A programmable optical angle clamp for rotary molecular motors

Steady-state running rate sets the speed and accuracy of accumulation of swimming bacteria

We study the chemotaxis of a population of genetically identical swimming bacteria undergoing run and tumble dynamics driven by stochastic switching between clockwise and counterclockwise rotation of the flagellar rotary system, where the steady-state rate of the switching changes in different environments. Understanding chemotaxis quantitatively requires that one links the measured steady-state switching rates of the rotary system, as well as the directional changes of individual swimming bacteria in a gradient of chemoattractant/repellant, to the efficiency of a population of bacteria in moving up/down the gradient. Here we achieve this by using a probabilistic model, parametrized with our experimental data, and show that the response of a population to the gradient is complex. We find the changes to the steady-state switching rate in the absence of gradients affect the average speed of the swimming bacterial population response as well as the width of the distribution. Both must be taken into account when optimizing the overall response of the population in complex environments.

Bacterial flagellar motor as a multimodal biosensor

Bacterial Flagellar Motor is one of nature's rare rotary molecular machines. It enables bacterial swimming and it is the key part of the bacterial chemotactic network, one of the best studied chemical signalling networks in biology, which enables bacteria to direct its movement in accordance with the chemical environment. The network can sense down to nanomolar concentrations of specific chemicals on the time scale of seconds. Motor's rotational speed is linearly proportional to the electrochemical gradients of either proton or sodium driving ions, while its direction is regulated by the chemotactic network. Recently, it has been discovered that motor is also a mechanosensor. Given these properties, we discuss the motor's potential to serve as a multifunctional biosensor and a tool for characterising and studying the external environment, the bacterial physiology itself and single molecular motor biophysics.

Single-Cell Bacterial Electrophysiology Reveals Mechanisms of Stress-Induced Damage

An electrochemical gradient of protons, or proton motive force (PMF), is at the basis of bacterial energetics. It powers vital cellular processes and defines the physiological state of the cell. Here, we use an electric circuit analogy of an Escherichia coli cell to mathematically describe the relationship between bacterial PMF, electric properties of the cell membrane, and catabolism. We combine the analogy with the use of bacterial flagellar motor as a single-cell "voltmeter" to measure cellular PMF in varied and dynamic external environments (for example, under different stresses). We find that butanol acts as an ionophore and functionally characterize membrane damage caused by the light of shorter wavelengths. Our approach coalesces noninvasive and fast single-cell voltmeter with a well-defined mathematical framework to enable quantitative bacterial electrophysiology.

Osmotaxis in Escherichia coli through changes in motor speed

Bacterial motility, and in particular repulsion or attraction toward specific chemicals, has been a subject of investigation for over 100 years, resulting in detailed understanding of bacterial chemotaxis and the corresponding sensory network in many bacterial species. For Escherichia coli most of the current understanding comes from the experiments with low levels of chemotactically active ligands. However, chemotactically inactive chemical species at concentrations found in the human gastrointestinal tract produce significant changes in E. coli's osmotic pressure and have been shown to lead to taxis. To understand how these nonspecific physical signals influence motility, we look at the response of individual bacterial flagellar motors under stepwise changes in external osmolarity. We combine these measurements with a population swimming assay under the same conditions. Unlike for chemotactic response, a long-term increase in swimming/motor speeds is observed, and in the motor rotational bias, both of which scale with the osmotic shock magnitude. We discuss how the speed changes we observe can lead to steady-state bacterial accumulation.

Applying torque to the Escherichia coli flagellar motor using magnetic tweezers

The bacterial flagellar motor of Escherichia coli is a nanoscale rotary engine essential for bacterial propulsion. Studies on the power output of single motors rely on the measurement of motor torque and rotation under external load. Here, we investigate the use of magnetic tweezers, which in principle allow the application and active control of a calibrated load torque, to study single flagellar motors in Escherichia coli. We manipulate the external load on the motor by adjusting the magnetic field experienced by a magnetic bead linked to the motor, and we probe the motor’s response. A simple model describes the average motor speed over the entire range of applied fields. We extract the motor torque at stall and find it to be similar to the motor torque at drag-limited speed. In addition, use of the magnetic tweezers allows us to force motor rotation in both forward and backward directions. We monitor the motor’s performance before and after periods of forced rotation and observe no destructive effects on the motor. Our experiments show how magnetic tweezers can provide active and fast control of the external load while also exposing remaining challenges in calibration. Through their non-invasive character and straightforward parallelization, magnetic tweezers provide an attractive platform to study nanoscale rotary motors at the single-motor level.

Origins of Escherichia coli growth rate and cell shape changes at high external osmolality

In Escherichia coli, a sudden increase in external concentration causes a pressure drop across the cell envelope, followed by an active recovery. After recovery, and if the external osmolality remains high, cells have been shown to grow more slowly, smaller, and at reduced turgor pressure. Despite the fact that the active recovery is a key stress response, the nature of these changes and how they relate to each other is not understood. Here, we use fluorescence imaging of single cells during hyperosmotic shocks, combined with custom made microfluidic devices, to show that cells fully recover their volume to the initial, preshock value and continue to grow at a slower rate immediately after the recovery. We show that the cell envelope material properties do not change after hyperosmotic shock, and that cell shape recovers along with cell volume. Taken together, these observations indicate that the turgor pressure recovers to its initial value so that reduced turgor is not responsible for the reduced growth rate observed immediately after recovery. To determine the point at which the reduction in cell size and turgor pressure occurs after shock, we measured the volume of E. coli cells at different stages of growth in bulk cultures. We show that cell volume reaches the same maximal level irrespective of the osmolality of the media. Based on these measurements, we propose that turgor pressure is used as a feedback variable for osmoregulatory pumps instead of being directly responsible for the reduction in growth rates. Reestablishment of turgor to its initial value might ensure correct attachment of the inner membrane and cell wall needed for cell wall biosynthesis.

Plasmolysis and cell shape depend on solute outer-membrane permeability during hyperosmotic shock in E. coli

The concentration of chemicals inside the bacterial cytoplasm generates an osmotic pressure, termed turgor, which inflates the cell and is necessary for cell growth and survival. In Escherichia coli, a sudden increase in external concentration causes a pressure drop across the cell envelope that drives changes in cell shape, such as plasmolysis, where the inner and outer membranes separate. Here, we use fluorescence imaging of single cells during hyperosmotic shock with a time resolution on the order of seconds to examine the response of cells to a range of different conditions. We show that shock using an outer-membrane impermeable solute results in total cell volume reduction with no plasmolysis, whereas a shock caused by outer-membrane permeable ions causes plasmolysis immediately upon shock. Slowly permeable solutes, such as sucrose, which cross the membrane in minutes, cause plasmolysis to occur gradually as the chemical potential equilibrates. In addition, we quantify the detailed morphological changes to cell shape during osmotic shock. Nonplasmolyzed cells shrink in length with an additional lateral size reduction as the magnitude of the shock increases. Quickly plasmolyzing cells shrink largely at the poles, whereas gradually plasmolyzing cells invaginate along the cell cylinder. Our results give a comprehensive picture of the initial response of E. coli to hyperosmotic shock and offer explanations for seemingly opposing results that have been reported previously.

High hydrostatic pressure induces counterclockwise to clockwise reversals of the Escherichia coli flagellar motor

The bacterial flagellar motor is a reversible rotary machine that rotates a left-handed helical filament, allowing bacteria to swim toward a more favorable environment. The direction of rotation reverses from counterclockwise (CCW) to clockwise (CW), and vice versa, in response to input from the chemotaxis signaling circuit. CW rotation is normally caused by binding of the phosphorylated response regulator CheY (CheY-P), and strains lacking CheY are typically locked in CCW rotation. The detailed mechanism of switching remains unresolved because it is technically difficult to regulate the level of CheY-P within the concentration range that produces flagellar reversals. Here, we demonstrate that high hydrostatic pressure can induce CW rotation even in the absence of CheY-P. The rotation of single flagellar motors in Escherichia coli cells with the cheY gene deleted was monitored at various pressures and temperatures. Application of >120 MPa pressure induced a reversal from CCW to CW at 20°C, although at that temperature, no motor rotated CW at ambient pressure (0.1 MPa). At lower temperatures, pressure-induced changes in direction were observed at pressures of <120 MPa. CW rotation increased with pressure in a sigmoidal fashion, as it does in response to increasing concentrations of CheY-P. Application of pressure generally promotes the formation of clusters of ordered water molecules on the surfaces of proteins. It is possible that hydration of the switch complex at high pressure induces structural changes similar to those caused by the binding of CheY-P.

Fast, multiphase volume adaptation to hyperosmotic shock by Escherichia coli

All living cells employ an array of different mechanisms to help them survive changes in extra cellular osmotic pressure. The difference in the concentration of chemicals in a bacterium's cytoplasm and the external environment generates an osmotic pressure that inflates the cell. It is thought that the bacterium Escherichia coli use a number of interconnected systems to adapt to changes in external pressure, allowing them to maintain turgor and live in surroundings that range more than two-hundred-fold in external osmolality. Here, we use fluorescence imaging to make the first measurements of cell volume changes over time during hyperosmotic shock and subsequent adaptation on a single cell level in vivo with a time resolution on the order of seconds. We directly observe two previously unseen phases of the cytoplasmic water efflux upon hyperosmotic shock. Furthermore, we monitor cell volume changes during the post-shock recovery and observe a two-phase response that depends on the shock magnitude. The initial phase of recovery is fast, on the order of 15–20 min and shows little cell-to-cell variation. For large sucrose shocks, a secondary phase that lasts several hours adds to the recovery. We find that cells are able to recover fully from shocks as high as 1 Osmol/kg using existing systems, but that for larger shocks, protein synthesis is required for full recovery.

A method to track rotational motion for use in single-molecule biophysics

The double helical nature of DNA links many cellular processes such as DNA replication, transcription, and repair to rotational motion and the accumulation of torsional strain. Magnetic tweezers (MTs) are a single-molecule technique that enables the application of precisely calibrated stretching forces to nucleic acid tethers and to control their rotational motion. However, conventional magnetic tweezers do not directly monitor rotation or measure torque. Here, we describe a method to directly measure rotational motion of particles in MT. The method relies on attaching small, non-magnetic beads to the magnetic beads to act as fiducial markers for rotational tracking. CCD images of the beads are analyzed with a tracking algorithm specifically designed to minimize crosstalk between translational and rotational motion: first, the in-plane center position of the magnetic bead is determined with a kernel-based tracker, while subsequently the height and rotation angle of the bead are determined via correlation-based algorithms. Evaluation of the tracking algorithm using both simulated images and recorded images of surface-immobilized beads demonstrates a rotational resolution of 0.1°, while maintaining a translational resolution of 1-2 nm. Example traces of the rotational fluctuations exhibited by DNA-tethered beads confined in magnetic potentials of varying stiffness demonstrate the robustness of the method and the potential for simultaneous tracking of multiple beads. Our rotation tracking algorithm enables the extension of MTs to magnetic torque tweezers (MTT) to directly measure the torque in single molecules. In addition, we envision uses of the algorithm in a range of biophysical measurements, including further extensions of MT, tethered particle motion, and optical trapping measurements.

Soft magnetic tweezers: a proof of principle

We present here the principle of soft magnetic tweezers which improve the traditional magnetic tweezers allowing the simultaneous application and measurement of an arbitrary torque to a deoxyribonucleic acid (DNA) molecule. They take advantage of a nonlinear coupling regime that appears when a fast rotating magnetic field is applied to a superparamagnetic bead immersed in a viscous fluid. In this work, we present the development of the technique and we compare it with other techniques capable of measuring the torque applied to the DNA molecule. In this proof of principle, we use standard electromagnets to achieve our experiments. Despite technical difficulties related to the present implementation of these electromagnets, the agreement of measurements with previous experiments is remarkable. Finally, we propose a simple way to modify the experimental design of electromagnets that should bring the performances of the device to a competitive level.

Conformational spread as a mechanism for cooperativity in the bacterial flagellar switch

The bacterial flagellar switch that controls the direction of flagellar rotation during chemotaxis has a highly cooperative response. This has previously been understood in terms of the classic two-state, concerted model of allosteric regulation. Here, we used high-resolution optical microscopy to observe switching of single motors and uncover the stochastic multistate nature of the switch. Our observations are in detailed quantitative agreement with a recent general model of allosteric cooperativity that exhibits conformational spread--the stochastic growth and shrinkage of domains of adjacent subunits sharing a particular conformational state. We expect that conformational spread will be important in explaining cooperativity in other large signaling complexes.

Highly birefringent vaterite microspheres: production, characterization and applications for optical micromanipulation

This paper reports on a simple synthesis and characterization of highly birefringent vaterite microspheres, which are composed of 20-30 nm sized nanocrystalls. Scanning electron microscopy shows a quite disordered assembly of nanocrystals within the microspheres. However, using optical tweezers, the effective birefringence of the microspheres was measured to be Deltan = 0.06, which compares to Deltan = 0.1 of vaterite single crystals. This suggests a very high orientation of the nanocrystals within the microspheres. A hyperbolic model of the direction of the optical axis throughout the vaterite spherulite best fits the experimental data. Results from polarized light microscopy further confirm the hyperbolic model.

Single molecule measurements of F1-ATPase reveal an interdependence between the power stroke and the dwell duration

Increases in the power stroke and dwell durations of single molecules of Escherichia coli F(1)-ATPase were measured in response to viscous loads applied to the motor and inhibition of ATP hydrolysis. The load was varied using different sizes of gold nanorods attached to the rotating gamma subunit and/or by increasing the viscosity of the medium using PEG-400, a noncompetitive inhibitor of ATPase activity. Conditions that increase the duration of the power stroke were found to cause 20-fold increases in the length of the dwell. These results suggest that the order of hydrolysis, product release, and substrate binding may change as the result of external load on the motor or inhibition of hydrolysis.

A molecular brake, not a clutch, stops the Rhodobacter sphaeroides flagellar motor

Many bacterial species swim by employing ion-driven molecular motors that power the rotation of helical filaments. Signals are transmitted to the motor from the external environment via the chemotaxis pathway. In bidirectional motors, the binding of phosphorylated CheY (CheY-P) to the motor is presumed to instigate conformational changes that result in a different rotor-stator interface, resulting in rotation in the alternative direction. Controlling when this switch occurs enables bacteria to accumulate in areas favorable for their survival. Unlike most species that swim with bidirectional motors, Rhodobacter sphaeroides employs a single stop-start flagellar motor. Here, we asked, how does the binding of CheY-P stop the motor in R. sphaeroides--using a clutch or a brake? By applying external force with viscous flow or optical tweezers, we show that the R. sphaeroides motor is stopped using a brake. The motor stops at 27-28 discrete angles, locked in place by a relatively high torque, approximately 2-3 times its stall torque.

Three-axis rapid steering of optically propelled micro/nanoparticles

This paper presents the design and implementation of a three-axis steering system, wherein a micro/nanoparticle is optically trapped and propelled to serve as a measurement probe. The actuators in the system consist of a deformable mirror enabling axial steering and a two-axis acousto-optic deflector for lateral steering. The actuation range is designed and calibrated to be over 20 microm along the two lateral axes and over 10 microm along the axial direction. The actuation bandwidth of the two lateral axes is over 50 kHz and the associated resolution is 0.016 nm (1sigma). The axial resolution is 0.16 nm, while the bandwidth is enhanced to over 3 kHz by model cancellation method. The performance of the three-axis steering system is illustrated by three sets of experiments. First, active Brownian motion control of the trapped probe is utilized to enhance trapping stability. Second, a large range three-dimensional (3D) steering of a 1.87 microm probe, contouring a complex 3D trajectory in a 6 x 6 x 4 microm3 volume, is demonstrated. Third, a closed-loop steering is implemented to achieve improved precision.

Nonequivalence of membrane voltage and ion-gradient as driving forces for the bacterial flagellar motor at low load

Many bacterial species swim using flagella. The flagellar motor couples ion flow across the cytoplasmic membrane to rotation. Ion flow is driven by both a membrane potential (V(m)) and a transmembrane concentration gradient. To investigate their relation to bacterial flagellar motor function we developed a fluorescence technique to measure V(m) in single cells, using the dye tetramethyl rhodamine methyl ester. We used a convolution model to determine the relationship between fluorescence intensity in images of cells and intracellular dye concentration, and calculated V(m) using the ratio of intracellular/extracellular dye concentration. We found V(m) = -140 +/- 14 mV in Escherichia coli at external pH 7.0 (pH(ex)), decreasing to -85 +/- 10 mV at pH(ex) 5.0. We also estimated the sodium-motive force (SMF) by combining single-cell measurements of V(m) and intracellular sodium concentration. We were able to vary the SMF between -187 +/- 15 mV and -53 +/- 15 mV by varying pH(ex) in the range 7.0-5.0 and extracellular sodium concentration in the range 1-85 mM. Rotation rates for 0.35-microm- and 1-microm-diameter beads attached to Na(+)-driven chimeric flagellar motors varied linearly with V(m). For the larger beads, the two components of the SMF were equivalent, whereas for smaller beads at a given SMF, the speed increased with sodium gradient and external sodium concentration.