Optimal estimation of drift and diffusion coefficients in the presence of static localization error

4Pi MINFLUX arrangement maximizes spatio-temporal localization precision of fluorescence emitter

We introduce MINFLUX localization with interferometric illumination through opposing objective lenses for maximizing the attainable precision in 3D-localization of single inelastic scatterers, such as fluorophores. Our 4Pi optical configuration employs three sequentially tilted counter-propagating beam pairs for illumination, each providing a narrow interference minimum of illumination intensity at the focal point. The localization precision is additionally improved by adding the inelastically scattered or fluorescence photons collected through both objective lenses. Our 4Pi configuration yields the currently highest precision per detected photon among all localization schemes. Tracking gold nanoparticles as non-blinking inelastic scatterers rendered a position uncertainty <0.4 nm3 in volume at a localization frequency of 2.9 kHz. We harnessed the record spatio-temporal precision of our 4Pi MINFLUX approach to examine the diffusion of single fluorophores and fluorescent nanobeads in solutions of sucrose in water, revealing local heterogeneities at the nanoscale. Our results show the applicability of 4Pi MINFLUX to study molecular nano-environments of diffusion and its potential for quantifying rapid movements of molecules in cells and other material composites.

Fitting an active Brownian particle's mean-squared displacement with improved parameter estimation

The active Brownian particle (ABP) model is widely used to describe the dynamics of active matter systems, such as Janus microswimmers. In particular, the analytical expression for an ABP's mean-squared displacement (MSD) is useful as it provides a means to describe the essential physics of a self-propelled, spherical Brownian particle. However, the truncated or "short-time" form of the MSD equation is typically fitted, which can lead to significant problems in parameter estimation. Furthermore, heteroscedasticity and the often statistically dependent observations of an ABP's MSD lead to a situation where standard ordinary least-squares regression leads to biased estimates and unreliable confidence intervals. Instead, we propose here to revert to always fitting the full expression of an ABP's MSD at short timescales, using bootstrapping to construct confidence intervals of the fitted parameters. Additionally, after comparison between different fitting strategies, we propose to extract the physical parameters of an ABP using its mean logarithmic squared displacement. These steps improve the estimation of an ABP's physical properties and provide more reliable confidence intervals, which are critical in the context of a growing interest in the interactions of microswimmers with confining boundaries and the influence on their motion.

Modeling charge separation in charged nanochannels for single-molecule electrometry

We model the transport of electrically charged solute molecules by a laminar flow within a nanoslit microfluidic channel with electrostatic surface potential. We derive the governing convection–diffusion equation, solve it numerically, and compare it with a Taylor–Aris-like approximation, which gives excellent results for small Péclet numbers. We discuss our results in light of designing an assay that can measure simultaneously the hydrodynamic size and electric charge of single molecules by tracking their motion in such nanoslit channels with electrostatic surface potential.