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

Physical mechanism reveals bacterial slowdown above a critical number of flagella

Numerous studies have explored the link between bacterial swimming and the number of flagella, a distinguishing feature of motile multi-flagellated bacteria. We revisit this open question using augmented slender-body theory simulations, in which we resolve the full hydrodynamic interactions within a bundle of helical filaments rotating and translating in synchrony. Unlike previous studies, our model considers the full torque-speed relationship of the bacterial flagellar motor, revealing its significant impact on multi-flagellated swimming. Because the viscous load per motor decreases with the flagellar number, the bacterial flagellar motor transitions from the high-load to the low-load regime at a critical number of filaments, leading to bacterial slowdown as further flagella are added to the bundle. We explain the physical mechanism behind the observed slowdown as an interplay between the load-dependent generation of torque by the motor, and the load-reducing cooperativity between flagella, which consists of both hydrodynamic and non-hydrodynamic components. The theoretically predicted critical number of flagella is remarkably close to the values reported for the model organism Escherichia coli. Our model further predicts that the critical number of flagella increases with viscosity, suggesting that bacteria can enhance their swimming capacity by growing more flagella in more viscous environments, consistent with empirical observations.

A multi-state dynamic process confers mechano-adaptation to a biological nanomachine

Adaptation is a defining feature of living systems. The bacterial flagellar motor adapts to changes in the external mechanical load by adding or removing torque-generating (stator) units. But the molecular mechanism behind this mechano-adaptation remains unclear. Here, we combine single motor eletrorotation experiments and theoretical modeling to show that mechano-adaptation of the flagellar motor is enabled by multiple mechanosensitive internal states. Dwell time statistics from experiments suggest the existence of at least two bound states with a high and a low unbinding rate, respectively. A first-passage-time analysis of a four-state model quantitatively explains the experimental data and determines the transition rates among all four states. The torque generated by bound stator units controls their effective unbinding rate by modulating the transition between the bound states, possibly via a catch bond mechanism. Similar force-mediated feedback enabled by multiple internal states may apply to adaptation in other macromolecular complexes.

Combining experiments with modeling, Wadhwa et al. propose a model for mechano-adaptation in the bacterial flagellar motor, finding that load-dependent transitions between multiple internal states govern the binding and unbinding of subunits.

Dynamic Hybrid Flagellar Motors-Fuel Switch and More

Flagellar motors are intricate rotating nanomachines that are powered by transmembrane ion gradients. The stator complexes are the powerhouses of the flagellar motor: They convert a transmembrane ion gradient, mainly of H⁺ or Na⁺, into rotation of the helical flagellar filament. They are thus essential for motor function. The number of stators synchronously engaged in the motor is surprisingly dynamic and depends on the load and the environmental concentration of the corresponding coupling ion. Thus, the rotor-stator interactions determine an important part of the properties of the motor. Numerous bacteria have been identified as possessing more than one set of stators, and some species have been demonstrated to use these different stators in various configurations to modify motor functions by dynamic in-flight swapping. Here, we review knowledge of the properties, the functions, and the evolution of these hybrid motors and discuss questions that remain unsolved.

Relaxation time asymmetry in stator dynamics of the bacterial flagellar motor

The bacterial flagellar motor is the membrane-embedded rotary motor, which turns the flagellum that provides thrust to many bacteria. This large multimeric complex, composed of a few dozen constituent proteins, is a hallmark of dynamic subunit exchange. The stator units are inner-membrane ion channels that dynamically bind to the peptidoglycan at the rotor periphery and apply torque. Their dynamic exchange is a function of the viscous load on the flagellum, allowing the bacterium to adapt to its local environment, although the molecular mechanisms of mechanosensitivity remain unknown. Here, by actively perturbing the steady-state stator stoichiometry of individual motors, we reveal a stoichiometry-dependent asymmetry in stator remodeling kinetics. We interrogate the potential effect of next-neighbor interactions and local stator unit depletion and find that neither can explain the observed asymmetry. We then simulate and fit two mechanistically diverse models that recapitulate the asymmetry, finding assembly dynamics to be particularly well described by a two-state catch-bond mechanism.

Stator Dynamics Depending on Sodium Concentration in Sodium-Driven Bacterial Flagellar Motors

Bacterial flagellar motor (BFM) is a large membrane-spanning molecular rotary machine for swimming motility. Torque is generated by the interaction between the rotor and multiple stator units powered by ion-motive force (IMF). The number of bound stator units is dynamically changed in response to the external load and the IMF. However, the detailed dynamics of stator unit exchange process remains unclear. Here, we directly measured the speed changes of sodium-driven chimeric BFMs under fast perfusion of different sodium concentration conditions using computer-controlled, high-throughput microfluidic devices. We found the sodium-driven chimeric BFMs maintained constant speed over a wide range of sodium concentrations by adjusting stator units in compensation to the sodium-motive force (SMF) changes. The BFM has the maximum number of stator units and is most stable at 5 mM sodium concentration rather than higher sodium concentration. Upon rapid exchange from high to low sodium concentration, the number of functional stator units shows a rapidly excessive reduction and then resurrection that is different from predictions of simple absorption model. This may imply the existence of a metastable hidden state of the stator unit during the sudden loss of sodium ions.

Bacterial motility: machinery and mechanisms

Bacteria have developed a large array of motility mechanisms to exploit available resources and environments. These mechanisms can be broadly classified into swimming in aqueous media and movement over solid surfaces. Swimming motility involves either the rotation of rigid helical filaments through the external medium or gyration of the cell body in response to the rotation of internal filaments. On surfaces, bacteria swarm collectively in a thin layer of fluid powered by the rotation of rigid helical filaments, they twitch by assembling and disassembling type IV pili, they glide by driving adhesins along tracks fixed to the cell surface and, finally, non-motile cells slide over surfaces in response to outward forces due to colony growth. Recent technological advances, especially in cryo-electron microscopy, have greatly improved our knowledge of the molecular machinery that powers the various forms of bacterial motility. In this Review, we describe the current understanding of the physical and molecular mechanisms that allow bacteria to move around.

ATP synthase: Evolution, energetics, and membrane interactions

The synthesis of ATP, life’s “universal energy currency,” is the most prevalent chemical reaction in biological systems and is responsible for fueling nearly all cellular processes, from nerve impulse propagation to DNA synthesis. ATP synthases, the family of enzymes that carry out this endless task, are nearly as ubiquitous as the energy-laden molecule they are responsible for making. The F-type ATP synthase (F-ATPase) is found in every domain of life and has facilitated the survival of organisms in a wide range of habitats, ranging from the deep-sea thermal vents to the human intestine. Accordingly, there has been a large amount of work dedicated toward understanding the structural and functional details of ATP synthases in a wide range of species. Less attention, however, has been paid toward integrating these advances in ATP synthase molecular biology within the context of its evolutionary history. In this review, we present an overview of several structural and functional features of the F-type ATPases that vary across taxa and are purported to be adaptive or otherwise evolutionarily significant: ion channel selectivity, rotor ring size and stoichiometry, ATPase dimeric structure and localization in the mitochondrial inner membrane, and interactions with membrane lipids. We emphasize the importance of studying these features within the context of the enzyme’s particular lipid environment. Just as the interactions between an organism and its physical environment shape its evolutionary trajectory, ATPases are impacted by the membranes within which they reside. We argue that a comprehensive understanding of the structure, function, and evolution of membrane proteins—including ATP synthase—requires such an integrative approach.

Improved bounds on entropy production in living systems

Living systems maintain or increase local order by working against the second law of thermodynamics. Thermodynamic consistency is restored as they consume free energy, thereby increasing the net entropy of their environment. Recently introduced estimators for the entropy production rate have provided major insights into the efficiency of important cellular processes. In experiments, however, many degrees of freedom typically remain hidden to the observer, and, in these cases, existing methods are not optimal. Here, by reformulating the problem within an optimization framework, we are able to infer improved bounds on the rate of entropy production from partial measurements of biological systems. Our approach yields provably optimal estimates given certain measurable transition statistics. In contrast to prevailing methods, the improved estimator reveals nonzero entropy production rates even when nonequilibrium processes appear time symmetric and therefore may pretend to obey detailed balance. We demonstrate the broad applicability of this framework by providing improved bounds on the energy consumption rates in a diverse range of biological systems including bacterial flagella motors, growing microtubules, and calcium oscillations within human embryonic kidney cells.

Mechanosensitive remodeling of the bacterial flagellar motor is independent of direction of rotation

Motility is important for the survival and dispersal of many bacteria, and it often plays a role during infections. Regulation of bacterial motility by chemical stimuli is well studied, but recent work has added a new dimension to the problem of motility control. The bidirectional flagellar motor of the bacterium Escherichia coli recruits or releases torque-generating units (stator units) in response to changes in load. Here, we show that this mechanosensitive remodeling of the flagellar motor is independent of direction of rotation. Remodeling rate constants in clockwise rotating motors and in counterclockwise rotating motors, measured previously, fall on the same curve if plotted against torque. Increased torque decreases the off rate of stator units from the motor, thereby increasing the number of active stator units at steady state. A simple mathematical model based on observed dynamics provides quantitative insight into the underlying molecular interactions. The torque-dependent remodeling mechanism represents a robust strategy to quickly regulate output (torque) in response to changes in demand (load).

Origins of eukaryotic excitability

All living cells interact dynamically with a constantly changing world. Eukaryotes, in particular, evolved radically new ways to sense and react to their environment. These advances enabled new and more complex forms of cellular behaviour in eukaryotes, including directional movement, active feeding, mating, and responses to predation. But what are the key events and innovations during eukaryogenesis that made all of this possible? Here we describe the ancestral repertoire of eukaryotic excitability and discuss five major cellular innovations that enabled its evolutionary origin. The innovations include a vastly expanded repertoire of ion channels, the emergence of cilia and pseudopodia, endomembranes as intracellular capacitors, a flexible plasma membrane and the relocation of chemiosmotic ATP synthesis to mitochondria, which liberated the plasma membrane for more complex electrical signalling involved in sensing and reacting. We conjecture that together with an increase in cell size, these new forms of excitability greatly amplified the degrees of freedom associated with cellular responses, allowing eukaryotes to vastly outperform prokaryotes in terms of both speed and accuracy. This comprehensive new perspective on the evolution of excitability enriches our view of eukaryogenesis and emphasizes behaviour and sensing as major contributors to the success of eukaryotes. This article is part of the theme issue 'Basal cognition: conceptual tools and the view from the single cell'.

Discovery of oscillations in rotational speed of body-tethered Caulobacter crescentus

Swarmer cells of Caulobacter crescentus have been found to tether to glass at a point on the cell body. The rolling of the freely rotating flagellum near the glass surface causes the cell body to rotate. We describe the discovery of damped oscillations in the rotational speed of these cell bodies. We show that the damped oscillations are robust over multiple cells and that they depend more on the cell's accumulated rotation angle than on time. We also find that their phase is determined by the moment the flagellar motor changes the direction of its rotation. The oscillations occur only for one direction of cell rotation, when the flagellum is in pulling mode. We discuss possible explanations for these oscillations, including fluctuations in flagellar motor torque and periodic changes in flagellar orientation, and illustrate both of these cases using simplified computer models. Finally, we present the hypothesis that the oscillations are the result of fluctuations in the proton motive force, initiated by a sudden change in proton current that occurs when the motor switches rotation direction.

Assembly and Dynamics of the Bacterial Flagellum

The bacterial flagellar motor is the most complex structure in the bacterial cell, driving the ion-driven rotation of the helical flagellum. The ordered expression of the regulon and the assembly of the series of interacting protein rings, spanning the inner and outer membranes to form the ∼45–50-nm protein complex, have made investigation of the structure and mechanism a major challenge since its recognition as a rotating nanomachine about 40 years ago. Painstaking molecular genetics, biochemistry, and electron microscopy revealed a tiny electric motor spinning in the bacterial membrane. Over the last decade, new single-molecule and in vivo biophysical methods have allowed investigation of the stability of this and other large protein complexes, working in their natural environment inside live cells. This has revealed that in the bacterial flagellar motor, protein molecules in both the rotor and stator exchange with freely circulating pools of spares on a timescale of minutes, even while motors are continuously rotating. This constant exchange has allowed the evolution of modified components allowing bacteria to keep swimming as the viscosity or the ion composition of the outside environment changes.