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Abstract:

The main motivation of this work was to address the challenge of single-molecule functional study of membrane proteins under stable and independently controlled electrical and chemical membrane potentials. Although transmembrane potential is often essential for the function of membrane proteins, current in vitro systems provide only limited options for studying them under biologically relevant conditions. Our experimental assay is based on the droplet-on-hydrogel bilayer technique (Leptihn et al. Nat Protoc 8:1048–1057, 2013), where a lipid bilayer forms between a sub-millimetre water droplet and a thin hydrogel layer on a glass cover slip, enabling high-resolution microscopy in total internal reflection mode. To extend the application of this assay beyond channels to other membrane proteins, we introduce a custom-built, electronically controlled perfusion system that is designed to directly connect to the droplet above the lipid bilayer. This system can supply a stable voltage to the bilayer and is suitable for delivery of fragile membrane proteins embedded in proteoliposomes via charged fusion (Ishmukhametov et al. Nat Commun 7:13025, 2016), introducing changes of chemical potentials, and timed introduction of labels or substrate into the droplet. This work represents one of the steps towards single-molecule functional study of F1Fo ATP synthase under variable transmembrane potentials. High-resolution single-molecule observation of its rotation steps on the microsecond timescale could provide valuable insights into the mechanisms of energy transport across the molecule.

Abstract:

The dipole anisotropy induced by our peculiar motion in the sky distribution of cosmologically distant sources is an important consistency test of the standard Friedmann-Lemaître-Robertson-Walker cosmology. In this work, we formalize how to compute the kinematic matter dipole in redshift bins. Apart from the usual terms arising from angular aberration and flux boosting, there is a contribution from the boosting of the redshifts that becomes important when considering a sample selected on observed redshift, leading to nonvanishing correction terms. We discuss examples and provide expressions to incorporate arbitrary redshift selection functions. We also discuss the effect of redshift measurement uncertainties in this context, in particular in upcoming surveys for which we provide estimates of the correction terms. Depending on the shape of a sample’s redshift distribution and on the applied redshift cuts, the correction terms can become substantial, even to the degree that the direction of the dipole is reversed. Lastly, we discuss how cuts on variables correlated with observed redshift, such as color, can induce additional correction terms. Published by the American Physical Society 2025