Polar features in the flagellar propulsion of E. coli bacteria

E. coli bacteria swim following a run and tumble pattern. In the run state all flagella join in a single helical bundle that propels the cell body along approximately straight paths. When one or more flagellar motors reverse direction the bundle unwinds and the cell randomizes its orientation. This basic picture represents an idealization of a much more complex dynamical problem. Although it has been shown that bundle formation can occur at either pole of the cell, it is still unclear whether this two run states correspond to asymmetric propulsion features. Using holographic microscopy we record the 3D motions of individual bacteria swimming in optical traps. We find that most cells possess two run states characterised by different propulsion forces, total torque and bundle conformations. We analyse the statistical properties of bundle reversal and compare the hydrodynamic features of forward and backward running states. Our method is naturally multi-particle and opens up the way towards controlled hydrodynamic studies of interacting swimming cells

Holographic tracking and sizing of optically trapped microprobes in diamond anvil cells

We demonstrate that Digital Holographic Microscopy can be used for accurate 3D tracking and sizing of a colloidal probe trapped in a diamond anvil cell (DAC). Polystyrene beads were optically trapped in water up to Gigapascal pressures while simultaneously recording in-line holograms at 1 KHz frame rate. Using Lorenz-Mie scattering theory to fit interference patterns, we detected a 10% shrinking in the bead’s radius due to the high applied pressure. Accurate bead sizing is crucial for obtaining reliable viscosity measurements and provides a convenient optical tool for the determination of the bulk modulus of probe material. Our technique may provide a new method for pressure measurements inside a DAC

The very long range nature of capillary interactions in liquid films

Micron-sized objects confined in thin liquid films interact through forces mediated by the deformed liquid-air interface. This capillary interactions provide a powerful driving mechanism for the self-assembly of ordered structures such as photonic materials or protein crystals. Direct probing of capillary interactions requires a controlled force field to independently manipulate small objects while avoiding any physical contact with the interface. We demonstrate how optical micro-manipulation allows the direct measurement of capillary interactions between two micron sized spheres in a free standing liquid film. The force falls off as an inverse power law in particles separation. We derive and validate an explicit expression for this exponent whose magnitude is mainly governed by particles size. For micron-sized objects we found an exponent close to, but smaller than one, making capillary interactions a unique example of strong and very long ranged forces in the mesoscopic world

Optical trapping at gigapascal pressures

Diamond anvil cells allow the behavior of materials to be studied at pressures up to hundreds of gigapascals in a small and convenient instrument. However, physical access to the sample is impossible once it is pressurized. We show that optical tweezers can be used to hold and manipulate particles in such a cell, confining micron-sized transparent beads in the focus of a laser beam. Here, we use a modified optical tweezers geometry, allowing us to trap through an objective lens with a higher working distance, overcoming the constraints imposed by the limited angular acceptance of the anvil cell. We demonstrate the effectiveness of the technique by measuring water’s viscosity at pressures of up to 1.3 GPa. In contrast to previous viscosity measurements in anvil cells, our technique measures absolute viscosity and does not require scaling to the accepted value at atmospheric pressure. This method could also measure the frequency dependence of viscosity as well as being sensitive to anisotropy in the medium’s viscosity

Thermodynamic limits of sperm swimming precision

Sperm swimming is crucial to fertilise the egg, in nature and in assisted reproductive technologies. Modelling the sperm dynamics involves elasticity, hydrodynamics, internal active forces, and out-of-equilibrium noise. Here we demonstrate experimentally the relevance of energy dissipation for sperm beating fluctuations. For each motile cell, we reconstruct the time-evolution of the two main tail's spatial modes, which together trace a noisy limit cycle characterised by a maximum level of precision $p_{max}$. Our results indicate $p_{max} \sim 10^2 s^{-1}$, remarkably close to the estimated precision of a dynein molecular motor actuating the flagellum, which is bounded by its energy dissipation rate according to the Thermodynamic Uncertainty Relation. Further experiments under oxygen deprivation show that $p_{max}$ decays with energy consumption, as it occurs for a single molecular motor. Both observations can be explained by conjecturing a high level of coordination among the conformational changes of dynein motors. This conjecture is supported by a theoretical model for the beating of an ideal flagellum actuated by a collection of motors, including a motor-motor nearest neighbour coupling of strength $K$: when $K$ is small the precision of a large flagellum is much higher than the single motor one. On the contrary, when $K$ is large the two become comparable.Comment: Main Text with Appendices (14 pages, 9 figures) plus Supplementary Information, Accepted for Publication in PRX-Lif

A transition to stable one-dimensional swimming enhances E. coli motility through narrow channels

Living organisms often display adaptive strategies that allow them to move efficiently even in strong confinement. With one single degree of freedom, the angle of a rotating bundle of flagella, bacteria provide one of the simplest examples of locomotion in the living world. Here we show that a purely physical mechanism, depending on a hydrodynamic stability condition, is responsible for a confinement induced transition between two swimming states in E. coli. While in large channels bacteria always crash onto confining walls, when the cross section falls below a threshold, they leave the walls to move swiftly on a stable swimming trajectory along the channel axis. We investigate this phenomenon for individual cells that are guided through a sequence of micro-fabricated tunnels of decreasing cross section. Our results challenge current theoretical predictions and suggest effective design principles for microrobots by showing that motility based on helical propellers provides a robust swimming strategy for exploring narrow spaces

A transition to stable one-dimensional swimming enhances E. coli motility through narrow channels

Living organisms often display adaptive strategies that allow them to move efficiently even in strong confinement. With one single degree of freedom, the angle of a rotating bundle of flagella, bacteria provide one of the simplest examples of locomotion in the living world. Here we show that a purely physical mechanism, depending on a hydrodynamic stability condition, is responsible for a confinement induced transition between two swimming states in E. coli. While in large channels bacteria always crash onto confining walls, when the cross section falls below a threshold, they leave the walls to move swiftly on a stable swimming trajectory along the channel axis. We investigate this phenomenon for individual cells that are guided through a sequence of micro-fabricated tunnels of decreasing cross section. Our results challenge current theoretical predictions and suggest effective design principles for microrobots by showing that motility based on helical propellers provides a robust swimming strategy for exploring narrow spaces. © 2020, The Author(s)

Four-directional stereo-microscopy for 3D particle tracking with real-time error evaluation

High-speed video stereo-microscopy relies on illumination from two distinct angles to create two views of a sample from different directions. The 3D trajectory of a microscopic object can then be reconstructed using parallax to combine 2D measurements of its position in each image. In this work, we evaluate the accuracy of 3D particle tracking using this technique, by extending the number of views from two to four directions. This allows us to record two independent sets of measurements of the 3D coordinates of tracked objects, and comparison of these enables measurement and minimisation of the tracking error in all dimensions. We demonstrate the method by tracking the motion of an optically trapped microsphere of 5 μm in diameter, and find an accuracy of 2–5 nm laterally, and 5–10 nm axially, representing a relative error of less than 2.5% of its range of motion in each dimension

Haloarchaea swim slowly for optimal chemotactic efficiency in low nutrient environments

Archaea have evolved to survive in some of the most extreme environments on earth. Life in extreme, nutrient-poor conditions gives the opportunity to probe fundamental energy limitations on movement and response to stimuli, two essential markers of living systems. Here we use three-dimensional holographic microscopy and computer simulations to reveal that halophilic archaea achieve chemotaxis with power requirements one hundred-fold lower than common eubacterial model systems. Their swimming direction is stabilised by their flagella (archaella), enhancing directional persistence in a manner similar to that displayed by eubacteria, albeit with a different motility apparatus. Our experiments and simulations reveal that the cells are capable of slow but deterministic chemotaxis up a chemical gradient, in a biased random walk at the thermodynamic limit