Dynamics Profiler Calculations

The diffusion coefficient D is calculated as indicated by the following formula:

The fluorofore concentration is given as:

• where
  
  is an average number of molecules and N_A ​​ is the Avogadro constant
• and
• 
  where S is the structural parameter.

The data quality is estimated using CPM values:

Data Quality	CPM Value
Bad (red)	Smaller than 1.
Not bad (yellow)	Between 1 and 3.
Good (green)	Higher than 3.

Detrending Filter

The detrending filter is applied to remove the trend (e.g. due to the photo bleaching) from the experiment data. The detrended signal I_d(t) is calculated as follows:

where the trend, Tr(t) is the gaussian smoothed signal:

with

The FilterWindowParameter [ms] is set by the user.

Dust Filter

The dust filter allows you to remove high intensity peaks (e.g. caused by aggregated objects) from the experiment data. Calculations are done on the 500x down sampled signal data. For comparison, intensity data shown in the count rate chart is down sampled with factor 2000x. The data bin is classified as dust (filtered out) if the following criteria is fulfilled:

UserParameter * I(t) > Mean(I(t))

If both the detrending and dust filter are activated, the dust filter is applied after the detrending filter.

In order to determine flow speed and direction, all possible cross-correlations are calculated at a distance of two fibers within three inner fiber rings. All correlations in the same direction are averaged, resulting in six correlation curves (30°, 90°, ..., 330°; by our definition, 0° means vertical flow direction). All six curves are fitted globally with the following model:

Parameter	Description
v	The flow speed (fit parameter).
ϕ	The angle between the flow and the vector connecting the fibers in this group of cross-correlations (fit parameter).
r0	The apparent distance between the fibers (calibration parameter).
Gdiff(τ)	The diffusion term (2D or 3D), see Fit Calculation.
Other parameters are defined as for the fit calculations, see Fit Calculation.

The pair correlation function (pCF) is a set of cross-correlations between the central fiber and all fibers located at a given distance from the center. For a better signal to noise ratio, cross-correlations are calculated in both directions and then averaged. The pCFs are used and displayed in the polar heatmaps of the Diffusion view.

The Diffusion view can display the data of two different sets of fibers. The group called Outer Elements comprises fibers with a slightly bigger distance from the center (blue element) and is illustrated with orange in the graphic below. The second group is called Inner Elements and comprises fibers with a slightly smaller distance from the center. They are illustrated with the green color in the graphic below.

Fiber Group	Fibers
Outer Elements	Comprises fibers 9, 11, 13, 15, 17 and 19.
Inner Elements	Comprises fibers 8, 10, 12, 14, 16 and 18.

The ω_r is calculated with the following formula:

During the ω_r calibration, τ_d is calculated in the one-component 3D diffusion model

and D (diffusion coefficient) needs to be provided and added in the ω_r Calibration tab. The diffusion coefficients of commonly used dyes are already specified in a dropdown list. The following requirements need to be fulfilled in order to generate a suitable calibration file:

• Spot measurement duration of at least 60 seconds
• Time Resolution of 0.5 µs (ω_r acquisition mode)
• The used dye concentration needs to be adjusted to match the expected FCS amplitude range (0.05 – 2)
• The emission wavelength of the selected dye should match the selected laser line

Four values are calculated and can be accessed by opening the calibration file with a text editor:

• W0Ring3: Effective radius of the observation spot (detector elements 1 to 19 binned together)
• W0Ring123: Average radius of the observation spot for a single detector element (average value for detector elements 1 to 19)
• R0Ring123: Effective distance between the detector elements for flow measurements
• StructuralParameter: Ratio between the observation spot waist in the axial and lateral direction

The generated ω_r calibration file can be used in the Correlation Tools tab to replace the default ω_r calibration values.

See also

• ωr Calibration Tab
• Correlation Tools Tab

The Dynamics Profiler autocorrelation curve is calculated according to the formula:

Correlation values are calculated for the lag times τ, commonly used in 16/8 multi-tau hardware correlators. This means the lag time τ is increased linearly with the τ =PixelDwellTime for the first 16 values. Then the lag time interval for τ is doubled, and the next eight lag times are calculated. The lag time interval is doubled after each next eight time lag values.

The very first correlation value, corresponding to the one PixelDwellTime, is skipped since it is biased due to correlation of the neighboring data points after low pass filter due to digitalization.