

Analysis models

Global Analysis of Fluorescence and Anisotropy decays [1, 2, 4] can be done by either MLE with Poissonian statistics of the noise
or LeastSquares methods [3].
Deconvolution via Instrumental response function:
Deconvolution via oneexponential Reference compound:
where:
I(t) is impulse response function of
the sample;
g(t) is measured Instrumental response
function (IRF);
f^{ref}(t)
is measured oneexponential reference
compound;
B(t)
is measured background;
D denotes the
time shift between sample
decay and IRF;
b is timeuncorrelated
background in the IRF or Reference compound;
g
is background multiplication factor;
c is timeuncorrelated background in
the sample decay;
n is
scattered light coefficient;
t_{ref}
is decay time of reference compound;
are fit parameters and
d(t)
is Dirac deltafunction.
Complete deconvolution for analysis of multiexcitation decays is also
supported.
The detailed protocol of the global analysis, programmed in TRFA Data Processor, is published in [4].
 Multiexponential
model for fluorescence decays
 Multiexponential
model for anisotropy decays
The form of the multiexponential model depends on the model
property Fluor Parameters Type, which can be either “Amplitudes
and decay times” or “Contributions and decay times” or “Ratio
and decay times”.
Switching between amplitudes and contributions is controlled by
Normalization property of the multiexponential model and can
be done independently for positive and negative preexponential
factors.

Associative and
nonassociative models for anisotropy
Two approaches for performing of anisotropy analysis are supported:
1. Two stage anisotropy analysis based on a sequential fit of the measured
sample total fluorescence decay and the measured sample parallel and
perpendicular polarization components to the
multiexponential model.
2. The anisotropy analysis based on a direct global fit of the sample parallel
and perpendicular polarization components.
This approach also supports an associative anisotropy analysis. The
fluorescence decay is calculated accordingly to the following equation:
where A is the normalization parameter;
a_{j} and
t_{j} are, respectively, contributions and decay times of
the corresponding fluorescence exponents;
Q is the polarization angle,
b_{k} and
j_{k} are, respectively, the amplitudes and rotational
correlation times of the corresponding anisotropy exponents and T_{jk}
controls the associations.
 Two compartmental
models
Fit parameters:
D
 the normalization parameter;
c_{i}
 the emission weighting factor of species i* (i=1,2);
b_{i}
 the concentration of species i* (i=1,2) at time zero;
k_{0i} 
the composite rate constant of species i* (i=1,2);
k_{12} 
firstorder rate constant for dissociation of 2* into 1* and
coreactant;
k_{21} 
secondorder rate constant for the association of 1* and coreactant
to 2*.

Three compartmental
models
Fit parameters:
D
 the normalization parameter;
c_{i}
 the emission weighting factor of species i* (i=1,…,3);
b_{i}
 the concentration of species i* (i=1,…,3) at time zero;
k_{0i} 
the composite rate constant of species i* (i=1,…,3);
k_{1i} 
firstorder rate constant for dissociation of i* (i=2,3) into 1* and coreactant;
k_{i1} 
secondorder rate constant for the association of 1* and coreactant to i* (i=2,3).
k_{23} 
interconversion rate constant from state 3* to 2*;
k_{32} 
interconversion rate constant from state 2* to 3*.
 Poisson distribution
of decay rates model
Fit parameters:
A
 the normalization parameter;
l_{1} 
the inverted decay time of first fluorescence component in
absence of energy transfer or other quenching;
b_{1} 
quenching efficiency of first fluorescence component;
m
 average number of quenchers;
e
 rate of quenching for a
probe interacting with one quencher;
a
 the relative contribution
of second fluorescence component;
l_{2} 
the inverted decay time of second fluorescence component in
absence of energy transfer or other quenching.
 Gaussian distribution
of decay rates model
Fit parameters:
A
 the normalization parameter;
s
 standard deviation on decay rate;
m
 average decay rate; k_{0}
 minimum decay rate;
a
 the relative contribution of second
fluorescence component;
l_{2} 
the inverted decay time of second fluorescence component.
Modular objectoriented architecture
allows for easy extension
of the model library

Instrumental models

 Instrumental response function via scattering solution
 Instrumental response function via single exponential reference compound
 Fitting of reference lifetime, time shift, level of dark noise in the instrumental response function, level of
timeuncorrelated background and scattered light coefficient

Methods


MLE nonlinear fitting with MarquardtLevenberg optimization
assuming Poissonian statistics of the noise

Leastsquares nonlinear fitting with MarquardtLevenberg
optimization (c^{2}
criterion)

Global fit: several fluorescence decays are combined and
simultaneously fitted

Anisotropy analysis via simultaneous fit of parallel and
perpendicular components of fluorescence

Automatically generated initial guesses for parameters

Parameter fixing, constraints and linkage

Constraints by a functional relationships between model parameters

Confidence intervals by exhaustive search and standard errors

The “Complete convolution” method for processing
multiexcitation decays

Quality of fit is judged by
c^{2}
or MLE criterion, visual inspection of residuals and
autocorrelation function of residuals, Zc^{2},
Durbin Watson and Runs tests, Heterosedasticity and
Normal probability function of the residuals

Buildin simulation of fluorescence decays and anisotropy curves

Interface

 Multidocument 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 F and fix them to some value
 Templates for quick saving and restoring analysis configurations
 Saving and loading experimental data and analysis results from databases
 Import of external data and export of analysis results
 Graphical representation of fit parameters depending on external parameters
 2D and 3D graphical data representation
 Saving and restoring interface settings

Databases

 Importing PicoQuant PHD files
 Import column organized text file (datasheet like)
 Import of text files with simple dataformat (like one,
two column list of double precision values with or without the
header)
 Storing and managing experimental data, analysis results and
oftenused 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

1. Beechem J. M., Gratton E., Ameloot M. et al. (2002) The Global Analysis of Fluorescence Intensity and Anisotropy Decay Data: SecondGeneration Theory and Programs. In: Lakowicz J. R. (ed) Topics in Fluorescence Spectroscopy Volume 2, Springer US, pp 241305.
2. Verveer P. J., Squire A., Bastiaens P. I. (2000) Global analysis of fluorescence lifetime imaging microscopy data. Biophys. J. 78(4), 21272137
3. Maus M., Cotlet M., Hofkens J. et al. (2001) An experimental comparison of the maximum likelihood estimation and nonlinear leastsquares fluorescence lifetime analysis of single molecules. Anal. Chem. 73(9), 20782086
4. Digris, A.V.,E.G. Novikov, V.V. Skakun, and V.V. Apanasovich. Global Analysis of TimeResolved Fluorescence Data // 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. 257277. DOI 10.1007/9781627036498_10
