Introduction
With the development of confocal microscopy and photodetection techniques, fluorescence correlation spectroscopy (FCS) has become cutting-edge technology with great potential, sensibility, and widespread application, starting from fluorescently labeled molecules in solution, on membranes, and inside living cells. Moreover, because of the enormous analytical and diagnostic potential, FCS can be put to practical use for in vitro and in vivo studies to measure diffusion, chemical kinetics, particle concentration and mobility, laminar flow, interactions between nucleic acid and proteins, and rapid enzyme screening from a very small sample in a short time (Elson and Magde, Reference Elson and Magde1974; Bieschke et al., Reference Bieschke, Schwille and Slavik1998; Kettling et al., Reference Kettling, Koltermann, Schwille and Eigen1998; Cooper, Reference Cooper2004). Concentration and diffusion variables are usually characterized by setting parameters into the pico to nanomolar scale limit. Quantitative results are often burdensome to gain due to extensive surveying parameters, which have to be judged by the size of the confocal volume. In biological specimens, measurement of the confocal volume in situ owing to its sensitivity to saturation and bleaching of the dye molecules, optical aberrations, and variations of the index refraction are imposing a burden.
Fluorescent fluctuation depends on the number, size, and speed of molecules undergoing Brownian motion by entering and leaving the observation volume element (OVE) by diffusion motion, reversible changes in the fluorescence emission in time by shifts in the triplet state, isomerization, and chromophore microenvironment. The volume element is a confocal bulk illuminated by a laser beam in which molecules move in a certain direction with a continuous motion. The volume element is based on the arrangements of excitation intensity and on the collection efficiency position of the excited fluorescence. Moreover, it depends on the sample quality trait belonging to the refractive index of a sample with a medium, photophysics of the fluorophore, cover slide thickness, and other experimental conditions. For that reason, we can acquire molecular quantitative data by expedient measurement of fluorescent signal if correlation functions of the time series signal are obtained (Cooper, Reference Cooper2004).
The aim of this study is to measure and determine the specific example variations of diffusion parameters of fluorescence particles in diverse sample concentrations, to examine glycerol solution viscosity and standard adjustment of Rhodamine 6G (Rh6G) and Alexa 633 dye as well as to stipulate Amyloid beta (Abeta) aggregates with Alexa 647 dye.
Theory
In FCS, the autocorrelation curve (ACC) of a comparatively minor femtoliter (fL) sample magnitude solution is determined by temporal autocorrelation analysis. The decay time of the ACC denotes the meantime that a molecule stays in the OVE due to molecular diffusion. The amplitude of ACC is inversely proportional to the average number of molecules (N) in the OVE and is representative of its concentration (Ries et al., Reference Ries and Schwille2012).
Diffusion is used to measure the characteristics of particles, as well as their size and mass. Since particles move at different speeds, their motion is not governed, and their speed can be described by the diffusion coefficient (D). The coincidental course of the individual molecule can be described as a solvent random walk in the solution, where solution molecules collide with the solvent and receive a series of small recoils in random directions (Figure 1) (Loman et al., Reference Loman, Gregor, Stuz, Mund and Enderlein2009). Particles are characterized by quick motion if the diffusion coefficient is considerable in size. The trajectory is typically distinctive by mean squared displacement (MSD) <r 2>, which represents the covered particle area at a certain time. MSD proportionality is given by the diffusion coefficient:
$$ <{r}^2>=6D\mathrm{T} $$
Molecule random walk in four constructed routes with a divergent diffusion coefficient that increases by a factor five from one subsequent walk to another. The circles assume the root MSD of the particles from its origin (http://www.wikiwand.com/en/Random_walk).
Fick’s law was used to delineate the macroscopic diffusion effect until the 20th century. The continuous and productive activity of single particle scale comprising fluctuations of molecular absorption, the fluorescence quantum yield, and local particle concentration can be interpreted as fluorescent particles undergoing Brownian motion in the focal region where fluorescent particles absorb light (Koppel et al., Reference Koppel1974). Albert Einstein obtained diffusion coefficient relation, which connects it with particles and solution properties in which they move so that Brownian motion can be expressed by an equation using the Stokes-Einstein relation:
$$ D=\frac{\mathrm{KbT}}{6\pi \eta \mathrm{Rh}} $$
where Kb = 1.3806504 × 10−23 J/K is Boltzmann’s constant, T is the absolute temperature, and η is the viscosity of the solvent. The basic units of matter are described by their hydrodynamic radius Rh, which is the radius of an identical globular body that has to resemble every relevant aspect of the diffusion coefficient of the examined molecule. For molecules with different globular body shapes, there will be deviations. Temperature dependence of D is not linear, and viscosity η shows strong temperature dependence. Conduction in fluids is related to the dynamic radii of the particle and is distinguished in size from fluid friction (Cooper, Reference Cooper2004). Calculating the existing radius of the particle is not feasible because of the reliance on experimental D. However, detailed analysis of particle dynamic radii can be used by utilizing diffusion coefficient (Elson and Magde, Reference Elson and Magde1974; Cooper, Reference Cooper2004; Bieschke et al., Reference Bieschke, Schwille and Slavik1998; Kettling et al., Reference Kettling, Koltermann, Schwille and Eigen1998; Ries et al., Reference Ries and Schwille2012).
If we assume that the volume of a particle (Vp) is linear with mass (m), we get
$$ \mathrm{Vp}=\frac{4}{3\;}\unicode{x03C0} \cdotp {\mathrm{Rh}}^3\propto \mathrm{m} $$
From this, we can easily derive the mass dependence of the diffusion coefficient:
$$ \mathrm{D}\propto \frac{1}{\sqrt[3]{\mathrm{m}}} $$
The association of diffusion time and viscosity is acquired by intermixing equations 1 and 2 (Cooper, Reference Cooper2004). Viscosities of various solutions are obtained by reference solutions with known viscosity through FCS experimental results (Jung et al., Reference Jung, Lee, Kang and Kim2014).
Particle number variations in observation volume
Sample properties in FCS can be obtained by utilization of fluorescence intensity I (t) fluctuation discharged by the particle commemoration. Overall intensity is commensurable to the observed number of particles N since every particle excited to an identical level donates an equivalent quantity of fluorescence to the measured signal. Over time, total particle number N (t) is cleaved into average value (N) and small fluctuations δN (t) around <N> (Figure 2) (Abney et al., Reference Abney, Scalettar, Park and Waxham1990).
$$ N\;(t)=<N>+\delta N\;(t) $$
The fundamental law of FCS. (A) Fluorescent particles (red and blue) in an observation volume with distinct diffusion coefficients. (B) Fluorescence intensity fluctuations as a function of time in an fL size sample solution. (C) Autocorrelation function G(t) to give up possession of the decay time, Td. Starting amplitude is vice versa correspondent to the number of particles (Krieger JW, et al (2015) Imaging fluorescence (cross-) correlation spectroscopy in live cells and organisms. Nature Protocols 10(12), 1948–1974.).
Intensity alterations give rise to particles arriving and departing from the observation volume Vobs. Depending on how distant the particles are from the observation volume, we can define D corresponding to its speed. Particles with bigger D will get in or out of the observation volume in a fixed observation time and show prompt fluctuation δN (t) while particles with lower D will exhibit slow fluctuations. The correlation analysis reveals fluctuation time scale which may be converted into a diffusion coefficient (Figure 2; Elson and Magde, Reference Elson and Magde1974; Cooper, Reference Cooper2004; Bieschke et al., Reference Bieschke, Schwille and Slavik1998).
Information of a single particle is acquired by the rise and fall in intensity arising from entering or leaving the focus δN single = 1. Variations originated from one particle are facile to disclose if the average N is low in the observation volume (Elson and Magde, Reference Elson and Magde1974).
Employing knowledge of particle amount in analyzed metric surface, sample volume Vsample and concentration Csample can be obtained (Ruttinger, Reference Ruttinger2007). For example, if we have a sample concentration of 100 nM and volume of 300 μl in the well
$$ <N>=300\bullet {10}^{-9}\cdotp 6.022\bullet {10}^{23}\cdotp 100\bullet {10}^{-6}\approx 18\cdotp {10}^{12}\hskip0.2em \mathrm{particles} $$
the relative fluctuation is 12·10−7 = 0.00012%.
Special attention should be given to reducing the sample volume to achieve suitable molar concentration. If we impair to Vsample 1 fl = 10−15 l = 1 μm3, we get around 10 particles in this volume with a reasonable concentration of Csample 18 nM. This means that if we want to work with concentrations in the nanomolar range, estimated volume has to be around Vsample 1 fl (Ruttinger, Reference Ruttinger2007).
Basis of confocal fluorescence microscopy
In FCS, the small focal volume of 1 fl is accomplished by a confocal microscope with a plane objective of high numerical aperture, NA (NA > 0.9). The confocal microscope can be transformed into the laser scanning confocal microscope (LSCM) for fluorescence imaging by deflecting the laser beam into more than one path forehead of objective lenses. Blue excitation light is focused by an objective lens into the sample (Figure 3). Size d of the focus is expressed with the wavelength of the light λ and sample solution refractive index n using Abbe’s law (Rainer, Reference Rainer2014):
$$ d=\frac{\unicode{x03BB}}{2n\cdotp NA} $$
Optical setup of the confocal microscope (https://cam.facilities.northwestern.edu/588-2/confocal-laser-scanning-microscopy/).
Fast detector (avalanche photodiode, APD) detects photons from submicrosecond to the second range thanks to emitted fluorescence imaged on pinhole, which filters green light out of focus. This information is processed by a computer. One dichroic mirror disconnects excitation and fluorescence light, while the second mirror contrasts various dyes by separating emitted light into detection channels. Due to sturdy power and stability, the Argon-Krypton ion laser with three main laser lines (488 nm, 568 nm, 647 nm) is used as a light source (Elson and Magde, Reference Elson and Magde1974; Cooper, Reference Cooper2004; Bieschke et al., Reference Bieschke, Schwille and Slavik1998).
Figure 3 exhibits crucial components of FCS instrument usage. The platform is composed of an inverted microscope to which the laser is coupled. The laser wavelength is dependent on employed fluorophore. Mirror and lenses lead the laser beam into the back aperture of the microscope objective through a dichroic mirror. The beam expander gives an opportunity to overfill or underfill the back opening of the objective that leads to drawing apart the laser beam in the OVE (Hess et al., Reference Hess and Watt2002). The NA of the objective is retained high to provide an upper limit collection of the photons given out by the fluorophores in the excitation volume. A confocal pinhole concentrates the emitted fluorescence and rejects light out of focus and resolution in the axial direction of OVE. The avalanche photodiodes detector accumulates fluorescence to the extent of quantum quality, which is important for the detection of a single photon.
Pinhole size is swapped among signal brightness and model equation fit quality (Gaussian curve of the detection volume) (Nagy, Reference Nagy, Wu and Berland2005). One of the significant parameters for distinguishing exceptional events (i.e., aggregate passing the focus) and excluding it from data analysis through an overlapping curve is the measurement time. Excellent options for quick diffusion dyes (i.e., 10 × 10s) are shorter consecutive measurement time and averaging, while for slow diffusion dyes are longer consecutive measurement time and the collection of a raw photon reaching time (Ries et al., Reference Ries, Bayer, Csucs, Dirkx, Solimena, Ewers and Schwille2010).
In order to hinder photobleaching, maximum signal brightness and minimum control of saturation, the highest laser power is utilized (Ries et al., Reference Ries, Bayer, Csucs, Dirkx, Solimena, Ewers and Schwille2010).
Count rate (CR) needs to be in the relatively less advanced scale below 200 kHz, while sample concentration is requested to suit laser power and CR. Low concentrations show elongated measurement times.
The brightness (CPM) is an indicator of the ACC and the signal quality. CPM expressed in kHz, appoints detected photon number per particle per time and is conditioned on enforceable excitation intensity, the fluorophore, and its environment. Variations of CPM can be used to observe aggregation flow.
Autocorrelation analysis
A number of particles can be computed indirectly by fluorescence intensity I (t) of emitted particles of an inner side of the excited laser focus. Particles constantly cycle between ground and excited state lasting 10 ns. APD determines gathered photon fraction from the objective lens. Fluctuation of I (t) is matched with fluctuation of N (t).
$$ I(t)=<I>+\delta I(t) $$
Autocorrelation analysis is used to investigate particle rate of movement in a sample by pulling out non-random data of particles passing the focus from the random intensity. Autocorrelation function G (t) is displayed from the magnitude of an identified signal I (t) by which information is computed by the computer software by:
$$ G\left(\tau \right)=\frac{<\delta I(t)\bullet \delta I\left(t+\tau \right){>}_t}{<I(t){>}_t^2} $$
where
$ <\delta I(t)\bullet \delta I\left(t+\tau \right){>}_t $
is a time average over time variable t, δI (t) is self-similarity of the fluctuation and
$ \unicode{x03C4} $
is lag time. The autocorrelation curve is minor, and lag time is extended when the signal appearance among
$ \delta I(t)\hskip0.52em \mathrm{and}\hskip0.52em \delta I\left(t+\tau \right) $
is deviating and vice versa (Figure 2) (Abney et al., Reference Abney, Scalettar, Park and Waxham1990; Ruttinger, Reference Ruttinger2007).
The autocorrelation function of diffusing particles
In order to assess an ACC and acquire D and N , we need to fit the theoretical models by including diffusion law (Equation 9) and integrals.
The homogenous mixture of a single-phase system with D and N in observation volume has:
$$ G(t)=\frac{1}{N}\cdotp {\left(1+\frac{4 D\tau}{w_{xy}^2}\right)}^{-1}\bullet {\left(1+\frac{4 D\tau}{z_0^2}\right)}^{-1/2} $$
where w xy is the latitude from one side of the observation volume to the other side in the XY direction and z 0 is the longitude in the z direction. The prior written formula is altered in a precise meaning of summarized retention time or diffusion time of particles in the fixed observation point:
$$ G(t)=\frac{1}{N}\cdotp {\left(1+\frac{4 D\tau}{\tau_d}\right)}^{-1}\bullet {\left(1+\frac{4 D\tau}{\gamma^2{\tau}_d}\right)}^{-1/2} $$
$$ D=\frac{w_{xy}^2}{4{\tau}_d} $$
$$ \gamma =\frac{z_0}{w_{xy}} $$
where
$ \hskip0.24em \boldsymbol{\gamma} $
is a structural factor or axis ratio of the focus. With the increase in diffusion time decay, the curve shifts to the right, while with a rise in the particle number, the amplitude decreases (Figure 4, Equation 11) (Jung et al., Reference Jung, Lee, Kang and Kim2014; Helmchen et al., Reference Helmchen and Denk2005).
Diffusion of particles: Left: rising τ D, constant N; Right: rising N, constant τ D (https://www.picoquant.com/applications/category/life-science/fluorescence-correlation-spectroscopy-fcs).
The size of the focus and the structure factor are utilized for calculating D. The value of the focus size is obtained by solution calibration with known D. We used 10 nM Rhodamine 6G on a day-to-day basis or when parts of the setup in our laboratory change (sample chamber). Having the information about the focus magnitude, solution volume V eff and concentration C can be assessed:
$$ {V}_{eff}={\pi}^{3/2}\bullet {w}_{xy}^2\bullet {z}_0={\pi}^{3/2}\bullet \gamma \bullet {w}_{xy}^3 $$
$$ c=\frac{N}{V_{eff}} $$
Experiments
Optical setup
For FCS measurements, we used ConfoCor 3 system (Carl Zeiss, Jena, Germany) consisting of an inverted microscope for passing light and epifluorescence (Axiovert 200 M); a VIS laser module consisting of the Argon/Argon Krypton (458, 488, and 514 nm), He Ne 543 nm and He Ne 633 nm lasers; scanning module LSM 510 META modified to potentiate detection utilizing silicon avalanche photodiodes (SPCM-AQR-1X; PerkinElmer, USA) and an FCS module with three detection channels (Figure 5). FCS is supplied with a C-Apochromat 40 x, NA = 1.2 water immersion UV–VIS-IR objective. Glycerol and Rhodamine were excited on 488 nm green light line of the Argon laser. Alexa 633 and Alexa 647 dyes were excited on 633 nm red light line of the He Ne laser. The HFT KP 700/488 plate was used as the main dichroic beam splitter that disjoins the incident and emitted light for glycerol and Rhodamine 6G, while the HFT 488/543/633 plate was used for the Alexa dye.
Zeiss LSM 510 Meta confocal 3 scope (http://nisms.stanford.edu/Equipment/LSM510Meta01v01.html).
The pinhole size in front of the detector for the green light was 72 and 90 μm (1 Airy) for the red light. Laser intensity measured at the objective was 30 and 6 μW retrospectively. Standard solutions of 10 nM Rhodamine 6G and Alexa 633 dye were used for instrumental calibration. The same optical setup for Rhodamine 6G was used for glycerol. Moreover, the same optical setup for Alexa 633 was used for Abeta Alexa 647. The diffusion time, CPM and CPS (counts per second), was determined, and the structure parameter was 7.
Autocorrelation analysis was used to survey fluorescence intensity fluctuation in 30 consecutive measurements, each lasting 10 s. Originated ACC was adjusted for one component-free 3D diffusion (Matthew et al., Reference Will, Clark and Swain2011).
$$ G(t)=\frac{1}{N}\cdotp \left(\frac{1}{\left(1+\frac{\tau }{\tau_D}\right)\bullet \left(\sqrt{1+\frac{\tau }{\gamma^2{\tau}_D}}\right)}\right)+1 $$
where
N
is the average number of aggregates in the detection volume,
$ {\boldsymbol{\tau}}_{\boldsymbol{D}} $
is the diffusion time, and
$ \boldsymbol{\gamma} $
is the structure parameter.
Materials
Reagents
Selection of dye should be based on the defined laser line and filter selection, while buffer should be with suitable refractive index and without fluorescence. Isopropanol is used for optics cleaning as recommended by the manufacturer Carl Zeiss. The compounds used in this experiment were Rhodamine 6G, glycerol, Alexa 633 dissolved in MiliQ water, and Amyloid beta Alexa 647 dye dissolved in 20 nM HEPES buffer, pH 7.0, T = 20 °C and RPMI medium phenol red free. The chemical structure of glycerol, Rh6G, and Alexa dyes are illustrated in Figures 6–9.
Chemical structure of glycerol (https://alchetron.com/Glycerol-2678521-W).
Chemical structure of Alexa Fluor 647 dye (http://www.atdbio.com/content/34/Alexa-dyes).
Emission spectra of Alexa Fluor dyes (https://www.thermofisher.com/rs/en/home/brands/molecular-probes/key-molecular-probes-products/alexa-fluor/alexa-fluor-dyes-across-the-spectrum.html).
Absorption and emission spectra for Rhodamine 6G dye. Inside: structure of Rhodamine 6G dye (Wang JH, et al (2005) The use of rhodamine 6G and fluorescence microscopy in the evaluation of phospholipid-based polymeric biomaterials. Journal of Microscopy 217(3), 216–224.).
Milli-Q water is ultra-pure water characterized by few supporting electric charged ions and is able to highly resist conducting electrical current. High purity is achieved with Q-Gard purification cartridges.
HEPES ((4-(2-hydroxyethyl)-1-piperazine-ethane sulfonic acid) buffer is utilized to preserve pH regardless of CO2 fluctuation. It is qualified with great solubility, membrane impregnability, poor visible and ultraviolet spectrum absorbance, stability and practical application (Christoph et al., Reference Christoph, Schmidt, Steinberner, Dilla and Karinen2006).
The most significant fluid characteristics which influence motion are density and viscosity. Viscosity is the most relevant physical asset of fluid. A fluid is a substance that undertakes constant opposition when faced with deformational change and induces friction. With a rise in temperature, the viscosity of liquids declines. Glycerol is a non-toxic, sweet, uncolored viscous liquid located in triglyceride lipids. It is broadly applied in the nourishment and pharmaceutical industries. Hydroxyl groups in glycerol are accountable for their solubility in water and hygroscopic behavior (Sibbett and Wallin, Reference Sibbett and Taylor1983). Fluorophore fluorescence lifetime can be influenced by the viscosity of the neighboring medium when the molecule experiences interior gyrate (Mutze et al., Reference Mutze, Ohrt and Schwille2011). The main purpose of our work was to display the effect of various water concentrations on viscosity in FCS by checking experimental data of aqueous glycerol solution. Ultrapure glycerol was purchased from ICN Biomedical (Irvine, CA). From 50% stock solution of glycerol, we prepared 50%, 40%, 30%, 20%, and 10% dilution concentrations with Milli-Q water.
Fluorophores can be intrinsic or extrinsic and absorb the laser excitation wavelength. Before the selection of specific reporter, a vast number of practical aspects need to be taken into account. Dye brightness is important for statistic measurements. High brightness is established by combining a high extinction coefficient, high quantum yield, low intersystem crossing, and high photo stability (Brackmann et al., Reference Brackmann, Brode and Blaschke2000). The best available fluorophores in terms of brightness and coverage of the wide range of the visible spectrum are Alexa dye, developed by the molecular probes (USA), Atto dyes manufactured by Attocec (Germany), and the HiLite Fluor dyes patented by Anaspec (USA). Photobleaching of the fluorophores under high excitation intensities or extended illumination in case of slow-moving particles can cause problems for the FCS data analysis. Dissolved molecular oxygen is the main culprit in irreversible photo damage because of photo oxidation and enzymatic oxygen-scavenging system (Brackmann et al., Reference Brackmann, Brode and Blaschke2000). Variants of the fluorescence protein are used as well as a marker. Green fluorescent protein (GFP) shows maximum brightness and photo stability as well as pH dependent fluorescent fluctuation. Red fluorescent protein (RFP) shows reduced brightness (Brackmann et al., Reference Brackmann, Brode and Blaschke2000). Alexa 647 and Alexa 633 are light, photo-stable, water-soluble red fluorescent dyes with well-known diffusion coefficients. The molecular weight of Alexa 647 is 1300 g/M, and molecular weight of Alexa 633 is 1200 g/M. Alexa dyes are pH insensitive to broad molar sweeps and have outstanding stability. Attached to other molecules in high concentrations, they allow for more sensitive detection without significant self-quenching. Alexa 647 is synthesized through the process of sulfonation. When Alexa 647 dye is excited with a He-Ne laser, it broadcasts maximum absorption at 650 nm and near IR maximum emission of 665 nm wavelength and has fixed excitation notwithstanding the material surface. Therefore, the samples of Beta Amyloid (1–40) HiLytetm Fluor 647 labeled the size of 0.1 mg stored at −20 C were taken with a top of the tip and diluted in a well with 300 μL of 20 nM Hepes buffer, pH = 7. When Alexa 633 dye is excited with the He-Ne laser, it broadcasts maximum absorption at 632 nm and far red maximum emission of 647 nm. From 1 μM concentration stock, solution of Alexa 633 dye dilutions of 1000 nM, 100 nM, 10 nM, and 1 nM was prepared with MiliQ water. Our study used Alexa 633 to provide a perspective of dye standard adjustment for the far red wavelength range. By plotting the diffusion time and CPM as a function of laser intensity, you can define sweep where diffusion times are constant and where saturation or bleaching is reached.
Rhodamine 6G (Rh6G) is a fluorescent dye, broadly applied as a medium to emit coherent light and as a fluorescent tracer (Penzkofer, Reference Penzkofer and Leupacher1987). Foregoing knowledge about its effect determines the usage of appropriate concentrations of dye and diluents. The medium generally used for an extensive range of Rh6G concentrations in the aqueous solution. An enormous number of researchers examined unitary solvents and constrained concentration sweeps (Culbertson et al., Reference Culbertson, Jacobson and Ramsey2002).
The absorption spectra of an aqueous Rh6G solution dissolved in water can be used to determine the concentration of Rh6G using Beer–Lambert law (A = ɛbc), where A is absorbance, b is the path length of the sample, c is the concentration of the compound in solution and ɛ is extinction coefficient. The Rh6G absorption spectrum in water is 440 nm to 570 nm, with a peak wavelength of 527 nm. The Rh6G emission spectrum in water at 480 nm excitation depending on the concentration is 490 to 810 nm with the peak wavelength at 570 nm (Penzkofer, Reference Penzkofer and Leupacher1987).
Our study used Rh6G to provide an overview of Rh6G standard adjustment to assist in the choice of adequate concentration for notorious demands. Rh6G is purchased from Invitrogen with purity of 95%, which is recommended for calibration experiments (Krchevsky et al., Reference Krchevsky and Bonnet2002). From 5 μM concentration stock of Rh6G dilutions of 50, 10, and 5 nM were prepared with MiliQ water.
Observation chambers
For our purpose, we used a disposable chamber with a cover slip from Nunc (Thermo Fisher Scientific). We pipette a 20 μl droplet of solution on a cover slip set straight on the objective. For the standard adjustment (pinhole, collimator, and correction collar), we used an identical cover slip as for the actual measurement.
Procedure reflection for FCS data derivation and curve fitting
Process of making setup ready for use
In order to make the setup ready for use, turn on the system and appropriate laser. During the next half hour, the system will obtain temperature balance. Repeating the calibration and pinhole adjustment, we can judge a state in which opposing temperatures are balanced.
Carefully choose the most suitable beam path
After laser activation, choose satisfactory dichroic and emission filters for employed dye. In order to bring about the strongest brightness as possible, apply wide band-pass filters and remove excitation wavelength by gathering fluorescence.
On ConfoCor 3 we selected the following combination for glycerol and Rhodamine 6G dye:
-
Main dichroic (HFT): KP 700/488 plate
-
Secondary dichroic (NFT): mirror
-
Red Chanel emission filter (channel 1): LP 505
-
Green Chanel emission filter (channel 2): LP 655
On ConfoCor 3 we selected the following combination for Alexa dyes:
-
Main dichroic (HFT): 488/543/633
-
Secondary dichroic (NFT): NFT 635 VIS
-
Red Chanel emission filter (channel 1): LP 655
-
Green Chanel emission filter (channel 2): BP 505–610
Laser illumination ability to produce an effect
In order to establish excitation laser line power, keep the room in complete darkness. From the options, choose HFT beam splitter, trigger one laser wavelength line, and open CR. Put the photo detector and move stage to the maximum power detection. To gain calibration curve for laser line set acousto-optical transmission filter (AOTF) settings and no objective or 10x objective can be used for quantification measurement. Fix the wavelength contingent transmission of various objectives from the producer.
Cover slip setting into appropriate manner, position, and direction
Use the same type of chamber for calibration and measurements. Find visual field between two chambers by seeing the glue so you can observe the volume inside. Move the visual field into the middle of the well and adjust to +200 μm so you can be inside the solution. This is an introduction adjustment of the correction collar of the objective for the cover density by the manufacturer.
The state of pinhole, collimator, and correction collar correction adjustment
Locate the pinholes in both lateral (X, Y) and axial (Z) routes. On the objective, put a cover slip with a high micromolar concentrated solution and keep the CR in a few hundred kHz with low laser intensity. While the position of the pinhole deviates, look at the CR. First, locate the pinhole in more sensitive lateral route and then in axial and finally repeat the lateral direction until the pinhole adjustment is completed.
Rough positioning of the collimator lens allows the pinholes maximum fluorescence in channels. After positioning the collimator lens, readjust the lateral direction of the pinholes. Fine positioning of the collimator lens reduces axial detection volume overlap and can affect contort the detection volume and CPM.
Autocorrelation analysis of test sample
As a test sample, aqueous solution for immersion without fluorescence is used and contains CR of few hundred kHz. CPM is optimized by diluted dye and rising excitation power. CPM estimation is based on multiplying the amplitude with CR. Moreover, CPM rises up to a point of saturation and bleaching with laser power increase. This kind of optimization is significant for signal quality when poor laser powers are applied to skip bleaching connected with slow diffusion of molecules. In cell measurements, the lowest value is 1 kHz.
Setting up the values for structure parameter and diffusion time
Generally, acquired ACC is fitted with the specific diffusion component model and set values of γ and
$ {\boldsymbol{\tau}}_{\boldsymbol{D}} $
. Structure parameter is used to fix parameters in real data. The diffusion time is applied for detection volume standardization. The diffusion coefficient of Rh6G and Alexa dye is 2.8 × 10
−10
m
2
s
−1
but newly determined diffusion coefficient in the literature is
$ \sim \mathbf{4}\bullet {\mathbf{10}}^{-\mathbf{1}\mathbf{0}}\;{\mathbf{m}}^{\mathbf{2}}{\mathbf{s}}^{-\mathbf{1}} $
(Krchevsky et al., Reference Krchevsky and Bonnet2002). Usually, the structure parameter is fixed between values of 5–7 in a well aligned system. The structure parameter is the ratio of axial to radial resolution.
At the maximum laser power, diffusion time and CR decreases as a result of photo bleaching.
Sample measurement on FCS
Acquire positive and negative control prior to sample analysis. After constructing the average value for FCS measurement, fit the autocorrelation curves to assess diffusion time and N eff . Decide what a good fit is and what is not. Prepare biological samples during temperature equilibration of the FCS machine.
Results and discussion
Introduced experiments in this study are concerned with describing exactly the nature of movement and interaction by molecule sizing, autocorrelation examination, and diffusion. FCS technique as a fashionable method was selected thanks to its tremendous selectivity and simplicity. The basic purpose of FCS analysis is to govern mobility-linked parameters of biological vital molecules in an aqueous solution. When working with biological material, it is imperative to differentiate diffusion from active transport, anomalous diffusion, or convection. Molecular pathways can only be understood by comprehension of the different transport mechanisms. Temporal resolution is constrained to a millisecond time scale so that the method is characterized by superior dynamics and stronger sensitivity (Petersen et al., Reference Petersen and Elson1986). For biological specimens, it is less stressful to have a small dye concentration and weaker laser power, so it is crucial to choose a proper dye molecule. In this situation, chromophores can indicate the kinetics of the system. FCS exploits fundamental characteristics of thermal fluctuation from a physics point of view: “Can the ideas of classical physics be sufficient for explaining the basic features of life” (Schrodinger, Reference Schrodinger1944). Moreover, measurement of the diffusion coefficient is indiscernible from unlimited dilution merit. ACC is correlated with the chance to detect photons from one molecule at a specific time, which emphasizes the character of FCS. Sometimes, signals do not correlate because they can originate from various molecules or laser light and will enclose a stable offset of G (Ƭ) independent on (Ƭ).
In Figure 10, the autocorrelation curves of glycerol, Rh6G dye, Alexa 633 dye in water solution, and Abeta Alexa 647 dye in 20 mM HEPES buffer solution and RPMI medium with/without phenol red solution are depicted. Fluorescence intensity fluctuations were recorded in a series of 30 consecutive measurements, each measurement lasting 10s. Corresponding data was assessed by a model for free 3D diffusion, Equation 16 where the structure parameter was fixed to 7 and N and diffusion time could be determined. FCS analysis revealed that reactive mixture contains fluorescent entities of various viscosities that can be dissimilar by distinction in diffusion time and abundance. A rough assessment of molecule mobility as a function of half merit decay time of the curves shows slight deviations between water, buffer, or a medium solution, so the characteristic decay time can be resolved by analyzing at the half-value latitude of G (t) or using diverse fitting models. The commensurate diffusing coefficient can be computed by Equation 1 from decomposition time from 3 x 106 cm2/s for free dye in water.
The autocorrelation curve on the milliseconds time scale. (A–C) Diffusion of aqueous solutions of 10%, 20%, 30%, 40%, 50% glycerol, 5 nM, 10 nM, 50 nM Rh6G dye and 1 nM, 10 nM, 100 nM, 1000 nM Alexa 633 dye. (D) Diffusion of RPMI medium with phenol red, RPMI medium phenol red free, and 20 mM HEPES, pH = 7.0, T = 20°C solution with unknown concentration of Abeta Alexa 647 dye.
Throughout the process of diffusion, the shape of ACC is dissimilar. It is evident that the movement of fluorophores is strongly conditional on the environment. Environment heterogeneities play a major role in the anomalous diffusion phenomenon as described in the literature for intracellular phenomena, membrane-bound receptors, and within plaque region pathology for progression of Alzheimer’s disease (Soula et al., Reference Soula, Caré, Beslon and Berry2013; Shoqhi-Jadid and Mehta, Reference Shoqhi-Jadid, Barrio, Kepe and Huang2006). Apart from environment heterogeneities, other unfamiliar phenomena can be explained by anomalous diffusion, like protein folding or unfolding. Therefore, in order to prove anomalous diffusion, it is important to take enough measurements to exclude possible artifacts.
Time of observing fluorescent molecules as a qualitative characteristic is depicted at ACC. If the analyzed molecules are in the vicinity of OVE, the upward number of photons is indicated. The number of photons decreases with time as molecules move out of the detection region. This decrease in ACC corresponds to molecular diffusion speed and size. Whichever process that interposes with fluorescence D can be subjected to FCS. The second notable characteristic of ACC is the reliance on the concentration of fluorescing molecules and viscosity of the solution. Fluorescent intensity of measured dye depends on the average N coming in or out of the OVE. If the N in OVE are comparatively few in number, the I (t) is stronger for molecules coming in or out of the detection volume. On the contrary, if the N in OVE is great in number (e.g., several hundred), the I (t) is weaker by molecules coming in or out of the detection volume. Distinction in diffusion time can be used to keep the different sizes of fluorescence molecules apart.
To acquire a credible standard for the estimation of a refractive index shift on the diffusion coefficient, we executed a systematic study of diffusion of MilliQ water solution containing a wide sweep of concentrations of glycerol, Rh6G dye, Alexa 33 dye; diffusion of RPMI medium with phenol red and diffusion of Abeta Alexa 647 dye containing RPMI medium phenol red-free and 20 mM HEPES buffer, pH = 7.0 solution.
Autocorrelation function and time
In Figure 10, links between autocorrelation decay and diffusion coefficient in terms of viscosity are depicted, and heterogeneous measurements are exhibited. From Figure 10A-C we have aqueous solutions of fluorescent dyes Rh6G and Alexa 633 and diverse concentrations of glycerol ranging from 10% - 50%, showing the differences in diffusion time on T = 20 °C. The fastest diffusing dye molecule is Rh6G, while Alexa 633 dye is located between 10% and 20% of glycerol. The curve shifts to the right, to a longer diffusion time due to the increase in viscosity with glycerol concentration. It’s the same molecule, but by raising the concentration, the glycerol becomes more viscose, which means it moves harder and slower in an aqueous solution. The viscosity of the solution is not subjected to change by various dye concentrations of Rh6G and Alexa 633 as seen in Figure 10B-C. Generally, the well-applied standard for molecular diffusion survey is 10 nM Rh6G as depicted in Figure 10A. Being aware of the precise diffusion coefficient of Rh6G is necessary to determine the absolute measurement of the diffusion coefficient. Measured values of viscosity for glycerol are in good agreement with the published data (Suhling and Phillips, Reference Suhling, Davis and Phillips2002).
The viscosity merit of aqueous glycerol is strongly dependent on concentration and temperature and can be equated with syrup. Temperature is the most contingent for higher glycerol concentration and moderately contingent for lower glycerol concentration (Longinotti and Corti, Reference Longinotti and Corti2014). When molecules undergo intrinsic rotation, viscosity can affect fluorophore lifetime fluorescence (Suhling and Phillips, Reference Suhling, Davis and Phillips2002). Glycerol is a feeble protein binder and higher concentrations can be added to the solution. It can change the optical characteristics by affecting the refractive index, light path, and focus. FCS stipulates molecular size based on the shape and size of a concentrated laser beam, and it is important to analyze solute influence. For high glycerol concentration, Equation 2 applies for diffusion coefficient and solution viscosity (Sherman et al., Reference Sherman, Itkin, Kuttner, Rhoades, Amir, Haas and Haran2008). Based on Figure 10, we can conclude that an increase in glycerol concentration affects the viscosity of a solution, while there is no effect on viscosity by the concentrations of Rh6G and Alexa dyes.
Consider the Roswell Park Memorial Institute (RPMI) cell medium, which is frequently used in cell laboratories. This RPMI medium can contain phenol red as a pH indicator. Phenol red can interfere with spectrophotometry and fluorescence assays depending on the laser wavelength and pH. Background fluorescence of culture media at the wavelength of 488 nm or 561 nm is negligible. However, phenol red is extremely fluorescent when excited at 440 nm or 633 nm with Argon or a He-Ne laser. Refractive index of phenol red with 440 nm and 633 nm wavelength cross interacts with pH shift due to irregular diffusion (Grattan and Palmer, Reference Grattan and Palmer2012). Therefore, it is better to use cell medium without phenol red. In Figure 10D, the curve for the RPMI medium with phenol red is an example of anomalous diffusion caused by the interaction of the auto-fluorescence of phenol red with the medium environment and the wavelength of a laser. The increased viscosity of the RPMI medium with phenol red compared to the 20 mM HEPES buffer solution and RPMI medium phenol red free with Abeta Alexa 647 dye resulted in the right shift of the G (t) towards longer times. Moreover, the form of the curve is shifting vigorously, so interaction with other phenol red molecules in the form of precipitates must be suspected. If the RPMI medium with phenol red is replaced with the RPMI medium phenol red free of 20 mM HEPES buffer, normal diffusion in the medium can be observed with Abeta Alexa 647 dye.
This information concludes that FCS is restricted to a tight sweep of the sample concentration from 1013 to 108. For other concentrations, the measurement time increases for acquiring a good ACC, which causes application constraints (e.g., low or high ligand concentrations) (Levene et al., Reference Levene, Levene, Turner, Craighead and Webb2003). The concentration range can be surmounted by fast scanning of the solution and reducing the observation volume while at the same time working at higher concentrations (Klar et al., Reference Klar, Engel and Hell2001).
Based on the sample volume and amplitude number of particles in the detection volume and by applying Equation 6, we obtained concentrations of every investigated molecule. Table 1 shows the concentration in mol/L and zM range of molecules analyzed by the FCS method.
Concentration of glycerol, Rh6G, and Alexa 647 molecules in solvents
Concentration in zM, mol/L range of glycerol, Rh6G, Alexa 647 molecules in diverse solvents (MiliQ water, 20 mM HEPES buffer, pH = 7.0, and RPMI medium).
Diffusion time and concentration
In order to further assess the fundamental kinetics, molecules are grouped according to their diffusion time and thus stated by their size. The observed number of molecules in th Equation 16. The average number of particles for a single concentration group was obtained by dividing the sum by the number of measurements. Changes in Ƭd and N according to concentration are shown in Figures 11 and 12.
Diffusion time variations on the concentration scale. (A–C) Diffusion of aqueous solution of 10%, 20%, 30%, 40%, 50% glycerol, 5 nM, 10 nM, 50 nM Rh6G dye and 1 nM, 10 nM, 100 nM, 1000 nM Alexa 633 dye. (D) Diffusion of RPMI medium with phenol red, RPMI medium phenol red free, and 20 mM HEPES, pH = 7.0, T = 20°C solution with unknown concentration of Abeta Alexa 647 dye.
Changes in the average number of particles depending on the concentration. (A–C) Aqueous solution of 10%, 20%, 30%, 40%, 50% glycerol, 5 nM, 10 nM, 50 nM Rh6G dye and 1 nM, 10 nM, 100 nM, 1000 nM Alexa 633 dye. (D) RPMI medium with phenol red, RPMI medium phenol red free, and 20 mM HEPES, pH = 7.0, T = 20°C solution with unknown concentration of Abeta Alexa 647 dye.
In Figure 11, diffusion time and concentration of glycerol, Alexa 633 dye, and Rh6G dye in MiliQ water and Abeta Alexa 647 in RPMI medium phenol red-free and 20 mM HEPES solution is presented. The slope of the plot for glycerol, Rh6G dye, and Alexa 633 dye increases with concentration increase. Viscosity and diffusion time of the aqueous glycerol solution rise linearly with concentration as indicated in the literature (Dean, Reference Dean1992). A solution of 50% glycerol has the biggest Td. For Alexa 633 dye, Td increases with the increase of concentration. However, smaller concentrations of the Alexa 633 dyes appear to be systematically biased towards larger values of Td. The diffusion time for glycerol and Rh6G estimated from individual G (t) shows wide distribution, while the overall curve has a typical sigmoid shape.
The RPMI medium with phenol red has the biggest diffusion time. Abeta Alexa 647 dye in 300 μL buffer and medium without the RPMI medium has the same diffusion time, while 200 μL of the buffer has the smallest diffusion time because molecules did not form Abeta aggregates as is the case with the medium and 300 μL of the buffer.
Number of particles and concentration
In Figure 12, changes in the average number of molecules in the OVE based on concentration group are shown. A solution of 10 nM Rh6G has the smallest N, while solutions of glycerol up to 40% have increasing N. However, 50% glycerol solutions have a decrease in N due to higher viscosity, slower molecule movement and shorter measurement time. Alexa 633 dye and Rh6G dye have a linear increase in N. The RPMI medium with phenol red has the approximate value as the 300 μL buffer and Abeta Alexa 647 dye and the smallest N value. A solution of the RPMI medium phenol red-free and Abeta Alexa 647 dye has the highest value of N.
A rough assessment of diffusion times can be achieved by organizing the aggregates into three groups based on their size (Figures 11D and 12D). Aggregates smaller in size with high Ƭd, behave as reactants since their concentration decreases during aggregation (Figure 11D, RPMI medium with phenol red). Aggregates larger in size behave as a product, since their concentration increases during aggregation (Figure 12D, RPMI medium phenol red free + Abeta Alexa 647 dye). Aggregates that belong in the group between the two act as intermediates with dynamic changes in concentration during aggregation (Figure 11D, buffer + Abeta Alexa 647 dye).
Brightness and concentration
When undergoing a modification in CPM, rely on the concentration of molecules as shown in Figure 13. The glycerol solution shows a linear decrease of CPM with viscosity in concentration increases up to 40%, and after that, it maintains CPM level. The Alexa 633 dye shows a linear increase in CPM to 100 nM and a sudden decrease to 1000 nM, while Rh6G depicts a linear increase in CPM. The RPMI medium with phenol red shows the smallest CPM since it does not contain Abeta Alexa 647. The Buffer and Abeta Alexa 647 dye exhibit the highest CPM.
Changes in the CPM [kHz] depending on the concentration. (A–C) Aqueous solution of 10%, 20%, 30%, 40%, 50% glycerol, 5 nM, 10 nM, 50 nM Rh6G dye and 1 nM, 10 nM, 100 nM, 1000 nM Alexa 633 dye. (D) RPMI medium with phenol red, RPMI medium phenol red free, and 20 mM HEPES, pH = 7.0, T = 20°C solution with unknown concentration of Abeta Alexa 647 dye.
We need to check concentrations above 50 nM of Rh6G aqueous solution since published data states that CPM decreases with concentration, accompanied by the decrease of quantum yield due to Forsters energy transfer between monomers and fluorescent stable dimmers at higher concentration (Culbertson et al., Reference Culbertson, Jacobson and Ramsey2002).
The aggregation of molecules extinguishes fluorescence and coherent properties associated with laser light systems. In an aqueous solution, dimerization of Rh6G starts when the concentration is at a border value of 1 × 105 mol/L (10,000 nM) and when two dye molecules are connected with a water molecule (Innocenzi et al., Reference Innocenzi, Kozuka and Yoko1993). Alexa 633 and Alexa 647 dyes are inclined to form dimer and monomer states with a decrease of fluorescence emission due to energy transfer between states (Conroy et al., Reference Conroy, Li, Kim and Algar2016).
We observe that as the concentration process continues, the number of small molecules decreases, and larger molecules appear while the number of observed particles decreases.
Count rate and concentration
Successive fluorescence intensity fluctuations were recorded. Concentration distribution histograms were generated by plotting the CR values as a function of corresponding concentrations obtained by fitting with Equation 16. The concentration distribution of all concentrations can be seen in Figure 14. A lower CR corresponds to a lower concentration of molecules in solution. An aqueous solution of 30% glycerol has the highest CR value after which CR decreases. Water solutions of Alexa 633 and a Rh6G dye show a linear rise in CR for a given concentration range. The RPMI medium with phenol red has the lowest CR, while the RPMI medium phenol red free with Abeta Alexa 647 has the highest CR.
Changes in the CR (kHz) depending on the concentration. (A–C) Aqueous solution of 10%, 20%, 30%, 40%, 50% glycerol, 5 nM, 10 nM, 50n M Rh6G dye and 1 nM, 10 nM, 100 nM, 1000 nM Alexa 633 dye. (D) RPMI medium with phenol red, RPMI medium phenol red free, and 20 mM HEPES, pH = 7.0, T = 20°C solution with unknown concentration of Abeta Alexa 647 dye.
Distribution of diffusion time and average number of particles
The N frequency distribution by means of diffusion time is depicted in Figure 15. This clearly shows that different concentrations of depicted molecules in different environments can affect the outcome of FCS measurement. Small distinction in the number of particles was observed for all Rh6G concentrations and for lower concentrations of glycerol and Alexa 633 dye. The biggest distinction in the number of particles is visible in higher concentrations where the maximum peak is reached at 40% glycerol and 1000 nM Alexa 633 dye. All Ƭd rises with N, with the only exception being Alexa 633 dye in 1 nM concentrations where the smaller molecules consistently bias to larger values of Ƭd. The diffusion time distribution of Alexa 633 dye depicts that when the initial concentration is 1 nM, the solution contains smaller aggregates. This is due to the faster aggregation process or to the decreased sensitivity of the FCS apparatus. The RPMI medium phenol red-free with Abeta Alexa 647 has the biggest difference in the number of particles. The ratio of Abeta Alexa 647 dye in buffer solution shows a decrease in the number of observed particles, but the overall diffusion time was not significantly affected.
Diffusion time allocation histogram produced by mapping N as a function of diffusion time. (A–C) Aqueous solution of 10%, 20%, 30%, 40%, 50% glycerol, 5 nM, 10 nM, 50 nM Rh6G dye, and 1 nM, 10 nM, 100 nM, 1000 nM Alexa 633 dye. (D) RPMI medium with phenol red, RPMI medium phenol red free, and 20 mM HEPES, pH = 7.0, T = 20°C solution with unknown concentration of Abeta Alexa 647 dye.
Diffusion time and brightness
Moreover, aspiring to stipulate the range where Ƭd is constant and where saturation and bleaching are achieved, we arrange Ƭd and CPM as a function of laser illumination power as depicted in Figure 16. When the plateau was reached with a 40% glycerol concentration, saturation was observed. This is not the case with other investigated molecules. Higher concentration needs to be explored to establish constant Ƭd, saturation, and bleaching levels.
Diffusion time allocation histogram produced by mapping CPM [kHz] as a function of diffusion time. (A-C) Aqueous solution of 10%, 20%, 30%, 40%, 50% glycerol, 5 nM, 10 nM, 50 nM Rh6G dye, and 1 nM, 10 nM, 100 nM, 1000 nM Alexa 633 dye. (D) RPMI medium with phenol red, RPMI medium phenol red free, and 20 mM HEPES, pH = 7.0, T = 20°C solution with unknown concentration of Abeta Alexa 647 dye.
Diffusion time and count rate
Figure 17 depicts the dependence of diffusion coefficient and fluorescence intensity of molecules moving in and out of the OVE. Overall, the graphs show that fluorescence intensity is the strongest in the 30% concentration of glycerol, in 1000 nM of Alexa 633 dye, in 50 nM of Rh6G dye, and in the RPMI medium phenol red-free with Abeta Alexa 647 dye. The 1 nM Alexa 633 dye shows the biggest diffusion time through OVE when compared to other dye concentrations, but the total CR was smaller.
Diffusion time allocation histogram produced by mapping CR [kHz] as a function of diffusion time. (A-C) Aqueous solution of 10%, 20%, 30%, 40%, 50% glycerol, 5 nM, 10 nM, 50 nM Rh6G dye, and 1 nM, 10 nM, 100 nM, 1000 nM Alexa 633 dye. (D) RPMI medium with phenol red, RPMI medium phenol red free and 20 mM HEPES, pH = 7.0, T = 20°C solution with unknown concentration of Abeta Alexa 647 dye.
Conclusion
The advantage of FCS is that it is a simple method to employ, sustain, and utilize, which provides its broad and comprehensive application. FCS can be applied for the following: basic studies of molecular diffusion in free solutions, various mechanisms in membranes in two dimensions, combining with micro fluid devices, and enzymatic reactions, and processes of folding and unfolding. The use of FCS in combination with other techniques is spreading in biochemical and biological fields to shed light upon diverse segments of macromolecules (Diez et al., Reference Diez, Borsch, Zimmermann, Turina, Dunn and Graber2004; Dertinger et al., Reference Dertinger, Hocht, Benda, Hof and Enderlein2006; Hamadani et al., Reference Hamadani and Weiss2008). Time scale sizing of molecules with FCS is an effective and trustworthy method for analyzing the diffusion of differently sized macromolecules (Donovan et al., Reference Donovan, Chehreghanianzabi, Rathinam and Zustiak2016). These broad FCS applications have limitations regarding the quantitative assessment of measurements. In order to obtain high sensitivity, we have to have prior knowledge about the size and the shape of detection volume to be able to see fluorescence photon molecules at a specific position in OVE.
Analysis of autocorrelation curve
Using FCS method for the methodological study of ACC, we perceived that all ACC can be fitted by a model of free 3D diffusion of a single component. There was a minimal effect of the selected method to establish ACC exponential decay time, so changes in the shape of glycerol ACC may stand out from short measurement times for higher viscosity solution. Assessment of ACC is simpler by utilizing short acquisition times and fitting models with a small number of free parameters when compared to longer acquisition times (Ries et al., Reference Ries and Schwille2008; Mittag et al., Reference Mittag, Milani, Walsh, Radler and McManus2014).
The precise quantification of FCS measurements is highly dependent on the optical parameters, refractive index, and cover slide thickness, which makes it harder to control. All those parameters influence the ACC and diffusion coefficient. One example is the refractive index of used immersion media. Water media aids detection by raising the detection volume and decreasing the diffusion coefficient. Thanks to that, reference measurements of the fluorescent molecule are employed to prevent changes, which is another important disadvantage (Enderlein et al., Reference Enderlein, Gregor, Patra and Fitter2004). There is no simple relationship between molecular weight and mobility, so it is hard to foretell the diffusion coefficient.
Effect of FCS measurement time on Autocorrelation curves
Fluorescence intensity variations are noted across a fixed measurable moment in time and mathematical examination is put into practical use to determine deviations in the data. This action is completed by applying temporal autocorrelation analysis to draw out data on Ƭd and N.
Extended measurement time and a suitable statistical analysis model may contribute to a less noisy ACC. When the static process is carefully considered, extended time can be employed. To whatever degree possible, when the dynamic changeable process is examined, the measurement time should be adjusted to suit a particular set of time process requirements. Since precise FCS analysis claims to employ the related mathematical principle of diverse fluctuations, it is of significant worth to have an understanding of the limit to reduce the continuance in measurement time lacking related deviations in the act of estimating the molecular number and diffusion times (Sengupta and Robinson, Reference Sengupta, Garai, Balaji, Periasamy and Maiti2002; Qian, Reference Qian, Elson and Frieden1992; Saffarian and Webb, Reference Saffarian and Elson2003; Wohland and Vogel, Reference Wohland, Rigler and Vogel2001).
The shortest distinguishing marked fitting decay time in our study was 24 μs for 5 nM Rh6G dye solution, and it was extending to a considerable distance of 670 μs for the 50% glycerol solution. The average number of molecules entering and exiting across the OVE perceived throughout the duration of 10 s measurements is 1500 for molecules marked with Ƭd = 24 μs, while the average number of molecules marked with Ƭd = 670 μs entering and exiting across the OVE perceived throughout the duration of 10 s measurements is 15,000. So 10 s measurement time is 1000 times extended than the distinguishing time of the slowest examined flow. In these circumstances, the standard deviation in N and Ƭd is indicated as less than 25% (16]. The allocation of diffusion times of Rh6G in water was resolved to be ƬdRh6G = (24 ± 2) μs (n = 460), the counts per molecule was CPM = (5.1 ± 0.6) kHz, and the structure parameter was S2 = 7 ± 1.
Effect of brightness on FCS analysis
The molecular brightness of fluorochrome can affect noise of the ACC (Jung et al., Reference Jung, Lee, Kang and Kim2014). Artifacts from photobleaching and optical saturation can originate by rising excitation intensity and brightness up to a limit (Nagy, Reference Nagy, Wu and Berland2005). Examined environment system can be homogeneous or heterogeneous containing an identical or diverse quantity of molecules of different sizes and brightness. Generally, we notice overlapping ACC, which shows the presence of the investigated molecule in large amounts. Moreover, some ACC can be distinguished in the amplitude and decay time, occasionally exhibiting instances of more numerous and brighter molecules.
Depending on the solution concentration, viscosity, and amplitude of the investigated molecule, the typical decay time will differ. With the increase of aggregates or the viscosity of a solution, longer decay times are indicated.
Distribution of brightness may influence the exact determination of particle numbers when two species of different light intensity exist together, because the apparent number of molecules in the OVE will be relatively lower than the total number of molecules, but higher than the metric composition of brighter molecules (Matthew et al., Reference Will, Clark and Swain2011).
Moreover, variability is not high when molecules are alike in brightness, and a small unreliability in the number of molecules in the lag phase can be anticipated. By increasing the number of aggregates in the solution, variability in brightness among small and large aggregates can be seen, while brightness decreases with increasing solution viscosity. Therefore, by applying Equation 16, individual ACC can be distinguished by decay time.
The combination of FCS with one photon excitation imaging method is a promising variation that can lead to punctual prosperity of signal quality and diffusion coefficient without prior information on solution volume size and complex environments. One of the fundamental properties of a molecule is size. By resolving size, you can get an insight into the conformational changes of a molecule, molecular interactions, or intermolecular reorganizations in diverse solution environments and concentrations. Optical saturation is the most notable cause for inaccuracy and irreproducibility in FCS analysis results. However, there is a state-of-the-art method variation called dual-focus fluorescence correlation spectroscopy, which diminishes the effects of said optical saturation.
Summary
In summary, we have presented FCS results of the analyzed behavior of glycerol, Alexa 633 dye, Rh6G dye, and Abeta Alexa 647 dye in various solution conditions that are crucial for the design of any application as well as experimental plans of action in combination with basic confined theory which makes quantification of molecular parameters possible, subjected to regular environmental requirements. Variations in fluorescence or other photophysical attributes can be of use in the result of fluorescence build assay. We have unraveled the underlying mechanism in the place of solution diffusion and viscosity, which provides the means to optimize the perceived fluorescence yield from a single molecule. Apart from molecular optimization, in the future, FCS can be included as one of the dynamic, innovative, and state-of-the-art methodologies used in cutting-edge laboratory research. Projects can involve clinical and non-clinical diagnostic and prognostic markers as well as statistical models for mapping actions of disease mechanisms. Collaboration with other research groups and further upscaling laboratory equipment and innovation engines can assist in discovering unknown signal pathways and molecular mechanisms for disease eradication. Learning to analyze and interpret data can help in performance assessment to clarify problems, evaluate new molecular alterations, and reduce the effect of errors in relating one variable to another. In the future, we should try to determine potential barriers to molecular characterization by using FCS. Emphasis can be given to image analysis for determining molecules based on visualization. Interpretation of the results is very important, as FCS generates enormous numbers of raw data that could be inappropriate and misleading. The goal is to learn how to normalize results by excluding non-biological variations such as non-specific and background hybridizations. Having understood the reaction mechanism properly, the expert model of detection will be modified, including the development of novel prognostic and diagnostic strategies for patients with disturbed molecular pathways. Comparing results from all variation methods of FCS will help assess their advantages and disadvantages as well as cost, sensitivity, reliability, and flexibility.
Growing collaboration between professionals worldwide will improve science and lead to better patient care. By working with other experts, we will be able to identify detection barriers and develop methodology refinement in data implementation with insights into solutions.
Abbreviations
AOTF, acousto-optical transmission filter; Abeta, Amyloid beta; ACC, autocorrelation curve; APD, avalanche photodiode fast detector; CPS, counts per second; CPM, counts per molecule, brightness; CR, count rate; D, diffusion coefficient; FCS, fluorescent correlation spectroscopy; fL, femtoliter; G (t), autocorrelation function; HEPES, 4-(2-hydroxyethyl)-1-piperazine-ethane sulfonic acid; HFT, main dichroic; I (t), fluorescence intensity; Kb, Boltzmann’s constant; LSCM, laser scanning confocal microscope; Λ, wavelength of the light; m, mass; MSD, mean squared displacement; N, average number of molecules; N (t), total particle number; NA, numerical aperture of the microscope lens; NFT, secondary dichroic; OVE, observation volume element; Rh, hydrodynamic radius; Rh6G, Rhodamine 6G; T, absolute temperature; Ƭ, lag time; Ƭd, diffusion time; Vp, volume of a particle; wxy, latitude in the XY direction; z0, longitude in the z direction; γ, structural factor or axis ratio of the focus; Ƞ, viscosity of the solvent; n, refractive index of the sample solution.
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