Motility in Macroorganisms

Figure 1: Typical infotactic trajectories in the absence (a) or presence (b) of wind, blowing in the negative y-direction. The background color represents the mean rate of detection of molecules emitted by the source. The searcher starts from the black upward triangle; times of detection of molecules are indicated by black circles. Note the long lags without any detection, typical of dilute conditions.

    Macroscopic animals sensing odors and/or pheromones in air or water, e.g. insects and birds, detect odor molecules very intermittently and sporadically, as patches of odor sweep by, carried by winds and currents. Furthermore, the randomness of the advection and mixing processes at macroscopic scales makes that, even if a patch is detected, local gradients do not point to the source of odors. Waiting and integrating the signal might of course amplify the signal-to-noise ratio. However, as average concentration typically decays rapidly with the distance away from the source, the waiting time would become huge. Furthermore, entomologists have observed that moths have a rapid time of response (order of ms) to stimuli, e.g. pheromones. The same challenging problem of locating a target by exploiting only sporadic cues and partial information arises also in the design of sniffers - robots that track chemicals emitted by drugs, chemical leaks, explosives and mines. Existing methods tend to mimic bacteria, employing strategies of search inspired by chemotaxis. The physical conditions described previously (quite different from those of bacteria) make that those strategies of search are severely limited.

     In [1], we proposed a different type of biomimetic strategy, more inspired by insects. strategy is dubbed “infotaxis” as it is based on the idea that the rate of acquisition of information on the location of the source, as estimated by the searcher, can play the same role as concentration in chemotaxis. The infotaxis strategy of motion maximizes the expected rate of information gain and leads to trajectories featuring zigzagging and casting paths similar to those observed in flights of moths and birds (see Fig. 1). Computational experiments demonstrate the superiority of the strategy to existing methods and to other alternatives based on local algorithms. We have also recently [2] generalized the infotaxis strategy to multiple searchers, cooperating in the search of a target. Sharing the probability map for the location of the target among the searchers leads to non-trivial interactions among them. Interactions tend to space the searchers by distances comparable to the correlation length of the environment to be sought and lead to impressive advantages in the search times.

[1] Infotaxis as a strategy for searching without gradients. M. Vergassola, E. Villermaux & B.I. Shraiman Nature, 445, 406-409, 2007.
[2] Chasing information to search in random environments. J.B. Masson, M. Bailly-Bechet, M. Vergassola, J. Phys. A, special issue on random search problems, to appear.

Our current and future objectives

     We are currently working with B.I. Shraiman at KITP (UCSB) on generalizations of the infottaxis strategy to other decision problems, such as for example the classical scheduling problem of multi-armed bandits. Preliminary results indicate that the infotaxis strategy performs extremely well as compared to state-of-the-art existing methods and saturates known mathematical bounds on the optimal performance of any possible strategy. We are also pursuing the application of the infotaxis strategy to real robots, in collaboration with A. Martinoli’s group at EPFL in Lausanne, who is testing performances in a wind tunnel in realistic conditions. A longer term objective that we are discussing with P.-M. Lledo at the Pasteur Institute is to directly assay the behavior of real animals and their strategies of decision. Details are not defined yet but the goal that we are after is to have both detections, e.g. of pheromones or odors, and trajectories of the animal and use these experimental data to get cues about their decisions, namely the amount of memory involved in their choice of direction of motion.