Method of map construction and analysis.

A: segment of a curve of the proliferation rate of rat liver cancer cell line Fao: 27 consecutive 6-day passages in culture. X-axis: passage number; Y-axis: proliferation rate, expressed as population doublings/passage (PD/passage). B: the corresponding map is constructed by displaying the proliferation rate data in the recurrent form x_i+1 versus x_i (e.g. the green lines x_i+1 to x_i that construct the point corresponding to the segment p13-p14). The successive points on the map are joined together, as a succession of vectors. When x_i is a local peak (i.e. if x_i−1i>x_i+1), then the vector points south-east (highlighted in red). Whereas when x_i is a trough, (i.e. if x_i−1>x_ii+1), the vector points north-west in the plane (highlighted in blue). The bisecting line, i.e. the line perpendicular to the mid-point of the vector, is drawn for each trough (blue dotted arrows) and peak (red dotted arrows) vector. Coordination, if any, of the bisecting lines defines a fixed point, i.e. a point on the diagonal where x_i = x_i+1 (which is therefore a stable level of cell growth), as shown here for convergence of the bisecting lines of trough vectors on coordinates 6.25/6.25. Note that there is no such coordination of the peak vectors in these cancer cells. (The complete analysis of the cell line was published in [14]).