Table 1.

CiliaQ output parameters

Parameter	Units	Description
x-, y-, z-center	$\mathrm{\mu }$m	Center of the cilium
Volume	Voxel, $\mathrm{\mu }{\text{m}}^3$	The volume of the cilium as number of voxels or metric volume (calculated as the product of the number of voxels, the voxel width, the voxel height, and the voxel depth)
# Surface voxels	–	The number of voxels belonging to the cilium that are localized at the ciliary surface
Surface	$\mathrm{\mu }{\text{m}}^2$	The surface of the cilium. Determined as the sum of the individual voxel surfaces with each voxel’s surface defined as the border surfaces of the voxel, at which no neighbored ciliary voxel exists
Shape complexity index	–	Comparing the surface of the cilium to the surface of a perfect sphere containing the volume of the cilium; this parameter gives a measure on how aspherical the cilium’s shape is. Determined as $\frac{\text{surface}}{4\pi ·{((3·\text{volume})/(4\pi ))}^{2/3}}$. An index of 1 represents a perfectly spherical shape. The higher the index, the less spherical the shape
Sphere radius	$\mathrm{\mu }\text{m}$	The radius of a sphere containing the same volume as the cilium
A: Colocalized volume	$\mathrm{\mu }{\text{m}}^3$, % of total volume	The volume of the cilium that is nonzero in channel A (only applicable if the intensity channel A is background-removed/binarized)
B: Colocalized volume	$\mathrm{\mu }{\text{m}}^3$, % of total volume	The volume of the cilium that is nonzero in channel B (only applicable if the supplied channel B is background-removed/binarized)
A: Colocalized compared to BG volume	$\mathrm{\mu }{\text{m}}^3$, % of total volume	The ciliary enrichment of a stained or fluorescent protein (labeled in channel A) compared to the expression level in the soma (BG volume $=$ Background volume). Determined as the ciliary volume with higher intensity than a threshold defined by the soma intensity. The threshold is calculated as follows:
		$\bullet$ Divide the entire image into 25 equally sized cuboids
		$\bullet$ Collect from each cuboid the 10% of voxels that feature the highest intensities in the cuboid and that are not part of any cilium object
		$\bullet$ Threshold $=$ Average $+$ 1.5-fold standard deviation of the intensities of the voxels collected from all cuboids
B: Colocalized compared to BG volume	$\mathrm{\mu }{\text{m}}^3$, % of total volume	The ciliary enrichment of a stained or fluorescent protein (labeled in channel B) compared to the expression level in the soma (BG volume $=$ Background volume). Determined as the ciliary volume with higher intensity than a threshold defined by the soma intensity. The threshold is calculated as follows:
		$\bullet$ Divide the entire image into 25 equally sized cuboids
		$\bullet$ Collect from each cuboid the 10% of voxels that feature the highest intensities in the cuboid and that are not part of any cilium object
		$\bullet$ Threshold $=$ Average $+$ 1.5-fold standard deviation of the intensities of the voxels collected from all cuboids
Minimum intensity (in reconstruction channel, channel A, or channel B)	a.u.	Minimum intensity of the voxels contained in the ciliary volume
Maximum intensity (in reconstruction channel, channel A, or channel B)	a.u.	Maximum intensity of the voxels contained in the ciliary volume
Average intensity (in reconstruction channel, channel A, or channel B)	a.u.	Average intensity of the voxels contained in the ciliary volume
Average intensity of the 10% of voxels with highest intensity (in reconstruction channel, channel A, or channel B)	a.u.	Average intensity of the 10% of all voxels contained in the ciliary volume with the highest intensities in the cilium
SD of intensity (in reconstruction channel, channel A, or channel B)	a.u.	Standard deviation (SD) of all voxels’ intensities in the ciliary volume
# of found skeletons (quality parameter)	–	If above 1, indicative for incomplete or incorrect cilium reconstruction. In turn, all skeleton-based parameters might be incorrect
# branches (quality parameter)	–	If above 1, the detected ciliary skeleton might contain side branches, which can be indicative for an incorrect ciliary detection
Tree length (quality parameter)	$\mathrm{\mu }\text{m}$	A large difference between the parameters tree length and “cilia length” can be indicative for an incorrect ciliary detection
Cilia length	$\mathrm{\mu }\text{m}$	The arcus length of the cilium. Determined as the largest shortest path of the largest skeleton detected for the cilium
Orientation vector (x, y, and z coordinate)	$\mathrm{\mu }\text{m}$	The orientation of the cilium in space. Determined as the vector from first (cilium base) to last (cilium tip) skeleton point
Cilia bending index	–	The bending/curvature of the cilium. Determined as the arcus length along the cilium divided by the Euclidian distance of first (cilium base) and last (cilium tip) skeleton point
Intensity threshold A	a.u.	The threshold determined to calculate the parameters “Colocalized compared to BG volume” and “Colocalized on centerline compared to BG volume” in channel A
		The threshold is calculated as follows:
		$\bullet$ Divide the entire image into 25 equally sized cuboids
		$\bullet$ Collect from each cuboid the 10% of voxels that feature the highest intensities in the cuboid and that are not part of any cilium object
		$\bullet$ Threshold $=$ Average $+$ 1.5-fold standard deviation of the intensities of the voxels collected from all cuboids
Intensity threshold B	a.u.	The threshold determined to calculate the parameters “Colocalized compared to BG volume” and “Colocalized on centerline compared to BG volume” in channel B
		The threshold is calculated as follows:
		$\bullet$ Divide the entire image into 25 equally sized cuboids
		$\bullet$ Collect from each cuboid the 10% of voxels that feature the highest intensities in the cuboid and that are not part of any cilium object
		$\bullet$ Threshold $=$ Average $+$ 1.5-fold standard deviation of the intensities of the voxels collected from all cuboids
Integrated A intensity	a.u.	The total intensity level in channel A along the ciliary centerline, determined as the sum of intensities along the largest shortest path of the detected skeleton
Average A intensity on centerline	a.u.	The average intensity level in channel A along the ciliary centerline, determined as the average of intensities along the largest shortest path of the detected skeleton
Integrated B intensity	a.u.	The total intensity level in channel B along the ciliary centerline, determined as the sum of intensities along the largest shortest path of the detected skeleton
Average B intensity on centerline	a.u.	The average intensity level in channel B along the ciliary centerline, determined as the average of intensities along the largest shortest path of the detected skeleton
A: Colocalized on centerline compared to BG volume	$\mathrm{\mu }\text{m}$, % total length	The ciliary enrichment of a stained or fluorescent protein (labeled in channel A) compared to the expression level in the soma (BG volume $=$ Background volume). Determined as the length/percentage of the ciliary centerline (the largest shortest path of the detected skeleton) featuring intensities above a threshold defined by the soma intensity
		The threshold is calculated as follows:
		$\bullet$ Divide the entire image into 25 equally sized cuboids
		$\bullet$ Collect from each cuboid the 10% of voxels that feature the highest intensities in the cuboid and that are not part of any cilium object
		Threshold $=$ Average $+$ 1.5-fold standard deviation of the intensities of the voxels collected from all cuboids
B: Colocalized on centerline compared to BG volume	$\mathrm{\mu }\text{m}$, % total length	The ciliary enrichment of a stained or fluorescent protein (labeled in channel B) compared to the expression level in the soma (BG volume $=$ Background volume). Determined as the length/percentage of the ciliary centerline (the largest shortest path of the detected skeleton) featuring intensities above a threshold defined by the soma intensity
		The threshold is calculated as follows:
		$\bullet$ Divide the entire image into 25 equally sized cuboids
		$\bullet$ Collect from each cuboid the 10% of voxels that feature the highest intensities in the cuboid and that are not part of any cilium object
		$\bullet$ Threshold $=$ Average $+$ 1.5-fold standard deviation of the intensities of the voxels collected from all cuboids
Profile A	a.u.	The intensities in channel A along the ciliary centerline (the largest shortest path of the detected skeleton). For each point of the largest shortest path, the intensity is interpolated from the four neighboring pixels in the closest stack image. For output, the profile is scaled in steps of the voxel width, for which adjacent points are averaged
Profile B	a.u.	The intensities in channel B along the ciliary centerline (the largest shortest path of the detected skeleton). For each point of the largest shortest path, the intensity is interpolated from the four neighboring pixels in the closest stack image. For output, the profile is scaled in steps of a voxel width, for which adjacent points are averaged
Arc length	$\mathrm{\mu }\text{m}$	The arc length position of each point on the ciliary centerline (the largest shortest path of the detected skeleton). Defined by the distance of a given point to the first ciliary point on the centerline
Tangent vector (x, y, and z coordinate)	$\mathrm{\mu }\text{m}$	The tangent vectors along the ciliary centerline (the largest shortest path of the detected skeleton). For each point of the largest shortest path, a tangent vector is determined as the vector from the point at a specific arc length distance upstream on the cilium to the point at a specific arc length distance downstream on the cilium (the specific distance is set by the user). The tangent vectors are normalized to a length of unity
Signed 3D Curvature	$\mathrm{\mu }{\text{m}}^{-1}$	The curvature along the ciliary centerline (the largest shortest path of the detected skeleton). At each point on the cilium the curvature is determined based on the equation for the geometric curvature. More specifically, the curvature is determined from the normalized tangent vectors of an upstream point P1 and downstream point P2 (tangent vectors T1 and T2, respectively) as: (T2 - T1) / 2 / (arc length distance P1 to P2 on the cilium). Finally, the curvature is signed by the sign of the cross product of T1 and T2

Some parameters are output in multiple ways with different units. For 2D analysis, the numeric values of volume parameters correspond to the area of the cilium in the image. The parameters Shape complexity index and Sphere radius are not applicable for 2D analysis. The parameters Arc length, Tangent vector, and Signed 3D Curvature are output for each individual point on the ciliary centerline. Abbreviations: a.u. (arbitrary units), voxel (a pixel in a 3D image)