4.3 Using the NPS with MFD data
4.3.4 The time deviation signal (TDS)
This method was used in an unpublished collaboration with the group of Prof. Dr. Gernot Längst (Universität Regensburg). To allow for a full understanding of the work presented in the thesis of Josef H. Exler parts of this chapter can also be found in the appendix of [24]. It additionally has been published as part of a collaboration with the group of Sandra Haake (Ludwig-Maximilians-University, Munich) [9].
A general problem with single molecule measurements are the binding constants of the respective sample contents. For many bio- molecules concentrations typically used in burst analysis or even FCS measurements are lower than the binding constant hence requiring some additional effort to allow for a successful experiment.
While for FCS measurements the focal volume dimensions can be reduced thereby allowing the sample concentration to increase [54] this is not possible for burst analysis methods where a rather long residence of the molecule in the focal volume is desired. Additionally, nucleosomes as under investigation in chapter 5 are prone to become instable at low concentrations as well as when interacting with sur- faces, thus in order to avoid artifacts the duration of the experiment has to be minimized while the concentration should be maximized.
Oftentimes a tradeoff has to be found where one has to keep in mind that with increasing concentrations the occurrence of multi- molecule bursts is not negligible. For a homogeneous population with only a single FRET species this is not a problem. In contrast, if
11determined in PBS pH 7.4, http://www.atto-
tec.com/fileadmin/user_upload/Katalog_Flyer_Support /Dye_Properties_01.pdf,
104 New developments and applications
several FRET states exist, multi-molecule events of different species will alter the determined FRET values. Moreover, impurities such as complexes labeled with only donor or acceptor observed simultane- ously with double-labeled complexes will also lead to changes in the detected FRET efficiencies.
However, as two independently diffusing complexes don’t enter and exit the excitation volume exactly at the same time it is possi- ble to differentiate these multi-molecular events from single molecule events and to exclude them from further analysis. Independently dif- fusing molecules involved in a multi-molecule event will yield differ- ent values for the mean-macro-time (MMT) (i.e. the time where 50% of the respective photons have arrived, see Figure 4.23) for all photons of a burst, as compared to that for the photons of one color. There- fore a characteristic time deviation signal (TDS) can be calculated by defining:
TDS= ((Dall−Dgreen) +|Tall−Tgreen|)∗(1−ǫ)
+ ((Dall−DFRET) +|Tall−TFRET|)∗ǫ∗γ (4.13)
where Dx is the burst duration,Txis the MMT,γ is a factor cor-
recting for the different detection efficiencies and QYs in the red and green channels (see chapter 3.2.4.3) andǫis the proximity ratio given by the number of photons in the burst as defined in equation 3.7.
Independently diffusing molecules involved in a multi molecule event will cause a deviation of the MMT calculated for all photons of a burst and the MMT for the individual photons of one color. As these burst properties are used to calculate the TDS for each burst by analyzing the differences between the values calculated from all photons and the ones calculated for individual channels one has to make sure that there is no influence of the respective FRET ef- ficiency. E.g. for a high FRET burst where only very few green photons are detected a simple green TDS calculated according to
TDSgreen = ((Dall−Dgreen) +|Tall−Tgreen|)will be very noisy due
to the poor statistics and does not contain much useful information. Similarly, for low FRET complexes a TDS calculated according to
4.3 Using the NPS with MFD data 105
all
all
Figure 4.23: Schematic of mean-macro-time and burst duration. The schematic development of fluorescence intensity with time is used to exem- plarily summarize the definitions of duration and MMT. For this schematic a theoretical multi-molecule event containing a donor only and a double labeled high FRET species is assumed. Positions of the MMT (Tx) as well as the durations, defined as the time difference between the first and the last photon in the respective channel of a burst (Dx), are marked.
TDSFRET = ((Dall−DFRET) +|Tall−TFRET|)would be noisy due to
the fact that in this case only few photons are detected in the red channel after green excitation. Therefore the TDS of these two chan- nels is computed simultaneously and the relative value of the green versus the red TDS is adjusted according to the percentage of photons detected (see equation 4.13).
Equation 4.13 is generally applicable to burst analysis data and allows for detection of almost all cases of bursts containing more than one molecule at a time except multi molecule events containing low (0%) FRET double labeled and donor only molecule mixtures. The latter species can only be identified using an experimental setup that employs PIE [84] [65]. Using a PIE setup one can define a second criterion using the additional information of red detection after red excitation (RR).
TDSred= ((Dall−Dred) +|Tall−Tred|) (4.14)
Here, the number of photons detected in the RR channel will be independent of the FRET efficiency.
106 New developments and applications
Together these two parameters (TDS,TDSred) can then be used to
remove multi-molecule events from burst analysis data by excluding bursts with a TDSand or TDSred above a given threshold from the
further analysis.
To demonstrate the capabilities of this method a sample contain- ing 23-NPS1-67 nucleosomes (see chapter 5.3, Ex0 Buffer chapter 5.2.3) as well as impurities of donor only and acceptor only complexes was measured. In order to stress the discussed effects for these test experiments the concentration of molecules was chosen to be high enough that most bursts detected show multi-molecule characteris- tics (∼150pM double labeled nucleosomes).
Previously, it had been common practice that data cleanup was done by selecting bursts through a stoichiometry criterion only [65]. For example in the described experiment histograms would have been calculated from bursts with stoichiometry values between∼0.45 and
∼0.77 (Figure 4.24 A, red) leading to a washed-out FRET efficiency
histogram especially in the medium FRET area and an unnaturally sharp cut off in the stoichiometry distribution. In comparison using stringent thresholds of TDS <0.1 and TDSred <0.1 a clean stoichiom-
etry distribution is received showing peaks of distinct FRET efficien- cies (Figure 4.24 B). In addition the resulting FRET histogram is al- most identical with data measured at far higher dilutions as shown in figure 4.24E.
While these tests were performed at concentrations higher than normal they nicely visualize the capabilities of this method. Under regular conditions where only a few percent of all events are multi- molecular the appropriate TDS thresholds are determined by itera- tive optimization of Stoichiometry-TDSx and Efficiency-TDSx plots.
Throughout this optimization one usually tries to find thresholds that remove as many multi-molecule events (stoichiometries higher or lower than the double labeled population) while maintaining as many events as possible. For the experiments presented in this thesis a starting value of 0.7 for TDSand TDSred turned out to be a good
4.3 Using the NPS with MFD data 107 A B C D 0 0.2 0.4 0.6 0.8 1 FRET efficiency Stoichiometry 1 0.8 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 1
FRET efficiency 0 0.2 0.4 0.6 0.8 1FRET efficiency 0 0.2 0.4 0.6 0.8 1FRET efficiency
1 0.8 0.6 0.4 0.2 0
frequency frequency frequency frequency
frequency
0 0.2 0.4 0.6 0.8 1 FRET efficiency
frequency
E
Figure 4.24: Effects of the TDS filter. The two dimensional plot of Stoi- chiometry versus FRET Efficiency recorded with a mononucleosome sam- ple containing 6-NPS1-67 nucleosomes (A-D, ∼ 150pM, Ex0 Buffer). (A)
Bursts within a limited Stoichiometry area (S = 0.45-0.80) that would have previously been selected for data analysis are highlighted in red and were used for one dimensional projections of FRET efficiency (top) and stoi- chiometry (right). Besides dual labeled nucleosomes, the sample contained also impurities of donor and acceptor only complexes. The high concen- tration of molecules in the sample combined with the significant amount of single labeled impurities cause strong multi-molecular trailing. (B) A significant improvement of the data quality is reached by removing the multi-molecule events using TDS <0.1 and TDSred<0.1 (B). The events re- moved by TDSred<0.1 (C) and TDS <0.1 (D) as well as a sample measured at far higher dilution (E,∼15pM) are additionally shown to allow for an
easier understanding of the TDS effect.