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FFS Data Processor
Analysis Methods and Models

Software performs the Global Analysis of auto(cross)correlation functions, photon counting distributions and fluorescence factorial cumulants. FCS, FCCS, TIR-FCS, PCH, PCMH, FIDA, FIMDA, FCA, TIFCA, coincidence bursts counting and coincidence analysis are supported in FFS Data Processor. The complete protocol of the global analysis of auto(cross)correlation functions and photon counting distributions is published in (Skakun et al. 2014).

1. Fluorescence Correlation Spectroscopy.

The model for analysis of correlation functions is defined by the following general equation:
where:

 is the level of autocorrelation function when ;
 denotes the average number of fluorescent particles;
 denotes the background correction multiplier;
 is kinetics term that denotes some kinetic process. The following kinetic terms are supported:
  • Pure-Diffusion: ;
  • Triplet-State: ;
  • Conformational: ;
  • Protonation: ;
  • Flow: .
 is motion term that describes the motion type of the particles. The following motion terms are supported:
  • Free 2D Diffusion;
  • Free 3D Diffusion;
  • Anomalous 2D Diffusion;
  • Anomalous 3D Diffusion;
  • Confined 2D Diffusion;
  • Confined 3D Diffusion.

2. Photon Counting Histogram

The PCH model is used to analyze Photon Counting Distribution (PCD). PCD here refers to the data to be analyzed, whereas PCH is a commonly used term to specify the method of analysis. The total PCD from a number of molecules is calculated by successive convolutions of a single molecule PCD (Chen et al., 1999, Perroud et al. 2003, Huang et al. 2004):

(1)

where Poi(n, l) denotes the Poisson distribution with the mean value l, T is the counting time interval, Vref is the reference observation volume, B(r) is the brightness profile function and Q is taken so that the product QVref is large enough to completely include the illuminated volume. The total distribution P(n) is the weighted average of convolved M times

(2)

An additional convolution to the background term can be taken in order to account for the background photons.
Four different combinations of fitted parameters are available:

  • Absolute N and q values,

  • N ratio,

  • q ratio,

  • N and q ratio.

The following brightness profile approximations are available:

  • 2D Gaussian,

  • 3D Gaussian,

  • Gaussian-Lorenzian, squared,

  • Polynomial (accordingly to Palo et al., 2000).

For the first three approximations the first and second order correction for the out-of-focus emission (and other types of profile nonideality) accordingly to Huang et al., 2005 is supported.
Normalization of model parameters (scaling) can be either to the effective volume, i.e. by setting Veff = 1 or to the first and second PSF moments, i.e. by setting 

Photon Counting Histogram with correction for out-of-focus emission
Out-of-focus correction is performed by introduction of additional fitting parameters Fk defined as relative difference between integral of the kth power of the actual observation profile χk and that of its approximation

,.(3)

In the most cases only the first order correction (all Fk equal zero except F1) is sufficient to get the best fit to the experimental data. F1 can be treated as an out-of-focus emission ratio. The second order correction (F1 and F2 are different from zero) can be also applied.

Photon Counting Histogram with polynomial profile
B
(r) is approximated by an exponential function of a single argument with polynomial transformation of a unit of volume (
Kask et al., 1999, Palo et al., 2000)

, (4)

where a1, a2 are instrumental parameters and B0 is the value of B(r) at r equal to 0. B0 and A0 are calculated from a system of normalization equations:

(5)

The total PCD is calculated by Eq. 1 and 2 taking into account Eq. 4,5. In this definition, results of PCH analysis with the polynomial profile are fully equivalent to results of FIDA.

 

Correction for a number of time-dependent processes:

  • Triplet, Conformation, Protonation

  • Free and anomalous 2D/3D diffusion 

can be applied. Correction for time-dependent processes is performed such that the first and second factorial cumulants of PCD are exact. According to this theory one has to calculate the so-called binning correction factor   where g(t) is a time dependent term of the autocorrelation function in FCS and to correct the brightness and the number of molecules in the following form:

 

where q(T) and N(T) are apparent parameters of the model dependent on bin time T and q0 and N0 are absolute values of brightness and concentration that are independent of T.

Correction for the detector dead time and afterpulsing can be additionally performed (accordingly to Palo et al., 2006).

Global analysis of a number of autocorrelation functions and a number of photon counting distributions with linking of all related parameters is possible (Skakun et al., 2005, 2011, 2014).



3. Fluorescence Cumulants Analysis

The fluorescence factorial cumulants (FFC) are analyzed by the following model (Muller, 2004, Wu et al., 2005)

(7)

where qi is the mean number of photons (expressed in counts per second per molecule) detected in a time interval T, Ni is the mean number of molecules of the i-th component in the open observation volume and Bg is the mean background count rate of the detector. γ-factors are calculated as ,

where B(r) is the normalized to unity brightness profile function and

is the diffusion correction term.  is the normalized correlation function of k-th order (Wu at al., 2005). For the limit of short bin times . We use normalization to the effective volume in order to relate Ni obtained by both FCA and FCS (additional factor γ2 in Eq. 7 is due to this type of normalization).

To correct for deviations of the actual observation profile from its ideal approximation three different approaches can be used:
1) γ-factors () can be fitted during the analysis (applicable only in the global analysis with linking all fitted γ-factors);
2) FIDA-like polynomial profile (Kask et al. 1999, Palo et al., 2000) can be used for the approximation of the actual PSF;
3) out-of focus correction of 2D/3D Gaussian or squared Gauss-Lorenzian profiles (Perroud et al. 2003, Huang et al. 2004) can be used.


 The following brightness profiles are supported:

2D/3D Gaussian. γ-factors are calculated by , where d is the dimensionality.

3D Gaussian fitted. γ-factors for two first comulants are calculated as respectively. All other γ-factors (actually products γ2γ3, γ2γ4, …) are fit parameters.

Squared Gauss-Lorenzian. γ-factors are calculated by  .

2D/3D Gaussian or squared Gauss-Lorenzian with out-of-focus correction.

For the out-of-focus correction Eq. 7 becomes

where Fk is a correction factor defined as relative difference between integral of the kth power of the actual observation profile χk and that of its approximation. In many cases just correction of the first integral of 3D Gaussian approximation of actual brightness profile is needed (all Fk = 0 except F1 – first order correction).

Polynomial profile. For the polynomial profile Eq. 7 becomes

where , and , (a1 and a2 are the fit parameters). A0 and B0 are chosen so that the normalization conditions assumed in FIDA () are satisfied.



4. Coincidence analysis

The coincidence histograms built from raw data can be fit by Gaussian model and separation quality parameter of two analyzed histograms can be calculated. Coincidence analysis is performed accordingly to Heinze et al. 2002.


5. Coincidence bursts counting

The relative number of coincidence bursts to the number of busts in a separate channel can be calculated.


Custom model with built-in script programming language provides creating user-defined models. Modular object-oriented architecture allows for easy extension of the model library

Raw data processing

  • Calculating statistical characteristics (autocorrelation and crosscorrelation functions, photon counting, first event, single event and inter-event time distributions, fluorescence cumulants and coincidence histograms) with correct weight factors from raw data  (Carl Zeiss ConfoCor2, Carl Zeiss ConfoCor3, ISS ALBA, PicoQuant PicoHarp 300, PicoQuant Time Harp 200, PicoQuant Symphotime 64, Becker & Hickl TCSPC modules, binary and text files containing photon arrival times) (updated)
  • Calculation of both blue-to-red and red-to-blue crosscorrelation functions from the raw data. Calculation of averaged (blue-to-red + red-to-blue)/2 crosscorrelation function. (new)
  • Import, processing and analysis of data from PicoQuant PicoHarp 300 without the header
  • Direct (without merging) import, processing and analysis of data from two SPC 130 cards (SPC 132) (new)
  • Sliding analysis of characteristics (PCD, AC(C)F, etc), calculated from the raw data either by the constant time shift or the constant amount of photons
  • Rejection of unwanted bursts of intensity while calculation of characteristics (PCD, AC(C)F, etc) from the raw data (updated)
  • Bursts analysis. Selection of bursts in the intensity trace and calculation of characteristics (PCD, AC(C)F, etc) from each burst (new)
  • Calculation of multiple characteristics (PCD, AC(C)F, etc) with binning time changed in a user defined range
  • Simulation of raw data (Shingaryov et al., 2014)
Methods

  • Global fit of correlation functions, photon counting distributions, fluorescence cumulants and coincidence histograms with the linked parameters (updated)
  • Sequential fit: independent analysis of datasets one by one with building dependencies of obtained fit parameters (updated)
  • Automated generating initial guesses for fit parameters (updated)
  • Parameter fixing, constraints and linkage
  • Confidence intervals by exhaustive search and standard errors (updated)
  • Quality of fit is judged by chi-square criterion and visual inspection of residuals
  • Built-in simulator of correlation functions
Interface

  • Multi-document interface
  • Advanced parameters management (sorting, quick linkage and easy navigation)
  • Advanced managing of parameters of a large number of fitted data, e.g. finding parameters with the name that begins with a specific symbol and fix them to some value
  • Automated creation of a global ACF + PCD analysis (FCS+PCH global analysis)
  • Templates for quick saving and restoring analysis configurations
  • Saving and loading experimental data and analysis results from databases
  • Database support for saving and restoring user-defined models
  • Import of external data and export of analysis results
  • Creation of a Fit Parameter Dependence (FPD) curve from a number of opened Experiments
  • Calculation of histograms of fit parameters (new)
  • Graphical representation of fit parameters depending on external parameters
  • 2D and 3D graphical data representation (updated)
  • Visualization of standard deviations and relative standard deviations of each point of calculated characteristic
  • Support for automatic calculation of a number of statistical characteristics with different bin time from the selected region of raw data (updated)
  • Support for automatic calculation of a number of statistical characteristics from the raw data either by the constant time shift or the constant amount of photons (sliding sheme). Multiple characteristics can now be calculated not only with different Time Step but also with different Start and End times accordingly to the chosen sliding scheme. (updated)
  • Rejection of unwanted bursts of intensity (updated)
  • Selection of bursts (new)
  • Selection and counting of coincidence bursts (updated)
  • Saving and restoring interface settings
Databases

  • Importing experimental data of following dataformats: Carl Zeiss ConfoCor tm, Carl Zeiss ConfoCor2 tm, Carl Zeiss ConfoCor3 tm, PicoQuant PicoHarp 300, PicoQuant Time Harp 200, PicoQuant Symphotime 64, ISS ALBA and B&H SPC (SPC 4x1, 4x2, 6x0 256 ch, 6x0 4096 ch, 130/134, 830)  (updated)
  • Import and processing of raw data of PicoQuant PicoHarp 300 without the header (new)
  • Direct (without merging) import, processing and analysis of data from two SPC 130 cards (SPC 132) (new)
  • Import column organized text file (datasheet like, can be used for import of ALV data) (updated)
  • Import of binary and text files with simple dataformat (like one column list of double precision values with or without the header) (new)
  • Direct (non-iterative) fast estimation of model parameters of measured (or calculated from raw data files) auto(cross)correlations, photon counting distributions and fluorescence cumulants.
  • Import of SIN files
  • Storing and managing experimental data, analysis results and often-used model and parameter linkage configurations (Templates)
  • Searching, sorting and filtering data
  • Support of data integrity and validity
  • Avoiding of data redundancy
  • 2D graphical data previewing
  • Report generation

References


Chen Y., J.D. Muller, P.T. So, and E. Gratton. 1999. The Photon Counting Histogram in Fluorescence Fluctuation Spectroscopy. Biophis. J. 77:553-567.

Perroud T.D., B. Huang, M.I. Wallace, and R.N. Zare. 2003. Photon Counting Histogram for One-Photon Excitation. ChemPhysChem. 4:1121-1123.

Huang B., T.D. Perroud, and R.N. Zare. 2004. Photon Counting Histogram: One-Photon Excitation. ChemPhysChem. 5:1523-1531.

Kask, P., K. Palo, D. Ullmann, and K. Gall. 1999. Fluorescence-intensity distribution analysis and its application in biomolecular detection technology. Proc. Natl. Acad. Sci. USA. 96:13756-13761.

Palo K., U. Mets, S. Jager, P. Kask, and K. Gall. 2000. Fluorescence intensity multiple distribution analysis: concurrent determination of diffusion times and molecular brightness. Boiphys. J. 79:2858-2866.

Muller J.D. 2004. Cumulant analysis in fluctuation spectroscopy. Biophys. J. 86:3981-3992.

Wu B., and J.D. Muller. 2005, Time-Integrated Fluorescence Cumulant Analysis in Fluorescence Fluctuation Spectroscopy. Biophys. J. 89: 2721-2735.

Heinze K.G., Markus Rarbach, Michael Jahnz, and Petra Schwille. 2002. Two-Photon Fluorescence Coincidence Analysis: Rapid Measurements of Enzyme Kinetics. Biophys. J. 83. 1671–1681.

Skakun V.V., M.A. Hink, A.V. Digris, R. Engel, E.G. Novikov, V.V. Apanasovich, A.J.W.G. Visser. 2005. Global Analysis of Fluorescence Fluctuation Data. Eur. Biophys. J. 34: 323–334.

Skakun V.V., R. Engel, A.V. Digris, J.W. Borst, A.J.W. Visser. 2011. Global analysis of autocorrelation functions and photon counting distributions. Frontiers in Bioscience (Elite Ed) 3: 489-505.

Skakun, V.V. Global Analysis of Autocorrelation Functions and Photon Counting Distributions in Fluorescence Fluctuation Spectroscopy / V.V. Skakun, A.V. Digris, and V.V. Apanasovich // In book Fluorescence Spectroscopy and Microscopy: Methods and Protocols: Methods in Molecular Biology, Springer Protocols, Yves Engelborghs and Antonie J.W.G. Visser (eds.). Springer Science+Business Media, LLC. vol. 1076. – 2014. P. 719-741. DOI 10.1007/978-1-62703-649-8_33

Shingaryov, I.P. Simulation of Autocorrelation Function and Photon Counting Distribution in Fluorescence Fluctuation Spectroscopy / I.P. Shingaryov, V.V. Skakun, and V.V. Apanasovich // In book Fluorescence Spectroscopy and Microscopy: Methods and Protocols: Methods in Molecular Biology, Springer Protocols, Yves Engelborghs and Antonie J.W.G. Visser (eds.). Springer Science+Business Media, LLC. vol. 1076. – 2014. P. 743-755. DOI 10.1007/978-1-62703-649-8_34