Figure 4
Indirect effects of goal-directed search on the immune cell’s covered area A(t) versus time (first column), on its mean squared displacement \(\overline{{R}^{2}}(\varDelta t)\) versus lag-time (second column), and on the probability density p(dNN) of the distance to the nearest target (third column). The top row (a–c) corresponds to temporal gradient search (TGS), the bottom row (d–f) to spatial gradient search (SGS). Orange lines were obtained with the optimized immune cell parameters, whereas blue lines were obtained with sensitivity parameters (cA1 for TGS, and cR1 for SGS) set to zero, effectively creating a blind search. In the double-logarithmic plots of the first two columns, the fine lines correspond to individual immune cells (10 per run) and simulation runs (10), whereas the thick lines are logarithmic averages. The search strategies TGS and SGS have little effect on the immune cell’s covered area ((a,d)), but lead to significantly reduced mean squared displacements at longer lag-times ((b,e)). The most drastic effect of TGS and SGS is seen in the distribution p(dNN), which is Rayleigh-like in blind search (blue histograms in (c,f)), but exponential-like in goal-directed search (orange histograms in (c,f)). These effects are caused by the attraction of the immune cells towards the targets, which in turn leads to a partial localization of the immune cell trajectory in the vicinity of targets.
