Correlation between Supercoiling and Conformational Motions of the Bacterial Flagellar Filament

The bacterial flagellar filament is a very large macromolecular assembly of a single protein, flagellin. Various supercoiled states of the filament exist, which are formed by two structurally different conformations of flagellin in different ratios. We investigated the correlation between supercoiling of the protofilaments and molecular dynamics in the flagellar filament using quasielastic and elastic incoherent neutron scattering on the picosecond and nanosecond timescales. Thermal fluctuations in the straight L- and R-type filaments were measured and compared to the resting state of the wild-type filament. Amplitudes of motion on the picosecond timescale were found to be similar in the different conformational states. Mean-square displacements and protein resilience on the 0.1 ns timescale demonstrate that the L-type state is more flexible and less resilient than the R-type, whereas the wild-type state lies in between. Our results provide strong support that supercoiling of the protofilaments in the flagellar filament is determined by the strength of molecular forces in and between the flagellin subunits.     

Modeling the Correlation Functions of Conformational Motions in Proteins

Abstract

A first principles calculation of the correlation function for conformational motion (CM) in proteins is carried out within the framework of a microscopic model of a protein as a heterogeneous system. The fragments of the protein are assumed to be identical hard spheres undergoing the CM within their conformational potentials about some mean equilibrium positions assigned by the tertiary structure. The memory friction function (MFF) for the generalized Langevin equation describing the CM of the particle is obtained on the basis of the direct calculation which is feasible for the present model of the protein due to the existence of a natural large parameter, viz. the ratio of the minimal distance between the mean equilibrium positions of the particles (～7A) to the amplitude of their CM (<1A). A relationship between the MFF and the correlation functions of the CM of the particles is derived which makes their calculation to be a self-consistent mathematical problem. The general analysis of the MFF is exemplified by a simple model case in which the mean equilibrium positions of the particles form a regular lattice so that the correlation functions for all particles are the same. In this case the MFF is shown to be an infinite series of the powers of the auto-correlation function whose coefficients are independent on temperature. The latter is a result of the abstraction of the interaction potential by that of hard spheres which actually corresponds to the high temperature limit. On the examples of cubic and triangular lattices the coefficients are shown to be non-negative values which increase with the increase of the packing density of the particles and quickly tend to zero with the increase of their index. Thus the MFF can be approximated by a polynomial of the correlation function and the resulting mathematical equation is analogous to the one from the dynamic theory of liquids. The correlation function of the CM is obtained by numerical solution of the equation. At realistic packing densities for proteins it exhibits transparent non-exponential decay and includes two relaxation processes: the first one on the intermediate timescale (tens of picoseconds) and the second on the long timescale (its characteristic time is about tens of nanoseconds at small values of the friction coefficient and increases by orders of the magnitude with the increase of the latter). Thus the present approach provides the microscopic basis for previous phenomenologi- cal models of cooperative dynamics in proteins.     

Steps in the Bacterial Flagellar Motor

The bacterial flagellar motor is a highly efficient rotary machine used by many bacteria to propel themselves. It has recently been shown that at low speeds its rotation proceeds in steps. Here we propose a simple physical model, based on the storage of energy in protein springs, that accounts for this stepping behavior as a random walk in a tilted corrugated potential that combines torque and contact forces. We argue that the absolute angular position of the rotor is crucial for understanding step properties and show this hypothesis to be consistent with the available data, in particular the observation that backward steps are smaller on average than forward steps. We also predict a sublinear speed versus torque relationship for fixed load at low torque, and a peak in rotor diffusion as a function of torque. Our model provides a comprehensive framework for understanding and analyzing stepping behavior in the bacterial flagellar motor and proposes novel, testable predictions. More broadly, the storage of energy in protein springs by the flagellar motor may provide useful general insights into the design of highly efficient molecular machines.     

Serological Study of Bacterial Flagellar Hooks

Bacterial hooks were partially purified from flagella isolated from Salmonella SJ25, by treatment with heat to depolymerize flagellar filaments and with n-butanol and calcium chloride to remove membranes. Antihook serum was obtained from a rabbit inoculated with a preparation of hooks. The serum contained antibodies directed against the flagellar filament and cell membrane. These antibodies could be removed from the serum by absorption with purified flagellar filaments and cells of a nonflagellated mutant strain. It was shown by electron microscopy that anti-SJ25-hook antibody reacts with hooks from a number of strains of Salmonella which differed from SJ25 in H and O antigens, flagellar shape, and motility. Hooks possessed by various strains of Salmonella have a common antigenicity. In addition, anti-SJ25-hook cross-reacted with hooks from Escherichia coli W3110 but did not react at all which those from strains of Serratia, Proteus, Aerobacter, and Klebsiella. It is well known that bacteria stop moving upon addition of antiflagella serum to the medium. However, the addition of purified antihook was found to have little effect on motility. At physiological ionic strength and pH, flagellin (Salmonella) can polymerize into flagellar filaments only in the presence of seeds. It was shown that a crude preparation of hooks was able to initiate in vitro polymerization of flagellin.     

Interaction between FliJ and FlhA,Components of the Bacterial Flagellar Type III Export Apparatus

A soluble protein, FliJ, along with a membrane protein, FlhA, plays a role in the energy coupling mechanism for bacterial flagellar protein export. The water-soluble FliH_X-FliI₆ ATPase ring complex allows FliJ to efficiently interact with FlhA. However, the FlhA binding site of FliJ remains unknown. Here, we carried out genetic analysis of a region formed by well-conserved residues—Gln38, Leu42, Tyr45, Tyr49, Phe72, Leu76, Ala79, and His83—of FliJ. A structural model of the FliI₆-FliJ ring complex suggests that they extend out of the FliI₆ ring. Glutathione S-transferase (GST)-FliJ inhibited the motility of and flagellar protein export by both wild-type cells and a fliH-fliI flhB(P28T) bypass mutant. Pulldown assays revealed that the reduced export activity of the export apparatus results from the binding of GST-FliJ to FlhA. The F72A and L76A mutations of FliJ significantly reduced the binding affinity of FliJ for FlhA, thereby suppressing the inhibitory effect of GST-FliJ on the protein export. The F72A and L76A mutations were tolerated in the presence of FliH and FliI but considerably reduced motility in their absence. These two mutations affected neither the interaction with FliI nor the FliI ATPase activity. These results suggest that FliJ(F72A) and FliJ(L76A) require the support of FliH and FliI to exert their export function. Therefore, we propose that the well-conserved surface of FliJ is involved in the interaction with FlhA.     

Motility Protein Complexes in the Bacterial Flagellar Motor

Among the many proteins needed for the assembly and function of bacterial flagella, only five have been suggested to be involved in torque generation. These are MotA, MotB, FliG, FliM and FliN. In this study, we have probed binding interactions among these proteins, by using protein fusions to glutathioneS-transferase or to oligo-histidine, in conjunction with co-isolation assays. The results show that FliG, FliM and FliN all bind to each other, and that each also self-associates. MotA and MotB also bind to each other, and MotA interacts, but only weakly, with FliG and FliM. Taken together with previous genetic, physiological and ultrastructural studies, these results provide strong support for the view that FliG, FliM and FliN function together in a complex on the rotor of the flagellar motor, whereas MotA and MotB form a distinct complex that functions as the stator. Torque generation in the flagellar motor is thus likely to involve interactions between these two protein complexes.     

Model Studies of the Dynamics of Bacterial Flagellar Motors

The bacterial flagellar motor is a rotary molecular machine that rotates the helical filaments that propel swimming bacteria. Extensive experimental and theoretical studies exist on the structure, assembly, energy input, power generation, and switching mechanism of the motor. In a previous article, we explained the general physics underneath the observed torque-speed curves with a simple two-state Fokker-Planck model. Here, we further analyze that model, showing that 1), the model predicts that the two components of the ion motive force can affect the motor dynamics differently, in agreement with latest experiments; 2), with explicit consideration of the stator spring, the model also explains the lack of dependence of the zero-load speed on stator number in the proton motor, as recently observed; and 3), the model reproduces the stepping behavior of the motor even with the existence of the stator springs and predicts the dwell-time distribution. The predicted stepping behavior of motors with two stators is discussed, and we suggest future experimental procedures for verification.     

Bacterial Nucleoid: Interplay of DNA Demixing and Supercoiling

This work addresses the question of the interplay of DNA demixing and supercoiling in bacterial cells. Demixing of DNA from other globular macromolecules results from the overall repulsion between all components of the system and leads to the formation of the nucleoid, which is the region of the cell that contains the genomic DNA in a rather compact form. Supercoiling describes the coiling of the axis of the DNA double helix to accommodate the torsional stress injected in the molecule by topoisomerases. Supercoiling is able to induce some compaction of the bacterial DNA, although to a lesser extent than demixing. In this work, we investigate the interplay of these two mechanisms with the goal of determining whether the total compaction ratio of the DNA is the mere sum or some more complex function of the compaction ratios due to each mechanism. To this end, we developed a coarse-grained bead-and-spring model and investigated its properties through Brownian dynamics simulations. This work reveals that there actually exist different regimes, depending on the crowder volume ratio and the DNA superhelical density. In particular, a regime in which the effects of DNA demixing and supercoiling on the compaction of the DNA coil simply add up is shown to exist up to moderate values of the superhelical density. In contrast, the mean radius of the DNA coil no longer decreases above this threshold and may even increase again for sufficiently large crowder concentrations. Finally, the model predicts that the DNA coil may depart from the spherical geometry very close to the jamming threshold as a trade-off between the need to minimize both the bending energy of the stiff plectonemes and the volume of the DNA coil to accommodate demixing.     

Switching of the Bacterial Flagellar Motor Near Zero Load

Flagellated bacteria, such as Escherichia coli, are able to swim up gradients of chemical attractants by modulating the direction of rotation of their flagellar motors, which spin alternately clockwise (CW) and counterclockwise (CCW). Chemotactic behavior has been studied under a variety of conditions, mostly at high loads (at large motor torques). Here, we examine motor switching at low loads. Nano-gold spheres of various sizes were attached to hooks (the flexible coupling at the base of the flagellar filament) of cells lacking flagellar filaments in media containing different concentrations of the viscous agent Ficoll. The speeds and directions of rotation of the spheres were measured. Contrary to the case at high loads, motor switching rates increased appreciably with load. Both the CW → CCW and CCW → CW switching rates increased linearly with motor torque. Evidently, the switch senses stator-rotor interactions as well as the CheY-P concentration.     

A Molecular Mechanism of Bacterial Flagellar Motor Switching

The high-resolution structures of nearly all the proteins that comprise the bacterial flagellar motor switch complex have been solved; yet a clear picture of the switching mechanism has not emerged. Here, we used NMR to characterize the interaction modes and solution properties of a number of these proteins, including several soluble fragments of the flagellar motor proteins FliM and FliG, and the response-regulator CheY. We find that activated CheY, the switch signal, binds to a previously unidentified region of FliM, adjacent to the FliM-FliM interface. We also find that activated CheY and FliG bind with mutual exclusivity to this site on FliM, because their respective binding surfaces partially overlap. These data support a model of CheY-driven motor switching wherein the binding of activated CheY to FliM displaces the carboxy-terminal domain of FliG (FliG_C) from FliM, modulating the FliG_C-MotA interaction, and causing the motor to switch rotational sense as required for chemotaxis.     

Gains of Bacterial Flagellar Motility in a Fungal World

The maintenance of energetically costly flagella by bacteria in non-water-saturated media, such as soil, still presents an evolutionary conundrum. Potential explanations have focused on rare flooding events allowing dispersal. Such scenarios, however, overlook bacterial dispersal along mycelia as a possible transport mechanism in soils. The hypothesis tested in this study is that dispersal along fungal hyphae may lead to an increase in the fitness of flagellated bacteria and thus offer an alternative explanation for the maintenance of flagella even in unsaturated soils. Dispersal along fungal hyphae was shown for a diverse array of motile bacteria. To measure the fitness effect of dispersal, additional experiments were conducted in a model system mimicking limited dispersal, using Pseudomonas putida KT2440 and its nonflagellated (ΔfliM) isogenic mutant in the absence or presence of Morchella crassipes mycelia. In the absence of the fungus, flagellar motility was beneficial solely under conditions of water saturation allowing dispersal, while under conditions limiting dispersal, the nonflagellated mutant exhibited a higher level of fitness than the wild-type strain. In contrast, in the presence of a mycelial network under conditions limiting dispersal, the flagellated strain was able to disperse using the mycelial network and had a higher level of fitness than the mutant. On the basis of these results, we propose that the benefit of mycelium-associated dispersal helps explain the persistence of flagellar motility in non-water-saturated environments.     

Temperature Dependences of Torque Generation and Membrane Voltage in the Bacterial Flagellar Motor

In their natural habitats bacteria are frequently exposed to sudden changes in temperature that have been shown to affect their swimming. With our believed to be new methods of rapid temperature control for single-molecule microscopy, we measured here the thermal response of the Na⁺-driven chimeric motor expressed in Escherichia coli cells. Motor torque at low load (0.35 μm bead) increased linearly with temperature, twofold between 15°C and 40°C, and torque at high load (1.0 μm bead) was independent of temperature, as reported for the H⁺-driven motor. Single cell membrane voltages were measured by fluorescence imaging and these were almost constant (∼120 mV) over the same temperature range. When the motor was heated above 40°C for 1–2 min the torque at high load dropped reversibly, recovering upon cooling below 40°C. This response was repeatable over as many as 10 heating cycles. Both increases and decreases in torque showed stepwise torque changes with unitary size ∼150 pN nm, close to the torque of a single stator at room temperature (∼180 pN nm), indicating that dynamic stator dissociation occurs at high temperature, with rebinding upon cooling. Our results suggest that the temperature-dependent assembly of stators is a general feature of flagellar motors.     

Temperature Dependences of Torque Generation and Membrane Voltage in the Bacterial Flagellar Motor

In their natural habitats bacteria are frequently exposed to sudden changes in temperature that have been shown to affect their swimming. With our believed to be new methods of rapid temperature control for single-molecule microscopy, we measured here the thermal response of the Na⁺-driven chimeric motor expressed in Escherichia coli cells. Motor torque at low load (0.35 μm bead) increased linearly with temperature, twofold between 15°C and 40°C, and torque at high load (1.0 μm bead) was independent of temperature, as reported for the H⁺-driven motor. Single cell membrane voltages were measured by fluorescence imaging and these were almost constant (∼120 mV) over the same temperature range. When the motor was heated above 40°C for 1–2 min the torque at high load dropped reversibly, recovering upon cooling below 40°C. This response was repeatable over as many as 10 heating cycles. Both increases and decreases in torque showed stepwise torque changes with unitary size ∼150 pN nm, close to the torque of a single stator at room temperature (∼180 pN nm), indicating that dynamic stator dissociation occurs at high temperature, with rebinding upon cooling. Our results suggest that the temperature-dependent assembly of stators is a general feature of flagellar motors.     

Structure Analysis of the Flagellar Cap–Filament Complex by Electron Cryomicroscopy and Single-Particle Image Analysis

The cap of the bacterial flagellum plays an essential role in the growth of the long helical filament by promoting the efficient self-assembly of flagellin transported to the distal end through the narrow central channel of the flagellum. The structure of the cap–filament complex was analyzed by electron cryomicroscopy and single-particle image analysis to understand how the cap stays attached while allowing the flagellin insertion between the cap and the filament end and also allowing the HAP proteins to pass through. In the images of the complex, the projection pattern of the helical subunit array in the filament portion occupied the major fraction but was variable depending on the azimuthal orientation of the filament; therefore the images showed a strong tendency to be misaligned. Various methods had to be newly developed to correctly align the images by overcoming this misalignment problem. The structure thus obtained clearly demonstrated the pentameric structure of the cap and how the cap operates. The new methods of analysis presented here would be generally applicable to cap structures of various filaments that play biologically important roles in cellular activities.     

Switching of Bacterial Flagellar Motors Is Triggered by Mutant FliG

Binding of the chemotaxis response regulator CheY-P promotes switching between rotational states in flagellar motors of the bacterium Escherichia coli. Here, we induced switching in the absence of CheY-P by introducing copies of a mutant FliG locked in the clockwise (CW) conformation (FliG^CW). The composition of the mixed FliG ring was estimated via fluorescence imaging, and the probability of CW rotation (CW_bias) was determined from the rotation of tethered cells. The results were interpreted in the framework of a 1D Ising model. The data could be fit by assuming that mutant subunits are more stable in the CW conformation than in the counterclockwise conformation. We found that CW_bias varies depending on the spatial arrangement of the assembled subunits in the FliG ring. This offers a possible explanation for a previous observation of hysteresis in the switch function in analogous mixed FliM motors—in motors containing identical fractions of mutant FliM^CW in otherwise wild-type motors, the CW_bias differed depending on whether mutant subunits were expressed in strains with native motors or native subunits were expressed in strains with mutant motors.     

Many Local Motions Cooperate to Produce the Adenylate Kinase Conformational Transition

Conformational transitions are functionally important in many proteins. In the enzyme adenylate kinase (AK), two small domains (LID and NMP) close over the larger CORE domain; the reverse (opening) motion limits the rate of catalytic turnover. Here, using double-well Gō simulations of Escherichia coli AK, we elaborate on previous investigations of the AK transition mechanism by characterizing the contributions of rigid-body (Cartesian), backbone dihedral, and contact motions to transition-state (TS) properties. In addition, we compare an apo simulation to a pseudo-ligand-bound simulation to reveal insights into allostery. In Cartesian space, LID closure precedes NMP closure in the bound simulation, consistent with prior coarse-grained models of the AK transition. However, NMP-first closure is preferred in the apo simulation. In backbone dihedral space, we find that, as expected, backbone fluctuations are reduced in the O/C transition in parts of all three domains. Among these “quenching” residues, most in the CORE, especially residues 11–13, are rigidified in the TS of the bound simulation, while residues 42–44 in the NMP are flexible in the TS. In contact space, in both apo and bound simulations, one nucleus of closed-state contacts includes parts of the NMP and CORE; CORE–LID contacts are absent in the TS of the apo simulation but formed in the TS of the bound simulation. From these results, we predict mutations that will perturb the opening and/or closing transition rates by changing the entropy of dihedrals and/or the enthalpy of contacts. Furthermore, regarding allostery, the fully closed structure is populated in the apo simulation, but our contact results imply that ligand binding shifts the preferred O/C transition pathway, thus precluding a simple conformational selection mechanism. Finally, the analytical approach and the insights derived from this work may inform the rational design of flexibility and allostery in proteins.     

Dimer Dynamics and Filament Organization of the Bacterial Cell Division Protein FtsA

FtsA is a bacterial actin homolog and one of the core proteins involved in cell division. While previous studies have demonstrated the capability of FtsA to polymerize, little is known about its polymerization state in vivo or if polymerization is necessary for FtsA function. Given that one function of FtsA is to tether FtsZ filaments to the membrane, in vivo polymerization of FtsA imposes geometric constraints and requires a specific polymer curvature direction. Here, we report a series of molecular dynamics simulations probing the structural dynamics of FtsA as a dimer and as a tetrameric single filament. We found that the FtsA polymer exhibits a preferred bending direction that would allow for its placement parallel with FtsZ polymers underneath the cytoplasmic membrane. We also identified key interfacial amino acids that mediate FtsA–FtsA interaction and propose that some amino acids play more critical roles than others. We performed in silico mutagenesis on FtsA and demonstrated that, while a moderate mutation at the polymerization interface does not significantly affect polymer properties such as bending direction and association strength, more drastic mutations change both features and could lead to non-functional FtsA.