Switching of Swimming Modes in Magnetospirillium gryphiswaldense

Controlling Confined Collective Organization with Taxis

Biased locomotion is a common feature of microorganisms, but little is known about its impact on self-organization. Inspired by recent experiments showing a transition to large-scale flows, we study theoretically the dynamics of magnetotactic bacteria confined to a drop. We reveal two symmetry-breaking mechanisms (one local chiral and one global achiral) leading to self-organization into global vortices and a net torque exerted on the drop. The collective behavior is ultimately controlled by the swimmers' microscopic chirality and, strikingly, the system can exhibit oscillations and memorylike features.

Differential dynamic microscopy for the characterisation of motility in biological systems

Differential Dynamic Microscopy (DDM) is a relatively new technique which measures the dynamics of suspended particles using a dynamic light scattering formalism. Videos are recorded using standard light microscopy at moderate frame rates, and fluctuations in pixel intensity are measured as a function of time. As only pixel intensity is analysed, it is not necessary to resolve individual particles. This allows for low magnifications and wide fields of view, and therefore dynamics can be measured on tens of thousands of scattering objects, providing robust statistics. A decade ago the technique was successfully applied to measure bacterial motility. Since then, it has been applied to a range of motile systems, but has not yet reached the wider biological community. This perspective reviews the work done so far, and provides the basic background to enable the broader application of this promising technique.

Experimental determination of the propulsion matrix of the body of helical Magnetospirillum magneticum cells

Helical-shaped magnetotactic bacteria provide a rare opportunity to precisely measure both the translational and rotational friction coefficients of micron-sized chiral particles. The possibility to align these cells with a uniform magnetic field allows clearly separating diffusion along and perpendicular to their longitudinal axis. Meanwhile, their corkscrew shape allows detecting rotations around their longitudinal axis, after which orientation correlation analysis can be used to retrieve rotational diffusion coefficients in the two principal directions. Using light microscopy, we measured the four principal friction coefficients of deflagellated Magnetospirillum magneticum cells, and compared our results to that expected for cylinders of comparable size. We show that for rotational motions, the overall dimensions of the cell body are what matters most, while the exact body shape has a larger influence on translational motions. To obtain a full characterization of the friction matrix of these elongated chiral particles, we also quantified the coupling between the rotation around and translation along the longitudinal axis of the cell. Our results suggest that for this bacterial species cell body rotation could significantly contribute to cellular propulsion.

Swimming behavior of the multicellular magnetotactic prokaryote 'Candidatus Magnetoglobus multicellularis' near solid boundaries and natural magnetic grains

The magnetotactic yet uncultured species 'Candidatus Magnetoglobus multicellularis' is a spherical, multicellular ensemble of bacterial cells able to align along magnetic field lines while swimming propelled by flagella. Magnetotaxis is due to intracytoplasmic, membrane-bound magnetic crystals called magnetosomes. The net magnetic moment of magnetosomes interacts with local magnetic fields, imparting the whole microorganism a torque. Previous works investigated 'Ca. M. multicellularis' behavior when free swimming in water; however, they occur in sediments where bumping into solid particles must be routine. In this work, we investigate the swimming trajectories of 'Ca. M. multicellularis' close to solid boundaries using video microscopy. We applied magnetic fields 0.25-8.0 mT parallel to the optical axis of a light microscope, such that microorganisms were driven upwards towards a coverslip. Because their swimming trajectories approach cylindrical helixes, circular profiles would be expected. Nevertheless, at fields 0.25-1.1 mT, most trajectory projections were roughly sinusoidal, and net movements were approximately perpendicular to applied magnetic fields. Closed loops appeared in some trajectory projections at 1.1 mT, which could indicate a transition to the loopy profiles observed at magnetic fields ≥ 2.15 mT. The behavior of 'Ca. M. multicellularis' near natural magnetic grains showed that they were temporarily trapped by the particle's magnetic field but could reverse the direction of movement to flee away. Our results show that interactions of 'Ca. M. multicellularis with solid boundaries and magnetic grains are complex and possibly involve mechano-taxis.

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.

Stokesian dynamics simulations of a magnetotactic bacterium

The swimming of bacteria provides insight into propulsion and steering under the conditions of low-Reynolds number hydrodynamics. Here we address the magnetically steered swimming of magnetotactic bacteria. We use Stokesian dynamics simulations to study the swimming of single-flagellated magnetotactic bacteria (MTB) in an external magnetic field. Our model MTB consists of a spherical cell body equipped with a magnetic dipole moment and a helical flagellum rotated by a rotary motor. The elasticity of the flagellum as well as magnetic and hydrodynamic interactions is taken into account in this model. We characterized how the swimming velocity is dependent on parameters of the model. We then studied the U-turn motion after a field reversal and found two regimes for weak and strong fields and, correspondingly, two characteristic time scales. In the two regimes, the U-turn time is dominated by the turning of the cell body and its magnetic moment or the turning of the flagellum, respectively. In the regime for weak fields, where turning is dominated by the magnetic relaxation, the U-turn time is approximately in agreement with a theoretical model based on torque balance. In the strong-field regime, strong deformations of the flagellum are observed. We further simulated the swimming of a bacterium with a magnetic moment that is inclined relative to the flagellar axis. This scenario leads to intriguing double helical trajectories that we characterize as functions of the magnetic moment inclination and the magnetic field. For small inclination angles ([Formula: see text]) and typical field strengths, the inclination of the magnetic moment has only a minor effect on the swimming of MTB in an external magnetic field. Large inclination angles result in a strong reduction in the velocity in direction of the magnetic field, consistent with recent observations that bacteria with large inclination angles use a different propulsion mechanism.

Intrinsically Magnetic Cells: A Review on Their Natural Occurrence and Synthetic Generation

The magnetization of non-magnetic cells has great potential to aid various processes in medicine, but also in bioprocess engineering. Current approaches to magnetize cells with magnetic nanoparticles (MNPs) require cellular uptake or adsorption through in vitro manipulation of cells. A relatively new field of research is "magnetogenetics" which focuses on in vivo production and accumulation of magnetic material. Natural intrinsically magnetic cells (IMCs) produce intracellular, MNPs, and are called magnetotactic bacteria (MTB). In recent years, researchers have unraveled function and structure of numerous proteins from MTB. Furthermore, protein engineering studies on such MTB proteins and other potentially magnetic proteins, like ferritins, highlight that in vivo magnetization of non-magnetic hosts is a thriving field of research. This review summarizes current knowledge on recombinant IMC generation and highlights future steps that can be taken to succeed in transforming non-magnetic cells to IMCs.

A Compass To Boost Navigation: Cell Biology of Bacterial Magnetotaxis

Magnetotactic bacteria are aquatic or sediment-dwelling microorganisms able to take advantage of the Earth's magnetic field for directed motility. The source of this amazing trait is magnetosomes, unique organelles used to synthesize single nanometer-sized crystals of magnetic iron minerals that are queued up to build an intracellular compass. Most of these microorganisms cannot be cultivated under controlled conditions, much less genetically engineered, with only few exceptions. However, two of the genetically amenable Magnetospirillum species have emerged as tractable model organisms to study magnetosome formation and magnetotaxis. Recently, much has been revealed about the process of magnetosome biogenesis and dedicated structures for magnetosome dynamics and positioning, which suggest an unexpected cellular intricacy of these organisms. In this minireview, we summarize new insights and place the molecular mechanisms of magnetosome formation in the context of the complex cell biology of Magnetospirillum spp. First, we provide an overview on magnetosome vesicle synthesis and magnetite biomineralization, followed by a discussion of the perceptions of dynamic organelle positioning and its biological implications, which highlight that magnetotactic bacteria have evolved sophisticated mechanisms to construct, incorporate, and inherit a unique navigational device. Finally, we discuss the impact of magnetotaxis on motility and its interconnection with chemotaxis, showing that magnetotactic bacteria are outstandingly adapted to lifestyle and habitat.

Quantifying the Benefit of a Dedicated "Magnetoskeleton" in Bacterial Magnetotaxis by Live-Cell Motility Tracking and Soft Agar Swimming Assay

The alphaproteobacterium Magnetospirillum gryphiswaldense has the intriguing ability to navigate within magnetic fields, a behavior named magnetotaxis, governed by the formation of magnetosomes, intracellular membrane-enveloped crystals of magnetite. Magnetosomes are aligned in chains along the cell's motility axis by a dedicated multipart cytoskeleton ("magnetoskeleton"); however, precise estimates of its significance for magnetotaxis have not been reported. Here, we estimated the alignment of strains deficient in various magnetoskeletal constituents by live-cell motility tracking within defined magnetic fields ranging from 50 μT (reflecting the geomagnetic field) up to 400 μT. Motility tracking revealed that ΔmamY and ΔmamK strains (which assemble mispositioned and fragmented chains, respectively) are partially impaired in magnetotaxis, with approximately equal contributions of both proteins. This impairment was reflected by a required magnetic field strength of 200 μT to achieve a similar degree of alignment as for the wild-type strain in a 50-μT magnetic field. In contrast, the ΔmamJ strain, which predominantly forms clusters of magnetosomes, was only weakly aligned under any of the tested field conditions and could barely be distinguished from a nonmagnetic mutant. Most findings were corroborated by a soft agar swimming assay to analyze magnetotaxis based on the degree of distortion of swim halos formed in magnetic fields. Motility tracking further revealed that swimming speeds of M. gryphiswaldense are highest within the field strength equaling the geomagnetic field. In conclusion, magnetic properties and intracellular positioning of magnetosomes by a dedicated magnetoskeleton are required and optimized for bacterial magnetotaxis and most efficient locomotion within the geomagnetic field.IMPORTANCE In Magnetospirillum gryphiswaldense, magnetosomes are aligned in quasi-linear chains in a helical cell by a complex cytoskeletal network, including the actin-like MamK and adapter MamJ for magnetosome chain concatenation and segregation and MamY to position magnetosome chains along the shortest cellular axis of motility. Magnetosome chain positioning is assumed to be required for efficient magnetic navigation; however, the significance and contribution of all key constituents have not been quantified within defined and weak magnetic fields reflecting the geomagnetic field. Employing two different motility-based methods to consider the flagellum-mediated propulsion of cells, we depict individual benefits of all magnetoskeletal constituents for magnetotaxis. Whereas lack of mamJ resulted almost in an inability to align cells in weak magnetic fields, an approximately 4-fold-increased magnetic field strength was required to compensate for the loss of mamK or mamY In summary, the magnetoskeleton and optimal positioning of magnetosome chains are required for efficient magnetotaxis.

Long-term observation of Magnetospirillum gryphiswaldense in a microfluidic channel

We controlled and observed individual magneto-tactic bacteria (Magnetospirillum gryphiswaldense) inside a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$5\, \upmu \hbox {m}$$\end{document}5μm-high microfluidic channel for over 4 h. After a period of constant velocity, the duration of which varied between bacteria, all observed bacteria showed a gradual decrease in their velocity of about \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$25\, \hbox {nm}/\hbox {s}^2$$\end{document}25nm/s2. After coming to a full stop, different behaviour was observed, ranging from rotation around the centre of mass synchronous with the direction of the external magnetic field, to being completely immobile. Our results suggest that the influence of the high-intensity illumination and the presence of the channel walls are important parameters to consider when performing observations of such long duration.

Magnetotactic Bacteria Powered Biohybrids Target E. coli Biofilms

Biofilm colonies are typically resistant to general antibiotic treatment and require targeted methods for their removal. One of these methods includes the use of nanoparticles as carriers for antibiotic delivery, where they randomly circulate in fluid until they make contact with the infected areas. However, the required proximity of the particles to the biofilm results in only moderate efficacy. We demonstrate here that the nonpathogenic magnetotactic bacteria Magnetosopirrillum gryphiswalense (MSR-1) can be integrated with drug-loaded mesoporous silica microtubes to build controllable microswimmers (biohybrids) capable of antibiotic delivery to target an infectious biofilm. Applying external magnetic guidance capability and swimming power of the MSR-1 cells, the biohybrids are directed to and forcefully pushed into matured Escherichia coli (E. coli) biofilms. Release of the antibiotic, ciprofloxacin, is triggered by the acidic microenvironment of the biofilm, ensuring an efficient drug delivery system. The results reveal the capabilities of a nonpathogenic bacteria species to target and dismantle harmful biofilms, indicating biohybrid systems have great potential for antibiofilm applications.

Investigation of moderately turbid suspensions by heterodyne near field scattering

Light scattering has proven to be a very powerful technique to characterize soft matter systems. However, many samples are turbid and hence suffer from multiple scattering which can affect the signal considerably. Multiple scattering can be reduced by diluting the sample or changing the solvent, but often this alters the sample and hence is precluded. Here we study the dynamics of a model system. In particular, we investigate the effects of moderate multiple scattering on small-angle heterodyne near field scattering (HNFS). Varying the particle concentration and size we change the degree of multiple scattering, which is quantified by the transmission of light. In dependence of the degree of multiple scattering, we analyze the statistical properties of the HNFS signal, which is the difference between two intensity patterns separated by a delay time. The distribution of intensity differences follows a Gaussian distribution if single scattering dominates and a Laplace distribution in the presence of extreme multiple scattering. We also investigate the effects of multiple scattering on the measured intermediate scattering function and the hydrodynamic radius of the particles. Reliable data are obtained for sample transmissions down to about 0.7. This is confirmed by a comparison with results from a far field cross-correlation instrument that suppresses multiple scattering contributions. Therefore, HNFS represents a technically simple but powerful method to investigate samples that are moderately multiple scattering.

Measurement of the magnetic moment of single Magnetospirillum gryphiswaldense cells by magnetic tweezers

Magnetospirillum gryphiswaldense is a helix-shaped magnetotactic bacterium that synthesizes iron-oxide nanocrystals, which allow navigation along the geomagnetic field. The bacterium has already been thoroughly investigated at the molecular and cellular levels. However, the fundamental physical property enabling it to perform magnetotaxis, its magnetic moment, remains to be elucidated at the single cell level. We present a method based on magnetic tweezers; in combination with Stokesian dynamics and Boundary Integral Method calculations, this method allows the simultaneous measurement of the magnetic moments of multiple single bacteria. The method is demonstrated by quantifying the distribution of the individual magnetic moments of several hundred cells of M. gryphiswaldense. In contrast to other techniques for measuring the average magnetic moment of bacterial populations, our method accounts for the size and the helical shape of each individual cell. In addition, we determined the distribution of the saturation magnetic moments of the bacteria from electron microscopy data. Our results are in agreement with the known relative magnetization behavior of the bacteria. Our method can be combined with single cell imaging techniques and thus can address novel questions about the functions of components of the molecular magnetosome biosynthesis machinery and their correlation with the resulting magnetic moment.

Inferring the Chemotactic Strategy of P. putida and E. coli Using Modified Kramers-Moyal Coefficients

Many bacteria perform a run-and-tumble random walk to explore their surrounding and to perform chemotaxis. In this article we present a novel method to infer the relevant parameters of bacterial motion from experimental trajectories including the tumbling events. We introduce a stochastic model for the orientation angle, where a shot-noise process initiates tumbles, and analytically calculate conditional moments, reminiscent of Kramers-Moyal coefficients. Matching them with the moments calculated from experimental trajectories of the bacteria E. coli and Pseudomonas putida, we are able to infer their respective tumble rates, the rotational diffusion constants, and the distributions of tumble angles in good agreement with results from conventional tumble recognizers. We also define a novel tumble recognizer, which explicitly quantifies the error in recognizing tumbles. In the presence of a chemical gradient we condition the moments on the bacterial direction of motion and thereby explore the chemotaxis strategy. For both bacteria we recover and quantify the classical chemotactic strategy, where the tumble rate is smallest along the chemical gradient. In addition, for E. coli we detect some cells, which bias their mean tumble angle towards smaller values. Our findings are supported by a scaling analysis of appropriate ratios of conditional moments, which are directly calculated from experimental data.

The movement strategies of bacteria have received increasing attention over the past decade, in particular with respect to the tracking of individual cells and the mathematical description of the resulting trajectories. Bacteria typically move in almost straight runs interrupted by sharp turning events (run-and-tumble). In order to characterize their motion on a single cell level, the tumble events in individual trajectories have to be identified. Traditionally, tumble recognition relies on threshold values that are applied to the swimming speed and the reorientation angle. They are chosen in an ad hoc fashion and introduce a certain degree of arbitrariness to the results of statistical motion analyses. Here, we propose a new stochastic model for the orientation angle of a bacterium and formulate conditonal moments, which we determine both in theory and from experimental trajectories. This provides an alternative way of quantifying the bacterial run-and-tumble strategy and of recognizing tumble events. Our approach no longer relies on arbitrarily chosen segmentation thresholds and rigorously quantifies the uncertainty in tumble recognition. We successfully apply our method not only to the paradigmatic case of E. coli but also to trajectories of the soil bacterium Pseudomonas putida, demonstrating that our approach provides a novel way to reliably characterize the tumbling statistics and chemotaxis strategies of bacterial swimmers across different species.

Differential dynamic microscopy of weakly scattering and polydisperse protein-rich clusters

Nanoparticle dynamics impact a wide range of biological transport processes and applications in nanomedicine and natural resource engineering. Differential dynamic microscopy (DDM) was recently developed to quantify the dynamics of submicron particles in solutions from fluctuations of intensity in optical micrographs. Differential dynamic microscopy is well established for monodisperse particle populations, but has not been applied to solutions containing weakly scattering polydisperse biological nanoparticles. Here we use bright-field DDM (BDDM) to measure the dynamics of protein-rich liquid clusters, whose size ranges from tens to hundreds of nanometers and whose total volume fraction is less than 10(-5). With solutions of two proteins, hemoglobin A and lysozyme, we evaluate the cluster diffusion coefficients from the dependence of the diffusive relaxation time on the scattering wave vector. We establish that for weakly scattering populations, an optimal thickness of the sample chamber exists at which the BDDM signal is maximized at the smallest sample volume. The average cluster diffusion coefficient measured using BDDM is consistently lower than that obtained from dynamic light scattering at a scattering angle of 90°. This apparent discrepancy is due to Mie scattering from the polydisperse cluster population, in which larger clusters preferentially scatter more light in the forward direction.