Molecular contribution function in RESOLFT nanoscopy.

The ultimate objective of a microscope of the highest resolution is to map the molecules of interest in the sample. Traditionally, linear imaging systems are characterized by their spatial frequency transfer function, which is given, in real space, by the point spread function (PSF). By extending the concept of the PSF towards the molecular contribution function (MCF), that quantifies the average contribution of a single fluorophore to the image, a straightforward concept for counting fluorophores is obtained. Using reversible saturable optical fluorescence transitions (RESOLFT), fluorophores are effectively activated only in a small, subdiffraction-sized volume before they are read out. During readout the signal exhibits an increased variance due to the stochastic nature of prior activation, which scales quadratically with the brightness of the active fluorophores while the mean of the signal scales only linearly with it. Using a two-state Markov model for the activation, showing comparable behavior to the switching kinetics of the switchable fluorescent protein rsEGFP2, we can approximate quantitatively the MCF of RESOLFT nanoscopy allowing to count the number of fluorophores within a subdiffraction-sized region of the sample. The method is validated on measurements of tubulin structures in Drosophila melagonaster larvae. Modeling and estimation of the MCF is a promising approach to quantitative microscopy.

Live-cell RESOLFT nanoscopy of transgenic Arabidopsis thaliana.

Subdiffraction super-resolution fluorescence microscopy, or nanoscopy, has seen remarkable developments in the last two decades. Yet, for the visualization of plant cells, nanoscopy is still rarely used. In this study, we established RESOLFT nanoscopy on living green plant tissue. Live-cell RESOLFT nanoscopy requires and utilizes comparatively low light doses and intensities to overcome the diffraction barrier. We generated a transgenic Arabidopsis thaliana plant line expressing the reversibly switchable fluorescent protein rsEGFP2 fused to the mammalian microtubule-associated protein 4 (MAP4) in order to ubiquitously label the microtubule cytoskeleton. We demonstrate the use of RESOLFT nanoscopy for extended time-lapse imaging of cortical microtubules in Arabidopsis leaf discs. By combining our approach with fluorescence lifetime gating, we were able to acquire live-cell RESOLFT images even close to chloroplasts, which exhibit very strong autofluorescence. The data demonstrate the feasibility of subdiffraction resolution imaging in transgenic plant material with minimal requirements for sample preparation.

Ultrafast ab Initio Quantum Chemistry Using Matrix Product States.

Ultrafast dynamics in chemical systems provide a unique access to fundamental processes at the molecular scale. A proper description of such systems is often very challenging because of the quantum nature of the problem. The concept of matrix product states (MPS), however, has proven its performance in describing such correlated quantum systems in recent years for a wide range of applications. In this work, we continue the development of the MPS approach to study ultrafast electron dynamics in quantum chemical systems. The method combines time evolution schemes, such as fourth-order Runge-Kutta and Krylov space time evolution, with MPS, in order to solve the time-dependent Schrödinger equation efficiently. This allows for describing electron dynamics in molecules on a full configurational interaction (CI) level for a few femtoseconds after excitation. As a benchmark, we compare MPS-based calculations to full CI calculations for a chain of hydrogen atoms and for the water molecule. Krylov space time evolution is in particular suited for the MPS approach, as it provides a wide range of opportunities to be adjusted to the reduced MPS dimension case. Finally, we apply the MPS approach to describe charge migration effects in iodoacetylene and find direct agreement between our results and experimental observations.