Quantifying gliding forces of filamentous cyanobacteria by self-buckling.

Filamentous cyanobacteria are one of the oldest and today still most abundant lifeforms on earth, with manifold implications in ecology and economics. Their flexible filaments, often several hundred cells long, exhibit gliding motility in contact with solid surfaces. The underlying force generating mechanism is not yet understood. Here, we demonstrate that propulsion forces and friction coefficients are strongly coupled in the gliding motility of filamentous cyanobacteria. We directly measure their bending moduli using micropipette force sensors, and quantify propulsion and friction forces by analyzing their self-buckling behavior, complemented with analytical theory and simulations. The results indicate that slime extrusion unlikely generates the gliding forces, but support adhesion-based hypotheses, similar to the better-studied single-celled myxobacteria. The critical self-buckling lengths align well with the peaks of natural length distributions, indicating the importance of self-buckling for the organization of their collective in natural and artificial settings.

The motility-matrix production switch in Bacillus subtilis-a modeling perspective.

Phenotype switching can be triggered by external stimuli and by intrinsic stochasticity. Here, we focus on the motility-matrix production switch in Bacillus subtilis. We use modeling to describe the SinR-SlrR bistable switch and its regulation by SinI and to distinguish different sources of stochasticity. Our simulations indicate that intrinsic fluctuations in the synthesis of SinI are insufficient to drive spontaneous switching and suggest that switching is triggered by upstream noise from the Spo0A phosphorelay. IMPORTANCE The switch from motility to matrix production is the first step toward biofilm formation and, thus, to multicellular behavior in Bacillus subtilis. The transition is governed by a bistable switch based on the interplay of the regulators SinR and SlrR, while SinI transmits upstream signals to that switch. Quantitative modeling can be used to study the switching dynamics. Here, we build such a model step by step to describe the dynamics of the switch and its regulation and to study how spontaneous switching is triggered by upstream noise from the Spo0A phosphorelay.

Keratin filament mechanics and energy dissipation are determined by metal-like plasticity.

Cell mechanics are determined by an intracellular biopolymer network, including intermediate filaments that are expressed in a cell-type-specific manner. A prominent pair of intermediate filaments are keratin and vimentin, as they are expressed by non-motile and motile cells, respectively. Therefore, the differential expression of these proteins coincides with a change in cellular mechanics and dynamic properties of the cells. This observation raises the question of how the mechanical properties already differ on the single filament level. Here, we use optical tweezers and a computational model to compare the stretching and dissipation behavior of the two filament types. We find that keratin and vimentin filaments behave in opposite ways: keratin filaments elongate but retain their stiffness, whereas vimentin filaments soften but retain their length. This finding is explained by fundamentally different ways to dissipate energy: viscous sliding of subunits within keratin filaments and non-equilibrium α helix unfolding in vimentin filaments.

Tug-of-War and Coordination in Bidirectional Transport by Molecular Motors.

Many cargoes in cells are transported in a bidirectional fashion by molecular motors pulling into opposite directions along a cytoskeletal filament, e.g., by kinesins and dyneins along microtubules. How opposite-polarity motors are coordinated has been under debate for a long time, with experimental evidence supporting both a tug-of-war between the motors as well as biochemical coordination mechanisms. Here we propose a model that extends a tug-of-war model by a mechanism of motor activation and inactivation and show that this model can explain some observations that are incompatible with a simple tug-of-war scenario, specifically long unidirectional runs and a directional memory after unbinding from the filament. Both features are present in two variants of the model in which motors are activated and inactivated individually and in opposite-direction pairs, respectively.

Interplay of surface interaction and magnetic torque in single-cell motion of magnetotactic bacteria in microfluidic confinement.

Swimming microorganisms often experience complex environments in their natural habitat. The same is true for microswimmers in envisioned biomedical applications. The simple aqueous conditions typically studied in the lab differ strongly from those found in these environments and often exclude the effects of small volume confinement or the influence that external fields have on their motion. In this work, we investigate magnetically steerable microswimmers, specifically magnetotactic bacteria, in strong spatial confinement and under the influence of an external magnetic field. We trap single cells in micrometer-sized microfluidic chambers and track and analyze their motion, which shows a variety of different trajectories, depending on the chamber size and the strength of the magnetic field. Combining these experimental observations with simulations using a variant of an active Brownian particle model, we explain the variety of trajectories by the interplay between the wall interactions and the magnetic torque. We also analyze the pronounced cell-to-cell heterogeneity, which makes single-cell tracking essential for an understanding of the motility patterns. In this way, our work establishes a basis for the analysis and prediction of microswimmer motility in more complex environments.

Role of bacterial persistence in spatial population expansion.

Bacterial persistence, tolerance to antibiotics via stochastic phenotype switching, provides a survival strategy and a fitness advantage in temporally fluctuating environments. Here we study its possible benefit in spatially varying environments using a Fisher wave approach. We study the spatial expansion of a population with stochastic switching between two phenotypes in spatially homogeneous conditions and in the presence of an antibiotic barrier. Our analytical results show that the expansion speed in growth-supporting conditions depends on the fraction of persister cells at the leading edge of the population wave. The leading edge contains a small fraction of persister cells, keeping the effect on the expansion speed minimal. The fraction of persisters increases gradually in the interior of the wave. This persister pool benefits the population when it is stalled by an antibiotic environment. In that case, the presence of persister enables the population to spread deeper into the antibiotic region and to cross an antibiotic region more rapidly. Further we observe that optimal switching rates maximize the expansion speed of the population in spatially varying environments with alternating regions of growth permitting conditions and antibiotics. Overall, our results show that stochastic switching can promote population expansion in the presence of antibiotic barriers or other stressful environments.

Quasi-essentiality of RNase Y in Bacillus subtilis is caused by its critical role in the control of mRNA homeostasis.

RNA turnover is essential in all domains of life. The endonuclease RNase Y (rny) is one of the key components involved in RNA metabolism of the model organism Bacillus subtilis. Essentiality of RNase Y has been a matter of discussion, since deletion of the rny gene is possible, but leads to severe phenotypic effects. In this work, we demonstrate that the rny mutant strain rapidly evolves suppressor mutations to at least partially alleviate these defects. All suppressor mutants had acquired a duplication of an about 60 kb long genomic region encompassing genes for all three core subunits of the RNA polymerase-α, ß, ß'. When the duplication of the RNA polymerase genes was prevented by relocation of the rpoA gene in the B. subtilis genome, all suppressor mutants carried distinct single point mutations in evolutionary conserved regions of genes coding either for the ß or ß' subunits of the RNA polymerase that were not tolerated by wild type bacteria. In vitro transcription assays with the mutated polymerase variants showed a severe decrease in transcription efficiency. Altogether, our results suggest a tight cooperation between RNase Y and the RNA polymerase to establish an optimal RNA homeostasis in B. subtilis cells.

Enhanced diffusion of a tracer particle in a lattice model of a crowded active system.

Living systems at the subcellular, cellular, and multicellular levels are often crowded systems that contain active particles. The active motion of these particles can also propel passive particles, which typically results in enhanced effective diffusion of the passive particles. Here we study the diffusion of a passive tracer particle in such a dense system of active crowders using a minimal lattice model incorporating particles pushing each other. We show that the model exhibits several regimes of motility and quantify the enhanced diffusion as a function of density and activity of the active crowders. Moreover, we demonstrate an interplay of tracer diffusion and clustering of active particles, which suppresses the enhanced diffusion. Simulations of mixtures of passive and active crowders show that a rather small fraction of active particles is sufficient for the observation of enhanced diffusion.

Vimentin intermediate filaments stabilize dynamic microtubules by direct interactions.

The cytoskeleton determines cell mechanics and lies at the heart of important cellular functions. Growing evidence suggests that the manifold tasks of the cytoskeleton rely on the interactions between its filamentous components-actin filaments, intermediate filaments, and microtubules. However, the nature of these interactions and their impact on cytoskeletal dynamics are largely unknown. Here, we show in a reconstituted in vitro system that vimentin intermediate filaments stabilize microtubules against depolymerization and support microtubule rescue. To understand these stabilizing effects, we directly measure the interaction forces between individual microtubules and vimentin filaments. Combined with numerical simulations, our observations provide detailed insight into the physical nature of the interactions and how they affect microtubule dynamics. Thus, we describe an additional, direct mechanism by which cells establish the fundamental cross talk of cytoskeletal components alongside linker proteins. Moreover, we suggest a strategy to estimate the binding energy of tubulin dimers within the microtubule lattice.

Multiscale mechanics and temporal evolution of vimentin intermediate filament networks.

The cytoskeleton, an intricate network of protein filaments, motor proteins, and cross-linkers, largely determines the mechanical properties of cells. Among the three filamentous components, F-actin, microtubules, and intermediate filaments (IFs), the IF network is by far the most extensible and resilient to stress. We present a multiscale approach to disentangle the three main contributions to vimentin IF network mechanics-single-filament mechanics, filament length, and interactions between filaments-including their temporal evolution. Combining particle tracking, quadruple optical trapping, and computational modeling, we derive quantitative information on the strength and kinetics of filament interactions. Specifically, we find that hydrophobic contributions to network mechanics enter mostly via filament-elongation kinetics, whereas electrostatics have a direct influence on filament-filament interactions.

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.

Simulations of structure formation by confined dipolar active particles.

Dipolar active particles describe a class of self-propelled, biological or artificial particles equipped with an internal (typically magnetic) dipole moment. Because of the interplay between self-propulsion and dipole-dipole interactions, complex collective behavior is expected to emerge in systems of such particles. Here, we use Brownian dynamics simulations to explore this collective behavior. We focus on the structures that form in small systems in spatial confinement. We quantify the type of structures that emerge and how they depend on the self-propulsion speed and the dipolar (magnetic) strength of the particles. We observe that the dipolar active particles self-assemble into chains and rings. The dominant configuration is quantified with an order parameter for chain and ring formation and shown to depend on the self-propulsion speed and the dipolar magnetic strength of the particles. In addition, we show that the structural configurations are also affected by the confining walls. To that end, we compare different confining geometries and study the impact of a reorienting 'wall torque' upon collisions of a particle with a wall. Our results indicate that dipolar interactions can further enhance the already rich variety of collective behaviors of active particles.

High-speed motility originates from cooperatively pushing and pulling flagella bundles in bilophotrichous bacteria.

Bacteria propel and change direction by rotating long, helical filaments, called flagella. The number of flagella, their arrangement on the cell body and their sense of rotation hypothetically determine the locomotion characteristics of a species. The movement of the most rapid microorganisms has in particular remained unexplored because of additional experimental limitations. We show that magnetotactic cocci with two flagella bundles on one pole swim faster than 500 µm·s-1 along a double helical path, making them one of the fastest natural microswimmers. We additionally reveal that the cells reorient in less than 5 ms, an order of magnitude faster than reported so far for any other bacteria. Using hydrodynamic modeling, we demonstrate that a mode where a pushing and a pulling bundle cooperate is the only possibility to enable both helical tracks and fast reorientations. The advantage of sheathed flagella bundles is the high rigidity, making high swimming speeds possible.

Coarse graining of biochemical systems described by discrete stochastic dynamics.

Many biological systems can be described by finite Markov models. A general method for simplifying master equations is presented that is based on merging adjacent states. The approach preserves the steady-state probability distribution and all steady-state fluxes except the one between the merged states. Different levels of coarse graining of the underlying microscopic dynamics can be obtained by iteration, with the result being independent of the order in which states are merged. A criterion for the optimal level of coarse graining or resolution of the process is proposed via a tradeoff between the simplicity of the coarse-grained model and the information loss relative to the original model. As a case study, the method is applied to the cycle kinetics of the molecular motor kinesin.

Chemotaxis in external fields: Simulations for active magnetic biological matter.

The movement of microswimmers is often described by active Brownian particle models. Here we introduce a variant of these models with several internal states of the swimmer to describe stochastic strategies for directional swimming such as run and tumble or run and reverse that are used by microorganisms for chemotaxis. The model includes a mechanism to generate a directional bias for chemotaxis and interactions with external fields (e.g., gravity, magnetic field, fluid flow) that impose forces or torques on the swimmer. We show how this modified model can be applied to various scenarios: First, the run and tumble motion of E. coli is used to establish a paradigm for chemotaxis and investigate how it is affected by external forces. Then, we study magneto-aerotaxis in magnetotactic bacteria, which is biased not only by an oxygen gradient towards a preferred concentration, but also by magnetic fields, which exert a torque on an intracellular chain of magnets. We study the competition of magnetic alignment with active reorientation and show that the magnetic orientation can improve chemotaxis and thereby provide an advantage to the bacteria, even at rather large inclination angles of the magnetic field relative to the oxygen gradient, a case reminiscent of what is expected for the bacteria at or close to the equator. The highest gain in chemotactic velocity is obtained for run and tumble with a magnetic field parallel to the gradient, but in general a mechanism for reverse motion is necessary to swim against the magnetic field and a run and reverse strategy is more advantageous in the presence of a magnetic torque. This finding is consistent with observations that the dominant mode of directional changes in magnetotactic bacteria is reversal rather than tumbles. Moreover, it provides guidance for the design of future magnetic biohybrid swimmers.

On Protein Folding in Crowded Conditions.

The interior of a cell is a highly packed environment that can be occupied up to 40% by different macromolecules. Such crowded media influence different biochemical processes like protein folding, enzymatic activity, and gene regulation. In this work, we use simulations to study protein stability under the presence of crowding agents that interact with the protein by excluded volume interactions. In general, the presence of crowding agents in the solution enhances the stability of the protein's native state. However, we find that the effects of excluded volume depend not only on crowding occupancy but also the crowders' geometry and size. Specifically, we find that polymeric crowders have stronger influence than spherical crowders and that this effect increases with polymer length, while it decreases with increasing size of spherical crowders. These opposing size effects are explained by the interplay of decreasing excluded volume and demixing, which together determine the change in the entropy of the crowders upon folding of the protein.

Lateral Subunit Coupling Determines Intermediate Filament Mechanics.

The cytoskeleton is a composite network of three types of protein filaments, among which intermediate filaments (IFs) are the most extensible ones. Two very important IFs are keratin and vimentin, which have similar molecular architectures but different mechanical behaviors. Here we compare the mechanical response of single keratin and vimentin filaments using optical tweezers. We show that the mechanics of vimentin strongly depends on the ionic strength of the buffer and that its force-strain curve suggests a high degree of cooperativity between subunits. Indeed, a computational model indicates that in contrast to keratin, vimentin is characterized by strong lateral subunit coupling of its charged monomers during unfolding of α helices. We conclude that cells can tune their mechanics by differential use of keratin versus vimentin.

Decoding Biomineralization: Interaction of a Mad10-Derived Peptide with Magnetite Thin Films.

Protein-surface interactions play a pivotal role in processes as diverse as biomineralization, biofouling, and the cellular response to medical implants. In biomineralization processes, biomacromolecules control mineral deposition and architecture via complex and often unknown mechanisms. For studying these mechanisms, the formation of magnetite nanoparticles in magnetotactic bacteria has become an excellent model system. Most interestingly, nanoparticle morphologies have been discovered that defy crystallographic rules (e.g., in the species Desulfamplus magnetovallimortis strain BW-1). In certain conditions, this strain mineralizes bullet-shaped magnetite nanoparticles, which exhibit defined (111) crystal faces and are elongated along the [100] direction. We hypothesize that surface-specific protein interactions break the nanoparticle symmetry, inhibiting the growth of certain crystal faces and thereby favoring the growth of others. Screening the genome of BW-1, we identified Mad10 (Magnetosome-associated deep-branching) as a potential magnetite-binding protein. Using atomic force microscope (AFM)-based single-molecule force spectroscopy, we show that a Mad10-derived peptide, which represents the most conserved region of Mad10, binds strongly to (100)- and (111)-oriented single-crystalline magnetite thin films. The peptide-magnetite interaction is thus material- but not crystal-face-specific. It is characterized by broad rupture force distributions that do not depend on the retraction speed of the AFM cantilever. To account for these experimental findings, we introduce a three-state model that incorporates fast rebinding. The model suggests that the peptide-surface interaction is strong in the absence of load, which is a direct result of this fast rebinding process. Overall, our study sheds light on the kinetic nature of peptide-surface interactions and introduces a new magnetite-binding peptide with potential use as a functional coating for magnetite nanoparticles in biotechnological and biomedical applications.

Is F1-ATPase a Rotary Motor with Nearly 100% Efficiency? Quantitative Analysis of Chemomechanical Coupling and Mechanical Slip.

We present a chemomechanical network model of the rotary molecular motor F1-ATPase which quantitatively describes not only the rotary motor dynamics driven by ATP hydrolysis but also the ATP synthesis caused by forced reverse rotations. We observe a high reversibility of F1-ATPase, that is, the main cycle of ATP synthesis corresponds to the reversal of the main cycle in the hydrolysis-driven motor rotation. However, our quantitative analysis indicates that torque-induced mechanical slip without chemomechanical coupling occurs under high external torque and reduces the maximal efficiency of the free energy transduction to 40-80% below the optimal efficiency. Heat irreversibly dissipates not only through the viscous friction of the probe but also directly from the motor due to torque-induced mechanical slip. Such irreversible heat dissipation is a crucial limitation for achieving a 100% free-energy transduction efficiency with biological nanomachines because biomolecules are easily deformed by external torque.