Mechanics of torque generation in the bacterial flagellar motor

Insertion of a Divergent GAF-like Domain Defines a Novel Family of YcgR Homologues That Bind c-di-GMP in Leptospirales

The Leptospiraceae family, which includes the genera Leptospira, Leptonema, and Turneriella, is an ecologically diverse group that includes saprophytic strains from soil and water as well as important pathogenic strains. Adaptation to these multiple environments relies strongly on signal transduction to adjust their morphology, motility, and metabolism to the changing environmental conditions. Members of the genus Leptospira distinguish themselves among spirochetes for having an elevated number of signal transduction genes. In this study, we describe a novel signal transduction protein that has gained multiple paralogues in the Leptospiraceae. These proteins are members of the YcgR/DgrA/MotI family, whose orthologs in several bacterial lineages have been shown to regulate the flagellar motor upon binding to c-di-GMP through their N-terminal PilZ domain. Unlike previously described versions of YcgR, the spirochetal proteins are characterized by the insertion of a divergent GAF domain within their N-terminal PilZ domain. We show that one member of this protein family from Leptospira interrogans is still a monomeric c-di-GMP binding protein and that these novel YcgR-like proteins have mostly replaced other members of the YcgR family in Leptospiraceae. Marked divergence among the paralogs suggests this family's expansion was accompanied by neofunctionalization, with the likely emergence of novel interactions in the signal transduction network controlling the flagellum rotor and other processes affected by changes in levels of c-di-GMP.

Intellectual frameworks to understand complex biochemical systems at the origin of life

Understanding the emergence of complex biochemical systems, such as protein translation, is a great challenge. Although synthetic approaches can provide insight into the potential early stages of life, they do not address the equally important question of why the complex systems of life would have evolved. In particular, the intricacies of the mechanisms governing the transfer of information from nucleic acid sequences to proteins make it difficult to imagine how coded protein synthesis could have emerged from a prebiotic soup. Here we discuss the use of intellectual frameworks in studying the emergence of life. We discuss how one such framework, namely the RNA world theory, has spurred research, and provide an overview of its limitations. We suggest that the emergence of coded protein synthesis could be broken into experimentally tractable problems by treating it as a molecular bricolage-a complex system integrating many different parts, each of which originally evolved for uses unrelated to its modern function-to promote a concrete understanding of its origin.

Theoretical insights into rotary mechanism of MotAB in the bacterial flagellar motor

Many bacteria enable locomotion by rotating their flagellum. It has been suggested that this rotation is realized by the rotary motion of the stator unit, MotAB, which is driven by proton transfer across the membrane. Recent cryo-electron microscopy studies have revealed a 5:2 MotAB configuration, in which a MotB dimer is encircled by a ring-shaped MotA pentamer. Although the structure implicates the rotary motion of the MotA wheel around the MotB axle, the molecular mechanisms of rotary motion and how they are coupled with proton transfer across the membrane remain elusive. In this study, we built a structure-based computational model for Campylobacter jejuni MotAB, conducted comprehensive protonation-state-dependent molecular dynamics simulations, and revealed a plausible proton-transfer-coupled rotation pathway. The model assumes rotation-dependent proton transfer, in which proton uptake from the periplasmic side to the conserved aspartic acid in MotB is followed by proton hopping to the MotA proton-carrying site, followed by proton export to the CP. We suggest that, by maintaining two of the proton-carrying sites of MotA in the deprotonated state, the MotA pentamer robustly rotates by ∼36° per proton transfer across the membrane. Our results provide a structure-based mechanistic model of the rotary motion of MotAB in bacterial flagellar motors and provide insights into various ion-driven rotary molecular motors.

Magnetic Control of Nonmagnetic Living Organisms

Living organisms inspire the design of microrobots, but their functionality is unmatched. Next-generation microrobots aim to leverage the sensing and communication abilities of organisms through magnetic hybridization, attaching magnetic particles to them for external control. However, the protocols used for magnetic hybridization are morphology specific and are not generalizable. We propose an alternative approach that leverages the principles of negative magnetostatics and magnetophoresis to control nonmagnetic organisms with external magnetic fields. To do this, we disperse model organisms in dispersions of Fe3O4 nanoparticles and expose them to either uniform or gradient magnetic fields. In uniform magnetic fields, living organisms align with the field due to external torque, while gradient magnetic fields generate a negative magnetophoretic force, pushing objects away from external magnets. The magnetic fields enable controlling the position and orientation of Caenorhabditis elegans larvae and flagellated bacteria through directional interactions and magnitude. This control is diminished in live spermatozoa and adult C. elegans due to stronger internal biological activity, i.e., force/torque. Our study presents a method for spatiotemporal organization of living organisms without requiring magnetic hybridization, opening the way for the development of controllable living microbiorobots.

Tuning the stator subunit of the flagellar motor with coiled-coil engineering

Many bacteria swim driven by an extracellular filament rotated by the bacterial flagellar motor. This motor is powered by the stator complex, MotA5 MotB2 , an heptameric complex which forms an ion channel which couples energy from the ion motive force to torque generation. Recent structural work revealed that stator complex consists of a ring of five MotA subunits which rotate around a central dimer of MotB subunits. Transmembrane (TM) domains TM3 and TM4 from MotA combine with the single TM domain from MotB to form two separate ion channels within this complex. Much is known about the ion binding site and ion specificity; however, to date, no modeling has been undertaken to explore the MotB-MotB dimer stability and the role of MotB conformational dynamics during rotation. Here, we modeled the central MotB dimer using coiled-coil engineering and modeling principles and calculated free energies to identify stable states in the operating cycle of the stator. We found three stable coiled-coil states with dimer interface angles of 28°, 56°, and 64°. We tested the effect of strategic mutagenesis on the comparative energy of the states and correlated motility with a specific hierarchy of stability between the three states. In general, our results indicate agreement with existing models describing a 36° rotation step of the MotA pentameric ring during the power stroke and provide an energetic basis for the coordinated rotation of the central MotB dimer based on coiled-coil modeling.

Questioning rotary functionality in the bacterial flagellar system and proposing a murburn model for motility

Bacterial flagellar system (BFS) was the primary example of a purported 'rotary-motor' functionality in a natural assembly. This mandates the translation of a circular motion of components inside into a linear displacement of the cell body outside, which is supposedly orchestrated with the following features of the BFS: (i) A chemical/electrical differential generates proton motive force (pmf, including a trans-membrane potential, TMP), which is electro-mechanically transduced by inward movement of protons via BFS. (ii) Membrane-bound proteins of BFS serve as stators and the slender filament acts as an external propeller, culminating into a hook-rod that pierces the membrane to connect to a 'broader assembly of deterministically movable rotor'. We had disclaimed the purported pmf/TMP-based respiratory/photosynthetic physiology involving Complex V, which was also perceived as a 'rotary machine' earlier. We pointed out that the murburn redox logic was operative therein. We pursue the following similar perspectives in BFS-context: (i) Low probability for the evolutionary attainment of an ordered/synchronized teaming of about two dozen types of proteins (assembled across five-seven distinct phases) towards the singular agendum of rotary motility. (ii) Vital redox activity (not the gambit of pmf/TMP!) powers the molecular and macroscopic activities of cells, including flagella. (iii) Flagellar movement is noted even in ambiances lacking/countering the directionality mandates sought by pmf/TMP. (iv) Structural features of BFS lack component(s) capable of harnessing/achieving pmf/TMP and functional rotation. A viable murburn model for conversion of molecular/biochemical activity into macroscopic/mechanical outcomes is proposed herein for understanding BFS-assisted motility. HIGHLIGHTSThe motor-like functionalism of bacterial flagellar system (BFS) is analyzedProton/Ion-differential based powering of BFS is unviable in bacteriaUncouplers-sponsored effects were misinterpreted, resulting in a detour in BFS researchThese findings mandate new explanation for nano-bio-mechanical movements in BFSA minimalist murburn model for the bacterial flagella-aided movement is proposedCommunicated by Ramaswamy H. Sarma.

The rapid evolution of flagellar ion selectivity in experimental populations of E. coli

Determining which cellular processes facilitate adaptation requires a tractable experimental model where an environmental cue can generate variants that rescue function. The bacterial flagellar motor (BFM) is an excellent candidate-an ancient and highly conserved molecular complex for bacterial propulsion toward favorable environments. Motor rotation is often powered by H⁺ or Na⁺ ion transit through the torque-generating stator subunit of the motor complex, and ion selectivity has adapted over evolutionary time scales. Here, we used CRISPR engineering to replace the native Escherichia coli H⁺-powered stator with Na⁺-powered stator genes and report the spontaneous reversion of our edit in a low-sodium environment. We followed the evolution of the stators during their reversion to H⁺-powered motility and used both whole-genome and RNA sequencing to identify genes involved in the cell's adaptation. Our transplant of an unfit protein and the cells' rapid response to this edit demonstrate the adaptability of the stator subunit and highlight the hierarchical modularity of the flagellar motor.

Inertialess gyrating engines

A typical model for a gyrating engine consists of an inertial wheel powered by an energy source that generates an angle-dependent torque. Examples of such engines include a pendulum with an externally applied torque, Stirling engines, and the Brownian gyrating engine. Variations in the torque are averaged out by the inertia of the system to produce limit cycle oscillations. While torque generating mechanisms are also ubiquitous in the biological world, where they typically feed on chemical gradients, inertia is not a property that one naturally associates with such processes. In the present work, seeking ways to dispense of the need for inertial effects, we study an inertia-less concept where the combined effect of coupled torque-producing components averages out variations in the ambient potential and helps overcome dissipative forces to allow sustained operation for vanishingly small inertia. We exemplify this inertia-less concept through analysis of two of the aforementioned engines, the Stirling engine, and the Brownian gyrating engine. An analogous principle may be sought in biomolecular processes as well as in modern-day technological engines, where for the latter, the coupled torque-producing components reduce vibrations that stem from the variability of the generated torque.

Exopolysaccharides amylovoran and levan contribute to sliding motility in the fire blight pathogen Erwinia amylovora

Erwinia amylovora, the causative agent of fire blight, uses flagella-based motilities to translocate to host plant natural openings; however, little is known about how this bacterium migrates systemically in the apoplast. Here, we reveal a novel surface motility mechanism, defined as sliding, in E. amylovora. Deletion of flagella assembly genes did not affect this movement, whereas deletion of biosynthesis genes for the exopolysaccharides (EPSs) amylovoran and levan resulted in non-sliding phenotypes. Since EPS production generates osmotic pressure that potentially powers sliding, we validated this mechanism by demonstrating that water potential positively contributes to sliding. In addition, no sliding was observed when the water potential of the surface was lower than -0.5 MPa. Sliding is a passive motility mechanism. We further show that the force of gravity plays a critical role in directing E. amylovora sliding on unconfined surfaces but has a negligible effect when cells are sliding in confined microcapillaries, in which EPS-dependent osmotic pressure acts as the main force. Although amylovoran and levan are both required for sliding, we demonstrate that they exhibit different roles in bacterial communities. In summary, our study provides fundamental knowledge for a better understanding of mechanisms that drive bacterial sliding motility.

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.

3D cryo-electron microscopic imaging of bacterial flagella: novel structural and mechanistic insights into cell motility

Bacterial flagella are nanomachines that enable cells to move at high speeds. Comprising ≳25 different types of proteins, the flagellum is a large supramolecular assembly organized into three widely conserved substructures: a basal body including the rotary motor, a connecting hook, and a long filament. The whole flagellum from Escherichia coli weighs ∼20 MDa, without considering its filament portion, which is by itself a ∼1.6 GDa structure arranged as a multimer of ∼30,000 flagellin protomers. Breakthroughs regarding flagellar structure and function have been achieved in the last few years, mainly due to the revolutionary improvements in 3D cryo-electron microscopy methods. This review discusses novel structures and mechanistic insights derived from such high-resolution studies, advancing our understanding of each one of the three major flagellar segments. The rotation mechanism of the motor has been unveiled with unprecedented detail, showing a two-cogwheel machine propelled by a Brownian ratchet device. Additionally, by imaging the flagellin-like protomers that make up the hook in its native bent configuration, their unexpected conformational plasticity challenges the paradigm of a two-state conformational rearrangement mechanism for flagellin-fold proteins. Finally, imaging of the filaments of periplasmic flagella, which endow Spirochete bacteria with their singular motility style, uncovered a strikingly asymmetric protein sheath that coats the flagellin core, challenging the view of filaments as simple homopolymeric structures that work as freely whirling whips. Further research will shed more light on the functional details of this amazing nanomachine, but our current understanding has definitely come a long way.

Probing nanomotion of single bacteria with graphene drums

Motion is a key characteristic of every form of life¹. Even at the microscale, it has been reported that colonies of bacteria can generate nanomotion on mechanical cantilevers², but the origin of these nanoscale vibrations has remained unresolved^3,4. Here, we present a new technique using drums made of ultrathin bilayer graphene, where the nanomotion of single bacteria can be measured in its aqueous growth environment. A single Escherichia coli cell is found to generate random oscillations with amplitudes of up to 60 nm, exerting forces of up to 6 nN to its environment. Using mutant strains that differ by single gene deletions that affect motility, we are able to pinpoint the bacterial flagella as the main source of nanomotion. By real-time tracing of changes in nanomotion on administering antibiotics, we demonstrate that graphene drums can perform antibiotic susceptibility testing with single-cell sensitivity. These findings deepen our understanding of processes underlying cellular dynamics, and pave the way towards high-throughput and parallelized rapid screening of the effectiveness of antibiotics in bacterial infections with graphene devices.

Modeling Bacterial Flagellar Motor With New Structure Information: Rotational Dynamics of Two Interacting Protein Nano-Rings

In this article, we develop a mathematical model for the rotary bacterial flagellar motor (BFM) based on the recently discovered structure of the stator complex (MotA₅MotB₂). The structure suggested that the stator also rotates. The BFM is modeled as two rotating nano-rings that interact with each other. Specifically, translocation of protons through the stator complex drives rotation of the MotA pentamer ring, which in turn drives rotation of the FliG ring in the rotor via interactions between the MotA ring of the stator and the FliG ring of the rotor. Preliminary results from the structure-informed model are consistent with the observed torque-speed relation. More importantly, the model predicts distinctive rotor and stator dynamics and their load dependence, which may be tested by future experiments. Possible approaches to verify and improve the model to further understand the molecular mechanism for torque generation in BFM are also discussed.

A physical mechanism underlying the torque generation of the bacterial flagellar motor

This study proposes a physical mechanism underlying the torque generation of a bacterial flagellar motor (BFM), in which the torque for the rotation of the rotor can be generated from impulsive forces resulting from collisions between the randomly moving stator and rotor. The torque required for the rotation of the rotor may be generated through two coexisting mechanisms: mechanism (A), in which the stator collides with the rotor, whose rotation axis fluctuates asymmetrically, generating a torque in the direction of the rod, and mechanism (B), in which physical collisions between the stator and the asymmetric [Formula: see text]and [Formula: see text] generate the torque in the direction of the rod. Mechanism (A) might be related the bidirectional rotation and the tumbling of the motion of the cell. Mechanism (B) might be related to occurrence of the steps in the time traces of the rotational angle, backward stepping or switching of the rotational direction, and the knee-shaped [Formula: see text]-[Formula: see text] relation. The above-mentioned characteristics of the rotation of BFM are reproduced in a model device designed to confirm the applicability of the proposed concept to real BFM. Moreover, a prediction of the disappearance of the knee-shaped [Formula: see text]-[Formula: see text] relation of the actual BFM at a high temperature is proposed.

Energy landscapes and dynamics of ion translocation through membrane transporters: a meeting ground for physics, chemistry, and biology

The dynamics of ion translocation through membrane transporters is visualized from a comprehensive point of view by a Gibbs energy landscape approach. The ΔG calculations have been performed with the Kirkwood-Tanford-Warshel (KTW) electrostatic theory that properly takes into account the self-energies of the ions. The Gibbs energy landscapes for translocation of a single charge and an ion pair are calculated, compared, and contrasted as a function of the order parameter, and the characteristics of the frustrated system with bistability for the ion pair are described and quantified in considerable detail. These calculations have been compared with experimental data on the ΔG of ion pairs in proteins. It is shown that, under suitable conditions, the adverse Gibbs energy barrier can be almost completely compensated by the sum of the electrostatic energy of the charge-charge interactions and the solvation energy of the ion pair. The maxima in ΔG_KTW with interionic distance in the bound H⁺ - A^- charge pair on the enzyme is interpreted in thermodynamic and molecular mechanistic terms, and biological implications for molecular mechanisms of ATP synthesis are discussed. The timescale at which the order parameter moves between two stable states has been estimated by solving the dynamical equations of motion, and a wealth of novel insights into energy transduction during ATP synthesis by the membrane-bound F_OF₁-ATP synthase transporter is offered. In summary, a unifying analytical framework that integrates physics, chemistry, and biology has been developed for ion translocation by membrane transporters for the first time by means of a Gibbs energy landscape approach.

Pseudomonas Flagella: Generalities and Specificities

Flagella-driven motility is an important trait for bacterial colonization and virulence. Flagella rotate and propel bacteria in liquid or semi-liquid media to ensure such bacterial fitness. Bacterial flagella are composed of three parts: a membrane complex, a flexible-hook, and a flagellin filament. The most widely studied models in terms of the flagellar apparatus are E. coli and Salmonella. However, there are many differences between these enteric bacteria and the bacteria of the Pseudomonas genus. Enteric bacteria possess peritrichous flagella, in contrast to Pseudomonads, which possess polar flagella. In addition, flagellar gene expression in Pseudomonas is under a four-tiered regulatory circuit, whereas enteric bacteria express flagellar genes in a three-step manner. Here, we use knowledge of E. coli and Salmonella flagella to describe the general properties of flagella and then focus on the specificities of Pseudomonas flagella. After a description of flagellar structure, which is highly conserved among Gram-negative bacteria, we focus on the steps of flagellar assembly that differ between enteric and polar-flagellated bacteria. In addition, we summarize generalities concerning the fuel used for the production and rotation of the flagellar macromolecular complex. The last part summarizes known regulatory pathways and potential links with the type-six secretion system (T6SS).

State of the art of bacterial chemotaxis

Bacterial chemotaxis is a biased movement of bacteria toward the beneficial chemical gradient or away from a toxic chemical gradient. This movement is achieved by sensing a chemical gradient by chemoreceptors. In most of the chemotaxis studies, Escherichia coli has been used as a model organism. E. coli have about 4-6 flagella on their surfaces, and the motility is achieved by rotating the flagella. Each flagellum has reversible flagellar motors at its base, which rotate the flagella in counterclockwise and clockwise directions to achieve "run" and "tumble." The chemotaxis of bacteria is regulated by a network of interacting proteins. The sensory signal is processed and transmitted to the flagellar motor by cytoplasmic proteins. Bacterial chemotaxis plays an important role in many biological processes such as biofilm formation, quorum sensing, bacterial pathogenesis, and host infection. Bacterial chemotaxis can be applied for bioremediation, horizontal gene transfer, drug delivery, or maybe some other industry in near future. This review contains an overview of bacterial chemotaxis, recent findings of the physiological importance of bacterial chemotaxis in other biological processes, and the application of bacterial chemotaxis.

Nonequilibrium Thermodynamics in Biochemical Systems and Its Application

Living systems are open systems, where the laws of nonequilibrium thermodynamics play the important role. Therefore, studying living systems from a nonequilibrium thermodynamic aspect is interesting and useful. In this review, we briefly introduce the history and current development of nonequilibrium thermodynamics, especially that in biochemical systems. We first introduce historically how people realized the importance to study biological systems in the thermodynamic point of view. We then introduce the development of stochastic thermodynamics, especially three landmarks: Jarzynski equality, Crooks' fluctuation theorem and thermodynamic uncertainty relation. We also summarize the current theoretical framework for stochastic thermodynamics in biochemical reaction networks, especially the thermodynamic concepts and instruments at nonequilibrium steady state. Finally, we show two applications and research paradigms for thermodynamic study in biological systems.

Structures of the stator complex that drives rotation of the bacterial flagellum

The bacterial flagellum is the prototypical protein nanomachine and comprises a rotating helical propeller attached to a membrane-embedded motor complex. The motor consists of a central rotor surrounded by stator units that couple ion flow across the cytoplasmic membrane to generate torque. Here, we present the structures of the stator complexes from Clostridium sporogenes, Bacillus subtilis and Vibrio mimicus, allowing interpretation of the extensive body of data on stator mechanism. The structures reveal an unexpected asymmetric A5B2 subunit assembly where the five A subunits enclose the two B subunits. Comparison to structures of other ion-driven motors indicates that this A5B2 architecture is fundamental to bacterial systems that couple energy from ion flow to generate mechanical work at a distance and suggests that such events involve rotation in the motor structures.

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.

Measurement of the Internal Frictional Drag of the Bacterial Flagellar Motor by Fluctuation Analysis

The bacterial flagellar motor generates the torque that drives the rotation of bacterial flagellar filaments. The torque it generates depends sensitively on the frictional viscous drag on the motor, which includes the frictional viscous drag on the filaments (external load) and the internal frictional viscous drag on the rotor (internal load). The internal load was roughly estimated previously by modeling it as a sphere of a radius of 20 nm rotating in a lipid of viscosity of 100 cp but was never measured experimentally. Here, we measured the internal load by fluctuation analysis of the motor velocity traces. A similar approach should be applicable to other molecular motors.

Taming the flagellar motor of pseudomonads with a nucleotide messenger

Pseudomonads rely on the flagellar motor to rotate a polar flagellum for swimming and swarming, and to sense surfaces for initiating the motile-to-sessile transition to adopt a surface-dwelling lifestyle. Deciphering the function and regulation of the flagellar motor is of paramount importance for understanding the behaviours of environmental and pathogenic pseudomonads. Recent studies disclosed the preeminent role played by the messenger c-di-GMP in controlling the real-time performance of the flagellar motor in pseudomonads. The studies revealed that c-di-GMP controls the dynamic exchange of flagellar stator units to regulate motor torque/speed and modulates the frequency of flagellar motor switching via the chemosensory signalling pathways. Apart from being a rotary motor, the flagellar motor is emerging as a mechanosensor that transduces surface-induced mechanical signals into an increase of cellular c-di-GMP concentration to initiate the cellular programs required for long-term colonization. Collectively, the studies generate long-awaited mechanistic insights into how c-di-GMP regulates bacterial motility and the motile-to-sessile transition. The new findings also raise the fundamental questions of how cellular c-di-GMP concentrations are dynamically coupled to flagellar output and the proton-motive force, and how c-di-GMP signalling is coordinated spatiotemporally to fine-tune flagellar response and the behaviour of pseudomonads in solutions and on surfaces.

Propulsive nanomachines: the convergent evolution of archaella, flagella and cilia

Echoing the repeated convergent evolution of flight and vision in large eukaryotes, propulsive swimming motility has evolved independently in microbes in each of the three domains of life. Filamentous appendages – archaella in Archaea, flagella in Bacteria and cilia in Eukaryotes – wave, whip or rotate to propel microbes, overcoming diffusion and enabling colonization of new environments. The implementations of the three propulsive nanomachines are distinct, however: archaella and flagella rotate, while cilia beat or wave; flagella and cilia assemble at their tips, while archaella assemble at their base; archaella and cilia use ATP for motility, while flagella use ion-motive force. These underlying differences reflect the tinkering required to evolve a molecular machine, in which pre-existing machines in the appropriate contexts were iteratively co-opted for new functions and whose origins are reflected in their resultant mechanisms. Contemporary homologies suggest that archaella evolved from a non-rotary pilus, flagella from a non-rotary appendage or secretion system, and cilia from a passive sensory structure. Here, we review the structure, assembly, mechanism and homologies of the three distinct solutions as a foundation to better understand how propulsive nanomachines evolved three times independently and to highlight principles of molecular evolution.

Evolution of the Stator Elements of Rotary Prokaryote Motors

The bacterial flagellar motor is driven by an ion flux that is converted to torque by motor-attendant complexes known as stators. The dynamics of stator assembly around the motor in response to external stimuli have been the subject of much recent research, but less is known about the evolutionary origins of stator complexes and how they select for specific ions. Here, we review the latest structural and biochemical data for the stator complexes and compare these with other ion transporters and microbial motors to examine possible evolutionary origins of the stator complex.

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.

Tuning the torque-speed characteristics of the bacterial flagellar motor to enhance swimming speed

In a classic paper, Purcell [Proc. Natl. Acad. Sci. U. S. A. 94, 11307 (1997)10.1073/pnas.94.21.11307] analyzed the dynamics of flagellated bacterial swimmers and derived a geometrical relationship which maximizes the propulsion efficiency. Experimental measurements for wild-type bacterial species E. coli have revealed that they closely satisfy this geometric optimality. However, dependence of the flagellar motor speed on the load and more generally the role of the torque-speed characteristics of the flagellar motor are not considered in Purcell's original analysis. Here we derive a tuned condition representing a match between the flagella geometry and the torque-speed characteristics of the flagellar motor to maximize the bacterial swimming speed for a given load. This condition is independent of the geometric optimality condition derived by Purcell. Interestingly, this condition is not satisfied by wild-type E. coli which swims 2-3 times slower than the maximum possible speed given the amount of available motor torque. Finally, we present experimental data on swimming dynamics of a cargo laden bacterial system which follows our analytical model. Our analysis also reveals the existence of an anomalous propulsion regime where the swim speed increases with increasing load (drag).

Mechanisms for bacterial gliding motility on soft substrates

The motility mechanism of certain prokaryotes has long been a mystery, since their motion, known as gliding, involves no external appendages. The physical principles behind gliding still remain poorly understood. Using myxobacteria as an example of such organisms, we identify here the physical principles behind gliding motility and develop a theoretical model that predicts a 2-regime behavior of the gliding speed as a function of the substrate stiffness. Our theory describes the elasto-capillary-hydrodynamic interactions between the membrane of the bacteria, the slime it secretes, and the soft substrate underneath. Defining gliding as the horizontal translation under zero net force, we find the 2-regime behavior is due to 2 distinct mechanisms of motility thrust. On mildly soft substrates, the thrust arises from bacterial shape deformations creating a flow of slime that exerts a pressure along the bacterial length. This pressure in conjunction with the bacterial shape provides the necessary thrust for propulsion. On very soft substrates, however, we show that capillary effects must be considered that lead to the formation of a ridge at the slime-substrate-air interface, thereby creating a thrust in the form of a localized pressure gradient at the bacterial leading edge. To test our theory, we perform experiments with isolated cells on agar substrates of varying stiffness and find the measured gliding speeds in good agreement with the predictions from our elasto-capillary-hydrodynamic model. The mechanisms reported here serve as an important step toward an accurate theory of friction and substrate-mediated interactions between bacteria proliferating in soft media.

Load-dependent adaptation near zero load in the bacterial flagellar motor

The bacterial flagellar motor is an ion-powered transmembrane protein complex which drives swimming in many bacterial species. The motor consists of a cytoplasmic 'rotor' ring and a number of 'stator' units, which are bound to the cell wall of the bacterium. Recently, it has been shown that the number of functional torque-generating stator units in the motor depends on the external load, and suggested that mechanosensing in the flagellar motor is driven via a 'catch bond' mechanism in the motor's stator units. We present a method that allows us to measure-on a single motor-stator unit dynamics across a large range of external loads, including near the zero-torque limit. By attaching superparamagnetic beads to the flagellar hook, we can control the motor's speed via a rotating magnetic field. We manipulate the motor to four different speed levels in two different ion-motive force (IMF) conditions. This framework allows for a deeper exploration into the mechanism behind load-dependent remodelling by separating out motor properties, such as rotation speed and energy availability in the form of IMF, that affect the motor torque.

Biophysics at the coffee shop: lessons learned working with George Oster

Over the past 50 years, the use of mathematical models, derived from physical reasoning, to describe molecular and cellular systems has evolved from an art of the few to a cornerstone of biological inquiry. George Oster stood out as a pioneer of this paradigm shift from descriptive to quantitative biology not only through his numerous research accomplishments, but also through the many students and postdocs he mentored over his long career. Those of us fortunate enough to have worked with George agree that his sharp intellect, physical intuition, and passion for scientific inquiry not only inspired us as scientists but also greatly influenced the way we conduct research. We would like to share a few important lessons we learned from George in honor of his memory and with the hope that they may inspire future generations of scientists.

Design principles and optimal performance for molecular motors under realistic constraints

The performance of a molecular motor, characterized by its power output and energy efficiency, is investigated in the motor design space spanned by the stepping rate function and the motor-track interaction potential. Analytic results and simulations show that a gating mechanism that restricts forward stepping in a narrow window in configuration space is needed for generating high power at physiologically relevant loads. By deriving general thermodynamics laws for nonequilibrium motors, we find that the maximum torque (force) at stall is less than its theoretical limit for any realistic motor-track interactions due to speed fluctuations. Our study reveals a tradeoff for the motor-track interaction: while a strong interaction generates a high power output for forward steps, it also leads to a higher probability of wasteful spontaneous back steps. Our analysis and simulations show that this tradeoff sets a fundamental limit to the maximum motor efficiency in the presence of spontaneous back steps, i.e., loose-coupling. Balancing this tradeoff leads to an optimal design of the motor-track interaction for achieving a maximum efficiency close to 1 for realistic motors that are not perfectly coupled with the energy source. Comparison with existing data and suggestions for future experiments are discussed.

Catch bond drives stator mechanosensitivity in the bacterial flagellar motor

The bacterial flagellar motor (BFM) is the rotary motor powering swimming of many motile bacteria. Many of the components of this molecular machine are dynamic, a property which allows the cell to optimize its behavior in accordance with the surrounding environment. A prime example is the stator unit, a membrane-bound ion channel that is responsible for applying torque to the rotor. The stator units are mechanosensitive, with the number of engaged units dependent on the viscous load on the motor. We measure the kinetics of the stators as a function of the viscous load and find that the mechanosensitivity of the BFM is governed by a catch bond: a counterintuitive type of bond that becomes stronger under force.

The bacterial flagellar motor (BFM) is the rotary motor that rotates each bacterial flagellum, powering the swimming and swarming of many motile bacteria. The torque is provided by stator units, ion motive force-powered ion channels known to assemble and disassemble dynamically in the BFM. This turnover is mechanosensitive, with the number of engaged units dependent on the viscous load experienced by the motor through the flagellum. However, the molecular mechanism driving BFM mechanosensitivity is unknown. Here, we directly measure the kinetics of arrival and departure of the stator units in individual motors via analysis of high-resolution recordings of motor speed, while dynamically varying the load on the motor via external magnetic torque. The kinetic rates obtained, robust with respect to the details of the applied adsorption model, indicate that the lifetime of an assembled stator unit increases when a higher force is applied to its anchoring point in the cell wall. This provides strong evidence that a catch bond (a bond strengthened instead of weakened by force) drives mechanosensitivity of the flagellar motor complex. These results add the BFM to a short, but growing, list of systems demonstrating catch bonds, suggesting that this “molecular strategy” is a widespread mechanism to sense and respond to mechanical stress. We propose that force-enhanced stator adhesion allows the cell to adapt to a heterogeneous environmental viscosity and may ultimately play a role in surface-sensing during swarming and biofilm formation.

Limiting (zero-load) speed of the rotary motor of Escherichia coli is independent of the number of torque-generating units

Rotation of the bacterial flagellar motor is driven by multiple torque-generating units (stator elements). The torque-generating dynamics can be understood in terms of the "duty ratio" of the stator elements, that is, the fraction of time a stator element engages with the rotor during its mechanochemical cycle. The dependence of the limiting speed (zero-load speed) of the motor on the number of stator elements is the determining test of the duty ratio, which has been controversial experimentally and theoretically over the past decade. Here, we developed a method combining laser dark-field microscopy and optical trapping to resolve this controversy. We found that the zero-load speed is independent of the number of stator elements for the bacterial flagellar motor in Escherichia coli, demonstrating that these elements have a duty ratio close to 1.

Torque, but not FliL, regulates mechanosensitive flagellar motor-function

The stator-complex in the bacterial flagellar motor is responsible for surface-sensing. It remodels in response to perturbations in viscous loads, recruiting additional stator-units as the load increases. Here, we tested a hypothesis that the amount of torque generated by each stator-unit modulates its association with the rotor. To do this, we measured stator-binding to the rotor in mutants in which motors reportedly develop lower torque compared to wildtype motors. First, we employed a strain lacking fliL. Contrary to earlier reports, measurements indicated that the torque generated by motors in the fliL strain was similar to that in the wildtype, at high loads. In these motors, stator-binding was unchanged. Next, experiments with a paralyzed strain indicated that the stator-binding was measurably weaker when motors were unable to generate torque. An analytical model was developed that incorporated an exponential dependence of the unit’s dissociation rate on the force delivered to the rotor. The model provided accurate fits to measurements of stator-rotor binding over a wide range of loads. Based on these results, we propose that the binding of each stator-unit is enhanced by the force it develops. Furthermore, FliL does not play a significant role in motor function in E. coli.

The Limiting Speed of the Bacterial Flagellar Motor

Recent experiments on the bacterial flagellar motor have shown that the structure of this nanomachine, which drives locomotion in a wide range of bacterial species, is more dynamic than previously believed. Specifically, the number of active torque-generating complexes (stators) was shown to vary across applied loads. This finding brings under scrutiny the experimental evidence reporting that limiting (zero-torque) speed is independent of the number of active stators. In this study, we propose that, contrary to previous assumptions, the maximum speed of the motor increases as additional stators are recruited. This result arises from our assumption that stators disengage from the motor for a significant portion of their mechanochemical cycles at low loads. We show that this assumption is consistent with current experimental evidence in chimeric motors, as well as with the requirement that a processive motor driving a large load via an elastic linkage must have a high duty ratio.

Resonance in the response of the bacterial flagellar motor to thermal oscillations

We have studied the dynamics of the Escherichia coli flagellar motor's angular velocity in response to thermal oscillations. We find that the oscillations' amplitude of the motor's angular velocity exhibits resonance when the temperature is oscillated at frequencies around 4 Hz. This resonance appears to be due to the existence of a natural mode of oscillation in the state of the motor, specifically in the torque generated by the motor. Natural modes of oscillation in torque generation cannot result from random fluctuations in the state of the motor. Their presence points to the existence of a coupling mechanism between the magnitude of the torque generated by the motor and the rates of transition between the different states of the motor components responsible for torque generation. The results presented here show resonance response in torque generation to external perturbations. They are explained with a simple phenomenological model, which can help future studies identify the source of the feedback mechanism between the torque and the interactions responsible for its generation. It can also help us to quantitatively estimate the strength of these interactions and how they are affected by the magnitude of the torque they generate.

Mutations targeting the plug-domain of the Shewanella oneidensis proton-driven stator allow swimming at increased viscosity and under anaerobic conditions

Shewanella oneidensis MR-1 possesses two different stator units to drive flagellar rotation, the Na⁺ -dependent PomAB stator and the H⁺ -driven MotAB stator, the latter possibly acquired by lateral gene transfer. Although either stator can independently drive swimming through liquid, MotAB-driven motors cannot support efficient motility in structured environments or swimming under anaerobic conditions. Using ΔpomAB cells we isolated spontaneous mutants able to move through soft agar. We show that a mutation that alters the structure of the plug domain in MotB affects motor functions and allows cells to swim through media of increased viscosity and under anaerobic conditions. The number and exchange rates of the mutant stator around the rotor were not significantly different from wild-type stators, suggesting that the number of stators engaged is not the cause of increased swimming efficiency. The swimming speeds of planktonic mutant MotAB-driven cells was reduced, and overexpression of some of these stators caused reduced growth rates, implying that mutant stators not engaged with the rotor allow some proton leakage. The results suggest that the mutations in the MotB plug domain alter the proton interactions with the stator ion channel in a way that both increases torque output and allows swimming at decreased pmf values.

The tetrameric MotA complex as the core of the flagellar motor stator from hyperthermophilic bacterium

Rotation of bacterial flagellar motor is driven by the interaction between the stator and rotor, and the driving energy is supplied by ion influx through the stator channel. The stator is composed of the MotA and MotB proteins, which form a hetero-hexameric complex with a stoichiometry of four MotA and two MotB molecules. MotA and MotB are four- and single-transmembrane proteins, respectively. To generate torque, the MotA/MotB stator unit changes its conformation in response to the ion influx, and interacts with the rotor protein FliG. Here, we overproduced and purified MotA of the hyperthermophilic bacterium Aquifex aeolicus. A chemical crosslinking experiment revealed that MotA formed a multimeric complex, most likely a tetramer. The three-dimensional structure of the purified MotA, reconstructed by electron microscopy single particle imaging, consisted of a slightly elongated globular domain and a pair of arch-like domains with spiky projections, likely to correspond to the transmembrane and cytoplasmic domains, respectively. We show that MotA molecules can form a stable tetrameric complex without MotB, and for the first time, demonstrate the cytoplasmic structure of the stator.