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Despite some promising results in federated learning using game-theoretical methods, most existing studies mainly employ a one-level game in either a cooperative or competitive environment, failing to capture the complex dynamics among participants in practice. To address this issue, we propose DualGFL, a novel federated learning framework with a dual-level game in cooperative-competitive environments. DualGFL includes a lower-level hedonic game where clients form coalitions and an upper-level multi-attribute auction game where coalitions bid for training participation.At the lower-level DualGFL, we introduce a new auction-aware utility function and propose a Pareto-optimal partitioning algorithm to find a Pareto-optimal partition based on clients' preference profiles.At the upper-level DualGFL, we formulate a multi-attribute auction game with resource constraints and derive equilibrium bids to maximize coalitions' winning probabilities and profits. A greedy algorithm is proposed to maximize the utility of the central server.Extensive experiments on real-world datasets demonstrate DualGFL's effectiveness in improving both server utility and client utility. 

Phosphatidylinositides constitute only 1%–3% of plasma membranes but play vital roles in cellular signaling. In particular, phosphatidylinositol 4,5-bisphosphate (PIP2) is involved in processes such as cytoskeleton organization and ion channel regulation. Pleckstrin homology (PH) domains are modular domains found in many proteins and are known for their strong affinity for PIP2 headgroups. The role of lipid composition in PH domain binding to PIP2, particularly the inclusion of phos phatidylserine (PS), is not well understood. This study explores the mechanisms of PH domain binding to PIP2 using fluores cence spectroscopy, Fourier transform infrared spectroscopy, two-dimensional infrared spectroscopy, and molecular dynamics simulations. We find that anionic PIP2 and PS alter the interfacial environment compared to phosphatidylcholines. Additionally, the PH domain promotes the localization of anionic lipid domains upon binding. Our results highlight the role of PSinlipid domain formation within membranes and its potential influence on protein binding affinities and lipid geometries. Spe cifically, we discovered a strong interaction between PIP2 and PS whereby hydrogen bonding within these anionic lipids drives localization in the membrane. This interaction also regulates protein binding at the membrane interface. Our findings suggest that cooperativity between PIP2 and PS is key to the formation of localized lipid domains and the recruitment of proteins such as the PH domain of phospholipase C-d1 

Cell membranes are incredibly complex environments containing hundreds of components. Despite substantial advances in the past decade, fundamental questions related to lipid-lipid interactions and heterogeneity persist. This review explores the complexity of lipid membranes, showcasing recent advances in vibrational spectroscopy to characterize the structure, dynamics, and interactions at the membrane interface. We include an overview of modern techniques such as surface-enhanced infrared spectroscopy as a steady-state technique with single-bilayer sensitivity, two-dimensional sum-frequency generation spectroscopy, and two-dimensional infrared spectroscopy to measure time-evolving structures and dynamics with femtosecond time resolution. Furthermore, we discuss the potential of multiscale molecular dynamics (MD) simulations, focusing on recently developed simulation algorithms, which have emerged as a powerful approach to interpret complex spectra. We highlight the ongoing challenges in studying heterogeneous environments in multicomponent membranes via current vibrational spectroscopic techniques and MD simulations. Overall, this review provides an up-to-date comprehensive overview of the powerful combination of vibrational spectroscopy and simulations, which has great potential to illuminate lipid-lipid, lipid-protein, and lipid-water interactions in the intricate conformational landscape of cell membranes. 

Cell signaling is an important process involving complex interactions between lipids and proteins. The myristoylated alanine-rich C-kinase substrate (MARCKS) has been established as a key signaling regulator, serving a range of biological roles. Its effector domain (ED), which anchors the protein to the plasma membrane, induces domain formation in membranes containing phosphatidylinositol 4,5-bisphosphate (PIP2) and phosphatidylserine (PS). The mechanisms governing the MARCKS-ED binding to membranes remain elusive. Here, we investigate the composition-dependent affinity and MARCKS-ED-binding-induced changes in interfacial environments using two-dimensional infrared spectroscopy and fluorescence anisotropy. Both negatively charged lipids facilitate the MARCKS-ED binding to lipid vesicles. Although the hydrogen-bonding structure at the lipid-water interface remains comparable across vesicles with varied lipid compositions, the dynamics of interfacial water show divergent patterns due to specific interactions between lipids and peptides. Our findings also reveal that PIP2 becomes sequestered by bound peptides, while the distribution of PS exhibits no discernible change upon peptide binding. Interestingly, PIP2 and PS become colocalized into domains both in the presence and absence of MARCKS-ED. More broadly, this work offers molecular insights into the effects of membrane composition on binding.