Track Properties

Track properties are features that describe a property of a trajectory. This can relate to e.g. the shape of the trajectory or number of points. In DiffusionLab, these track properties are used to segment the tracks into smaller populations with similar motion behavior.

Note

A good set of track properties for segmentation describes properties that are different between the intended populations. DiffusionLab provides a large selection of track properties, and depending on the intended populations the best subset of track properties can differ between data sets.

Standard Track Properties

The standard track properties are computed in the same way regardless the settings in DiffusionLab via Compute properties.

Number of points

Description: number of consecutive localizations.

Physical interpretation:

  • Mobility

  • Photostability

  • Statistical significance

Units: -.

Supported dimensions: 2/3.

Length

Description: the sum of all the individual displacements.

Physical interpretation:

  • Mobility

  • Photostability

Units: length.

Supported dimensions: 2/3.

MinBoundCircleRadius

Description: radius of the smallest enclosing circle that can be drawn around the localization coordinates, i.e. minimum bounding circle (MBC).

Physical interpretation:

  • spatial extension of localization coordinates

Units: length.

Supported dimensions: 2/(3 is converted to XY plane).

MBC minus CoM

Description: the distance between the center of the MinBoundCircleRadius and the center of mass, calculated as a percentage of the MBC radius. 1

Physical interpretation:

  • Evenness spatial distribution localizations. It gives an indication of how homogeneously points are spatially distributed.

Units: -.

Supported dimensions: 2/(3 is converted to XY plane).

Entropy

Description: Shannon’s entropy of the distribution of the localization coordinates within the enclosing square that is defined by two times MinBoundCircleRadius. 2

Physical interpretation:

  • Statistical measurement of spatial randomness

Units: -.

Supported dimensions: 2/(3 is converted to XY plane).

Tortuosity

Description: the ratio of the distance between start and end points versus the length of the track.

Physical interpretation:

  • start-to-end directionality.

Units: -.

Supported dimensions: 2/3.

Elongation

Description: weight of the first principal component of localization coordinates.

Physical interpretation:

  • Directionality of localizations

Units: -.

Supported dimensions: 2/(3 is converted to XY plane).

Elongation angle

Description: direction of the first principal component of localization coordinates

Physical interpretation:

  • Direction of localizations

Units: -.

Supported dimensions: 2/(3 is converted to XY plane).

Other Track Properties

The optional track properties are specified in the diffusion constant estimator and are dependent on the settings thereof.

Diffusion constant

Description: magnitude of the diffusion.

Units: length^2/time.

Localization error

Description: imprecision in the localization. The deviation of a localization estimate from its true position is ideally normally distributed in one dimension. The localization error is defined as the standard deviation of this normal distribution.

Units: length.

Supported dimensions: 2/3.

Diffusion SNR

Description: signal-to-noise (SNR) of the displacements as given in Vestergaard et al. 3

Physical interpretation:

  • relative magnitude of diffusion to the localization error

Units: -.

Supported dimensions: 2/3.

Underlying Descriptors

The standard track properties categorized by their main descriptors are given in Table 1.

Table 1 Standard track properties categorized by their main underlying descriptor.

Descriptor

Track property

Mobility, photostability

Number of points, length

Spatial directionality

Tortuosity, elongation, elongation angle

Uniformity spatial distribution

Minimum bounding circle radius, MBCC minus CoM, entropy

References (in footnotes)

1

Hendriks, F.C., Meirer, F., Kubarev, A.V., Ristanović, Z., Roeffaers, M.B., Vogt, E.T., Bruijnincx, P.C. and Weckhuysen, B.M., 2017. Single-molecule fluorescence microscopy reveals local diffusion coefficients in the pore network of an individual catalyst particle. Journal of the American Chemical Society, 139, pp.13632-13635.

2

Same as ref. 1.

3

Vestergaard, C.L., Blainey, P.C. and Flyvbjerg, H., 2014. Optimal estimation of diffusion coefficients from single-particle trajectories. Physical Review E, 89, p.022726.