Interaction of Pair Particles Mediated by Signal Molecules

A mesoscopic model is set up to study the predator–prey-like phenomenon between two chemically active objects. A target sphere (T) secretes chemical signal molecules that are detected and traced by a hunter sphere (H). The distribution of signal molecules diffusing around the target is simulated and analyzed. The chemotactic behavior of the hunter along the gradient of signal molecules results in the capture of the target. The dependences of capture time t_\rm c on different conditions are focused on. It is found that the values of capture time rely on their initial separation d as a power law t_\rm c\propto d^\alpha. The exponent \alpha depends on decay rate of signal molecules. The capture time increases with the decay rate. The increases of target and hunter size both lead to the decrease of the capture time, which is also shown by the power law behavior. The detailed chemotaxis process is investigated.