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Leishangthem P, Xu X. Thermodynamic Effects Are Essential for Surface Entrapment of Bacteria. PHYSICAL REVIEW LETTERS 2024; 132:238302. [PMID: 38905690 DOI: 10.1103/physrevlett.132.238302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2023] [Revised: 03/12/2024] [Accepted: 04/17/2024] [Indexed: 06/23/2024]
Abstract
The entrapment of bacteria near boundary surfaces is of biological and practical importance, yet the underlying physics is not well understood. We demonstrate that it is crucial to include a commonly neglected thermodynamic effect related to the spatial variation of hydrodynamic interactions, through a model that provides analytic explanation of bacterial entrapment in two dimensionless parameters: α_{1} the ratio of thermal energy to self-propulsion, and α_{2} an intrinsic shape factor. For α_{1} and α_{2} that match an Escherichia coli at room temperature, our model quantitatively reproduces existing experimental observations, including two key features that have not been previously resolved: The bacterial "nose-down" configuration, and the anticorrelation between the pitch angle and the wobbling angle. Furthermore, our model analytically predicts the existence of an entrapment zone in the parameter space defined by {α_{1},α_{2}}.
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Affiliation(s)
- Premkumar Leishangthem
- Complex Systems Division, Beijing Computational Science Research Center, Beijing 100193, China
| | - Xinliang Xu
- Complex Systems Division, Beijing Computational Science Research Center, Beijing 100193, China
- Department of Physics, Beijing Normal University, Beijing 100875, China
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Niu Y, Zhang R, Yuan J. Flagellar motors of swimming bacteria contain an incomplete set of stator units to ensure robust motility. SCIENCE ADVANCES 2023; 9:eadi6724. [PMID: 37922360 PMCID: PMC10624342 DOI: 10.1126/sciadv.adi6724] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/10/2023] [Accepted: 10/03/2023] [Indexed: 11/05/2023]
Abstract
Flagellated bacteria, like Escherichia coli, swim by rotating helical flagellar filaments powered by rotary flagellar motors at their base. Motor dynamics are sensitive to the load it drives. It was previously thought that motor load was high when driving filament rotation in free liquid environments. However, torque measurements from swimming bacteria revealed substantially lower values compared to single-motor studies. We addressed this inconsistency through motor resurrection experiments, abruptly attaching a 1-micrometer-diameter bead to the filament to ensure high load. Unexpectedly, we found that the motor works with only half the complement of stator units when driving filament rotation. This suggests that the motor is not under high load during bacterial swimming, which we confirmed by measuring the torque-speed relationship by varying media viscosity. Therefore, the motor operates in an intermediate-load region, adaptively regulating its stator number on the basis of external load conditions. This ensures the robustness of bacterial motility when swimming in diverse load conditions and varying flagella numbers.
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Affiliation(s)
- Yuhui Niu
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Rongjing Zhang
- Hefei National Research Center for Physical Sciences at the Microscale and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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Nord AL, Biquet-Bisquert A, Abkarian M, Pigaglio T, Seduk F, Magalon A, Pedaci F. Dynamic stiffening of the flagellar hook. Nat Commun 2022; 13:2925. [PMID: 35614041 PMCID: PMC9133114 DOI: 10.1038/s41467-022-30295-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2021] [Accepted: 04/22/2022] [Indexed: 11/09/2022] Open
Abstract
For many bacteria, motility stems from one or more flagella, each rotated by the bacterial flagellar motor, a powerful rotary molecular machine. The hook, a soft polymer at the base of each flagellum, acts as a universal joint, coupling rotation between the rigid membrane-spanning rotor and rigid flagellum. In multi-flagellated species, where thrust arises from a hydrodynamically coordinated flagellar bundle, hook flexibility is crucial, as flagella rotate significantly off-axis. However, consequently, the thrust applies a significant bending moment. Therefore, the hook must simultaneously be compliant to enable bundle formation yet rigid to withstand large hydrodynamical forces. Here, via high-resolution measurements and analysis of hook fluctuations under dynamical conditions, we elucidate how it fulfills this double functionality: the hook shows a dynamic increase in bending stiffness under increasing torsional stress. Such strain-stiffening allows the system to be flexible when needed yet reduce deformation under high loads, enabling high speed motility. Bacterial motility relies on the mechanics of the “hook” the 60 nm biopolymer at the base of rotating flagella. Here, authors observe the hook stiffening as it is twisted by the rotation of the flagellum, a mechanical feat evolved for its function.
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Affiliation(s)
- Ashley L Nord
- Centre de Biologie Structurale, Univ. Montpellier, CNRS, INSERM, Montpellier, France
| | - Anaïs Biquet-Bisquert
- Centre de Biologie Structurale, Univ. Montpellier, CNRS, INSERM, Montpellier, France
| | - Manouk Abkarian
- Centre de Biologie Structurale, Univ. Montpellier, CNRS, INSERM, Montpellier, France
| | - Théo Pigaglio
- Aix Marseille Université, CNRS, Laboratoire de Chimie Bactérienne (UMR7283), IMM, IM2B, 13402, Marseille, France
| | - Farida Seduk
- Aix Marseille Université, CNRS, Laboratoire de Chimie Bactérienne (UMR7283), IMM, IM2B, 13402, Marseille, France
| | - Axel Magalon
- Aix Marseille Université, CNRS, Laboratoire de Chimie Bactérienne (UMR7283), IMM, IM2B, 13402, Marseille, France
| | - Francesco Pedaci
- Centre de Biologie Structurale, Univ. Montpellier, CNRS, INSERM, Montpellier, France.
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Kamdar S, Shin S, Leishangthem P, Francis LF, Xu X, Cheng X. The colloidal nature of complex fluids enhances bacterial motility. Nature 2022; 603:819-823. [PMID: 35355005 DOI: 10.1038/s41586-022-04509-3] [Citation(s) in RCA: 22] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2021] [Accepted: 02/03/2022] [Indexed: 12/24/2022]
Abstract
The natural habitats of microorganisms in the human microbiome, ocean and soil ecosystems are full of colloids and macromolecules. Such environments exhibit non-Newtonian flow properties, drastically affecting the locomotion of microorganisms1-5. Although the low-Reynolds-number hydrodynamics of swimming flagellated bacteria in simple Newtonian fluids has been well developed6-9, our understanding of bacterial motility in complex non-Newtonian fluids is less mature10,11. Even after six decades of research, fundamental questions about the nature and origin of bacterial motility enhancement in polymer solutions are still under debate12-23. Here we show that flagellated bacteria in dilute colloidal suspensions display quantitatively similar motile behaviours to those in dilute polymer solutions, in particular a universal particle-size-dependent motility enhancement up to 80% accompanied by a strong suppression of bacterial wobbling18,24. By virtue of the hard-sphere nature of colloids, whose size and volume fraction we vary across experiments, our results shed light on the long-standing controversy over bacterial motility enhancement in complex fluids and suggest that polymer dynamics may not be essential for capturing the phenomenon12-23. A physical model that incorporates the colloidal nature of complex fluids quantitatively explains bacterial wobbling dynamics and mobility enhancement in both colloidal and polymeric fluids. Our findings contribute to the understanding of motile behaviours of bacteria in complex fluids, which are relevant for a wide range of microbiological processes25 and for engineering bacterial swimming in complex environments26,27.
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Affiliation(s)
- Shashank Kamdar
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN, USA
| | - Seunghwan Shin
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN, USA
| | | | - Lorraine F Francis
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN, USA
| | - Xinliang Xu
- Complex Systems Division, Beijing Computational Science Research Center, Beijing, China. .,Department of Physics, Beijing Normal University, Beijing, China.
| | - Xiang Cheng
- Department of Chemical Engineering and Materials Science, University of Minnesota, Minneapolis, MN, USA.
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Ishikawa T, Omori T, Kikuchi K. Bacterial biomechanics-From individual behaviors to biofilm and the gut flora. APL Bioeng 2020; 4:041504. [PMID: 33163845 PMCID: PMC7595747 DOI: 10.1063/5.0026953] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2020] [Accepted: 10/16/2020] [Indexed: 02/07/2023] Open
Abstract
Bacteria inhabit a variety of locations and play important roles in the environment and health. Our understanding of bacterial biomechanics has improved markedly in the last decade and has revealed that biomechanics play a significant role in microbial biology. The obtained knowledge has enabled investigation of complex phenomena, such as biofilm formation and the dynamics of the gut flora. A bottom-up strategy, i.e., from the cellular to the macroscale, facilitates understanding of macroscopic bacterial phenomena. In this Review, we first cover the biomechanics of individual bacteria in the bulk liquid and on surfaces as the base of complex phenomena. The collective behaviors of bacteria in simple environments are next introduced. We then introduce recent advances in biofilm biomechanics, in which adhesion force and the flow environment play crucial roles. We also review transport phenomena in the intestine and the dynamics of the gut flora, focusing on that in zebrafish. Finally, we provide an overview of the future prospects for the field.
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Affiliation(s)
| | - Toshihiro Omori
- Department Finemechanics, Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
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Reorientation behavior in the helical motility of light-responsive spiral droplets. Nat Commun 2019; 10:5238. [PMID: 31748502 PMCID: PMC6868138 DOI: 10.1038/s41467-019-13201-6] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/03/2019] [Accepted: 10/25/2019] [Indexed: 01/07/2023] Open
Abstract
The physico-chemical processes supporting life's purposeful movement remain essentially unknown. Self-propelling chiral droplets offer a minimalistic model of swimming cells and, in surfactant-rich water, droplets of chiral nematic liquid crystals follow the threads of a screw. We demonstrate that the geometry of their trajectory is determined by both the number of turns in, and the handedness of, their spiral organization. Using molecular motors as photo-invertible chiral dopants allows converting between right-handed and left-handed trajectories dynamically, and droplets subjected to such an inversion reorient in a direction that is also encoded by the number of spiral turns. This motile behavior stems from dynamic transmission of chirality, from the artificial molecular motors to the liquid crystal in confinement and eventually to the helical trajectory, in analogy with the chirality-operated motion and reorientation of swimming cells and unicellular organisms.
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Jabbarzadeh M, Fu HC. Dynamic instability in the hook-flagellum system that triggers bacterial flicks. Phys Rev E 2018; 97:012402. [PMID: 29448321 DOI: 10.1103/physreve.97.012402] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2017] [Indexed: 11/06/2022]
Abstract
Dynamical bending, buckling, and polymorphic transformations of the flagellum are known to affect bacterial motility, but run-reverse-flick motility of monotrichous bacteria also involves the even more flexible hook connecting the flagellum to its rotary motor. Although flick initiation has been hypothesized to involve either static Euler buckling or dynamic bending of the hook, the precise mechanism of flick initiation remains unknown. Here, we find that flicks initiate via a dynamic instability requiring flexibility in both the hook and flagellum. We obtain accurate estimates of forces and torques on the hook that suggest that flicks occur for stresses below the (static) Euler buckling criterion, then provide a mechanistic model for flick initiation that requires combined bending of the hook and flagellum. We calculate the triggering torque-stiffness ratio and find that our predicted onset of dynamic instability corresponds well with experimental observations.
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Affiliation(s)
- Mehdi Jabbarzadeh
- Department of Mechanical Engineering, University of Utah, Salt Lake City, Utah 84112, USA
| | - Henry Chien Fu
- Department of Mechanical Engineering, University of Utah, Salt Lake City, Utah 84112, USA
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Abstract
The rotary motor of bacteria is a natural nano-technological marvel that enables cell locomotion by powering the rotation of semi-rigid helical flagellar filaments in fluid environments. It is well known that the motor operates essentially at constant torque in counter-clockwise direction but past work have reported a large range of values of this torque. Focusing on Escherichia coli cells that are swimming and cells that are stuck on a glass surface for which all geometrical and environmental parameters are known (N. C. Darnton et al., J. Bacteriol., 2007, 189, 1756-1764), we use two validated numerical methods to compute the value of the motor torque consistent with experiments. Specifically, we use (and compare) a numerical method based on the boundary integral representation of Stokes flow and also develop a hybrid method combining boundary element and slender body theory to model the cell body and flagellar filament, respectively. Using measured rotation speed of the motor, our computations predict a value of the motor torque in the range 440 pN nm to 829 pN nm, depending critically on the distance between the flagellar filaments and the nearby surface.
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Affiliation(s)
- Debasish Das
- Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK.
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Abstract
As discovered over the past 25 years, the cytoskeletons of bacteria and archaea are complex systems of proteins whose central components are dynamic cytomotive filaments. They perform roles in cell division, DNA partitioning, cell shape determination and the organisation of intracellular components. The protofilament structures and polymerisation activities of various actin-like, tubulin-like and ESCRT-like proteins of prokaryotes closely resemble their eukaryotic counterparts but show greater diversity. Their activities are modulated by a wide range of accessory proteins but these do not include homologues of the motor proteins that supplement filament dynamics to aid eukaryotic cell motility. Numerous other filamentous proteins, some related to eukaryotic IF-proteins/lamins and dynamins etc, seem to perform structural roles similar to those in eukaryotes.
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Affiliation(s)
- Linda A Amos
- MRC Laboratory of Molecular Biology, Francis Crick Avenue, Cambridge, CB2 0QH, UK.
| | - Jan Löwe
- MRC Laboratory of Molecular Biology, Francis Crick Avenue, Cambridge, CB2 0QH, UK.
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