Linearity

Dear All,

Congratulations on the software! It works really well! Thanks so much
I have doing some analysis on cell motility and would like to know what does the ‘linearity’ measurement mean? Thanks in advance for your help.

susana

Hi Susana,

The linearity measurement is calculated as the distance from an object’s initial location to its final location, divided by the integrated object distance (that is, the total path length travelled). If it is close to 1, then the path was more or less linear, and goes to 0 with increasing meander (e.g, an extreme case would be if the object wandered around significantly before returning to its starting point)

Hope this helps!
-Mark

Thanks, Mark!
I have so trouble in understanding exactly what you mean. So if it’s close to 1 and decreases to 0 is a linear path? Is that what you meant? I have attached 2 examples, in this case cell 2 would be an example of a linear path and how would you describe cell3?
Thanks once again

susana




Ah, I see what you mean; thanks for clarifying. My mistake; I should have added that this measure is made at each time point.

For a given time point, the linearity is computed using:

  • The start position is taken at the first frame the object appears.
  • The end frame is the current time point
    . - The integrated distance is the path length traveled up to that time-point
    .

So what you are seeing is essentially a measure that is evolving over time. The true linearity measure should be evaluated at the time point when the object terminates, i.e., the last frame.
-Mark

Thanks, Mark!
I understand what you mean but I still have a question.
If the cell doesn’t take the same direction during the time-acquisition then you can’t really use the first and last timepoints to assess linearity, isn’t it? Is there any other measurement possible to do?
So it makes sense that the graphs tend to 0 with a higher or lower slope depending on the velocity and how much are they displaced, right? Also, looking to the data you think it is possible to conclude that cell 3 change direction during the time-lapse acquisition?
Does the *integrated distance * take into consideration the directionality?

Thanks a lot for your time

susana

The idea is that if a cell follows a linear track over the course of its life, then the first and last time points will be the endpoints of a line, and the integrated distance will reflect the simple distance along this line. So, it should be sufficient for the purpose of the measurement as described.

We do not have currently measurements available to measure how linear a cell track is during only a portion of its existence. However, the (x,y) frame-to-frame displacements are available. If you output the measurements to a spreadsheet, you may able to work with them in Excel to measure the linearity of part of a track.

Assuming that your cells meander non-linearly as part of their behavior, then yes, this is correct.

Not necessarily. The deflections to higher values (such as around frame 40 or 70) could be due to a jump in the position of the cell, leading to a large start-end distance but it doesn’t follow that the jump was in a different direction, just that it was large. I would be more interested in whether the cell actually experienced that significant a displacement in the first place; you might want to check the (x,y) coordinates to confirm.

No, the intergrated distance is merely the sum of frame-to-frame displacements, regardless of direction.
-Mark