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We extend the standard solid-state quantum mechanical Hamiltonian containing only Coulomb interactions between the charged particles by inclusion of the (transverse) current-current diamagnetic interaction starting from the non-relativistic QED restricted to the states without photons and neglecting the retardation in the photon propagator. This derivation is supplemented with a derivation of an analogous result along the non-rigorous old classical Darwin-Landau-Lifshitz argumentation within the physical Coulomb gauge.
The rapid spread of the Coronavirus (COVID-19) confronts policy makers with the problem of measuring the effectiveness of containment strategies, balancing public health considerations with the economic costs of social distancing measures. We introduce a modified epidemic model that we name the controlled-SIR model, in which the disease reproduction rate evolves dynamically in response to political and societal reactions. An analytic solution is presented. The model reproduces official COVID-19 cases counts of a large number of regions and countries that surpassed the first peak of the outbreak. A single unbiased feedback parameter is extracted from field data and used to formulate an index that measures the efficiency of containment strategies (the CEI index). CEI values for a range of countries are given. For two variants of the controlled-SIR model, detailed estimates of the total medical and socio-economic costs are evaluated over the entire course of the epidemic. Costs comprise medical care cost, the economic cost of social distancing, as well as the economic value of lives saved. Under plausible parameters, strict measures fare better than a hands-off policy. Strategies based on current case numbers lead to substantially higher total costs than strategies based on the overall history of the epidemic.
Living cells constantly remodel the shape of their lipid membranes. In the endo-plasmic reticulum (ER), the reticulon homology domain (RHD) of the reticulophagy regulator 1 (RETR1/FAM134B) forms dense autophagic puncta that are associated with membrane removal by ER-phagy. In molecular dynamics (MD) simulations, we find that FAM134B-RHD spontaneously forms clusters, driven in part by curvature-mediated attraction. At a critical size, the FAM134B-RHD clusters induce the formation of membrane buds. The kinetics of budding depends sensitively on protein concentration and bilayer asymmetry. Our MD simulations shed light on the role of FAM134B-RHD in ER-phagy and show that membrane asymmetry can be used to modulate the kinetics barrier for membrane remodeling.
Living cells constantly remodel the shape of their lipid membranes. In the endoplasmic reticulum (ER), the reticulon homology domain (RHD) of the reticulophagy regulator 1 (RETR1/FAM134B) forms dense autophagic puncta that are associated with membrane removal by ER-phagy. In molecular dynamics (MD) simulations, we find that FAM134B-RHD spontaneously forms clusters, driven in part by curvature-mediated attractions. At a critical size, as in a nucleation process, the FAM134B-RHD clusters induce the formation of membrane buds. The kinetics of budding depends sensitively on protein concentration and bilayer asymmetry. Our MD simulations shed light on the role of FAM134B-RHD in ER-phagy and show that membrane asymmetry can be used to modulate the kinetic barrier for membrane remodeling.
Nuclear pore complexes (NPCs) mediate nucleocytoplasmic transport. Their intricate 120 MDa architecture remains incompletely understood. Here, we report a near-complete structural model of the human NPC scaffold with explicit membrane and in multiple conformational states. We combined AI-based structure prediction with in situ and in cellulo cryo-electron tomography and integrative modeling. We show that linker Nups spatially organize the scaffold within and across subcomplexes to establish the higher-order structure. Microsecond-long molecular dynamics simulations suggest that the scaffold is not required to stabilize the inner and outer nuclear membrane fusion, but rather widens the central pore. Our work exemplifies how AI-based modeling can be integrated with in situ structural biology to understand subcellular architecture across spatial organization levels.
Binding of the spike protein of SARS-CoV-2 to the human angiotensin-converting enzyme 2 (ACE2) receptor triggers translocation of the virus into cells. Both the ACE2 receptor and the spike protein are heavily glycosylated, including at sites near their binding interface. We built fully glycosylated models of the ACE2 receptor bound to the receptor binding domain (RBD) of the SARS-CoV-2 spike protein. Using atomistic molecular dynamics (MD) simulations, we found that the glycosylation of the human ACE2 receptor contributes substantially to the binding of the virus. Interestingly, the glycans at two glycosylation sites, N90 and N322, have opposite effects on spike protein binding. The glycan at the N90 site partly covers the binding interface of the spike RBD. Therefore, this glycan can interfere with the binding of the spike protein and protect against docking of the virus to the cell. By contrast, the glycan at the N322 site interacts tightly with the RBD of the ACE2-bound spike protein and strengthens the complex. Remarkably, the N322 glycan binds to a conserved region of the spike protein identified previously as a cryptic epitope for a neutralizing antibody. By mapping the glycan binding sites, our MD simulations aid in the targeted development of neutralizing antibodies and SARS-CoV-2 fusion inhibitors.
Cysteine cross-linking in native membranes establishes the transmembrane architecture of Ire1
(2021)
The ER is a key organelle of membrane biogenesis and crucial for the folding of both membrane and secretory proteins. Sensors of the unfolded protein response (UPR) monitor the unfolded protein load in the ER and convey effector functions for maintaining ER homeostasis. Aberrant compositions of the ER membrane, referred to as lipid bilayer stress, are equally potent activators of the UPR. How the distinct signals from lipid bilayer stress and unfolded proteins are processed by the conserved UPR transducer Ire1 remains unknown. Here, we have generated a functional, cysteine-less variant of Ire1 and performed systematic cysteine cross-linking experiments in native membranes to establish its transmembrane architecture in signaling-active clusters. We show that the transmembrane helices of two neighboring Ire1 molecules adopt an X-shaped configuration independent of the primary cause for ER stress. This suggests that different forms of stress converge in a common, signaling-active transmembrane architecture of Ire1.
Background: Organoids are morphologically heterogeneous three-dimensional cell culture systems and serve as an ideal model for understanding the principles of collective cell behaviour in mammalian organs during development, homeostasis, regeneration, and pathogenesis. To investigate the underlying cell organisation principles of organoids, we imaged hundreds of pancreas and cholangiocarcinoma organoids in parallel using light sheet and bright-field microscopy for up to 7 days.
Results: We quantified organoid behaviour at single-cell (microscale), individual-organoid (mesoscale), and entire-culture (macroscale) levels. At single-cell resolution, we monitored formation, monolayer polarisation, and degeneration and identified diverse behaviours, including lumen expansion and decline (size oscillation), migration, rotation, and multi-organoid fusion. Detailed individual organoid quantifications lead to a mechanical 3D agent-based model. A derived scaling law and simulations support the hypotheses that size oscillations depend on organoid properties and cell division dynamics, which is confirmed by bright-field microscopy analysis of entire cultures.
Conclusion: Our multiscale analysis provides a systematic picture of the diversity of cell organisation in organoids by identifying and quantifying the core regulatory principles of organoid morphogenesis.
In dieser Bachelorarbeit werden verschiedene Methoden zur Bestimmung der Betriebsfrequenz von CH-Kavitäten untersucht. Aufgrund der geometrisch komplexen Form der Beschleunigungsstruktur, können die Eigenfrequenzen nicht mithilfe von analytischen Methoden bestimmt werden. Üblicherweise werden die Eigenfrequenzen, ihre Ladungsund Stromdichten, sowie die elektromagnetischen Felder über numerische Methoden der Computational Electromagnetics (CEM) ermittelt. Die CEM ist eine junge Disziplin, deren Performanz und Anwendungsgebiete in den letzten 20 Jahren rapide gewachsen sind. Hauptverantwortlich hierfür ist zum einen das exponentielle Wachstum der Rechenleitung bei gleichbleibenden Kosten, zum anderen die Entwicklung und Verbesserung der Algorithmen. Bis zum Ende des letzten Jahrhunderts wurden elektronische Komponenten hauptsächlich dadurch entwickelt, indem Prototypen angefertigt und analysiert wurden. Diese zeitaufwendige und kostspielige Herangehensweise ist heutzutage nahezu vollständig durch CEM-Simulationen ersetzt worden. Die Hauptmethoden der CEM sind die Finite-Differenzen-Methode (FDM), die Momenten-Methode (MoM) und die Finite-Elemente-Methode (FEM). Für die Bestimmung der Eigenwerte und Eigenvektoren der Beschleunigungsstrukturen eignet sich aufgrund der Stabilität von diesen Dreien am besten die Methode der finiten Elemente. Da die FEM ein rechen- und speicherintensives Verfahren ist, wurde in dieser Arbeit nach einer schnelleren Methode gesucht, um die Betriebsfrequenz von CH-Kavitäten zu bestimmen. Hierfür wurden 84 CH-Kavitäten mithilfe von CST Studio Suite erstellt und simuliert. Es handelt sich hierbei um vier Grundtypen, drei wurden bei einer fixierten Sollfrequenz von 300 MHz konstruiert; die Sollfrequenz des vierten Grundtyps betrug 175 MHz. Die Teilchengeschwindigkeit wurde jeweils in 0,01er-Schrtitten von 0,05 c bis 0,25 c variiert. Aus den Untersuchungen der EM-Felder wurde anschließend ein semi-analytisches Modell entwickelt, das aufgrund der Geometrie der CH-Kavität die Betriebsfrequenz liefern soll.
The direct study of transcription or DNA–protein-binding events, requires imaging of individual genes at molecular resolution. Electron microscopy (EM) can show local detail of the genome. However, direct visualization and analysis of specific individual genes is currently not feasible as they cannot be unambiguously localized in the crowded, landmark-free environment of the nucleus. Here, we present a method for the genomic insertion of gene clusters that can be localized and imaged together with their associated protein complexes in the EM. The method uses CRISPR/Cas9 technology to incorporate several genes of interest near the 35S rRNA gene, which is a frequently occurring, easy-to-identify genomic locus within the nucleolus that can be used as a landmark in micrographs. As a proof of principle, we demonstrate the incorporation of the locus-native gene RDN5 and the locus-foreign gene HSX1. This led to a greater than 7-fold enrichment of RNA polymerase III (Pol III) complexes associated with the genes within the field of view, allowing for a significant increase in the analysis yield. This method thereby allows for the insertion and direct visualization of gene clusters for a range of analyses, such as changes in gene activity upon alteration of cellular or external factors.