1/150 μm⁻¹). In contrast, the cell stiffness increased and then decreased. Thus, at the intermediate curvature (1/750 μm⁻¹) the ASMCs were the least motile, but most stiff. The contractility instead decreased consistently as the curvature increased. The level of F-actin, and vinculin expression within the ASMCs appeared to correlate with the contractility and motility, respectively, in relation to the curvature. These results may provide valuable insights to understanding the heterogeneity of airway constrictions in asthma as well as the developing and functioning of other tubular organs and tissue engineering.     

The single-process biochemical reaction of Rubisco: a unified theory and model with the effects of irradiance, CO₂ and rate-limiting step on the kinetics of C₃ and C₄ photosynthesis from gas exchange

Photosynthesis is the origin of oxygenic life on the planet, and its models are the core of all models of plant biology, agriculture, environmental quality and global climate change. A theory is presented here, based on single process biochemical reactions of Rubisco, recognizing that: In the light, Rubisco activase helps separate Rubisco from the stored ribulose-1,5-bisphosphate (RuBP), activates Rubisco with carbamylation and addition of Mg²⁺, and then produces two products, in two steps: (Step 1) Reaction of Rubisco with RuBP produces a Rubisco-enediol complex, which is the carboxylase-oxygenase enzyme (Enco) and (Step 2) Enco captures CO₂ and/or O₂ and produces intermediate products leading to production and release of 3-phosphoglycerate (PGA) and Rubisco. PGA interactively controls (1) the carboxylation-oxygenation, (2) electron transport, and (3) triosephosphate pathway of the Calvin-Benson cycle that leads to the release of glucose and regeneration of RuBP. Initially, the total enzyme participates in the two steps of the reaction transitionally and its rate follows Michaelis-Menten kinetics. But, for a continuous steady state, Rubisco must be divided into two concurrently active segments for the two steps. This causes a deviation of the steady state from the transitional rate. Kinetic models are developed that integrate the transitional and the steady state reactions. They are tested and successfully validated with verifiable experimental data. The single-process theory is compared to the widely used two-process theory of Farquhar et al. (1980. Planta 149, 78-90), which assumes that the carboxylation rate is either Rubisco-limited at low CO₂ levels such as CO₂ compensation point, or RuBP regeneration-limited at high CO₂. Since the photosynthesis rate cannot increase beyond the two-process theory's Rubisco limit at the CO₂ compensation point, net photosynthesis cannot increase above zero in daylight, and since there is always respiration at night, it leads to progressively negative daily CO₂ fixation with no possibility of oxygenic life on the planet. The Rubisco-limited theory at low CO₂ also contradicts all experimental evidence for low substrate reactions, and for all known enzymes, Rubisco included.     

Mechanism of negative membrane curvature generation by I-BAR domains

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