Helical and oscillatory microswimmer motility statistics from differential dynamic microscopy

Abstract

The experimental characterisation of the swimming statistics of populations of micro-organisms or artificially propelled particles is essential for understanding the physics of active systems and their exploitation. Here, we construct a theoretical framework to extract information on the threedimensional motion of micro-swimmers from the intermediate scattering function (ISF) obtained from differential dynamic microscopy (DDM). We derive theoretical expressions for the ISF of helical and oscillatory breaststroke swimmers, and test the theoretical framework by applying it to video sequences generated from simulated swimmers with precisely-controlled dynamics. We then discuss how our theory can be applied to the experimental study of helical swimmers, such as active Janus colloids or suspensions of motile microalgae. In particular, we show how fitting DDM data to a simple, non-helical ISF model can be used to derive three-dimensional helical motility parameters, which can therefore be obtained without specialised 3D microscopy equipment. Finally, we discus how our results aid the study of active matter and describe applications of biological and ecological importance.

Nonequilibrium dynamical structure of a dilute suspension of active particles in a viscoelastic fluid

“…an oscillatory behavior of the intermediate scattering function emerges as a function of τ , which is similar to the oscillations found at intermediate wave numbers for other models of active particles in a viscous environment [42,[50][51][52]. This can be checked in Fig.…”

“…For instance, dynamical light scattering (DLS) [37], differential dynamic microscopy (DDM) [38], and super-heterodyne laser-Doppler-velocimetry (SH-LDV) [39], have been successfully applied to the characterization of aqueous suspensions of Janus colloidal particles [40][41][42][43], motile bacteria [44][45][46][47], and cytoskeletal filamentous actin [48]. Furthermore, analytical expressions for the intermediate scattering function, a quantity directly accessible by DDM, have been derived for stochastic models of active matter, such as run-and-tumble particles [49], active Brownian particles [50,51], and oscillatory breaststroke microswimmers [52]. Although such ensemble techniques have proved to be valuable for investigating specific dynamical details of active particles in viscous solvents under homogeneous conditions, other situations of practical interests remain largely unexplored.…”

Helical trajectories of swimming cells with a flexible flagellar hook

“…where U 0 and Ω 0 are related to F 0 and M 0 via ( 17)-( 18), U f 0 and Ω f 0 are related to F f 0 and M f 0 via ( 37)- (38). These equations represent, in order: total force balance, total torque balance about the cell body centroid, torque balance on the flagellum about the basal connection point, and the kinematic constraint of flagellum attachment to the cell body.…”

“…The "wobbling" and "wiggling" of cell bodies has been investigated numerically by Hyon et al, in an effort which included comparison to new experiments using B. subtilis cells [32], and precession was also noted in simulations by Shum & Gaffney [33]. More recently, Constantino et al have observed and rationalized the helical trajectories of H. pylori [34], Rossi et al have investigated the same for E. gracila cells [35,36], synthetic models have been designed to explore helical trajectories [37], and new techniques have been developed for inferring motility parameters statistically [38]. Properly tuned undulatory beating can also result in helical navigation, as found in the swimming of Chlamydomonas reinhardtii cells [39].…”

Characterization of active matter in dense suspensions with heterodyne laser Doppler velocimetry

“…Properties and performance of individual particles and small ensembles are readily accessible by (confocal or holographic) microscopy utilizing particle tracking and image analysis for structural and dynamical characterization [18][19][20]. Particle image velocimetry [21] or dynamic differential microscopy (DDM) is suitable for studies of larger ensembles of individually propelling swimmers [17,22,23]. Both approaches, however, reveal severe technical drawbacks (e.g.…”