We demonstrate how optical tweezers combined with a three-dimensional force detection system and high-speed camera are used to study the swimming force and behavior of trapped micro-organisms. By utilizing position sensitive detection, we measure the motility force of trapped particles, regardless of orientation. This has the advantage of not requiring complex beam shaping or microfluidic controls for aligning trapped particles in a particular orientation, leading to unambiguous measurements of the propulsive force at any time. Correlating the direct force measurements with position data from a high-speed camera enables us to determine changes in the particle’s behavior. We demonstrate our technique by measuring the swimming force and observing distinctions between swimming and tumbling modes of the Escherichia coli (E. coli) strain MC4100. Our method shows promise for application in future studies of trappable but otherwise arbitrary-shaped biological swimmers and other active matter.

A R T I C L E I N F OKeywords: optical trapping dual beam trap annular beams spatial light modulator dynamic orientation motile particles A B S T R A C TOptical tweezers are a versatile tool that can be used to manipulate small particles including both motile and non-motile bacteria and cells. The orientation of a non-spherical particle within a beam depends on the shape of the particle and the shape of the light field. By using multiple beams, sculpted light fields or dynamically changing beams, it is possible to control the orientation of certain particles. In this paper we discuss the orientation of the rod-shaped bacteria Escherichia coli (E. coli) using dynamically shifting annular beam optical tweezers. We begin with examples of different beams used for the orientation of rod-shaped particles. We discuss the differences between orientation of motile and non-motile particles, and explore annular beams and the circumstances when they may be beneficial for manipulation of non-spherical particles or cells. Using simulations we map out the trajectory the E. coli takes. Estimating the trap stiffness along the trajectory gives us an insight into how stable an intermediate rotation is with respect to the desired orientation. Using this method, we predict and experimentally verify the change in the orientation of motile E. coli from vertical to near-horizontal with only one intermediate step.The method is not specific to exploring the orientation of particles and could be easily extended to quantify the stability of an arbitrary particle trajectory.

The trap stiffness us the key property in using optical tweezers as a force transducer. Force reconstruction via maximum-likelihood-estimator analysis (FORMA) determines the optical trap stiffness based on estimation of the particle velocity from statistical trajectories. Using a modification of this technique, we determine the trap stiffness for a two micron particle within 2 ms to a precision of ∼10% using camera measurements at 10 kfps with the contribution of pixel noise to the signal being larger the level Brownian motion. This is done by observing a particle fall into an optical trap once at a high stiffness. This type of calibration is attractive, as it avoids the use of a nanopositioning stage, which makes it ideal for systems of large numbers of particles, e.g., micro-fluidics or active matter systems.

Escherichia coli and many other bacteria swim through media with the use of flagella, which are deformable helical propellers. When the viscosity of media is increased, a peculiar phenomenon can be observed in which the organism's motility appears to improve. This improvement in the cell's swimming speed has previously been explained by modified versions of resistive force theory (RFT) which accounts for the interaction between flagella and molecules associated with the viscosity increase. Using optical tweezers, we measure the swimming force of individual E. coli in solutions of varying viscosity. By using probe-free force measurements, we are able to quantitatively validate and compare RFT and proposed modifications to the theory. We find that the force produced by the flagellum remains relatively constant even when the viscosity of the medium increases by approximately two orders of magnitude, contrary to predictions of RFT and variants. We conclude that the observed swimming forces can be explained by allowing the flagella geometry to deform as the viscosity of the surrounding medium is increased.