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Software | Probability Distribution Analysis

Package PDA (560 Mbyte), Installation notes

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An accurate description of the histogram profile based on the statistical distributions of fluorescence and background signals is sensitive to small changes in fluorescence signal even when signal counts are low. The PDA formalism allows monitoring the changes in the emission spectra of single molecules, dynamical changes of the system, etc.

Software for probability distribution analysis (PDA) is presented for quantitative and precise description of the photon counting histograms (PCH) from fluorescence resonance energy transfer experiments (FRET) [1] or fluorescence polarization experiments [2]. Taking explicitly background and shot noise contributions into account, PDA accurately predicts the shape of one-dimensional histograms of various parameters, such as FRET efficiency or fluorescence anisotropy. In order to describe complex experimental single-molecule FRET or polarization data obtained for systems consisting of multiple non-interconverting fluorescent states, several extensions to the PDA theory are presented [3]. Effects of brightness variations and multiple molecule events are considered independently of the detection volume parameters, using only the overall experimental signal intensity distribution [4]. The extended PDA theory can now be applied to analyze any mixture, by using any a priori model or a model-free deconvolution approach based on the maximum entropy method (MEM). The accuracy of the analysis and the number of free parameters is limited only by data quality. Correction of the PDA model function for the presence of multiple molecule events allows one to measure at "high" SM concentrations to avoid artifacts due to a very long measurement time. Tools such as MEM and combined mean donor fluorescence lifetime analysis have been developed to distinguish whether extra broadening of PDA histograms could be attributed to structural heterogeneities or dye artifacts [5]. In this way an ultimate resolution in FRET experiments in the range of a few Ångström is achieved which allows for molecular Ångström optics distinguishing between a set of fixed distances and a distribution of distances [6]. The extended theory is verified by analyzing simulations and experimental data.

Features in Tatiana 4.8 (SUPER Global) are:

  • Probability distribution analysis (PDA) method for the analysis of fluorescence resonance energy transfer (FRET) signals to determine with high precision the originating value of a shot-noise-limited signal distribution. PDA theoretical distributions are calculated explicitly including crosstalk, stochastic variations, and background and represent the minimum width that a FRET distribution must have. In this way an unambiguous distinction is made between shot-noise distributions and distributions broadened by heterogeneities.
  • Simultaneously and effectively extracts highly resolved information from FRET distributions.
  • Gaussian distribution of Donor-Acceptor distances is modeled in the PDA method.
  • Corresponding fit routines for single state, N states, N Gaussian distributed states, Model Free distributed states (Maximum of Entropy) and two states with dynamics are realized.
  • Rate constants can be recovered accurately.
  • Steady state anisotropy is defined with very high precision from single molecule data.
  • Global analysis of the FRET labeled molecule SMD (MgCl2, inhibitor, ect.) titration experiments data sets is possible assuming linear, logarithmic or logistic dependence of rates on agent concentration.
  • Super global analysis of SMD (MgCl2, inhibitor, ect.) titration experiments data sets from FRET labeled at different positions molecules is possible assuming linear, logarithmic or logistic dependence of rates on agent concentration [7].


 [1] Antonik M., et al., J. Phys. Chem. B 110, 6970 (2006)

 [5] Kalinin S., et al., J. Phys. Chem. B. 114, 7983–7995 (2010)

 [2] Kalinin S., et al., Phys. Chem. B 111, 10253-10262 (2007)

 [6] Sindbert S., et al., J. Am. Chem. Soc. 133, 2463–2480 (2011)

 [3] Kalinin S., et al., J. Phys. Chem. B 112, 8361-8374 (2008)

 [7] Kilic, S., et al., Nat. Commun. 9, e235 (2018)

 [4] Kalinin S., et al., J. Phys. Chem. B. 114, 6197–6206 (2010)