Modeling of the tachyzoite trajectory during cell penetration highlights a change in body curvature and a final rotation independently of cell type and junction behavior. Time lapses of: GFP tachyzoites entering in (A) a M2 cell with a stable junction, (B) RON2mC tachyzoite entering with a capped junction in a HFF cell, (C) a Ptk-1 cell with a capped junction, (D) Δ toxofilin RON2mC tachyzoite entering with a capped junction in a HFF cell. The lines define the parasite apex trajectory (blue line) and final rotation (white line); white curve arrows show the rotation direction while blue arrows indicate the change in body curvature, all scale bars: 5 μm. Below each time lapse is presented the corresponding graph: (A) of the x and y coordinates separately as a function of time, of the xy coordinates Y = f(X) that represents the tracked trajectory (blue), all with their respective best fitting polynomial curves (red crosses), and of the radius curvature (RC) as a function of time for which the change in line color matches with the sign of RC over time. The blue arrows mark the time of RC shift; (B-D) left graphs show the tachyzoite speed over time with parasite apex (blue lines) and junction (pink lines) trajectories, pink arrows indicate the starting and ending time points; right graphs display the RC as a function of time. HFF, human foreskin fibroblasts; Ptk-1, rat kangaroo kidney epithelial cell; RON2, RhOptry Neck.