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The authors have declared that no competing interests exist.

Cell migration is a central biological process that requires fine coordination of molecular events in time and space. A deregulation of the migratory phenotype is also associated with pathological conditions including cancer where cell motility has a causal role in tumor spreading and metastasis formation. Thus cell migration is of critical and strategic importance across the complex disease spectrum as well as for the basic understanding of cell phenotype. Experimental studies of the migration of cells in monolayers are often conducted with ‘wound healing’ assays. Analysis of these assays has traditionally relied on how the wound area changes over time. However this method does not take into account the shape of the wound. Given the many options for creating a wound healing assay and the fact that wound shape invariably changes as cells migrate this is a significant flaw. Here we present a novel software package for analyzing concerted cell velocity in wound healing assays. Our method encompasses a wound detection algorithm based on cell confluency thresholding and employs a Bayesian approach in order to estimate concerted cell velocity with an associated likelihood. We have applied this method to study the effect of siRNA knockdown on the migration of a breast cancer cell line and demonstrate that cell velocity can track wound healing independently of wound shape and provides a more robust quantification with significantly higher signal to noise ratios than conventional analyses of wound area. The software presented here will enable other researchers in any field of cell biology to quantitatively analyze and track live cell migratory processes and is therefore expected to have a significant impact on the study of cell migration, including cancer relevant processes. Installation instructions, documentation and source code can be found at

This is a

The coordinated movement of cells is required for almost any morphogenetic processes [

The migration of cells in monolayers is commonly studied using a ‘scratch assay’, where a wound is created by scratching a confluent layer of cells [

Here we argue that a more accurate representation of wound closure is the concerted cell velocity derived from wound area and perimeter, as shown in

Cells moving at a constant velocity can cause significantly different changes in wound area depending on the initial perimeter as illustrated in the following examples: The wound shown in (A) decreases in area by 48%. The wound in (B) has the same shape as in (A) and a smaller perimeter, and decreases in area by 75%. Similarly, the wound in (C) has the same perimeter length as in (A) but a different shape and decreases in area by 58%. Finally the wound in (D) is the same shape as in (C) and a smaller perimeter, and decreases in area by 86%. The velocity of the moving cells is identical in all cases.

As such we believe that our wound detection algorithm can address a key deficiency in currently available tools. Given that there is no standardized experimental method for creating wounds in a scratch assay quantifying cell velocity would also allow for better reproducibility of experimental data between laboratories, given that cell velocity is independent of wound geometry. We demonstrate the use of our algorithm in a study of migration in a cancer cell model, and using the TScratch sample data [

The Bowhead cell velocity method was implemented as an open source Python package with methods to detect, fit and predict concerted cell velocity. The program can analyze any type of image that fits, or can be processed to fit, the general assumption that cell regions have higher intensity counts than wound regions. The program structure facilitates easy incorporation into imaging pipelines for use in screening assays. For each time point analyzed by the package wound perimeter and area were quantified. Measurement variance could then be estimated by repeating the detection at slightly different thresholding values in order to mimic the inherent uncertainty of the wound boundary.

The detection algorithm, shown in _{i} was the intensity value of a pixel at position

Given a user defined relative intensity scaling factor _{c}. The largest connected region of pixels, in a Von Neumann neighbourhood, below this threshold was then classified as the wound. The unclassified area was then filled such that its topology was simply connected. Wound area could then be defined by

To determine the wound perimeter the wound region was traced with the Marching Squares algorithm [_{S} was the number of pixels in

In order to limit the detection of erroneous wounds a reference coordinate _{1} and _{2}

After wound detection, Gaussian Process Regression (GPR) [_{α}(_{ϕ}(_{α} and _{ϕ} are constants. The fitted GPs allow for posterior predictions with Bayesian estimated uncertainty of area and perimeter (red lines

(A) Detected wound at 1 hour (blue line) progressing to 15 hours (white line). The algorithm utilizes a combination of measured data (blue) and predicted data (red) in order determine the change in wound perimeter (B), wound area (C) and the derived cell velocity (D). Expected data which is found to be missing can be imputed by the model (green). All error bars signify one standard deviation of data and predictions colored accordingly.

Using our method we investigated the concerted velocity of MDA-MB-231 cells, an epithelial-like breast cancer cell line with a very strong migrating phenotype [

Cells were transfected with pooled Silencer Select siRNAs (three siRNAs per pool, 10nM final concentration) using lipofectamine RNAiMAX for 48 hours prior to experimentation. In addition to the three siRNAs previously described cells were also transfected with a non-targeting siRNA, which should represent the migratory potential of unperturbed MDA-MB-231 cells. Following gene knockdown the zone exclusion was removed and cells were imaged for 16 hours in 1 hour intervals on a high content screening system (PerkinElmer Opera) at 10x magnification (1.3μm per pixel resolution) to detect red fluorescent protein tagged histone (nuclear staining) and diffuse green fluorescent protein (cytoplasmic staining).

Each of the four knockdowns was repeated 28 times generating 112 time series in total. The exclusion wounds were detected using the following settings,

To compare the computed cell velocities with the more conventional readout of change in area over time the mean change of area was found by taking the slope of a linear least square regression from the area data for each time series. For velocity the weighted average of the velocity was calculated for each time series weighted by the velocity precision

(A) Mean area change. (B) Mean velocity. Blue lines illustrate PLK1 mean response and red lines illustrate 3 times PLK1 response. (C) Signal to noise comparison of the area change and mean velocity.

(A) Wound detection in non-fluorescent images. (B) Mean area change. (C) Mean velocity. Blue lines illustrate starve response median value and red lines illustrate 110% of this value. (D) Signal to noise comparison of the area change and mean velocity.

These analyses demonstrate that determining cell velocity enables better separation of conditions in high content screening assays and would thus facilitate more accurate detection of potential therapeutic targets or treatment strategies. We note that wound geometry can change over time for no obvious biological reason (see imaging data associated with this paper on bowhead.lindinglab.science for examples), wounds that are circular to begin with become more square or triangular over time. In these cases the imaging method, mainly the number of time points used to calculate the wound closure, would have a significant impact on the result if area change was used, and may also affect the signal-to-noise ratio. In comparison, velocity is an absolute measurement that was not affected by the different imaging methods, and instrumentation, employed to generate the two datasets tested here.

For platform independence the wound detection algorithm was constructed using Python. Documentation, source code, data used in the paper and examples are hosted online at

The original image (A) is first flattened to gray scale, then convoluted with a Gaussian filter at chosen standard deviation

(TIF)

Both are available with Bowhead.

(TIF)

Cells with PLK1 knockdown are not migrating. MYH9 and POU5F1 knockdown cells are migrating faster and slower respectively compared to non-targeting cells.

(TIF)

Non-targeting cells migrating into the wound with detected border in blue, 1 to 11 hours.

(MP4)

Non-targeting cells migrating into the wound with detected border in blue, 1 to 17 hours.

(MP4)