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arXiv:2306.05614 · AVS Quantum Science

Estimation of the number of single-photon emitters for multiple fluorophores with the same spectral signature

Wenchao Li, Shuo Li, Timothy C. Brown, Qiang Sun, Xuezhi Wang, Vladislav V. Yakovlev, Allison Kealy, Bill Moran, Andrew D. Greentree

Published Nov 14, 2023• 4 citations
arXivHTMLPDF

Abstract

Fluorescence microscopy is of vital importance for understanding biological function. However, most fluorescence experiments are only qualitative inasmuch as the absolute number of fluorescent particles can often not be determined. Additionally, conventional approaches to measuring fluorescence intensity cannot distinguish between two or more fluorophores that are excited and emit in the same spectral window, as only the total intensity in a spectral window can be obtained. Here we show that, by using photon number resolving experiments, we are able to determine the number of emitters and their probability of emission for a number of different species, all with the same measured spectral signature. We illustrate our ideas by showing the determination of the number of emitters per species and the probability of photon collection from that species, for one, two and three otherwise unresolvable fluorophores. The convolution binomial model is presented to represent the counted photons emitted by multiple species. Then, the expectation-maximization (EM) algorithm is used to match the measured photon counts to the expected convolution binomial distribution function. In applying the EM algorithm, to leverage the problem of being trapped in a sub-optimal solution, the moment method is introduced to yield an initial guess for the EM algorithm. Additionally, the associated Cramér-Rao lower bound is derived and compared with the simulation results.

DOI
10.1116/5.0162501

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Fluorescence microscopy is of vital importance for understanding biological function. However, most fluorescence experiments are only qualitative inasmuch as the absolute number of fluorescent particles can often not be determined. Additionally, conventional approaches to measuring fluorescence intensity cannot distinguish between two or more fluorophores that are excited and emit in the same spectral window, as only the total intensity in a spectral window can be obtained. Here we show that, by using photon number resolving experiments, we are able to determine the number of emitters and their probability of emission for a number of different species, all with the same measured spectral signature. We illustrate our ideas by showing the determination of the number of emitters per species and the probability of photon collection from that species, for one, two and three otherwise unresolvable fluorophores. The convolution binomial model is presented to represent the counted photons emitted by multiple species. Then, the expectation-maximization (EM) algorithm is used to match the measured photon counts to the expected convolution binomial distribution function. In applying the EM algorithm, to leverage the problem of being trapped in a sub-optimal solution, the moment method is introduced to yield an initial guess for the EM algorithm. Additionally, the associated Cramér-Rao lower bound is derived and compared with the simulation results.
The fundamental understanding of biological pathways requires minimally invasive nanoscopic optical resolution imaging. Many approaches to high-resolution imaging rely on localization of single emitters, such as fluorescent molecules or quantum dots. Additionally, the exact determination of the number of such emitters in an imaging volume is essential for a number of applications; however, in standard intensity-based microscopy it is not possible to determine the number of individual emitters within a diffraction limited spot without initial knowledge of system parameters. Here we explore how quantum measurements of the emitted photons using photon number resolving detectors can be used to address this challenging task. In the proposed new approach, the problem of counting emitters reduces to the task of determining differences between the emitted photon distribution and the Poisson limit. We show that quantum measurements of the number of photons emitted from an ensemble of emitters enable the determination of both the number of emitters and the probability of emission. This method can be applied for any type of single-photon emitters. The scaling laws of this new approach are presented by the Cramer-Rao Lower Bounds, and this technique has great potential in quantum optical imaging with nanoscopic resolution.
Typical problems in molecular biology, like oligomerization of proteins, appear on non-resolvable length scales. Therefore a method which allows counting numbers of fluorescent emitters beyond this barrier can help to unveil these questions. One approach engaging this task makes use of the photon antibunching (PAB) effect. Most fluorophores are single photon emitters. Therefore upon a narrow excitation pulse they might only run through one excitation cycle and emit one photon at a time. This behavior is known as PAB. By analyzing coincident events of photon detections (Coincidence Analysis, CCA ) over many excitation cycles the number of fluorophores residing in the confocal volume can be estimated. Simulations have shown that up to 40 fluorophores can be distinguished with a reasonable error. In follow-up experiments five fluorophores could be distinguished by CCA. In this work the method is applied to a whole sample set and statistical variance and robustness are determined. CCA is critical to several parameters like photo stability, background noise, label efficiency and photopysical properties of the dye, like brightness and blinking. Therefore a reasonable scheme for analysis is introduced and setup parameters are optimized. To proof the superiority of CCA, it has been applied to estimate the number of dyes for a well-defined probe and the results have been compared with bleach step analysis (BS analysis), a method based on the ability to observe single bleach-steps.
In single-molecule fluorescence spectroscopy photon-antibunching is frequently used to prove the occurrence of single fluorophores. Furthermore, the relative frequency of coincident photon pairs was also used to determine the number of fluorophores in the diffraction limited observation volume of a confocal microscope. However, the ability to count fluorophores is so far limited to approximately 3 molecules due to saturation of the calibration curve with increasing number of fluorophores. Recently, we introduced a novel theoretical framework for counting the number of emitting molecules by analyzing photon-distributions acquired with a confocal microscope using four single-photon detectors. Here, we present the experimental realization of the proposed scheme in a confocal setup using novel multi-channel photon-counting electronics and DNA constructs that were labelled with five fluorophores. Our experimental results give a clear correlation between the number of estimated fluorophores and the number of bleaching steps for DNA probes conjugated with five ATTO647N labels with an error of approximately 20%. Moreover, we could acquire experimental data for up to 15 fluorophores indicating the simultaneous occurrence of three DNA probes. Our experiments put into perspective that the analysis of photon-distributions acquired with four detection channels is suited to count the number of fluorescently labelled molecules in larger aggregates or clusters with potential for applications in molecular and cell biology and for time-resolved analysis of multi-chromophoric compounds in material sciences.
The lack of reliable quantitative methods in fluorescence microscopy prevents the detailed investigation of basic molecular processes. Single-molecule fluorescence spectroscopy offers several techniques to determine the stoichiometry of fluorescent probes. Among them, an approach using the single-photon emission of an individual quantum system, also known as photon antibunching, yields access to both the emitter number and their molecular brightness. Previous work demonstrated the feasibility of the method to estimate up to five dyes without further physical characterization. In this work, I investigated and improved the reliability and robustness of this method. I developed different fluorescent probes with a defined label stoichiometry to explore the performance of our approach \nin experiments. I could demonstrate, in combination with simulations, that it can provide reliable estimates of up to 18 fluorescent emitters at a time resolution of approximately 200 ms. Furthermore, I inspected the dependency of the estimation bias and precision on the laser intensity, the analysis time and the number of expected molecules in detail. My results designate the scope for future stoichiometry determinations. In initial experiments, I analyzed the labeling distributions of different fluorescent probes. In addition, I could combine our counting approach with super-resolution STED-microscopy and identify critical parameters for possible applications
Single-molecule fluorescence microscopy has been established in life science as an essential tool for studying the characteristics and dynamics of individual fluorescent emitters both in vitro as well as in vivo. Acquiring quantitative information from the confocal observation volume is still a challenging task and knowing the absolute number or concentration of proteins in, e.g., cellular structures can significantly improve our understanding of cell biology, which is an important step towards quantitative microscopy. In this talk, a new quantitative analytical tool called Counting by Photon Statistics (CoPS) will be presented. The approach relies on a statistical analysis of detected photon coincidences to estimate the number of independent fluorescent labels in the observation volume [1]. CoPS does exploit the photon antibunching effect: a single photon emitter can only generate one photon at a time. Originally developed for point measurements, CoPS has recently been extended to an imaging scheme [2]. Using a confocal fluorescence microscopy setup with pulsed excitation, four single-photon, detectors and parallellized time-correlated single photon counting electronics (MicroTime 200, PicoQuant), we prove the applicability of the method with artificial model systems (immobilized DNA origami) and present first steps towards biological samples. [1] Ta, H., Wolfrum, J., Herten, D.-P., An extended scheme for counting fluorescent molecules by photon-antibunching Laser Phys. 20:119 (2010). [2] Ta, H. et al., Mapping molecules in scanning far-field fluorescence nanoscopy. Nat. Commun. 6:7977 (2015).
Quantitative information is key to unravel molecular processes in all fields of research. Counting by Photon Statistics (CoPS) is a single molecule technique that provides such quantification for fluorescent species. CoPS exploits the photon antibunching effect to infer \nthe number of independent emitters and their molecular brightness from multiple photon detection events. I laid the foundation for high quality results by improving the microscope detection efficiency more than threefold compared to earlier measurements. Using both simulations \nand experiments with defined, DNA-based probes, I investigated the critical interplay of fluorophore properties and analysis parameters. I discovered that measurements at high molecular brightness can be ten times faster than previously established which opens new possibilities for time resolved quantification. The findings stress that the choice of analysis parameters is vital and provide an objective measure of fluorophore eligibility for CoPS. I characterized sixteen \norganic dyes across the visible spectrum based on their molecular brightness and photostability. This study accomplished the transition of CoPS from a proof of concept technique to a widely applicable quantification method. Experiments demonstrated that CoPS can reveal \nthe label number distribution of fluorescent markers, a prerequisite for quantitative investigations in biology. Moreover, I showed that CoPS offers new perspectives for characterization of photophysical processes in photoluminescent materials.