Time and dose influence by means of gradient

Once the DDRA is identified, the influence of time on the fold-change is studied by analysing the vector field of gradients in the region. For each point, the magnitude and the angle of the gradient are computed and used to evaluate the time-dose response score as follows:

where g_i and mod_i are the angle and magnitude of the gradient in the i-th point in the DDRA and n is the number of points in the same region. This score can be used to categorize the genes on the basis of the dose and time effect on their fold-change. According to the time-dose response score, the active genes are divided into 4 groups, corresponding to the 4 quadrants of Cartesian space. In the first quadrant the fold-change increases with both time and dose (0 < td_s ≤ 90); in the second quadrant the fold-change increases with time but decreases with dose (90 < td_s ≤ 180); in the third quadrant the fold-change decreases with both time and dose (180 < td_s ≤ 270); in the fourth quadrant the fold-change increases with dose and decreases with time (270 < td_s ≤ 360). The 4 quadrants can be further dissected in 3 smaller sectors: 1 in which the dose has a stronger effect than the time, 1 in which they have the same effect, and 1 in which the time has a stronger effect than the dose. We assign a label to each gene composed by the letters d and t,standing for dose and time, respectively, and a positive or negative sign. If the influence of 1 of the 2 components is stronger than the other, this is highlighted by using capital letters. For example, the label d + T + stands for fold-change increasing with both dose and time, with a stronger effect from the time.