Signal to noise analysis of multiple color fluorescence imaging microscopy

BACKGROUND: Various approaches that were recently developed demonstrate the ability to simultaneously detect all human (or other species) chromosomes by using combinatorial labeling and fluorescence in situ hybridization (FISH). With the growing interest in this field, it is important to develop tools for optimizing and estimating the accuracy of different experimental methods. METHODS: We have analyzed the principles of multiple color fluorescence imaging microscopy. First, formalism based on the physical principles of fluorescence microscopy and noise analysis is introduced. Next, a signal to noise (S/N) analysis is performed and summarized in a simple accuracy criterion. The analysis assumes shot noise to be the dominant source of noise. RESULTS: The accuracy criterion was used to calculate the S/N of multicolor FISH (M-FISH), spectral karyotyping, ratio imaging, and a method based on using a set of broad band filters. Spectral karyotyping is tested on various types of samples and shows accurate classifications. We have also tested classification accuracy as a function of total measurement time. CONCLUSIONS: The accuracy criterion that we have developed can be used for optimizing and analyzing different multiple color fluorescence microscopy methods. The assumption that shot noise is dominant in these measurements is supported by our measurements.     

Optimum spectral windows to minimize quantum noise of ratiometric intracellular fluorescent probes

When fluorescent indicators are used to measure intracellular ligands in single cells, the quality of the data is usually limited by quantum (shot) noise. For indicators which shift excitation or emission wavelengths upon ligand binding, a ratiometric method is usually employed. In choosing the spectral windows for excitation or collection of fluorescence, there is a trade-off between maximum sensitivity to ligand binding, and maximum collection of light. We show that there is a well-defined optimum choice of windows which minimizes the error caused by quantum noise in the estimated ligand concentration. An algorithm for determining these optimum windows is presented. As an example, we consider the measurement of intracellular calcium by indo-1 fluorescence emission ratio in cardiac myocytes. The optimum wavelength bands for collection of fluorescence are considerably wider than those commonly employed. The use of these windows in a pulsed-excitation time-resolved calcium measurement instrument resulted in improved signal to noise ratio of the calcium signal.     

Fluorescence intensity resolution in flow systems.

The factor which can limit fluorescence intensity resolution in a flow cytometer of the type in which cells pass perpendicularly through a focussed laser beam depends on signal intensity. For the brightest sources (e.g. fluorescent DNA stains), the coefficient of variation (CV) is limited in our system to around 3% by stream hydrodynamics, unstable illumination intensity, nonstoichiometric staining, etc. The weakest detectable sources (e.g. fluorescent cell-surface labels) are limited in coefficient of variation by shot noise in the photomultiplier due to constant background light levels. Finally, over a fairly wide brightness range between these extremes, resolution is determined primarily by photoelectron statistical variation on the signal itself (i.e. "photon statistics"). Thus photon collection and detection efficiency (solid angle, barrier filter passband, detector quantum efficiency) become of primary importance.     

Polarized fluorescence resonance energy transfer microscopy

Current methods for fluorescence resonance energy transfer (FRET) microscopy of living cells involve taking a series of images with alternating excitation colors in separate camera exposures. Here we present a new FRET method based on polarization that requires only one camera exposure and thereby offers the possibility for better time resolution of dynamic associations among subcellular components. Polarized FRET (p-FRET) uses a simultaneous combination of excitation wavelengths from two orthogonally polarized sources, along with an emission channel tri-image splitter outfitted with appropriate polarizers, to concurrently excite and collect fluorescence from free donors, free acceptors, and FRET pairs. Based upon the throughput in each emission channel as premeasured on pure samples of each of the three species, decoupling of an unknown sample's three polarized fluorescence images can be performed to calculate the pixel-by-pixel concentrations of donor, acceptor, and FRET pairs. The theory of this approach is presented here, and its feasibility is experimentally confirmed by measurements on mixtures of cyan fluorescent protein (CFP), citrine ((Cit) a yellow fluorescent protein variant), and linked fusion proteins (CFP-L16-Cit, CFP-L7-Cit, CFP-L54-Cit) in living cells. The effects of shot noise, acceptor polarization, and FRET efficiency on the statistical accuracy of p-FRET experimental results are investigated by a noise-simulation program.     

Probing complexes with single fluorophores: factors contributing to dispersion of FRET in DNA/RNA duplexes

Single molecule fluorescent microscopy is a method for the analysis of the dynamics of biological macromolecules by detecting the fluorescence signal produced by fluorophores associated with the macromolecule. Two fluorophores located in a close proximity may result in Förster resonance energy transfer (FRET), which can be detected at the single molecule level and the efficiency of energy transfer calculated. In most cases, the experimentally observed distribution of FRET efficiency exhibits a significant width corresponding to 0.07–0.2 (on a scale of 0–1). Here, we present a general approach describing the analysis of experimental data for a DNA/RNA duplex. We have found that for a 15 bp duplex with Cy3 and Cy5 fluorophores attached to the opposite ends of the helix, the width of the energy transfer distribution is mainly determined by the photon shot noise and the orientation factor, whereas the variation of inter-dye distances plays a minor role.     

Localization Precision in Stepwise Photobleaching Experiments

The precise determination of the position of fluorescent labels is essential for the quantitative study of biomolecular structures by various localization microscopy techniques. Localization by stepwise photobleaching is especially suited for measuring nanometer-scale distances between two labels; however, the precision of this method has remained elusive. Here, we show that shot noise from other emitters and error propagation compromise the localization precision in stepwise photobleaching. Incorporation of point spread function-shaped shot noise into the variance term in the Fisher matrix yielded fundamental Cràmer-Rao lower bounds (CRLBs) that were in general anisotropic and depended on emitter intensity and position. We performed simulations to benchmark the extent to which different analysis procedures reached these ideal CRLBs. The accumulation of noise from several images accounted for the worse localization precision in image subtraction. Propagation of fitting errors compromised the CRLBs in sequential fitting using fixed parameters. Global fitting of all images was also governed by error propagation, but made optimal use of the available information. The precision of individual distance measurements depended critically on the exact bleaching kinetics and was correctly quantified by the CRLBs. The methods presented here provide a consistent framework for quantitatively analyzing stepwise photobleaching experiments and shed light on the localization precision in some other bleaching- or blinking-assisted techniques.     

Localization Precision in Stepwise Photobleaching Experiments

The precise determination of the position of fluorescent labels is essential for the quantitative study of biomolecular structures by various localization microscopy techniques. Localization by stepwise photobleaching is especially suited for measuring nanometer-scale distances between two labels; however, the precision of this method has remained elusive. Here, we show that shot noise from other emitters and error propagation compromise the localization precision in stepwise photobleaching. Incorporation of point spread function-shaped shot noise into the variance term in the Fisher matrix yielded fundamental Cràmer-Rao lower bounds (CRLBs) that were in general anisotropic and depended on emitter intensity and position. We performed simulations to benchmark the extent to which different analysis procedures reached these ideal CRLBs. The accumulation of noise from several images accounted for the worse localization precision in image subtraction. Propagation of fitting errors compromised the CRLBs in sequential fitting using fixed parameters. Global fitting of all images was also governed by error propagation, but made optimal use of the available information. The precision of individual distance measurements depended critically on the exact bleaching kinetics and was correctly quantified by the CRLBs. The methods presented here provide a consistent framework for quantitatively analyzing stepwise photobleaching experiments and shed light on the localization precision in some other bleaching- or blinking-assisted techniques.     

Enhanced Archaerhodopsin Fluorescent Protein Voltage Indicators

A longstanding goal in neuroscience has been to develop techniques for imaging the voltage dynamics of genetically defined subsets of neurons. Optical sensors of transmembrane voltage would enhance studies of neural activity in contexts ranging from individual neurons cultured in vitro to neuronal populations in awake-behaving animals. Recent progress has identified Archaerhodopsin (Arch) based sensors as a promising, genetically encoded class of fluorescent voltage indicators that can report single action potentials. Wild-type Arch exhibits sub-millisecond fluorescence responses to trans-membrane voltage, but its light-activated proton pump also responds to the imaging illumination. An Arch mutant (Arch-D95N) exhibits no photocurrent, but has a slower, ~40 ms response to voltage transients. Here we present Arch-derived voltage sensors with trafficking signals that enhance their localization to the neural membrane. We also describe Arch mutant sensors (Arch-EEN and -EEQ) that exhibit faster kinetics and greater fluorescence dynamic range than Arch-D95N, and no photocurrent at the illumination intensities normally used for imaging. We benchmarked these voltage sensors regarding their spike detection fidelity by using a signal detection theoretic framework that takes into account the experimentally measured photon shot noise and optical waveforms for single action potentials. This analysis revealed that by combining the sequence mutations and enhanced trafficking sequences, the new sensors improved the fidelity of spike detection by nearly three-fold in comparison to Arch-D95N.     

Metal ion-mediated carbon dot nanoprobe for fluorescent turn-on sensing of N-acetyl-l-cysteine

In this work, carbon dots (CDs) was easily synthesized from aspartic acid through a pyrolysis method. Based on their favourable fluorescence properties, CDs were utilized to design a metal ion-mediated fluorescent probe for N-acetyl-l -cysteine (NAC) detection. The fluorescence intensity of CDs was firstly quenched by manganese ions (Mn²⁺) through static quenching effect and subsequently restored by NAC via the combination with Mn²⁺ due to the coordination effect. Therefore, the fluorescent turn-on sensing of NAC was actuated based on the fluorescence quenching stimulated by Mn²⁺ and recovery induced by coordination. The fluorescence recovery efficiencies showed a proportional range to the concentration of NAC in the range 0.04–5 mmol L⁻¹ and the detection limit was 0.03 mmol L⁻¹. Furthermore, this metal ion-mediated fluorescent nanoprobe was applied to human urine sample detection and the standard recovery rates were located in the range 97.62–102.34%. This was the first time that Mn²⁺ was used to construct a fluorescent nanoprobe for NAC. Compared with other heavy metal ions, Mn²⁺ with good biosecurity prevented the risk of application, which made the nanoprobe green and biopractical. The facile synthesis of CDs and novel metal ion-mediated sensing mode made it a promising method for pharmaceutical analysis.     

On the analysis of high order moments of fluorescence fluctuations.

A simple, straightforward analysis to characterize the distribution of aggregate sizes in a reversible aggregation system at equilibrium is presented. The method, an extension of fluorescence correlation spectroscopy (FCS), is based on measurements of higher order moments of spontaneous fluctuations of fluorescence intensity emitted from a defined open region of the sample. These fluctuations indicate fluctuations of the numbers of the fluorescent molecules in the observation region. Shot noise resulting from the random character of fluorescence emission and from the photoelectric detection system is modeled as a Poisson distribution and is subtracted from the measured photon count fluctuation moments to yield the desired fluorescence fluctuation moments. This analysis can also be used to estimate the fraction of immobile fluorophores in FCS measurements.     

Measurement of instantaneous velocity vectors of organelle transport: mitochondrial transport and bioenergetics in hippocampal neurons

Impaired transport of mitochondria, in dendrites and axons of neurons, and bioenergetic deficit are increasingly recognized to be of pathological importance in neurodegenerative diseases. To study the relationship between transport and bioenergetics, we have developed what to our knowledge is a novel technique to quantify organelle velocity in cultured cells. The aim was to combine measurement of motion and bioenergetic parameters while minimizing photodynamic oxidative artifacts evoked by fluorescence excitation. Velocity determination from sequential fluorescence images is not trivial, and here we describe an application of “optical flow”, the flow of gray values in grayscale images, to this problem. Based on the principles of photon shot noise occurring in low light level fluorescence microscopy, we describe and validate here an optical flow-based, robust method to measure velocity vectors for organelles expressing fluorescent proteins. This method features instantaneous velocity determination from a pair of images by detecting motion of edges, with no assumptions about the separation or shapes of the objects in the image. Optical flow was used in combination with single mitochondrion assay of mitochondrial thiol redox status by mitochondrially targeted redox-sensitive green fluorescent protein and measurement of mitochondrial membrane potential by tetramethylrhodamine methyl ester. Mitochondrial populations of resting cultured hippocampal neurons were analyzed. It was found that mitochondria with more oxidized thiol redox status have lower membrane potentials and are smaller in size. These mitochondria are more motile than the average; however, mitochondrial motility is only slightly dependent on the observed bioenergetic parameters and is correlated the best to the size of the mitochondria.     

Interference of Shot Noise of Open-Channel Current with Analysis of Fast Gating: Patchers do not (Yet) Have to Care

Microsecond gating of ion channels can be evaluated by fitting beta distributions to amplitude histograms of measured time series. The shape of these histograms is determined not only by the rate constants of the gating process (in relation to the filter frequency) but also by baseline noise and shot noise, resulting from the stochastic nature of ion flow. Under normal temporal resolution, the small shot noise can be ignored. This simplification may no longer be legitimate when rate constants reach the range above 1 μs⁻¹. Here, the influence of shot noise is studied by means of simulated time series for several values of single-channel current of the fully open state and baseline noise. Under realistic optimal conditions (16 pA current, 1 pA noise, 50 kHz bandwidth), ignoring the shot noise leads to an underestimation of the rate constants above 1 μs⁻¹ by a factor of about 2.5. However, in that range, the scatter of the evaluated rate constants is at least of the same magnitude, obscuring the systematic error. The incorporation of shot noise into the analysis will become more important when amplifiers with significantly reduced noise become available.     

Resolution of complex fluorescence spectra recorded on single unpigmented living cells using a computerised method

The identification and quantification of fluorescent compounds in a complex fluorescence spectra are always difficult, especially in the case of low signal:noise ratio. We propose a computerised method that allows the resolution of low light level complex fluorescence spectra into its components. Based on a linear combination of N possible characteristic fluorescence spectra, and using N weighting functions, this method allows the integration of fluorescence intensities over the entire fluorescence spectra and the generation of n equations with N unknowns. The compounds that participate in complex fluorescence spectra are identified and quantified. Because fluorescence intensities can be integrated we can resolve complex fluorescence spectra presenting a low signal:noise ratio. The reliability and sensitivity of our method are shown through examples of resolution of complex intracellular fluorescence of single living cells pretreated with benzo(a)pyrene. Depending on the cell type and treatment, two, four, or five components can be identified in the complex fluorescence spectra.     

Statistical analysis of fluorescence correlation spectroscopy: the standard deviation and bias

We present a detailed statistical analysis of fluorescence correlation spectroscopy for a wide range of timescales. The derivation is completely analytical and can provide an excellent tool for planning and analysis of FCS experiments. The dependence of the signal-to-noise ratio on different measurement conditions is extensively studied. We find that in addition to the shot noise and the noise associated with correlated molecular dynamics there is another source of noise that appears at very large lag times. We call this the "particle noise," as its behavior is governed by the number of particles that have entered and left the laser beam sample volume during large dwell times. The standard deviations of all the points on the correlation function are calculated analytically and shown to be in good agreement with experiments. We have also investigated the bias associated with experimental correlation function measurements. A "phase diagram" for FCS experiments is constructed that demonstrates the significance of the bias for any given experiment. We demonstrate that the value of the bias can be calculated and added back as a first-order correction to the experimental correlation function.     

Membrane potential can be determined in individual cells from the nernstian distribution of cationic dyes.

The distribution of a selection of cationic fluorescent dyes can be used to measure the membrane potential of individual cells with a microfluorometer. The essential attributes of these dyes include membrane permeability, low membrane binding, spectral properties which are insensitive to environment, and, of course, strong fluorescence. A series of dyes were screened on HeLa cells for their ability to meet these criteria and several commercially available dyes were found to be satisfactory. In addition, two new dyes were synthesized for this work by esterification of tetramethyl rhodamine. The analysis of the measured fluorescent intensities requires correction for fluorescence collected from outside the plane of focus of the cell and for nonpotentiometric binding of the dye. The measurements and analysis were performed on three different cell types for which there exists a body of literature on membrane potential; the potentials determined in this work were always within the range of literature values. The rhodamine esters are nontoxic, highly fluorescent dyes which do not form aggregates or display binding-dependent changes in fluorescence efficiency. Thus, their reversible accumulation is quantitatively related to the contrast between intracellular and extracellular fluorescence and allows membrane potentials in individual cells to be continuously monitored.     

Waveguide excitation fluorescence microscopy: a new tool for sensing and imaging the biointerface

A novel biosensing and imaging technique, the waveguide excitation fluorescence microscope, has been developed for the dynamic and quantitative investigation of bio-interfacial events in situ, ranging from ligand-receptor binding to focal adhesion formation in cell-surface interactions. The technique makes use of the evanescent field created when light travels in a mono-mode, planar optical waveguide to excite fluorescence in the near interface region. Advantages of the technique include high target sensitivity for fluorescence detection (femtomolar range), high surface specificity (ca. 100 nm perpendicular to the waveguide), large area analysis with submicron resolution, 'built-in' calibration of fluorescent light gain, and the capability to perform multi-colour imaging in situ and in real time. In this work, the sensitivity of the system has already been demonstrated through dynamic measurements of the streptavidin-biotin binding event to below 20 pM concentrations, signal to noise comparisons with conventional fluorescence microscopy have shown more than a 10-fold improvement, and surface specificity of the technique has also been illustrated in a comparison of fibroblast focal adhesion images. Thus, this new tool can be used to illuminate processes occurring at the interface between biology and synthetic surfaces in a unique manner.     

DNA sequencing with solid-phase-capturable dideoxynucleotides and energy transfer primers

False terminations occurring in fluorescent dye-primer DNA sequencing, and nonsequencing primer extension DNA fragments generated in dye-terminator sequencing cause background noise in fluorescent electropherograms, leading to errors in sequence determination. We describe here a DNA sequencing chemistry that produces accurate and clean sequencing data on a fluorescent DNA sequencer, eliminating the false terminations and background noise. The procedure involves coupling fluorescence energy transfer (ET) primers that produce high fluorescent signals with solid-phase-capturable biotinylated dideoxynucleotides to generate Sanger DNA sequencing fragments. After the sequencing reaction,the DNA extension fragments that carry a biotin at the 3' end are captured with streptavidin-coated magnetic beads, while the other components in the sequencing reaction are washed away. Only pure DNA extension products terminated by the biotinylated dideoxynucleotides are released from the magnetic beads and are loaded onto a sequencing gel to produce accurate sequencing data.     

荧光热漂移实验体外检测核小体的解聚

核小体是真核生物染色质的基本组成单元。核小体的解聚可以动态调控诸如DNA复制、转录、重组等以DNA为模板的生物学过程。特定荧光探针分子与蛋白质疏水残基结合后可被激发荧光信号。荧光热漂移（fluorescence thermal shift,FTS）是一种利用该原理检测温度上升时蛋白质变性过程的方法。本文以Widom 601序列为DNA模板,盐透析法体外装配核小体;分别在实时荧光定量PCR仪的VIC和TAMRA通道激发下,利用FTS检测了核小体在Tris-NaCl（TN）缓冲液和HEPES缓冲液中的解聚状态。研究结果发现,DNA对照序列在TN缓冲液中产生的背景噪声较大,VIC通道激发下组蛋白八聚体产生的荧光信号相对较强。FTS检测核小体的结果显示,随着温度的上升核小体的解聚过程分为2个阶段,～71℃和～84℃是核小体解聚速度最快的温度范围,而75℃～80℃是降解速度较慢的阶段。基于FTS基本原理,本研究发展了一种新颖的可用于检测核小体结构稳定性的方法,为核小体与染色质结构相关问题的研究奠定了一定的技术基础。     

Measuring fast calcium fluxes in cardiomyocytes

Cardiomyocytes have multiple Ca(2+) fluxes of varying duration that work together to optimize function (1,2). Changes in Ca(2+) activity in response to extracellular agents is predominantly regulated by the phospholipase Cβ- Gα(q;) pathway localized on the plasma membrane which is stimulated by agents such as acetylcholine (3,4). We have recently found that plasma membrane protein domains called caveolae(5,6) can entrap activated Gα(q;)(7). This entrapment has the effect of stabilizing the activated state of Gα(q;) and resulting in prolonged Ca(2+) signals in cardiomyocytes and other cell types(8). We uncovered this surprising result by measuring dynamic calcium responses on a fast scale in living cardiomyocytes. Briefly, cells are loaded with a fluorescent Ca(2+) indicator. In our studies, we used Ca(2+) Green (Invitrogen, Inc.) which exhibits an increase in fluorescence emission intensity upon binding of calcium ions. The fluorescence intensity is then recorded for using a line-scan mode of a laser scanning confocal microscope. This method allows rapid acquisition of the time course of fluorescence intensity in pixels along a selected line, producing several hundreds of time traces on the microsecond time scale. These very fast traces are transferred into excel and then into Sigmaplot for analysis, and are compared to traces obtained for electronic noise, free dye, and other controls. To dissect Ca(2+) responses of different flux rates, we performed a histogram analysis that binned pixel intensities with time. Binning allows us to group over 500 traces of scans and visualize the compiled results spatially and temporally on a single plot. Thus, the slow Ca(2+) waves that are difficult to discern when the scans are overlaid due to different peak placement and noise, can be readily seen in the binned histograms. Very fast fluxes in the time scale of the measurement show a narrow distribution of intensities in the very short time bins whereas longer Ca(2+) waves show binned data with a broad distribution over longer time bins. These different time distributions allow us to dissect the timing of Ca(2+)fluxes in the cells, and to determine their impact on various cellular events.