Optimal strategies for driving a mobile agent in a guidance by repulsion model

We present a guidance by repulsion model based on a driver-evader interaction where the driver, assumed to be faster than the evader, follows the evader but cannot be arbitrarily close to it, and the evader tries to move away from the driver beyond a short distance. The key ingredient allowing the driver to guide the evader is that the driver is able to display a circumvention maneuver around the evader, in such a way that the trajectory of the evader is modified in the direction of the repulsion that the driver exerts on the evader. The evader can thus be driven towards any given target or along a sufficiently smooth path by controlling a single discrete parameter acting on driver's behavior. The control parameter serves both to activate/deactivate the circumvention mode and to select the clockwise/counterclockwise direction of the circumvention maneuver. Assuming that the circumvention mode is more expensive than the pursuit mode, and that the activation of the circumvention mode has a high cost, we formulate an optimal control problem for the optimal strategy to drive the evader to a given target. By means of numerical shooting methods, we find the optimal open-loop control which reduces the number of activations of the circumvention mode to one and which minimizes the time spent in the active~mode. Our numerical simulations show that the system is highly sensitive to small variations of the control function, and that the cost function has a nonlinear regime which contributes to the complexity of the behavior of the system, so that a general open-loop control would not be of practical interest. We then propose a feedback control law that corrects from deviations while preventing from an excesive use of the circumvention mode, finding numerically that the feedback law significantly reduces the cost obtained with the open-loop control

Multiparametric Modulation of Magnetic Transduction for Biomolecular Sensing in Liquids

The recent COVID19 pandemic has remarkably boosted the research on in vitro diagnosis assays to detect biomarkers in biological fluids. Specificity and sensitivity are mandatory for diagnostic kits aiming to reach clinical stages. Whilst the modulation of sensitivity can significantly improve the detection of biomarkers in liquids, this has been scarcely explored. Here, we report on the proof of concept and parametrization of a novel biosensing methodology based on the changes of AC magnetic hysteresis areas observed for magnetic nanoparticles following biomolecular recognition in liquids. Several parameters are shown to significantly modulate the transducing capacity of magnetic nanoparticles to detect analytes dispersed in saline buffer at concentrations of clinical relevance. Magnetic nanoparticles were bio-conjugated with an engineered recognition peptide as a receptor. Analytes are engineered tetratricopeptide binding domains fused to the fluorescent protein whose dimerization state allows mono- or divalent variants. Our results unveil that the number of receptors per particle, analyte valency and concentration, nanoparticle composition and concentration, and field conditions play a key role in the formation of assemblies driven by biomolecular recognition. Consequently, all these parameters modulate the nanoparticle transduction capacity. Our study provides essential insights into the potential of AC magnetometry for customizing biomarker detection in liquids.Peer reviewe