Applying torque to the Escherichia coli flagellar motor using magnetic tweezers

Magnetic Quincke rollers with tunable single-particle dynamics and collective states

Electrohydrodynamically driven active particles based on Quincke rotation have quickly become an important model system for emergent collective behavior in nonequilibrium colloidal systems. Like most active particles, Quincke rollers are intrinsically nonmagnetic, preventing the use of magnetic fields to control their complex dynamics on the fly. Here, we report on magnetic Quincke rollers based on silica particles doped with superparamagnetic iron oxide nanoparticles. We show that their magnetic nature enables the application of both externally controllable forces and torques at high spatial and temporal precision, leading to several versatile control mechanisms for their single-particle dynamics and collective states. These include tunable interparticle interactions, potential energy landscapes, and advanced programmable and teleoperated behaviors, allowing us to discover and probe active chaining, anisotropic active sedimentation-diffusion equilibria, and collective states in various geometries and dimensionalities.

Direct Measurement of the Stall Torque of the Flagellar Motor in Escherichia coli with Magnetic Tweezers

The flagellar motor drives the rotation of flagellar filaments, propelling the swimming of flagellated bacteria. The maximum torque the motor generates, the stall torque, is a key characteristic of the motor function. Direct measurements of the stall torque carried out 3 decades ago suffered from large experimental uncertainties, and subsequently there were only indirect measurements. Here, we applied magnetic tweezers to directly measure the stall torque in E. coli. We precisely calibrated the torsional stiffness of the magnetic tweezers and performed motor resurrection experiments at stall, accomplishing a precise determination of the stall torque per torque-generating unit (stator unit). From our measurements, each stator passes 2 protons per step, indicating a tight coupling between motor rotation and proton flux. IMPORTANCE The maximum torque the bacterial flagellar motor generates, the stall torque, is a critical parameter that describes the motor energetics. As the motor operates in equilibrium near stall, from the stall torque one can determine how many protons each torque-generating unit (stator) of the motor passes per revolution and then test whether motor rotation and proton flux are tightly or loosely coupled, which has been controversial in recent years. Direct measurements performed 3 decades ago suffered from large uncertainties, and subsequently, only indirect measurements were attempted, obtaining a range of values inconsistent with the previous direct measurements. Here, we developed a method that used magnetic tweezers to perform motor resurrection experiments at stall, resulting in a direct precise measurement of the stall torque per stator. Our study resolved the previous inconsistencies and provided direct experimental support for the tight coupling mechanism between motor rotation and proton flux.

Surface Sensing and Adaptation in Bacteria

Bacteria thrive both in liquids and attached to surfaces. The concentration of bacteria on surfaces is generally much higher than in the surrounding environment, offering bacteria ample opportunity for mutualistic, symbiotic, and pathogenic interactions. To efficiently populate surfaces, they have evolved mechanisms to sense mechanical or chemical cues upon contact with solid substrata. This is of particular importance for pathogens that interact with host tissue surfaces. In this review we discuss how bacteria are able to sense surfaces and how they use this information to adapt their physiology and behavior to this new environment. We first survey mechanosensing and chemosensing mechanisms and outline how specific macromolecular structures can inform bacteria about surfaces. We then discuss how mechanical cues are converted to biochemical signals to activate specific cellular processes in a defined chronological order and describe the role of two key second messengers, c-di-GMP and cAMP, in this process.

The bank of swimming organisms at the micron scale (BOSO-Micro)

Unicellular microscopic organisms living in aqueous environments outnumber all other creatures on Earth. A large proportion of them are able to self-propel in fluids with a vast diversity of swimming gaits and motility patterns. In this paper we present a biophysical survey of the available experimental data produced to date on the characteristics of motile behaviour in unicellular microswimmers. We assemble from the available literature empirical data on the motility of four broad categories of organisms: bacteria (and archaea), flagellated eukaryotes, spermatozoa and ciliates. Whenever possible, we gather the following biological, morphological, kinematic and dynamical parameters: species, geometry and size of the organisms, swimming speeds, actuation frequencies, actuation amplitudes, number of flagella and properties of the surrounding fluid. We then organise the data using the established fluid mechanics principles for propulsion at low Reynolds number. Specifically, we use theoretical biophysical models for the locomotion of cells within the same taxonomic groups of organisms as a means of rationalising the raw material we have assembled, while demonstrating the variability for organisms of different species within the same group. The material gathered in our work is an attempt to summarise the available experimental data in the field, providing a convenient and practical reference point for future studies.

Magnetic Measurement and Stimulation of Cellular and Intracellular Structures

From single-pole magnetic tweezers to robotic magnetic-field generation systems, the development of magnetic micromanipulation systems, using electromagnets or permanent magnets, has enabled a multitude of applications for cellular and intracellular measurement and stimulation. Controlled by different configurations of magnetic-field generation systems, magnetic particles have been actuated by an external magnetic field to exert forces/torques and perform mechanical measurements on the cell membrane, cytoplasm, cytoskeleton, nucleus, intracellular motors, etc. The particles have also been controlled to generate aggregations to trigger cell signaling pathways and produce heat to cause cancer cell apoptosis for hyperthermia treatment. Magnetic micromanipulation has become an important tool in the repertoire of toolsets for cell measurement and stimulation and will continue to be used widely for further explorations of cellular/intracellular structures and their functions. Existing review papers in the literature focus on fabrication and position control of magnetic particles/structures (often termed micronanorobots) and the synthesis and functionalization of magnetic particles. Differently, this paper reviews the principles and systems of magnetic micromanipulation specifically for cellular and intracellular measurement and stimulation. Discoveries enabled by magnetic measurement and stimulation of cellular and intracellular structures are also summarized. This paper ends with discussions on future opportunities and challenges of magnetic micromanipulation in the exploration of cellular biophysics, mechanotransduction, and disease therapeutics.

The Dissociation Rate of Acetylacetonate Ligands Governs the Size of Ferrimagnetic Zinc Ferrite Nanocubes

Magnetic nanoparticles are critical to a broad range of applications from medical diagnostics and therapeutics to biotechnological processes and single-molecule manipulation. To advance these applications, facile and robust routes to synthesize highly magnetic nanoparticles over a wide size range are needed. Here, we demonstrate that changing the degassing temperature of thermal decomposition of metal acetylacetonate precursors from 90 to 25 °C tunes the size of ferrimagnetic Zn_xFe_3-xO₄ nanocubes from 25 to 100 nm, respectively. We show that degassing at 90 °C nearly entirely removes acetylacetone ligands from the reaction, which results in an early formation of monomers and a reaction-controlled growth following LaMer's model toward small nanocubes. In contrast, degassing at 25 °C only partially dissociates acetylacetone ligands from the metal center and triggers a delayed formation of monomers, which leads to intermediate assembled structures made of tiny irregular crystallites and an eventual formation of large nanocubes via a diffusion-controlled growth mechanism. Using complementary techniques, we determine the substitution fraction x of Zn²⁺ to be in the range of 0.35-0.37. Our method reduces the complexity of the thermal decomposition method by narrowing the synthesis parameter space to a single physical parameter and enables fabrication of highly magnetic and uniform zinc ferrite nanocubes over a broad size range. The resulting particles are promising for a range of applications from magnetic fluid hyperthermia to actuation of macromolecules.

Mechanisms and Dynamics of the Bacterial Flagellar Motor

Many bacteria are able to actively propel themselves through their complex environment, in search of resources and suitable niches. The source of this propulsion is the Bacterial Flagellar Motor (BFM), a molecular complex embedded in the bacterial membrane which rotates a flagellum. In this chapter we review the known physical mechanisms at work in the motor. The BFM shows a highly dynamic behavior in its power output, its structure, and in the stoichiometry of its components. Changes in speed, rotation direction, constituent protein conformations, and the number of constituent subunits are dynamically controlled in accordance to external chemical and mechanical cues. The mechano-sensitivity of the motor is likely related to the surface-sensing ability of bacteria, relevant in the initial stage of biofilm formation.

Patterned Optoelectronic Tweezers: A New Scheme for Selecting, Moving, and Storing Dielectric Particles and Cells

Optical micromanipulation has become popular for a wide range of applications. In this work, a new type of optical micromanipulation platform, patterned optoelectronic tweezers (p-OET), is introduced. In p-OET devices, the photoconductive layer (that is continuous in a conventional OET device) is patterned, forming regions in which the electrode layer is locally exposed. It is demonstrated that micropatterns in the photoconductive layer are useful for repelling unwanted particles/cells, and also for keeping selected particles/cells in place after turning off the light source, minimizing light-induced heating. To clarify the physical mechanism behind these effects, systematic simulations are carried out, which indicate the existence of strong nonuniform electric fields at the boundary of micropatterns. The simulations are consistent with experimental observations, which are explored for a wide variety of geometries and conditions. It is proposed that the new technique may be useful for myriad applications in the rapidly growing area of optical micromanipulation.

Computing the motor torque of Escherichia coli

The rotary motor of bacteria is a natural nano-technological marvel that enables cell locomotion by powering the rotation of semi-rigid helical flagellar filaments in fluid environments. It is well known that the motor operates essentially at constant torque in counter-clockwise direction but past work have reported a large range of values of this torque. Focusing on Escherichia coli cells that are swimming and cells that are stuck on a glass surface for which all geometrical and environmental parameters are known (N. C. Darnton et al., J. Bacteriol., 2007, 189, 1756-1764), we use two validated numerical methods to compute the value of the motor torque consistent with experiments. Specifically, we use (and compare) a numerical method based on the boundary integral representation of Stokes flow and also develop a hybrid method combining boundary element and slender body theory to model the cell body and flagellar filament, respectively. Using measured rotation speed of the motor, our computations predict a value of the motor torque in the range 440 pN nm to 829 pN nm, depending critically on the distance between the flagellar filaments and the nearby surface.

Measuring Single-Molecule Twist and Torque in Multiplexed Magnetic Tweezers

Magnetic tweezers permit application of precisely calibrated stretching forces to nucleic acid molecules tethered between a surface and superparamagnetic beads. In addition, magnetic tweezers can control the tethers' twist. Here, we focus on recent extensions of the technique that expand the capabilities of conventional magnetic tweezers by enabling direct measurements of single-molecule torque and twist. Magnetic torque tweezers (MTT) still control the DNA or RNA tether's twist, but directly measure molecular torque by monitoring changes in the equilibrium rotation angle upon overwinding and underwinding of the tether. In freely orbiting magnetic tweezers (FOMT), one end of the tether is allowed to rotate freely, while still applying stretching forces and monitoring rotation angle. Both MTT and FOMT have provided unique insights into the mechanical properties, structural transitions, and interactions of DNA and RNA. Here, we provide step-by-step protocols to carry out FOMT and MTT measurements. In particular, we focus on multiplexed measurements, i.e., measurements that record data for multiple nucleic acid tethers at the same time, to improve statistics and to facilitate the observation of rare events.