Switch interactions control energy frustration and multiple flagellar filament structures

Differential Bending Stiffness of the Bacterial Flagellar Hook under Counterclockwise and Clockwise Rotations

The bacterial hook, as a universal joint coupling rotation of the flagellar motor and the filament, is an important component of the flagellum that propels the bacteria to swim. The mechanical properties of the hook are essential for the flagellum to achieve normal functions. In multiflagellated bacteria such as Escherichia coli, the hook must be compliant so that it can bend for the filaments to form a coherently rotating bundle to generate the thrust when the motor rotates counterclockwise (CCW), yet it also must be rigid so that the bundle can disrupt for the bacteria to tumble to change swimming direction when the motor rotates clockwise (CW). Here, by combining an elastic rod model with high-resolution bead assay to accurately measure the bending stiffness of the hook under CCW or CW rotation in vivo, we elucidate how the hook accomplishes this dual functionality: the hook stiffens under CW rotation, with bending stiffness under CW rotation twice as large as that under CCW rotation. This enables a robust run-and-tumble swimming motility for multiflagellated bacteria.

Bacterial Flagellar Filament: A Supramolecular Multifunctional Nanostructure

The bacterial flagellum is a complex and dynamic nanomachine that propels bacteria through liquids. It consists of a basal body, a hook, and a long filament. The flagellar filament is composed of thousands of copies of the protein flagellin (FliC) arranged helically and ending with a filament cap composed of an oligomer of the protein FliD. The overall structure of the filament core is preserved across bacterial species, while the outer domains exhibit high variability, and in some cases are even completely absent. Flagellar assembly is a complex and energetically costly process triggered by environmental stimuli and, accordingly, highly regulated on transcriptional, translational and post-translational levels. Apart from its role in locomotion, the filament is critically important in several other aspects of bacterial survival, reproduction and pathogenicity, such as adhesion to surfaces, secretion of virulence factors and formation of biofilms. Additionally, due to its ability to provoke potent immune responses, flagellins have a role as adjuvants in vaccine development. In this review, we summarize the latest knowledge on the structure of flagellins, capping proteins and filaments, as well as their regulation and role during the colonization and infection of the host.

Distinct chemotactic behavior in the original Escherichia coli K-12 depending on forward-and-backward swimming, not on run-tumble movements

Most motile bacteria are propelled by rigid, helical, flagellar filaments and display distinct swimming patterns to explore their favorable environments. Escherichia coli cells have a reversible rotary motor at the base of each filament. They exhibit a run-tumble swimming pattern, driven by switching of the rotational direction, which causes polymorphic flagellar transformation. Here we report a novel swimming mode in E. coli ATCC10798, which is one of the original K-12 clones. High-speed tracking of single ATCC10798 cells showed forward and backward swimming with an average turning angle of 150°. The flagellar helicity remained right-handed with a 1.3 μm pitch and 0.14 μm helix radius, which is consistent with the feature of a curly type, regardless of motor switching; the flagella of ATCC10798 did not show polymorphic transformation. The torque and rotational switching of the motor was almost identical to the E. coli W3110 strain, which is a derivative of K-12 and a wild-type for chemotaxis. The single point mutation of N87K in FliC, one of the filament subunits, is critical to the change in flagellar morphology and swimming pattern, and lack of flagellar polymorphism. E. coli cells expressing FliC(N87K) sensed ascending a chemotactic gradient in liquid but did not spread on a semi-solid surface. Based on these results, we concluded that a flagellar polymorphism is essential for spreading in structured environments.

Bioinspired reorientation strategies for application in micro/nanorobotic control

Engineers have recently been inspired by swimming methodologies of microorganisms in creating micro-/nanorobots for biomedical applications. Future medicine may be revolutionized by the application of these small machines in diagnosing, monitoring, and treating diseases. Studies over the past decade have often concentrated on propulsion generation. However, there are many other challenges to address before the practical use of robots at the micro-/nanoscale. The control and reorientation ability of such robots remain as some of these challenges. This paper reviews the strategies of swimming microorganisms for reorientation, including tumbling, reverse and flick, direction control of helical-path swimmers, by speed modulation, using complex flagella, and the help of mastigonemes. Then, inspired by direction change in microorganisms, methods for orientation control for microrobots and possible directions for future studies are discussed. Further, the effects of solid boundaries on the swimming trajectories of microorganisms and microrobots are examined. In addition to propulsion systems for artificial microswimmers, swimming microorganisms are promising sources of control methodologies at the micro-/nanoscale.

Bacterial flagellar axial structure and its construction

The bacterial flagellum is a motile organelle composed of thousands of protein subunits. The filamentous part that extends from the cell membrane is called the axial structure and consists of three major parts, the filament, hook, and rod, and other minor components. Each of the three main parts shares a similar self-assembly mechanism and a common basic architecture of subunit arrangement while showing quite distinct mechanical properties to achieve its specific function. Structural and molecular mechanisms to produce these various mechanical properties of the axial structure, such as the filament, the hook, and the rod, have been revealed by the complementary use of X-ray crystallography and cryo-electron microscopy. In addition, the mechanism of growth of the axial structure is beginning to be revealed based on the molecular structure.

Molecular dynamics simulation of bacterial flagella

The bacterial flagellum is a biological nanomachine for the locomotion of bacteria, and is seen in organisms like Salmonella and Escherichia coli. The flagellum consists of tens of thousands of protein molecules and more than 30 different kinds of proteins. The basal body of the flagellum contains a protein export apparatus and a rotary motor that is powered by ion motive force across the cytoplasmic membrane. The filament functions as a propeller whose helicity is controlled by the direction of the torque. The hook that connects the motor and filament acts as a universal joint, transmitting torque generated by the motor to different directions. This report describes the use of molecular dynamics to study the bacterial flagellum. Molecular dynamics simulation is a powerful method that permits the investigation, at atomic resolution, of the molecular mechanisms of biomolecular systems containing many proteins and solvent. When applied to the flagellum, these studies successfully unveiled the polymorphic supercoiling and transportation mechanism of the filament, the universal joint mechanism of the hook, the ion transfer mechanism of the motor stator, the flexible nature of the transport apparatus proteins, and activation of proteins involved in chemotaxis.

A structural model of flagellar filament switching across multiple bacterial species

The bacterial flagellar filament has long been studied to understand how a polymer composed of a single protein can switch between different supercoiled states with high cooperativity. Here we present near-atomic resolution cryo-EM structures for flagellar filaments from both Gram-positive Bacillus subtilis and Gram-negative Pseudomonas aeruginosa. Seven mutant flagellar filaments in B. subtilis and two in P. aeruginosa capture two different states of the filament. These reliable atomic models of both states reveal conserved molecular interactions in the interior of the filament among B. subtilis, P. aeruginosa and Salmonella enterica. Using the detailed information about the molecular interactions in two filament states, we successfully predict point mutations that shift the equilibrium between those two states. Further, we observe the dimerization of P. aeruginosa outer domains without any perturbation of the conserved interior of the filament. Our results give new insights into how the flagellin sequence has been "tuned" over evolution.Bacterial flagellar filaments are composed almost entirely of a single protein-flagellin-which can switch between different supercoiled states in a highly cooperative manner. Here the authors present near-atomic resolution cryo-EM structures of nine flagellar filaments, and begin to shed light on the molecular basis of filament switching.

Curcumin Reduces the Motility of Salmonella enterica Serovar Typhimurium by Binding to the Flagella, Thereby Leading to Flagellar Fragility and Shedding

One of the important virulence properties of the pathogen is its ability to travel to a favorable environment, cross the viscous mucus barrier (intestinal barrier for enteric pathogens), and reach the epithelia to initiate pathogenesis with the help of an appendage, like flagella. Nonetheless, flagella can act as an "Achilles heel," revealing the pathogen's presence to the host through the stimulation of innate and adaptive immune responses. We assessed whether curcumin, a dietary polyphenol, could alter the motility of Salmonella, a foodborne pathogen. It reduced the motility of Salmonella enterica serovar Typhimurium by shortening the length of the flagellar filament (from ∼8 μm to ∼5 μm) and decreasing its density (4 or 5 flagella/bacterium instead of 8 or 9 flagella/bacterium). Upon curcumin treatment, the percentage of flagellated bacteria declined from ∼84% to 59%. However, no change was detected in the expression of the flagellin gene and protein. A fluorescence binding assay demonstrated binding of curcumin to the flagellar filament. This might make the filament fragile, breaking it into smaller fragments. Computational analysis predicted the binding of curcumin, its analogues, and its degraded products to a flagellin molecule at an interface between domains D1 and D2. Site-directed mutagenesis and a fluorescence binding assay confirmed the binding of curcumin to flagellin at residues ASN120, ASP123, ASN163, SER164, ASN173, and GLN175.

IMPORTANCE

This work, to our knowledge the first report of its kind, examines how curcumin targets flagellar density and affects the pathogenesis of bacteria. We found that curcumin does not affect any of the flagellar synthesis genes. Instead, it binds to the flagellum and makes it fragile. It increases the torsional stress on the flagellar filament that then breaks, leaving fewer flagella around the bacteria. Flagella, which are crucial ligands for Toll-like receptor 5, are some of the most important appendages of Salmonella Curcumin is an important component of turmeric, which is a major spice used in Asian cooking. The loss of flagella can, in turn, change the pathogenesis of bacteria, making them more robust and fit in the host.

Chemical reactivity drives spatiotemporal organisation of bacterial metabolism

In this review, we examine how bacterial metabolism is shaped by chemical constraints acting on the material and dynamic layout of enzymatic networks and beyond. These are moulded not only for optimisation of given metabolic objectives (e.g. synthesis of a particular amino acid or nucleotide) but also for curbing the detrimental reactivity of chemical intermediates. Besides substrate channelling, toxicity is avoided by barriers to free diffusion (i.e. compartments) that separate otherwise incompatible reactions, along with ways for distinguishing damaging vs. harmless molecules. On the other hand, enzymes age and their operating lifetime must be tuned to upstream and downstream reactions. This time dependence of metabolic pathways creates time-linked information, learning and memory. These features suggest that the physical structure of existing biosystems, from operon assemblies to multicellular development may ultimately stem from the need to restrain chemical damage and limit the waste inherent to basic metabolic functions. This provides a new twist of our comprehension of fundamental biological processes in live systems as well as practical take-home lessons for the forward DNA-based engineering of novel biological objects.

Nonlinear dynamics of a rotating elastic rod in a viscous fluid

The dynamics of an elastic rod in a viscous fluid at zero Reynolds number is investigated when the bottom end of the rod is tethered at a point in space and rotates at a prescribed angular frequency, while the other part of the rod freely moves through the fluid. A rotating elastic rod, which is intrinsically straight, exhibits three dynamical motions: twirling, overwhirling, and whirling. The first two motions are stable, whereas the last motion is unstable. The stability of dynamical motions is determined by material and geometrical properties of the rod, fluid properties, and the angular frequency of the rod. We employ the regularized Stokes flow to describe the fluid motion and the Kirchhoff rod model to describe the elastic rod. Our simulation results display subcritical Hopf bifurcation diagrams indicating the bistability region. We also investigate the whirling motion generated by the rotation of an intrinsically bent rod. It is observed that the angular frequency determines the handedness of the whirling rod and thus the flow direction and that there is a critical frequency which separates the positive (upward) flow at frequencies above it from the negative (downward) flow at frequencies below it.

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.

Frustration-induced protein intrinsic disorder

Spontaneous folding into a specific native structure is the most important property of protein to perform their biological functions within organisms. Spontaneous folding is understood on the basis of an energy landscape picture based on the minimum frustration principle. Therefore, frustration seemingly only leads to protein functional disorder. However, frustration has recently been suggested to have a function in allosteric regulation. Functional frustration has the possibility to be a key to our deeper understanding of protein function. To explore another functional frustration, we theoretically examined structural frustration, which is designed to induce intrinsic disorder of a protein and its function through the coupled folding and binding. We extended the Wako-Saitô-Muñoz-Eaton model to take into account a frustration effect. With the model, we analyzed the binding part of neuron-restrictive silencer factor and showed that designed structural frustration in it induces intrinsic disorder. Furthermore, we showed that the folding and the binding are cooperative in interacting with a target protein. The cooperativity enables an intrinsically disordered protein to exhibit a sharp switch-like folding response to binding chemical potential change. Through this switch-like response, the structural frustration may contribute to the regulation function of interprotein interaction of the intrinsically disordered protein.

Key amino acid residues involved in the transitions of L- to R-type protofilaments of the Salmonella flagellar filament

The flagellar filament enables bacteria to swim by functioning as a helical propeller. The filament is a supercoiled assembly of a single protein, flagellin, and is formed by 11 protofilaments arranged in a circle. Bacterial swimming and tumbling correlate with changes of the various helical structures, called polymorphic transformation, that are determined by the ratios of two distinct forms of protofilaments, the L and R types. The polymorphic transformation is caused by transition of the protofilament between L and R types. Elucidation of this transition mechanism has been addressed by comparing the atomic structures of L- and R-type straight filaments or using massive molecular dynamic simulation. Here, we found amino acid residues required for the transition of the protofilament using fliC-intragenic suppressor analysis. We isolated a number of revertants producing supercoiled filaments from mutants with straight filaments and identified the second-site mutations in all of the revertants. The results suggest that Asp107, Gly426, and Ser448 and Ser106, Ala416, Ala427, and Arg431 are the key residues involved in inducing supercoiled filaments from the R- and the L-type straight filaments, respectively. Considering the structures of the R- and L-type protofilaments and the relationship between the rotation of the flagellar motor and the polymorphic transformation, we propose that Gly426, Ala427, and Arg431 contribute to the first stage of the transition and that Ser106, Asp107, and Ala416 play a role in propagating the transitions along the flagellar filament.

Rise of the RNA machines: exploring the structure of long non-coding RNAs

Novel, profound and unexpected roles of long non-coding RNAs (lncRNAs) are emerging in critical aspects of gene regulation. Thousands of lncRNAs have been recently discovered in a wide range of mammalian systems, related to development, epigenetics, cancer, brain function and hereditary disease. The structural biology of these lncRNAs presents a brave new RNA world, which may contain a diverse zoo of new architectures and mechanisms. While structural studies of lncRNAs are in their infancy, we describe existing structural data for lncRNAs, as well as crystallographic studies of other RNA machines and their implications for lncRNAs. We also discuss the importance of dynamics in RNA machine mechanism. Determining commonalities between lncRNA systems will help elucidate the evolution and mechanistic role of lncRNAs in disease, creating a structural framework necessary to pursue lncRNA-based therapeutics.

Microscopic analysis of bacterial motility at high pressure

The bacterial flagellar motor is a molecular machine that converts an ion flux to the rotation of a helical flagellar filament. Counterclockwise rotation of the filaments allows them to join in a bundle and propel the cell forward. Loss of motility can be caused by environmental factors such as temperature, pH, and solvation. Hydrostatic pressure is also a physical inhibitor of bacterial motility, but the detailed mechanism of this inhibition is still unknown. Here, we developed a high-pressure microscope that enables us to acquire high-resolution microscopic images, regardless of applied pressures. We also characterized the pressure dependence of the motility of swimming Escherichia coli cells and the rotation of single flagellar motors. The fraction and speed of swimming cells decreased with increased pressure. At 80 MPa, all cells stopped swimming and simply diffused in solution. After the release of pressure, most cells immediately recovered their initial motility. Direct observation of the motility of single flagellar motors revealed that at 80 MPa, the motors generate torque that should be sufficient to join rotating filaments in a bundle. The discrepancy in the behavior of free swimming cells and individual motors could be due to the applied pressure inhibiting the formation of rotating filament bundles that can propel the cell body in an aqueous environment.

Three mutations in Escherichia coli that generate transformable functional flagella

Hydrodynamics predicts that swimming bacteria generate a propulsion force when a helical flagellum rotates because rotating helices necessarily translate at a low Reynolds number. It is generally believed that the flagella of motile bacteria are semirigid helices with a fixed pitch determined by hydrodynamic principles. Here, we report the characterization of three mutations in laboratory strains of Escherichia coli that produce different steady-state flagella without losing cell motility. E. coli flagella rotate counterclockwise during forward swimming, and the normal form of the flagella is a left-handed helix. A single amino acid exchange A45G and a double mutation of A48S and S110A change the resting flagella to right-handed helices. The stationary flagella of the triple mutant were often straight or slightly curved at neutral pH. Deprotonation facilitates the helix formation of it. The helical and curved flagella can be transformed to the normal form by torsion upon rotation and thus propel the cell. These mutations arose in the long-term laboratory cultivation. However, flagella are under strong selection pressure as extracellular appendages, and similar transformable flagella would be common in natural environments.

Multiple Conformations of F-actin

Actin works within eukaryotic cells to facilitate a variety of cellular processes, which are driven by the assembly of G-actin (monomeric form) into F-actin (fibrous form), and the disassembly of F-actin into G-actin. F-actin adopts multiple conformations, which are specified by interactions with various actin-binding proteins. Knowledge of the multiple conformations of actin is the key for understanding its cellular functions. Recently, we published a refined model for F-actin. In this review, based on this model, we discuss the origin, mechanism, and possible physiological significance of the multiple conformations of F-actin.

Enhanced resolution of molecular recognition to distinguish structurally similar molecules by different conformational responses of a protein upon ligand binding

MutT distinguishes substrate 8-oxo-dGTP from dGTP and also 8-oxo-dGMP from dGMP despite small differences of chemical structures between them. In this paper we show by the method of molecular dynamics simulation that the transition between conformational substates of MutT is a key mechanism for a high-resolution molecular recognition of the differences between the very similar chemical compounds. (1) The native state MutT has two conformational substates with similar free energies, each characterized by either open or closed of two loops surrounding the substrate binding active site. Between the two substates, the open substate is more stable in free MutT and in dGMP-MutT complex, and the closed substate is more stable in 8-oxo-dGMP-MutT complex. (2) Conformational fluctuation of the open substate is much larger than that of the closed substate. An estimate of associated entropy difference was found to be consistent with the experimentally found difference of entropy contribution to the binding free energies of the two molecules. (3) A hydrogen bond between H7 atom of 8-oxo-dGMP and the sidechain of Asn119 plays a crucial role for maintaining the closed substate in 8-oxo-dGMP-MutT complex. When this hydrogen bond is absent in the H7-deficient dGMP-MutT complex, the closed substate is no more maintained and transition to the more entropically-favored open substate is induced. (4) Thus, this mechanism of the hydrogen bond controlling the relative stabilities of the drastically different two conformational substates enhances the resolution to recognize the small difference of the chemical structures between the two molecules, dGMP and 8-oxo-dGMP.

Conformational change of flagellin for polymorphic supercoiling of the flagellar filament

The bacterial flagellar filament is a helical propeller rotated by the flagellar motor for bacterial locomotion. The filament is a supercoiled assembly of a single protein, flagellin, and is formed by 11 protofilaments. For bacterial taxis, the reversal of motor rotation switches the supercoil between left- and right-handed, both of which arise from combinations of two distinct conformations and packing interactions of the L-type and R-type protofilaments. Here we report an atomic model of the L-type straight filament by electron cryomicroscopy and helical image analysis. Comparison with the R-type structure shows interesting features: an orientation change of the outer core domains (D1) against the inner core domains (D0) showing almost invariant orientation and packing, a conformational switching within domain D1, and the conformational flexibility of domains D0 and D1 with their spoke-like connection for tight molecular packing.

Regulation of the protein-conducting channel by a bound ribosome

During protein synthesis, it is often necessary for the ribosome to form a complex with a membrane-bound channel, the SecY/Sec61 complex, in order to translocate nascent proteins across a cellular membrane. Structural data on the ribosome-channel complex are currently limited to low-resolution cryo-electron microscopy maps, including one showing a bacterial ribosome bound to a monomeric SecY complex. Using that map along with available atomic-level models of the ribosome and SecY, we have determined, through molecular dynamics flexible fitting (MDFF), an atomic-resolution model of the ribosome-channel complex. We characterized computationally the sites of ribosome-SecY interaction within the complex and determined the effect of ribosome binding on the SecY channel. We also constructed a model of a ribosome in complex with a SecY dimer by adding a second copy of SecY to the MDFF-derived model. The study involved 2.7-million-atom simulations over altogether nearly 50 ns.

Mechanical unfolding of bacterial flagellar filament protein by molecular dynamics simulation

Bacterial flagellum is a nano-scale motility device constructed by self-assembly. During construction of the cell-exterior filament (the 'propeller'), subunit proteins (called flagellin) are thought to be exported through the hollow flagellum to the growing filament tip in an unfolded state. To gain insight into the unfolded state preceding any force-spectroscopy experiments on flagellin, we employed force-probe molecular dynamics simulations. Two schemes to attain an unfolded state suitable for efficient transport were examined: (i) stretching flagellin along its length; (ii) unzipping flagellin from its adjacently placed termini. Atomic-level unfolding pathways and the mechanical efforts involved under each scheme were obtained for the four-domain flagellin from S. typhimurium. Flagellin appeared stiffer and required larger unfolding forces when stretched as the relative sliding of beta-strands require the breaking of multiple hydrogen bonds at once. In contrast, unzipping requires lower unfolding forces as it mainly involves unraveling beta-sheets by breaking hydrogen bonds one by one.

Bacterial flagellar motor

The bacterial flagellar motor is a reversible rotary nano-machine, about 45 nm in diameter, embedded in the bacterial cell envelope. It is powered by the flux of H+or Na+ions across the cytoplasmic membrane driven by an electrochemical gradient, the proton-motive force or the sodium-motive force. Each motor rotates a helical filament at several hundreds of revolutions per second (hertz). In many species, the motor switches direction stochastically, with the switching rates controlled by a network of sensory and signalling proteins. The bacterial flagellar motor was confirmed as a rotary motor in the early 1970s, the first direct observation of the function of a single molecular motor. However, because of the large size and complexity of the motor, much remains to be discovered, in particular, the structural details of the torque-generating mechanism. This review outlines what has been learned about the structure and function of the motor using a combination of genetics, single-molecule and biophysical techniques, with a focus on recent results and single-molecule techniques.

Large-scale molecular dynamics simulations of self-assembling systems

Relentless increases in the size and performance of multiprocessor computers, coupled with new algorithms and methods, have led to novel applications of simulations across chemistry. This Perspective focuses on the use of classical molecular dynamics and so-called coarse-grain models to explore phenomena involving self-assembly in complex fluids and biological systems.

Thermal unfolding simulations of bacterial flagellin: insight into its refolding before assembly

Flagellin is the subunit of the bacterial filament, the micrometer-long propeller of a bacterial flagellum. The protein is believed to undergo unfolding for transport through the channel of the filament and to refold in a chamber at the end of the channel before being assembled into the growing filament. We report a thermal unfolding simulation study of S. typhimurium flagellin in aqueous solution as an attempt to gain atomic-level insight into the refolding process. Each molecule comprises two filament-core domains {D0, D1} and two hypervariable-region domains {D2, D3}. D2 can be separated into subdomains D2a and D2b. We observed a similar unfolding order of the domains as reported in experimental thermal denaturation. D2a and D3 exhibited high thermal stability and contained persistent three-stranded beta-sheets in the denatured state which could serve as folding cores to guide refolding. A recent mutagenesis study on flagellin stability seems to suggest the importance of the folding cores. Using crude size estimates, our data suggests that the chamber might be large enough for either denatured hypervariable-region domains or filament-core domains, but not whole flagellin; this implicates a two-staged refolding process.

Strain-dependent twist-stretch elasticity in chiral filaments

Coupling between axial and torsional degrees of freedom often modifies the conformation and expression of natural and synthetic filamentous aggregates. Recent studies on chiral single-walled carbon nanotubes and B-DNA reveal a reversal in the sign of the twist-stretch coupling at large strains. The similarity in the response in these two distinct supramolecular assemblies and at high strains suggests a fundamental, chirality-dependent nonlinear elastic behaviour. Here we seek the link between the microscopic origin of the nonlinearities and the effective twist-stretch coupling using energy-based theoretical frameworks and model simulations. Our analysis reveals a sensitive interplay between the deformation energetics and the sign of the coupling, highlighting robust design principles that determine both the sign and extent of these couplings. These design principles have already been exploited by nature to dynamically engineer such couplings, and have broad implications in mechanically coupled actuation, propulsion and transport in biology and technology.

Design and chance in the self-assembly of macromolecules

The principles of self-assembly are described for naturally occurring macromolecules and for complex assemblies formed from simple synthetic constituents. Many biological molecules owe their function and specificity to their three-dimensional folds, and, in many cases, these folds are specified entirely by the sequence of the constituent amino acids or nucleic acids, and without the requirement for additional machinery to guide the formation of the structure. Thus sequence may often be sufficient to guide the assembly process, starting from denatured components having little or no folds, to the completion state with the stable, equilibrium fold that encompasses functional activity. Self-assembly of homopolymeric structures does not necessarily preserve symmetry, and some polymeric assemblies are organized so that their chemically identical subunits pack stably in geometrically non-equivalent ways. Self-assembly can also involve scaffolds that lack structure, as seen in the multi-enzyme assembly, the degradosome. The stable self-assembly of lipids into dynamic membraneous sheets is also described, and an example is shown in which a synthetic detergent can assemble into membrane layers.

DNA−Protein Interactions as the Source of Large-Length-Scale Chirality Evident in the Liquid Crystal Behavior of Filamentous Bacteriophages

Although all filamentous phages are constructed of chiral components, this study of eight of these phages (fd, IKe, I(2)2, X-2, Pf1, Pf3, tf-1, and X) shows that some form nematic liquid crystals, which are apparently oblivious to the chirality of the components, while others form cholesteric liquid crystals revealing a type of structural chirality not normally encountered. Additions of dopants that interact with the DNA or protein components of the viruses change the liquid crystal properties of seven of the phages. In these seven, DNA-capsid symmetry differences do not allow strict structural equivalency among the protein subunits. The polymorphism arising from this nonequivalency is proposed here to give rise to coiling of the filaments, a large-length-scale chirality that is responsible for forming cholesteric liquid crystal phases. Only one phage of those studied here, Pf1, which is distinguished from the others in its DNA-capsid interactions, forms nematic phases under all conditions tried. The formation of liquid crystals has been developed as a method to detect subtle overall shape effects arising from DNA-subunit-derived polymorphism, an unusual role for the mesogenic state and a new tool for the study of filamentous phage structure.

A Deletion Variant Study of the Functional Role of the Salmonella Flagellin Hypervariable Domain Region in Motility

The eubacterial flagellum is a complex structure with an elongated extracellular filament that is composed primarily of many subunits of a flagellin protein. The highly conserved N and C termini of flagellin are important in its export and self-assembly, whereas the middle sequence region varies greatly in size and composition in different species and is known to be deletion-tolerant. In Salmonella typhimurium phase 1 flagellin, this "hypervariable" region encodes two solvent-exposed domains, D2 and D3, that form a knob-like feature on flagella fibers. The functional role of this structural feature in motility remains unclear. We investigated the structural and physiological role of the hypervariable region in flagella assembly, stability and cellular motility. A library of random internal deletion variants of S. typhimurium flagellin was constructed and screened for functional variants using a swarming agar motility assay. The relative cellular motility and propulsive force of ten representative variants were determined in semi-solid and liquid medium using colony swarming motility assays, video microscopy and optical trapping of single cells. All ten variants exhibited diminished motility, with varying extents of motility observed for internal deletions less than 75 residues and nearly complete loss of motility for deletions greater than 100 residues. The mechanical stability of the variant flagella fibers also decreased with increasing size of deletion. Comparison of the variant sequences with the wild-type sequence and structure indicated that all deletions involved loss of hydrophobic core residues, and removal of both partial and complete segments of secondary structure in the D2 and D3 domains. Homology modeling predicted disruptions of secondary structures in each variant. The hypervariable region D2 and D3 domains appear to stabilize the folded conformation of the flagellin protein and contribute to the mechanical stability and propulsive force of the flagella fibers.

Gap compression/extension mechanism of bacterial flagellar hook as the molecular universal joint

Bacterial flagellar hook acts as a molecular universal joint, transmitting torque produced by the flagellar basal body, a rotary motor, to the flagellar filament. The hook forms polymorphic supercoil structures and can be considered as an assembly of 11 circularly arranged protofilaments. We investigated the molecular mechanism of the universal joint function of the hook by a approximately two-million-atom molecular dynamics simulation. On the inner side of the supercoil, protein subunits are highly packed along the protofilament and no gaps remain for further compression, whereas subunits are slightly separated and are hydrogen bonded through one layer of water molecules on the outer side. As for the intersubunit interactions between protofilaments, subunits are packed along the 6-start helix in a left-handed supercoil whereas they are highly packed along the 5-start helix in a right-handed supercoil. We conclude that the supercoiled structures of the hook in the left- and right-handed forms make maximal use of the gaps between subunits, which we call "gap compression/extension mechanism". Mutual sliding of subunits at the subunit interface accompanying rearrangements of intersubunit hydrogen bonds is interpreted as a mechanism to allow continuous structural change of the hook during flagellar rotation at low energy cost.

Coarse-grained molecular dynamics simulations of a rotating bacterial flagellum

Many types of bacteria propel themselves using elongated structures known as flagella. The bacterial flagellar filament is a relatively simple and well-studied macromolecular assembly, which assumes different helical shapes when rotated in different directions. This polymorphism enables a bacterium to switch between running and tumbling modes; however, the mechanism governing the filament polymorphism is not completely understood. Here we report a study of the bacterial flagellar filament using numerical simulations that employ a novel coarse-grained molecular dynamics method. The simulations reveal the dynamics of a half-micrometer-long flagellum segment on a timescale of tens of microseconds. Depending on the rotation direction, specific modes of filament coiling and arrangement of monomers are observed, in qualitative agreement with experimental observations of flagellar polymorphism. We find that solvent-protein interactions are likely to contribute to the polymorphic helical shapes of the filament.