WO2014058371A1

WO2014058371A1 - Scattering interference correlation spectroscopy (sics)

Info

Publication number: WO2014058371A1
Application number: PCT/SE2013/000155
Authority: WO
Inventors: Stefan Wennmalm
Original assignee: Individual
Current assignee: Individual
Priority date: 2012-10-13
Filing date: 2013-10-14
Publication date: 2014-04-17
Anticipated expiration: 2015-04-13

Description

Scattering Interference Correlation Spectroscopy (SICS) Field of the Invention:

The invention relates to analysis of diffusing particles and biomolecules in solution or in cells. In biophysics, biochemistry, and cell biology, methods are needed for analyzing the interaction of biomolecules. A particular requirement on such methods is the possibility to measure interactions even at low concentrations, down to nano-molar and lower concentrations.

The invention also relates to the field of analyzing particles that may not be biological, for example particles in solutions and emulsions. For example there is a need to determine the concentration and size of particles in engine-fuels, for environmental and health purposes. Another example is analysis of aggregation of particles in for example cosmetic products such as skin lotions.

Even though the description of the invention below will focus on its application to analysis of particles in solution, it may also be of interest to analyze particles or biomolecules in a solid, or in a substance which is not fluid. This can be realized by moving the solid sample relative to the laser focus, which can be accomplished by moving the sample relative to the fixed laser focus, or by moving the laser focus across the immobile, solid sample.

Background of the Invention, and Description of Prior Art:

Light scattering techniques for analysis of unlabeled particles:

A large number of techniques exist for analysing particles, nanoparticles (smaller than 100 nm diameter), biological particles and biomolecules in solution (all of these will below be referred to as "particles"). The majority of these techniques are based on light scattering in different forms.

One example of such a technique is dynamic light scattering (DLS), also called quasi- elastic light scattering (QELS), which detects only the scattered light from particles in solution, and is used to estimate the size of particles from their diffusion coefficient. Another technique is laser diffraction (for example utilized in instruments from the company Malvern), which utilizes the fact that the angle relative to the incoming laser in which light is scattered from particles in solution is dependent on the particle size.

Therefore many detectors are positioned at positions corresponding to different scattering angels around the sample, and the time-averaged intensity distribution on these detectors is used to identify the mean size of the particles in the sample. Particle size is here given as the projected cross-section, so no information of the diffusion coefficient is obtained. A third technique is laser Doppler velicometry, which can be used together with phase analysis light scattering (PALS), and these are used to estimate the velocity of particles in a flow. None of these techniques can determine the particle concentration, and for nanoparticles (smaller than 200 nm diameter), no technique can estimate particle concentration independently from particle size; existing techniques require pre-knowledge about particle size in order to estimate concentration, and vice versa.

Moreover, none of these techniques can be combined with fluorescence detection to allow simultaneous fluctuation analysis of light scattering and fluorescence.

Fluorescence Correlation Spectroscopy for analysis of labelled particles:

The above mentioned techniques analyze unlabeled particles in solution by light scattering techniques. A different technique which is based on fluorescence is

fluorescence correlation spectroscopy (FCS). Even though the invention analyzes a scattering signal and not a fluorescence signal, FCS is mentioned here because it has similarities to the invention. In addition, one part of the invention is to combine the invention with FCS, in order to allow simultaneous analysis of labelled and unlabeled particles.

FCS detects transient fluorescence signals from fluorescently labelled particles (most commonly biomolecules) in solution as they diffuse through an open detection volume that usually has a size in the range 0.2 femto liter to a few femtoliter. The duration of the generated fluorescence bursts is indicative of the size of the diffusing species, since the diffusion coefficient is inversely proportional to the particle radius. The detection volume is restricted by the size of the laser focus and also by the confocal detection with a pinhole in the image plane. In this part, FCS resembles the invention, because the invention also detects a signal from particles as they diffuse through a detection volume, and the detection volume is, or can at least be, restricted as in FCS by the dimensions of the laser focus and by the pinhole (the detection may however be different, because the forward scattered light may be analyzed, which requires a second lens or objective, on the other side of the sample. However, the detection may also be similar to that of FCS in that back scattered light may be detected by the same objective as used for the incoming laser). The invention also resembles FCS in that the signal may (but does not have to) be analyzed by autocorrelation or cross-correlation.

More on FCS:

The concept and principal experiments of FCS were presented in 1972 (Magde, Elson and Webb, 1972, Elson and Magde 1974) however the real breakthrough had to await the early 1990's, when FCS was combined with confocal microscopy and later two-photon microscopy (Rigler, Mets, Widengren and Kask, 1993). Since then about 3000 papers using FCS have been published according to Web of Science, March 2012. FCS instruments are in 2012 built and sold at least by Zeiss, Leica, Picoquant, ISS and

Hamamatsu, and FCS has become an important tool in biophysics and cell biology, in academia as well as in industry. In FCS, a laser is focused by a microscope objective, which generates a focus inside the liquid sample. The axial radius of the laser focus cannot be smaller than about 0.2 μιη due to the diffraction limit. The focus can however be enlarged, to have a radius of several micrometers. Fluorescent molecules, for example organic fluorophores, labelled biomolecules, or fusions of a protein with a fluorescent protein like GFP, generate fluorescence bursts as they transit through the excitation focus. A part of the emitted fluorescence is collected by the same objective, focused through a pinhole in the image plane, and thereafter focused again onto detectors. Because the emitted fluorescence has slightly longer wavelength than the exciting laser, the collected fluorescence can be spectrally discriminated from scattered laser light by using dichroic mirrors and emission filters between the objective and the pinhole. The final detection volume is restricted both by the dimensions of the laser focus and by the size of the pinhole in the image plane, which in the diffraction limited case results in a detection volume of -0.3 fl (fig 1).

The detected fluorescence bursts can give information about the mobility and

concentration of the diffusion molecules, and about any dynamic process generating fluorescence fluctuations between high- and low-fluorescent states.

Fig 1. Description of a common experimental setup for FCS. Laser light (blue) is reflected by a dicroic mirror and focused by a microscope objective into a sample containing diffusing fluorescent particles or molecules. The emitted fluorescence light (green) from fluorescent particles diffusing through the excitation focus is collected by the same objective and transmitted through the dichroic mirror. An emission filter selects fluorescence emission and blocks scattered laser light. The emission is then focused through a pinhole, which discriminates out-of-focus photons, and focused onto a photo detector. From the detected fluorescence light the autocorrelation function (ACF) is calculated. Fitting of the ACF to an appropriate model gives information about concentrations and mobilities of the diffusing particles.

FCS is for example used to analyze interactions between biomolecules: When a small, fluorescently labeled molecule interacts with, or binds to, a larger, unlabeled molecule or particle, the mobility of the smaller molecule will decrease since large molecules have lower mobility than small molecules. In this way the process of binding over time between the smaller, labeled, molecule and the larger, unlabelled molecule can be detected and analyzed.

A version of FCS is Fluorescence Cross-Correlation Spectroscopy, where two excitation foci of different wavelength (often 488 nm and 633 nm) are superimposed in the sample. Interacting partner-molecules are labeled with a 488-excitable dye and a 633-excitable dye respectively, and their respective emissions are spectrally filtered and detected by two separate detectors. This allows analysis of interacting molecules independent of their respective sizes (see any of several review papers by Petra Schwille). Summary of the invention (Abstract):

A drawback of present scattering based methods is that they cannot estimate the size in two ways simultaneously, for example from the diffusion coefficient and from the scattering intensity simultaneously. This results, for example, in that they cannot determine the particle concentration independently from the particle size, because these two both affect the scattering from the sample.

In contrast, the invention, SICS, does estimate the particle size both from the diffusion coefficient and from a signal based on scattering, and can thus estimate not only the particle size but also simultaneously estimate the particle concentration (see the manuscript below for details). In short, typically, a laser is focused to form a detection volume inside a liquid sample, and while most of the laser light is transmitted through the sample, some light is scattered in the forward direction from particles or biomolecules inside the detection volume. This scattered light interferes with the transmitted laser light, forming the detected fluctuations which give information about the particles or biomolecules that gave rise to the scattering.

Moreover, by comparing the measured diffusion coefficient and the scattering-based signal can give information about particle shape. In principle, any sample parameter can be investigated that affects the two measures of particle size differently.

Furthermore, the invention can conveniently be combined with FCS, and allows thereby unlabelled and labelled particles or biomolecules to be analysed simultaneously, which enables the fraction of labelled particles or biomolecules to be estimated. Furthermore, the affinity between unlabelled particles or biomolecules and fluorescently labelled ligands can be estimated from a single measurement, as described in detail in the manuscript.

Detailed summary of the Invention

As a first aspect of the invention, there is provided a method for analysing particles or biomolecules in a liquid sample, comprising:

detecting a signal and fluctuations in the signal from a detection volume in the sample; wherein the signal is laser light transmitted through the detection volume and the fluctuations are reductions or increases in the signal due to the presence of particles or biomolecules in the detection volume; and analyzing the detected fluctuations to obtain information about the analytes in the sample.

It may be added to the first aspect above that the fluctuations caused by the presence of particles or biomolecules in the detection volume may arise due to scattering of the incoming laser light from the particles or biomolecules which then interferes with the transmitted laser light.

As a second aspect of the invention, there is provided a method for analyzing particles, biomolecules or molecules in a solid material, comprising

scanning a detection volume across the solid material: detecting a signal generated from the solid material and fluctuations in the signal; wherein the fluctuations arise due to scattering from some molecules in the detection volume which then interferes with the laser light transmitted through the detection volume; and analyzing the detected fluctuations in the signal from the solid material to obtain information about the molecules.

As a third aspect of the invention, there is provided a Scattering Interference Correlation Spectroscopy system comprising a laser, a coverslip sandwich in between which a sample resides, focusing means for focusing the laser inside the sample inside the coverslip sandwich, means for collecting the scattering and interference signals and any fluorescence signals from analytes within the coverslip sandwich, detectors for detecting the scattering and interference signals and any fluorescence signals, and means for autocorrelating the detected signals.

As a fourth aspect of the invention, the system described in the third aspect of the invention may be combined with Fluorescence Correlation Spectroscopy (FCS) in a single instrument, such that while the SICS-part of the instrument analyses the size and concentration of the analytes present in the sample (labeled as well as unlabeled), the FCS-part of the instrument analyses simultaneously the fluorescently labeled fraction.

The fourth aspect of the invention, ie the combination of SICS and FCS, allows determining the fraction of labeled analytes in the sample. Furthermore, if unlabeled particles or biomolecules are analyzed in the presence of labeled, small ligands, where the ligands bind to the unlabeled particles or biomolecules, the affinity (K_d) can be estimated from one single measurement, as described in the manuscript below.

As a fifth aspect of the invention, there is provided a device for analyzing the detected signal, comprising:

a data storage device which in addition may be a data analysis device, for storage and possibly also analysis of the detected signal, where the analysis may be in the form of autocorrelation analysis, where the amplitude and the decay time of the autocorrelation function give two separate estimations of the size of the analytes in the sample, and the amplitude of the autocorrelation function also can give information about the concentration of analytes in the sample, or the analysis may be in the form of intensity distribution analysis or analysis of photon counting histograms, which can give information about the size of the analytes in the sample, and the shape of the analytes in the sample, or the analysis may be in the form of cross-correlation with another signal.

If the instrument described above comprising is not sufficiently unique, it may be specified further, by in addition specifying that the detector should consist of a photo diode which can detect count rates as high a 10¹⁵ photons per second or higher, or a photo multiplier tube running in dc mode, capable of detecting 10¹² photons per second or more. An important feature of the invention is that the signal from fluctuations caused by interference of the scattered light with the transmitted or reflected laser light is detected from a limited detection volume. This allows analysis resembling that in FCS, to determine the average transit time of particles through that detection volume, and also to determine the average number of particles in this detection volume. The detection volume may be restricted by the dimensions of a focused laser beam, for example a diffraction limited laser focus, and also by a pinhole or similar positioned between the sample and the detector, for example at the image plane of the detection focus, and likely positioned in the forward direction due to forward scattering, but back scattering may also be analyzed, in which case the scattered light is collected by the same focusing means as was used for creating the detection focus, and the scattered light is then focused through a pinhole in the backward direction.

A fibre-coupled detector may also be used, in which case the fibre opening may be used instead of the pinhole or similar, and the fibre opening may for example have a diameter of 5, 10, 20 or 50 μπι. In the measurements which are described in fig 1A in the manuscript attached below, a fibre coupled detector was used, even though the fibre cannot be seen in the drawing of fig 1A.

Another important feature of the invention is that the diffusion coefficient and the signal based on scattering give two separate and independent measures of particle size. Due to this it is possible to determine parameters that are affected differently by these two size measures, for example the shape of particles.

Another important feature of the invention is that particle size and particle concentration can be determined using a single technique. If the instrument is calibrated, then size and concentration of an unknown sample (with known refractive index and fairly spherical particles) can in principle be determined in a single measurement. This is done by taking the size as estimated from the diffusion coefficient and inserting this size estimate into the expression for the amplitude of the autocorrelation function, which allows the concentration to be derived.

Another important feature of the invention is that the technique is very similar to FCS but does not require fluorescence labelling. This will allow the invention to be combined with FCS, and allow simultaneous analysis of labelled and unlabeled particles. This will for example make possible to determine the percentage of particles or biomolecules that carry a fluorescently labelled ligand, or the percentage of particles of biomolecules that are fluorescently labelled.

Combining the invention and FCS may be accomplished using an instrument for the invention (called SICS in the manuscript attached below) as is described in fig la in the manuscript, but where not only the forward scattered light (label-free detection) is utilized, but also the fluorescence signal from fluorescently labelled particles in the sample is detected. In fig la in the manuscript, the mirror that reflects the laser light from the laser down into the objective may be a dichroic mirror, as in the FCS instrument in fig 1 above. Thus, a fluorescence signal generated in the sample may be collected by the objective, passed through the dichroic mirror, focused through the pinhole and finally focused again onto the detector, as shown in fig 1 above (green line for the collected fluorescence emission). If instead the FCS instrument in fig 1 above is taken as starting point for combining FCS and the invention, then the combination of FCS and the invention may be accomplished by collecting the transmitted and scattered laser light below the sample in fig 1 above, as described in the manuscript (plus using a "coverslip sandwich" as described in the manuscript). The instrument in fig 1 above is already an FCS instrument, so adding the collection and analysis of the transmitted and scattered light would yield a combination of the invention and FCS.

The pinholes or similar and detectors may be optimized such that both detectors (the detector that detects the interference signal from scattering and the transmitted beam, and the detector that detects fluorescence) detect a signal from the same, or almost the same open volume.

As described above, the FCS signals and the signals detected by the invention (SICS) may either be analyzed separately and compared, which in a single measurement would yield the total concentration of particles and the concentration of label-carrying particles, which allows the percentage of label-carrying particles to be determined. Alternatively, the two signals can be cross-correlated, which may yield additional information. For example, this could as in inverse-FCS (see references in the manuscript below) allow the volume of the analyzed labelled particles to be determined, since the SICS-signal is proportional to the particle volume (and the amplitude of the autocorrelation function is proportional to the square of the particle volume). Such cross-correlation analysis may also be a good way to determine that binding between a small, fluorescently labelled ligand and a larger non-labeled particle has occurred. Alternatively, if a larger,

fluorescently labelled particle binds to a smaller, non-labeled ligand, this may also be advantageously analyzed by cross-correlaiton analysis, since the volume change upon binding will have a strong effect on the fluctuations detected in SICS+FCS which are proportional to particle volume, stronger than the effect that the same binding event would have on the diffusion time in an FCS measurement, since the diffusion time only scales with the cubic root of the particle mass.

As described in the manuscript below, the volume of particles in SICS may also be derived by fitting of single-species or multiple-species models to intensity distribution histograms.

In principle, SICS could also be applied to analysis of particles on a surface, which may be a solid surface or a fluid surface. This could either be realized by sweeping the laser over surface, or moving the surface relative to the laser.

It is assumed throughout this provisional patent application that in the invention, SICS, the fluctuations are generated from interference between the light scattered from particles and the transmitted laser light. However, if it would turn out that this is not the cause of the fluctuations, the instrument as described in fig la in the manuscript below is nonetheless novel in that detection of the scattered and transmitted laser light followed by statistical analysis of the detected fluctuations (such as autocorrelation, cross- correlation or intensity distribution analysis) allows determination of the diffusion coefficient, the amplitude of the fluctuations, and of the concentration, and that a detection volume is defined in the instrument in the same way as in FCS.

Using photo detectors capable of detecting higher count rates than what APDs are capable of should allow higher laser powers to be used. This will reduce the relative influence of noise (called shot noise or photon noise) relative to the signal and thus allow SICS to analyze even smaller particles than what is presently possible using APDs. Such photodetectors may be PMTs in DC-mode (ie, not single photon counting PMTs), or photo diodes, both which may be used together with analogue to digital converters.

It may also be advantageous to use so called lock-in detection, to improve sensitivity and allow analysis of even smaller particles. Lock-in detection is a common approach which circumvents the problem that small fluctuations of interest may drown in other, larger fluctuations, for example caused by the laser.

Another way of reducing the influence of noise from the laser light during a

measurement with the SICS technique is to split the laser light before the sample, such that one fraction of the beam (probably the majority of the original intensity) is focused inside the sample as usual, but the other fraction is not, and the intensity of the latter can then be recorded with one detector simultaneously as the SICS-measurement is performed, which allows slow fluctuations from the laser to be subtracted from the SICS- signal, or otherwise compensated for.

Other objects and advantages of the present invention will become obvious to the reader from the description below, and it is intended that these objects and advantages are within the scope of the present invention.

The invention called SICS and its combination with FCS is described in the manuscript attached at the end of this document. The main novel parts of the invention (SICS), and the main possible developments and applications are described in the points below. The source generating electromagnetic radiation will in most cases below be called "laser". The manuscript is published, Wennmalm and Widengren, J. Am. Chem. Soc. (2012), 134, 19516-19519.

Brief description of drawings

Figure 1 describes a standard FCS setup.

Brief description of drawings in the manuscript below

Figure 1 A describes a combined SICS- and FCS-instrument, where SICS is the part of the instrument below the sample and FCS is the part of the instrument above the sample.

Interferometry and fluorescence detection for simultaneous analysis of labeled and unlabeled nanoparticles in solution

Stefan Wennmalm^* and Jerker Widengren

Royal Institute of Technology, Albanova University Center, Department of Applied Physics, Experimental Biomolecular Physics, 106 91 Stockholm, Sweden.

Keywords: nanoparticles, label-free, interferometry, particle sizing, light scattering, fluorescence correlation spectroscopy

Supporting Information Placeholder

The two most popular techniques for label-free analysis of particles in solution are dynamic light scattering¹ (DLS) and laser diffraction spectroscopy². While DLS derives particle size from the diffusion coefficient, laser diffraction measures the particles' projected cross-section. None of the techniques estimate however the concentration of particles, and they cannot easily be combined with fluorescence techniques. In the last few years, interferometric techniques for analysis of single metal and polymer nanoparticles (NPs) and viruses have gained much interest. They offer high sensitivity detection of unlabeled nano-sized objects³' ⁴, but also allow metal NPs to be used as an alternative label, free from fluorescence bleaching, blinking and saturation^5"8. Recently photothermal correlation spectroscopy⁹ (PCS) and photothermal absorption correlation spectroscopy¹⁰ (PhACS) were demonstrated as interferometric techniques for solution analysis of gold NPs as an alternative specific label.

Here scattering interference correlation spectroscopy (SICS) is introduced as a label- free technique, where fluctuations are likely caused by interference between the phase shifted forward scattering from NPs and the transmitted laser light (reference beam) as in PCS and PhACS (fig 1 a). Autocorrelation of the forward scattered and transmitted light yields information not only about the NPs' hydrodynamic radius, but also about their effective cross-section and concentration. Furthermore we demonstrate how the technique easily can be combined with fluorescence correlation spectroscopy (FCS), to allow simultaneous analysis of labeled and unlabeled NPs.

Figure 1. A) Experimental setup for SICS and its combination with FCS. B) Intensity trace and C) histogram of a measurement on 93 nm NPs, 8 ms bin time, diffusion time T_d=8-9 ms, N=0.18. D) Intensity trace and E) histogram of a measurement on pure buffer solution, 8 ms bin time. Measurement times were 120 s.

Figure 2. ACF curves from four measurements on 62 nm (left) and 26 nm diameter (middle) unlabeled NPs. Insets: G(0)-1 vs N for the respective NP sizes. A_q for all four NP sizes was obtained from the slope which equals A_q ². Right: A_q plotted versus the NP diameter for the four NP sizes. A_q scales with the NP volume, evidencing that the fluctuations are caused by interference.

The amplitude of the autocorrelation function is given by

3/² (0)

G(0) - 1 =

(1)

where / is the detected intensity, 6I(t) is the deviation from the mean intensity at a certain time point t, and brackets denote mean value.

The signal caused by a single unlabeled NP is a_p-P_tot/A_dv = P_tot A_q, where σ_ρ is an effective cross-section, P_tot is the applied laser power, A_dv is the area of the laser focus, and A_q is the normalized effective cross-section A_q= Op/A_dv. With a mean number of particles N in the detection volume, the fluctuation of the detected power P equals δΡ= Ptot'Aq- N, since the standard deviation of N equals 5N= N because N is Poisson distributed. The mean detected power P is dominated by the transmitted light and can be approximated as P_tot. Insertion into eq. 1 gives

P² - A² - N

G(0) - 1 =—— ² = A²N

K ^■ (2)

First, polystyrene NPs diluted to concentrations such that on average N = 0.18 NPs resided in the detection volume were measured. For 93 nm NPs, negative fluctuations in the detected laser light are directly visible in the intensity trace (fig lb), while a measurement on pure buffer solution shows only laser noise (fig Id and e). A histogram of the detected intensity for 93 nm NPs shows a broader distribution with a tail towards lower counts per bin, indicating that NPs transiting the detection volume give rise to negative fluctuations¹¹ (fig lc). Positive fluctuations may also be present, but this cannot be concluded given the limited signal to noise ratio in these measurements.

Next, the dependence of the autocorrelation function (ACF) amplitude on particle concentration was investigated by measurements on unlabeled NPs with diameters 210, 93, 62 (fig 2, left) and 26 nm (fig 2, middle). In agreement with eq. 2, the ACF amplitudes scale linearly with particle concentration. The resulting slopes from plotting G(0)-1 vs N (insets, fig 2) give A_q = 0.162 (210 nm NPs, data not shown), A_q = 0.0135 (93 nm, data not shown), A_q = 4.5 10^"3 (62 nm), and A_q = 4.0· 10^"4 (26 nm). If these different A_q- values are now plotted against the NP diameter d, and fitted with A_q=k d^p, an exponent β close to three should be obtained. Such a fit yielded β=3.03 ± 0.03 (fig 2, right), and accordingly the fluctuations scale with the NP volume. This indicates that the observed fluctuations are caused by interference of the scattered light with the transmitted light, in contrast to scattering alone which scales as the square of the polarizability and hence as the square of the volume ' ' .

The decay-time dependence of the ACF curves on particle size was investigated by measurements on the 210, 93, 62 and 26 nm diameter NPs. The respective diffusion times were 26, 8.6, 6.4, and 2.8 ms (fig 3, upper). From these diffusion times of NPs with known diameters, the radius ω₀ of the detection volume was calculated using the Stokes- Einstein equation, yielding ω₀=0.43 μιη ± 0.015 μιη, and V_dv=2.21 fL (the 210 nm NPs are too large to be considered point-like 12 and were not used for estimation of co₀).

For spherical particles, the diffusion coefficient gives a separate estimate of the particle size, which can be used together with eq. 2 to derive the particle concentration from the ACF amplitude. In cases with homogeneous samples of known refractive index, the instrument can even be calibrated to yield the diffusion time, normalized effective cross- section A_q and concentration of an unknown sample, by utilizing that the diffusion time for point like particles is linear with the particle diameter d, and that A_q scales as d³. By calibrating the instrument using A_q = 4.0· 10^'4 and x_D=2.8 ms of the 26 nm NPs, the diffusion time and A_q of the 62 nm NPs could be predicted, which were then used to convert the ACF-amplitudes of the 62 nm NPs into concentrations. The result is shown for the 62 nm NPs (fig 3, lower left), and also for the 26 nm NPs used as calibration standard (fig 3, lower right).

Figure 3. Upper: Normalized ACF curves from measurements on NPs of different sizes, with diffusion times x_D = 2.8, 6.4, 8.6 and 26 ms respectively. Inset: x_D vs NP diameter for the four NP sizes. Measurement times were 60 s. Lower: Plot of the measured versus the pipetted concentrations of 62 nm NPs (left), and the 26 nm NPs (right).

SICS measurements were also performed on unlabeled Ml 3 bacteriophages. Ml 3 is a filamentous type bacteriophage of 880 nm length and 6.6 nm diameter, with a persistence length of ~2.2 μιη and thus Ml 3 has the form of a rod. Measurements were performed at concentrations of ~10 viable phages/ml (~1.7 nM), which should correspond to a mean number of phages in the detection volume of N=2.2. Based on an estimated polarizability¹⁴ of the phages of 4πε₀· (5.1 10^"18 cm³), the amplitudes in fig 4 indicate together with eq. 2 a concentration of ~3· 10 12 /ml (fig 4, left. See supporting information for detailed calculations). This is within the specified range ~10¹²/ml because the total number of phages may be higher than the estimated number of viable phages.

Finally, SICS was combined with FCS. Mixtures of 26 nm non-fluorescent and 24 nm fluorescent NPs were prepared to contain 10, 25, 39 and 65 % fluorescent NPs respectively, with a constant total NP concentration. Analysis of the SICS-curves indicated that the total NP concentration was constant at ~500 nM (fig 4, middle, inset), while FCS analysis of the fluorescent fraction as expected indicated a larger variation (fig 4, middle). The combined SICS and FCS analysis yielded that 9, 22, 35 and 64 % of the NPs in the four samples respectively were fluorescent, which agrees well with the pipetted fractions. SICS + FCS was also used to measure the affinity of 62 nm negatively charged nonfluorescent NPs to ligands in the form of the positively charged fluorophore FIL488 at pH 7.3 (fig 4, right). Nonfluorescent NPs at 55 nM were mixed with ligands at concentrations varying from 8 μΜ down to 1 nM, and each sample was analyzed by SICS + FCS. The FCS-curves give the concentration of free ligand [L] and of the ligand- NP complexes [L*NP] respectively, while the SICS-curves give the total concentration of NPs. Thus the dissociation constant K_d=[NP][L]/[L*NP] can be measured from each single measurement, which is not possible using single color FCS. The eight measurements yielded K_<r=3.1 ± 3.6 nM (fig 4, right).

The fluctuations detected in SICS scale with the NP volume (fig 2, right), which indicates that they are caused by interference of the forward scattered laser light with the transmitted laser light 3 ' 5 ' 7. Similar interference signals have been utilized for single NP detection 16 , for NP correlation analysis 1 , and in phase analysis light scattering for measurement of particle velocity¹⁸. Also in PCS⁹ and PhACS¹⁰ the generated signal is attributed to interference between the scattered and the transmitted light, however, recently an alternative theory interprets the photothermal fluctuations as originating from a nano-lensing effect¹⁹.

The S/N should increase as the square root of the laser power and accordingly, use of photo diodes which can sustain count rates higher than 10¹⁶ Hz should substantially enhance the S/N ratio and sensitivity in SICS.

In principle it should be possible to obtain the normalized effective cross-section A_q by performing multi-component analysis of intensity distribution histograms (fig 1C ). Such analysis will be important for very non-spherical particles, whose size cannot be estimated from the diffusion coefficient. For such particles, comparison of A_q with the diffusion coefficient will then yield information about the particles' shape² . For the elongated Ml 3 phages, the theoretically estimated A_q (see above) corresponds to that of a sphere of 70 nm diameter. Such a sphere would have had a diffusion time of 7-8 ms in the instrument used here, however the measured diffusion times of the phages were almost ten times longer, indicating an extremely elongated shape .

A related technique i •s inverse-FCS 12 ' 21 ' 22 which also combines analysis of labelled and unlabeled NPs. Inverse-FCS allows the absolute volume of particles and even protein molecules in solution to be measured using zero-mode waveguides¹¹. SICS as presented here has however an advantage in that NPs and possibly biomolecules can be analyzed in a simpler, diffraction limited detection volume.

In summary, given that the refractive index is known, SICS allows analysis of both size and concentration of unlabeled nanoparticles in solution. Furthermore, simultaneous analysis of labeled and unlabeled nanoparticles was shown by combining SICS and FCS. Measurements were performed on Ml 3 phage viruses and on unlabeled and labeled polystyrene NPs down to 24 nm diameter. The contrast in SICS likely arises from interference between the scattered light from particles and the transmitted laser light, as indicated by the fact that the fluctuations scale with the particle volume.

Fig 4. Left: SICS-measurement of unlabeled M13 bacteriophages at specified

12 1 1

concentrations of 10 phages/ml (upper curve), 5-10 phages/ml (middle curve), and 2.5-10¹¹ phages/ml (lower curve). Oscillations are due to laser noise. Middle: Four mixtures of labelled (24 nm) and unlabeled (26 nm) NPs. The FCS-curves indicate a varying labeled fraction, while the SICS-curves (inset) display a fairly constant total NP concentration of ~500 nM. Right: FCS curves of unlabeled 62 nm polystyrene NPs binding to ligands in the form of the positively charged HL488-fluorophore at varying concentrations. Inset: The corresponding SICS-curves give the total bead concentration, which allows K_d to be estimated from each single measurement. Measurement times were 60 s.

The combination of SICS and FCS allows the percentage of label-carrying particles or viruses to be determined, and single-measurement estimation of K_D though only one species is labeled. The discussed possibilities for improvement should allow analysis of even smaller NPs and biomolecules, which for example will allow the success of post- translational labelling of protein molecules to be measured.

ASSOCIATED CONTENT

Supporting Information. Materials and methods and Discussion. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION

Corresponding Author

* stewen@kth.se

ACKNOWLEDGMENT

We are very grateful to Sebastian Grimm and Per-Ake Nygren for providing the Ml 3 phages, and to Per Thyberg for many important discussions.

ABBREVIATIONS

FCS, fluorescence correlation spectroscopy.

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Claims

1. A method for analyzing a sample, comprising:

detecting a signal and fluctuations in the signal from a detection volume in the sample; wherein the signal is electromagnetic radiation guided into and transmitted through the detection volume and the fluctuations are reductions or increases in the signal due to the presence of analytes in the detection volume; and analyzing the detected fluctuations to obtain information about the analytes in the sample.

2. A method according to claim 1, wherein the fluctuations arise when a fraction of the electromagnetic radiation directed into the detection volume scatters from analytes in the detection volume and then interferes with the non-scattered electromagnetic radiation transmitted through the detection volume.

3. A method according to claim 1, wherein the fluctuations are transient.

4. A method according to claim 1, wherein the detected fluctuations are

proportional to the volume of the analytes.

5. A method according to claim 1, wherein the electromagnetic radiation is

generated by a laser.

6. A method according to claim 1 , wherein the electromagnetic radiation, after being directed into the detection volume, is reflected on a surface such that the signal and the fluctuations are detected on the same side of the sample as the laser.

7. A method according to any previous claim, wherein the detection volume is restricted by the dimensions of a laser focus.

8. A method according to any previous claim, wherein the detection volume is restricted by a pinhole in the plane of a focus after the sample.

9. A method according to any previous claim, wherein the detection volume is about 0.01 - lO fL.

10. A method according to any previous claim, wherein the detection volume is determined by using zero-mode waveguides.

1 1. A method according to any previous claim, wherein analyzing the detected fluctuations comprises calculating the autocorrelation function (ACF) or calculating the standard deviation of the detected fluctuations.

12. A method according to any previous claim, wherein analyzing the detected fluctuations comprises intensity distribution analysis such as the Photon

Counting Histogram (PCH) or Fluorescence Intensity Distribution Analysis (FIDA).

13. A method according to any previous claim, wherein the concentration of the analytes are in the range 1 picomolar - 10 micromolar.

14. A method according to any previous claim, further comprising

simultaneously detecting a second or further signal and fluctuations in the second or further signal from a detection volume in the sample; wherein the second or further signal is generated due to the presence of signal-generating analytes in the detection volume; and wherein

analyzing the detected fluctuations comprises cross-correlating the detected fluctuations originating from scattering and interference with the detected fluctuations originating from the presence of signal-generating analytes in the detection volume, and analyzing the detected fluctuations to obtain information about the analytes in the sample.

15. A method according to claim 14, wherein the second or further signal comprise a fluorescence signal or a Raman signal from the analytes in the sample.

16. A method according to any previous claim, wherein the analytes are labeled.

17. A method according to any previous claim, wherein the analytes are unlabeled.

18. A Scattering Interference Correlation Spectroscopy system comprising a laser, a coverslip sandwich in between which a sample resides, focusing means for focusing the laser inside the sample inside the coverslip sandwich, means for collecting the scattering and interference signals and any fluorescence signals from analytes within the coverslip sandwich, detectors for detecting the scattering and interference signals and any fluorescence signals, and means for autocorrelating the detected signals.

19. A Scattering Interference Correlation Spectroscopy system according to claim

18 wherein the sample does not reside between two coverslips but lies on top of a coverslip or hangs below a coverslip.

20. A Scattering Interference Correlation Spectroscopy system according to claim 18 or claim 19 wherein other transparent items are used instead of coverslips.

21. A Scattering Interference Correlation Spectroscopy system according to claim 18 wherein the detector comprises a simple photodiode or a photomultiplier tube.

22. A Scattering Interference Correlation Spectroscopy system according to claim 18 wherein the photomultiplier tube is in dc-mode.

23. A Scattering Interference Correlation Spectroscopy system according to claim 18 wherein the photodiode or the photomultiplier tube is combined with an analogue to digital converter.

24. A Scattering Interference Correlation Spectroscopy system according to claim 18 wherein the signals are analyzed by intensity distribution analysis.

25. A method according to any of the previous claims wherein the analytes are particles or biomolecules.

26. A method according to claim 18 where the signals in addition to those from scattering and interference are Raman signals instead of fluorescence signals.

27. A Scattering Interference Correlation Spectroscopy system according to claim 18 which is combined with a Fluorescence Correlation Spectroscopy (FCS) system and where the FCS part of the system is used for detecting and analyzing the fluorescence signals from the analytes.

28. A method according to any previous claim, wherein the sample is a biological sample, such as for example a cell or a cell surface.

29. A method according to claim 1, wherein the light scattered from analytes is scattered in the forward direction and interferes with the laser light transmitted in the forward direction.

30. A method according to claim 1 , wherein the light scattered from analytes is scattered in the backward direction and interferes with the laser light transmitted but reflected in the backward direction.