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Protein–protein interactions (PPIs) regulate signalling pathways and cell phenotypes, and the visualization of spatially resolved dynamics of PPIs would thus shed light on the activation and crosstalk of signalling networks. Here we report a method that leverages a sequential proximity ligation assay for the multiplexed profiling of PPIs with up to 47 proteins involved in multisignalling crosstalk pathways. We applied the method, followed by conventional immunofluorescence, to cell cultures and tissues of non-small-cell lung cancers with a mutated epidermal growth-factor receptor to determine the co-localization of PPIs in subcellular volumes and to reconstruct changes in the subcellular distributions of PPIs in response to perturbations by the tyrosine kinase inhibitor osimertinib. We also show that a graph convolutional network encoding spatially resolved PPIs can accurately predict the cell-treatment status of single cells. Multiplexed proximity ligation assays aided by graph-based deep learning can provide insights into the subcellular organization of PPIs towards the design of drugs for targeting the protein interactome. 

The recently demonstrated chiral modes of lattice motion carry angular momentum and therefore directly couple to magnetic fields. Notably, their magnetic moments are predicted to be strongly influenced by electronic contributions. Here, we have studied the magnetic response of transverse optical phonons in a set of Pb_1−xSn_xTe films, which is a topological crystalline insulator forx> 0.32 and has a ferroelectric transition at anx-dependent critical temperature. Polarization-dependent terahertz magnetospectroscopy measurements revealed Zeeman splittings and diamagnetic shifts, demonstrating a large phonon magnetic moment. Films in the topological phase exhibited phonon magnetic moment values that were larger than those in the topologically trivial samples by two orders of magnitude. Furthermore, the sign of the effective phonong-factor was opposite in the two phases, a signature of the topological transition according to our model. These results strongly indicate the existence of interplay between the magnetic properties of chiral phonons and the topology of the electronic band structure. 

It has been proposed that classical filtering methods, like the Kalman filter and 3DVAR, can be used to solve linear statistical inverse problems. In the work of Iglesias, Lin, Lu, and Stuart (Commun. Math. Sci. 15(7):1867–1896, 2017), error estimates were obtained for this approach. By optimally tuning a regularization parameter in the filters, the authors were able to show that the mean squared error could be systematically reduced. Building on the aforementioned work of Iglesias, Lin, Lu, and Stuart, we prove that by (i) considering the problem in a weaker norm and (ii) applying simple iterate averaging of the filter output, 3DVAR will converge in mean square, unconditionally on the choice of parameter. Without iterate averaging, 3DVAR cannot converge by running additional iterations with a fixed choice of parameter. We also establish that the Kalman filter’s performance in this setting cannot be improved through iterate averaging. We illustrate our results with numerical experiments that suggest our convergence rates are sharp.