Variational calculus approach to Zernike polynomials with application to fluorescence correlation spectroscopy.

Zernike polynomials are a sequence of orthogonal polynomials that play a crucial role in optics and in particular in modeling microscopy systems. Introduced by Frits Zernike in 1934, they are particularly useful in expressing wavefront aberrations and thus imperfections of imaging systems. However, their origin and properties are rarely discussed and proven. Here, we present a novel approach to Zernike polynomials using variational calculus, and apply them to describe aberrations in fluorescence microscopy. In particular, we model the impact of various optical aberrations on the performance of one-photon and two-photon excitation fluorescence microscopy.

Rotational and translational diffusion of biomolecules in complex liquids and HeLa cells.

Diffusive motion accompanies many physical and biological processes. The Stokes-Sutherland-Einstein relation for the translational diffusion coefficient, DT, agrees with experiments done in simple fluids but fails for complex fluids. Moreover, the interdependence between DT and rotational diffusion coefficient, DR, also deviates in complex fluids from the classical relation of DT/DR = 4r2/3 known in simple fluids. Makuch et al. Soft Matter, 2020, 16, 114-124 presented a generalization of the classical translational and rotational diffusion theory for complex fluids. In this work, we empirically verify this model based on simultaneous translational and rotational diffusion measurements. We use fluorescently stained cowpea chlorotic mottle virus (CCMV) particles as monodisperse probes and aqueous polyethylene glycol (PEG) solutions as a model complex fluid. The theory and experimental data obtained from fluorescence correlation spectroscopy (FCS) measurements agreed. Finally, we used the same model and analyzed the diffusion of Yo-Pro-1 stained large ribosomal subunits (LSU) in the cytoplasm and nucleus of living HeLa cells.

Cholesterol-Induced Nanoscale Variations in the Thickness of Phospholipid Membranes.

Graphene-induced energy transfer (GIET) is a recently developed fluorescence-spectroscopic technique that achieves subnanometric optical localization of fluorophores along the optical axis of a microscope. GIET is based on the near-field energy transfer from an optically excited fluorescent molecule to a single sheet of graphene. It has been successfully used for estimating interleaflet distances of single lipid bilayers and for investigating the membrane organization of living mitochondria. In this study, we use GIET to measure the cholesterol-induced subtle changes of membrane thickness at the nanoscale. We quantify membrane thickness variations in supported lipid bilayers (SLBs) as a function of lipid composition and increasing cholesterol content. Our findings demonstrate that GIET is an extremely sensitive tool for investigating nanometric structural changes in biomembranes.

Local Water Content in Polymer Gels Measured with Super-Resolved Fluorescence Lifetime Imaging.

Water molecules play an important role in the structure, function, and dynamics of (bio-) materials. A direct access to the number of water molecules in nanoscopic volumes can thus give new molecular insights into materials and allow for fine-tuning their properties in sophisticated applications. The determination of the local water content has become possible by the finding that H2 O quenches the fluorescence of red-emitting dyes. Since deuterated water, D2 O, does not induce significant fluorescence quenching, fluorescence lifetime measurements performed in different H2 O/D2 O-ratios yield the local water concentration. We combined this effect with the recently developed fluorescence lifetime single molecule localization microscopy imaging (FL-SMLM) in order to nanoscopically determine the local water content in microgels, i.e. soft hydrogel particles consisting of a cross-linked polymer swollen in water. The change in water content of thermo-responsive microgels when changing from their swollen state at room temperature to a collapsed state at elevated temperature could be analyzed. A clear decrease in water content was found that was, to our surprise, rather uniform throughout the entire microgel volume. Only a slightly higher water content around the dye was found in the periphery with respect to the center of the swollen microgels.

Fluorophore position of headgroup-labeled Gb3 glycosphingolipids in lipid bilayers.

Fluorescent lipid probes are an invaluable tool for investigating lipid membranes. In particular, localizing certain receptor lipids such as glycosphingolipids within phase-separated membranes is of pivotal interest to understanding the influence of protein-receptor lipid binding on membrane organization. However, fluorescent labeling can readily alter the phase behavior of a lipid membrane because of the interaction of the fluorescent moiety with the membrane interface. Here, we investigated Gb3 glycosphingolipids, serving as receptor lipids for the protein Shiga toxin, with a headgroup attached BODIPY fluorophore separated by a polyethylene glycol (PEG) spacer of different lengths. We found that the diffusion coefficients of the fluorescently labeled Gb3 species in 1,2-dioleoyl-sn-glycero-3-phosphocholine/Gb3 (98:2, n/n) supported lipid bilayers are unaltered by the PEG spacer length. However, quenching as well as graphene-induced energy transfer experiments indicated that the length of the PEG spacer (n = 3 and n = 13) alters the position of the BODIPY fluorophore. In particular, the graphene-induced energy transfer technique provided accurate end-to-end distances between the fluorophores in the two leaflets of the bilayer thus enabling us to quantify the distance between the membrane interface and the fluorophore with sub-nanometer resolution. The spacer with three oligo ethylene glycol groups positioned the BODIPY fluorophore directly at the membrane interface favoring its interaction with the bilayer and thus may disturb lipid packing. However, the longer PEG spacer (n = 13) separated the BODIPY moiety from the membrane surface by 1.5 nm.

Photophysical Studies at Cryogenic Temperature Reveal a Novel Photoswitching Mechanism of rsEGFP2.

Single-molecule localization microscopy (SMLM) at cryogenic temperature opens new avenues to investigate intact biological samples at the nanoscale and perform cryo-correlative studies. Genetically encoded fluorescent proteins (FPs) are markers of choice for cryo-SMLM, but their reduced conformational flexibility below the glass-transition temperature hampers efficient cryo-photoswitching. We investigated cryo-switching of rsEGFP2, one of the most efficient reversibly switchable fluorescent proteins at ambient temperature due to facile cis-trans isomerization of the chromophore. UV-visible microspectrophotometry and X-ray crystallography revealed a completely different switching mechanism at ∼110 K. At this cryogenic temperature, on-off photoswitching involves the formation of two off-states in cis conformation with blue-shifted absorption relative to that of the trans protonated chromophore populated at ambient temperature. Only one of these off-states can be switched back to the fluorescent on-state by 405 nm light, while both of them are sensitive to UV light at 355 nm. Superior recovery to the fluorescent on-state by 355 nm light was confirmed at the single-molecule level. This suggests, as also shown by simulations, that employing 355 nm light in cryo-SMLM experiments using rsEGFP2 and possibly other FPs could improve the effective labeling efficiency achievable with this technique. The rsEGFP2 photoswitching mechanism discovered in this work adds to the panoply of known switching mechanisms in fluorescent proteins.

Single-Molecule Fluorescence Lifetime Imaging Using Wide-Field and Confocal-Laser Scanning Microscopy: A Comparative Analysis.

A recent addition to the toolbox of super-resolution microscopy methods is fluorescence-lifetime single-molecule localization microscopy (FL-SMLM). The synergy of SMLM and fluorescence-lifetime imaging microscopy (FLIM) combines superior image resolution with lifetime information and can be realized using two complementary experimental approaches: confocal-laser scanning microscopy (CLSM) or wide-field microscopy. Here, we systematically and comprehensively compare these two novel FL-SMLM approaches in different spectral regions. For wide-field FL-SMLM, we use a commercial lifetime camera, and for CLSM-based FL-SMLM we employ a home-built system equipped with a rapid scan unit and a single-photon detector. We characterize the performances of the two systems in localizing single emitters in 3D by combining FL-SMLM with metal-induced energy transfer (MIET) for localization along the third dimension and in the lifetime-based multiplexed bioimaging using DNA-PAINT. Finally, we discuss advantages and disadvantages of wide-field and confocal FL-SMLM and provide practical advice on rational FL-SMLM experiment design.

Electrically controlling and optically observing the membrane potential of supported lipid bilayers.

Supported lipid bilayers are a well-developed model system for the study of membranes and their associated proteins, such as membrane channels, enzymes, and receptors. These versatile model membranes can be made from various components, ranging from simple synthetic phospholipids to complex mixtures of constituents, mimicking the cell membrane with its relevant physiochemical and molecular phenomena. In addition, the high stability of supported lipid bilayers allows for their study via a wide array of experimental probes. In this work, we describe a platform for supported lipid bilayers that is accessible both electrically and optically, and demonstrate direct optical observation of the transmembrane potential of supported lipid bilayers. We show that the polarization of the supported membrane can be electrically controlled and optically probed using voltage-sensitive dyes. Membrane polarization dynamics is understood through electrochemical impedance spectroscopy and the analysis of an equivalent electrical circuit model. In addition, we describe the effect of the conducting electrode layer on the fluorescence of the optical probe through metal-induced energy transfer, and show that while this energy transfer has an adverse effect on the voltage sensitivity of the fluorescent probe, its strong distance dependency allows for axial localization of fluorescent emitters with ultrahigh accuracy. We conclude with a discussion on possible applications of this platform for the study of voltage-dependent membrane proteins and other processes in membrane biology and surface science.

Excited state lifetime modulation in semiconductor nanocrystals for super-resolution imaging.

We report on proof of principle measurements of a concept for a super-resolution imaging method that is based on excitation field density-dependent lifetime modulation of semiconductor nanocrystals. The prerequisite of the technique is access to semiconductor nanocrystals with emission lifetimes that depend on the excitation intensity. Experimentally, the method requires a confocal microscope with fluorescence-lifetime measurement capability that makes it easily accessible to a broad optical imaging community. We demonstrate with single particle imaging that the method allows one to achieve a spatial resolution of the order of several tens of nanometers at moderate fluorescence excitation intensity.

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.

Mapping Activity-Dependent Quasi-stationary States of Mitochondrial Membranes with Graphene-Induced Energy Transfer Imaging.

Graphene-induced energy transfer (GIET) was recently introduced for sub-nanometric axial localization of fluorescent molecules. GIET relies on near-field energy transfer from an optically excited fluorophore to a single sheet of graphene. Recently, we demonstrated its potential by determining the distance between two leaflets of supported lipid bilayers. Here, we use GIET imaging for mapping quasi-stationary states of the inner and outer mitochondrial membranes before and during adenosine triphosphate (ATP) synthesis. We trigger the ATP synthesis state in vitro by activating mitochondria with precursor molecules. Our results demonstrate that the inner membrane approaches the outer membrane, while the outer membrane does not show any measurable change in average axial position upon activation. The inter-membrane space is reduced by ∼2 nm. This direct experimental observation of the subtle dynamics of mitochondrial membranes and the change in intermembrane distance upon activation is relevant for our understanding of mitochondrial function.

Nanoparticles for super-resolution microscopy and single-molecule tracking.

We review the use of luminescent nanoparticles in super-resolution imaging and single-molecule tracking, and showcase novel approaches to super-resolution imaging that leverage the brightness, stability, and unique optical-switching properties of these nanoparticles. We also discuss the challenges associated with their use in biological systems, including intracellular delivery and molecular targeting. In doing so, we hope to provide practical guidance for biologists and continue to bridge the fields of super-resolution imaging and nanoparticle engineering to support their mutual advancement.

Transmembrane ß-peptide helices as molecular rulers at the membrane surface.

ß-Peptides are known to form 14-helices with high conformational rigidity, helical persistence length, and well-defined spacing and orientation regularity of amino acid side chains. Therefore, ß-peptides are well suited to serve as backbone structures for molecular rulers. On the one hand, they can be functionalized in a site-specific manner with molecular probes or fluorophores, and on the other hand, the ß-peptide helices can be recognized and anchored in a biological environment of interest. In this study, the ß-peptide helices were anchored in lipid bilayer membranes, and the helices were elongated in the outer membrane environment. The distances of the covalently bound probes to the membrane surface were determined using graphene-induced energy transfer (GIET) spectroscopy, a method based on the distance-dependent quenching of a fluorescent molecule by a nearby single graphene sheet. As a proof of principle, the predicted distances were determined for two fluorophores bound to the membrane-anchored ß-peptide molecular ruler.

Plasmon-Driven Modulation of Reaction Pathways of Individual Pt-Modified Au Nanorods.

Understanding the underlying kinetic mechanism of plasmon-enhanced catalysis is important for designing optimized bimetal nanostructures. Here, we characterize product formation rate at both the single-particle and ensemble level. The single-particle measurement allows us to reveal the underlying catalytic kinetic mechanisms of a bimetal nanostructure. Combining this with ensemble observations of two different catalytic behaviors of this catalyst with and without illumination shows that energetic charge carriers induce a transition from a competitive reactant adsorption type to a noncompetitive adsorption type, which leads to the suppression of catalytic rate decay at high reactant concentration. Theoretical modeling as well as analysis of hole acceptability of scavengers on Pt and Au surfaces indicates that the Pt light absorptivity is enhanced near Au and the energetic charges may form directly from the Pt part of the Au-Pt nanostructure. The presented study deepens our understanding of plasmon-enhanced catalysis by bimetal nanostructures.

Multi-Color, Bleaching-Resistant Super-Resolution Optical Fluctuation Imaging with Oligonucleotide-Based Exchangeable Fluorophores.

Super-resolution optical fluctuation imaging (SOFI) is a super-resolution microscopy technique that overcomes the diffraction limit by analyzing intensity fluctuations of statistically independent emitters in a time series of images. The final images are background-free and show confocality and enhanced spatial resolution (super-resolution). Fluorophore photobleaching, however, is a key limitation for recording long time series of images that will allow for the calculation of higher order SOFI results with correspondingly increased resolution. Here, we demonstrate that photobleaching can be circumvented by using fluorophore labels that reversibly and transiently bind to a target, and which are being replenished from a buffer which serves as a reservoir. Using fluorophore-labeled short DNA oligonucleotides, we labeled cellular structures with target-specific antibodies that contain complementary DNA sequences and record the fluctuation events caused by transient emitter binding. We show that this concept bypasses extensive photobleaching and facilitates two-color imaging of cellular structures with SOFI.

Dimerization of Human Drebrin-like Protein Governs Its Biological Activity.

Drebrin-like protein (DBNL) is a multidomain F-actin-binding protein, which also interacts with other molecules within different intracellular pathways. Here, we present quantitative measurements on the size and conformation of human DBNL. Using dual-focus fluorescence correlation spectroscopy, we determined the hydrodynamic radius of the DBNL monomer. Native gel electrophoresis and dual-color fluorescence cross-correlation spectroscopy show that both endogenous DBNL and recombinant DBNL exist as dimers under physiological conditions. We demonstrate that C-terminal truncations of DBNL downstream of the coiled-coil domain result in its oligomerization at nanomolar concentrations. In contrast, the ADF-H domain alone is a monomer, which displays a concentration-dependent self-assembly. In vivo FLIM-FRET imaging shows that the presence of only actin-binding domains is not sufficient for DBNL to localize properly at the actin filament inside the cell. In summary, our work provides detailed insight into the structure-function relationship of human drebrin-like protein.

Rapid nonlinear image scanning microscopy.

Image scanning microscopy (ISM) doubles the resolution of a conventional confocal microscope for super-resolution imaging. Here, we describe an all-optical ISM design based on rescanning microscopy for two-photon-excited fluorescence and second-harmonic generation that allows straightforward implementation into existing microscopes. The design offers improved sensitivity and high frame rates relative to those of existing systems. We demonstrate its utility using fixed and living specimens as well as collagen hydrogels.

Quantitative analysis of hidden particles diffusing behind a scattering layer using speckle correlation.

Speckle-correlation imaging is a family of methods that makes use of the "memory effect" to image objects hidden behind visually opaque layers. Here, we show that a correlation analysis can be applied to quantitative imaging of an ensemble of dynamic fluorescent beads diffusing on a 2D surface. We use an epi-fluorescence microscope where both the illumination and detection light patterns are speckled, due to light scattering by a thin disordered layer. The spatio-temporal cross-correlation of the detection speckle pattern is calculated as a function of lag time and spatial shift and is used to determine the diffusion constant and number of fluorescent particles in the sample without requiring any phase retrieval procedure. It is worth to note that the "memory effect" range is not required to extend beyond a distance of few speckle grains, thus making our method potentially useful for nearly arbitrary values of the thickness of the scattering layer.

Wide-Field Fluorescence Lifetime Imaging of Single Molecules.

Fluorescence lifetime imaging (FLIM) has become an important microscopy technique in bioimaging. The two most important of its applications are lifetime-multiplexing for imaging many different structures in parallel, and lifetime-based measurements of Förster resonance energy transfer. There are two principal FLIM techniques, one based on confocal-laser scanning microscopy (CLSM) and time-correlated single-photon counting (TCSPC) and the other based on wide-field microscopy and phase fluorometry. Although the first approach (CLSM-TCSPC) assures high sensitivity and allows one to detect single molecules, it is slow and has a small photon yield. The second allows, in principal, high frame rates (by 2-3 orders of magnitude faster than CLSM), but it suffers from low sensitivity, which precludes its application for single-molecule imaging. Here, we demonstrate that a novel wide-field TCSPC camera (LINCam25, Photonscore GmbH) can be successfully used for single-molecule FLIM, although its quantum yield of detection in the red spectral region is only ∼5%. This is due to the virtually absent background and readout noise of the camera, assuring high signal-to-noise ratio even at low detection efficiency. We performed single-molecule FLIM of different red fluorophores, and we use the lifetime information for successfully distinguishing between different molecular species. Finally, we demonstrate single-molecule metal-induced energy transfer (MIET) imaging which is a first step for three-dimensional single-molecule localization microscopy (SMLM) with nanometer resolution.

Size and mobility of lipid domains tuned by geometrical constraints.

In the plasma membrane of eukaryotic cells, proteins and lipids are organized in clusters, the latter ones often called lipid domains or "lipid rafts." Recent findings highlight the dynamic nature of such domains and the key role of membrane geometry and spatial boundaries. In this study, we used porous substrates with different pore radii to address precisely the extent of the geometric constraint, permitting us to modulate and investigate the size and mobility of lipid domains in phase-separated continuous pore-spanning membranes (PSMs). Fluorescence video microscopy revealed two types of liquid-ordered (lo) domains in the freestanding parts of the PSMs: (i) immobile domains that were attached to the pore rims and (ii) mobile, round-shaped lo domains within the center of the PSMs. Analysis of the diffusion of the mobile lo domains by video microscopy and particle tracking showed that the domains' mobility is slowed down by orders of magnitude compared with the unrestricted case. We attribute the reduced mobility to the geometric confinement of the PSM, because the drag force is increased substantially due to hydrodynamic effects generated by the presence of these boundaries. Our system can serve as an experimental test bed for diffusion of 2D objects in confined geometry. The impact of hydrodynamics on the mobility of enclosed lipid domains can have great implications for the formation and lateral transport of signaling platforms.