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1. Causal models with constraints

   S. Beckers; C. Hitchcock; J. Y. Halpern (April 2023, Proceedings of the Second Conference on Causal Learning and Reasoning)

   Causal models have proven extremely useful in offering formal representations of causal relationships between a set of variables. Yet in many situations, there are non-causal relationships among variables. For example, we may want variables LDL, HDL, and TOT that represent the level of low-density lipoprotein cholesterol, the level of lipoprotein high-density lipoprotein cholesterol, and total cholesterol level, with the relation LDL+HDL=\OT. This cannot be done in standard causal models, because we can intervene simultaneously on all three variables. The goal of this paper is to extend standard causal models to allow for constraints on settings of variables. Although the extension is relatively straightforward, to make it useful we have to define a new intervention operation that disconnects a variable from a causal equation. We give examples showing the usefulness of this extension, and provide a sound and complete axiomatization for causal models with constraints. 

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2. Probing the Interactions of LRP1 Ectodomain-Derived Peptides with Fibrillar Tau Protein and Its Impact on Cellular Internalization

   https://doi.org/10.3390/app13020853  

   Boder, E. Josephine; Goncalves, Beatriz G.; Lebedenko, Charlotta G.; Banerjee, Ipsita A. (January 2023, Applied Sciences)

   Cellular internalization and the spreading of misfolded tau have become increasingly important for elucidating the mechanism of Tau pathology involved in Alzheimer’s disease (AD). The low-density lipoprotein-related receptor 1 (LRP1) has been implicated in the internalization of fibrillar tau. In this work, we utilized homology modeling to model the Cluster 2 domain of LRP1 and determined that a 23-amino-acid sequence is involved in binding to paired helical filaments (PHF) of Tau. Fourteen short peptide segments derived from this ectodomain region were then designed and docked with PHF Tau. Molecular dynamics studies of the optimal peptides bound to PHF Tau demonstrated that the peptides formed critical contacts through Lys and Gln residues with Tau. Based on the computational results, flow cytometry, AFM, SPR analysis and CD studies were conducted to examine binding and cellular internalization. The results showed that the peptide sequence TauRP (1–14) (DNSDEENCES) was not only associated with fibrillar Tau but was also able to mitigate its cellular internalization in LRP1-expressed HEK-293 cells. Preliminary docking studies with Aβ (1–42) revealed that the peptides also bound to Aβ (1–42). While this study focused on the CCR2 domain of LRP1 to design peptide sequences to mitigate Tau internalization, the work can be extended to other domains of the LRP1 receptor or other receptors to examine if the cellular internalization of fibrillar Tau can be deterred. These findings show that short peptides derived from the LRP1 receptor can alter the internalization of its ligands. 

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3. Lipid-Mediated Modulation of mGluR2 Embedded in Micelle and Bilayer Environments: Insights from Molecular Dynamics

   https://doi.org/10.1101/2025.04.06.647485  

   Khodadadi, Ehsaneh; badiee, Shadi A; Khodadadi, Ehsan; Moradi, Mahmoud (April 2025, bioRxiv)

   Abstract Metabotropic glutamate receptor 2 (mGluR2), a subclass C member of the G protein-coupled receptor (GPCR) superfamily, is essential for regulating neurotransmitter signaling and facilitating synaptic adaptability in the central nervous system. This receptor, like other GPCRs, is highly sensitive to its surrounding lipid environment, where specific lipid compositions can influence its stability, conformational dynamics, and function. In particular, cholesteryl hemisuccinate (CHS) plays a critical role in stabilizing mGluR2 and modulating its structural states within cellular membranes and micellar environments. However, the molecular basis for this lipid-mediated modulation remains largely unexplored. To investigate the effects of CHS and lipid composition on mGluR2, we employed all-atom molecular dynamics simulations of mGluR2 embedded in both detergent micelles (BLMNG and CHS) and a POPC lipid bilayer containing 0%, 10%, and 25% CHS. These simulations were conducted for both active and inactive states of the receptor. Our findings reveal that CHS concentration modulates mGluR2’s structural stability and conformational behavior, with a marked impact observed within transmembrane helices TM1, TM2, and TM3, which constitute the core of the receptor’s transmembrane domain. In micelle environments, mGluR2 displayed unique conformational dynamics influenced by CHS, underscoring the receptor’s sensitivity to its lipid surroundings. Notably, a CHS concentration of 10% elicited more pronounced conformational changes than either cholesterol-depleted (0%) or cholesterol-enriched (25%) systems, indicating an optimal CHS range for maintaining structural stability. Our study provides atomistic insights into how lipid composition and CHS concentration impact mGluR2’s conformational landscape in distinct micelle and bilayer environments. These findings advance our understanding of lipid-mediated modulation in GPCR function, highlighting potential avenues for receptor-targeted drug design, particularly in cases where lipid interactions play a significant role in therapeutic efficacy. 

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4. Cholesterol Dependence of the Conformational Changes in Metabotropic Glutamate Receptor 1

   https://doi.org/10.1101/2024.04.17.589854  

   Isu, Ugochi H; Badiee, Shadi A; Polasa, Adithya; Tabari, Seyed H; Derakhshani-Molayousefi, Mortaza; Moradi, Mahmoud (April 2024, bioRxiv)

   Abstract Metabotropic glutamate receptors (mGluRs) are class C G protein-coupled receptors that function as obligate dimers in regulating neurotransmission and synaptic plasticity in the central nervous system. The mGluR1 subtype has been shown to be modulated by the membrane lipid environment, particularly cholesterol, though the molecular mechanisms remain elusive. In this study, we employed all-atom molecular dynamics simulations to investigate the effects of cholesterol on the conformational dynamics of the mGluR1 seven-transmembrane (7TM) domain in an inactive state model. Simulations were performed with three different cholesterol concentrations (0%, 10%, and 25%) in a palmitoyl-oleoyl phosphatidylcholine (POPC) lipid bilayer system. Our results demonstrate that cholesterol induces conformational changes in the mGluR1 dimer more significantly than in the individual protomers. Notably, cholesterol modulates the dynamics and conformations of the TM1 and TM2 helices at the dimer interface. Interestingly, an intermediate cholesterol concentration of 10% elicits more pronounced conformational changes compared to both cholesterol-depleted (0%) and cholesterol-enriched (25%) systems. Specific electrostatic interaction unique to the 10% cholesterol system further corroborate these conformational differences. Given the high sequence conservation of the 7TM domains across mGluR subtypes, the cholesterol-dependent effects observed in mGluR1 are likely applicable to other members of this receptor family. Our findings provide atomistic insights into how cholesterol modulates the conformational landscape of mGluRs, which could impact their function and signaling mechanisms. 

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5. Crystallization of ApoA1 and ApoE4 Nanolipoprotein Particles and Initial XFEL-Based Structural Studies

   https://doi.org/10.3390/cryst10100886  

   Shelby, Megan; Gilbile, Deepshika; Grant, Thomas; Bauer, William; Segelke, Brent; He, Wei; Evans, Angela; Crespo, Natalia; Fischer, Pontus; Pakendorf, Tim; et al (October 2020, Crystals)

   Nanolipoprotein particles (NLPs), also called “nanodiscs”, are discoidal particles with a patch of lipid bilayer corralled by apolipoproteins. NLPs have long been of interest due to both their utility as membrane-model systems into which membrane proteins can be inserted and solubilized and their physiological role in lipid and cholesterol transport via high-density lipoprotein (HDL) and low-density lipoprotein (LDL) maturation, which are important for human health. Serial femtosecond crystallography (SFX) at X-ray free electron lasers (XFELs) is a powerful approach for structural biology of membrane proteins, which are traditionally difficult to crystallize as large single crystals capable of producing high-quality diffraction suitable for structure determination. To facilitate understanding of the specific role of two apolipoprotein/lipid complexes, ApoA1 and ApoE4, in lipid binding and HDL/LDL particle maturation dynamics, and to develop new SFX methods involving NLP membrane protein encapsulation, we have prepared and crystallized homogeneous populations of ApoA1 and ApoE4 NLPs. Crystallization of empty NLPs yields semi-ordered objects that appear crystalline and give highly anisotropic and diffuse X-ray diffraction, similar to fiber diffraction. Several unit cell parameters were approximately determined for both NLPs from these measurements. Thus, low-background, sample conservative methods of delivery are critical. Here we implemented a fixed target sample delivery scheme utilizing the Roadrunner fast-scanning system and ultra-thin polymer/graphene support films, providing a low-volume, low-background approach to membrane protein SFX. This study represents initial steps in obtaining structural information for ApoA1 and ApoE4 NLPs and developing this system as a supporting scaffold for future structural studies of membrane proteins crystalized in a native lipid environment. 

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