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arxiv: 2606.20070 · v2 · pith:6WK7R53Hnew · submitted 2026-06-18 · ❄️ cond-mat.soft

E. coli bacterium near corrugated surfaces: near-suface swimming, escape, and hydrodynamic trapping

Pierre Martin , Gon\c{c}alo C. Antunes , Holger Stark This is my paper

Pith reviewed 2026-06-26 15:36 UTC · model grok-4.3

classification ❄️ cond-mat.soft
keywords E. coli motilitynear-surface swimminghydrodynamic trappingcorrugated surfacessurface curvatureflagellar propulsionbacterial adhesionmulti-particle collision dynamics
0
0 comments X

The pith

Higher curvature in undulating surfaces traps non-tumbling E. coli by promoting oscillatory groove swimming and reversing rotation direction from clockwise to counter-clockwise.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper uses hydrodynamic simulations to study how a detailed model of E. coli swims near sinusoidal no-slip surfaces of varying curvature. At low curvatures bacteria show the expected persistent clockwise near-surface motion seen on flat walls. At higher curvatures some escape is possible near ridges, but still larger curvatures induce back-and-forth swimming along grooves that reduces escape chances and strengthens trapping. Two minimal models confirm that groove confinement alone flips the rotation sense. The work therefore shows that realistic three-dimensional surface shape controls bacterial surface exploration and adhesion.

Core claim

At larger curvatures the surface geometry promotes oscillatory swimming along the groove direction, which reduces escape opportunities and therefore enhances bacterial trapping; the confinement around the groove reverses the swimming of the bacterium from clockwise to counter-clockwise.

What carries the argument

Hydrodynamic interaction between a rigid spherocylindrical cell body plus flexible flagella (Kirchhoff rod model) and an undulating no-slip wall, simulated by multi-particle collision dynamics.

If this is right

  • At low curvatures bacteria exhibit persistent near-surface clockwise trajectories.
  • There exists a critical curvature above which escape from ridges becomes probable.
  • At still higher curvatures oscillatory motion along grooves reduces escape and increases trapping.
  • Groove confinement alone is sufficient to reverse rotation sense, as shown by two minimal models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Surface roughness of this scale could be used to design textures that locally retain or repel bacteria in microfluidic or biomedical settings.
  • The same curvature-induced reversal mechanism may operate for other flagellated swimmers whose propulsion relies on similar hydrodynamic coupling to boundaries.
  • Biofilm initiation rates on real surfaces may depend more on groove curvature than on average roughness amplitude.

Load-bearing premise

The multi-particle collision dynamics method together with the Kirchhoff rod model accurately captures the hydrodynamic interactions and mechanics of a non-tumbling E. coli near no-slip boundaries.

What would settle it

Direct observation of whether bacteria near sufficiently curved grooves exhibit sustained counter-clockwise oscillatory trajectories instead of the clockwise circles seen on flat walls.

read the original abstract

Bacteria often swim in complex environments where surfaces are ubiquitous and rarely flat. Surface topography and curvature can strongly affect bacterial motility, with important consequences for surface exploration, adhesion, and biofilm formation. Here, we investigate the swimming of a non-tumbling Escherichia coli bacterium near an undulating no-slip surface using hydrodynamic simulations of a detailed model bacterium. The latter is described by a rigid spherocylindrical cell body and flexible flagella modeled with the Kirchhoff rod theory, while the surrounding fluid is simulated using the method of multi-particle collision dynamics. At low curvatures of the sinusoidal surface modulations, the bacterium exhibits persistent near-surface swimming and clockwise trajectories, consistent with the known behavior near flat no-slip walls. As the curvature increases, bacteria swimming toward a ridge can escape from the surface, which we use to estimate a critical curvature where surface detachment is more likely. At larger curvatures, we find that the surface geometry promotes oscillatory swimming along the groove direction, which reduces escape opportunities and, therefore, enhances bacterial trapping. Indeed, the confinement around the groove reverses the swimming of the bacterium from clockwise to counter-clockwise, as we demonstrate by two minimal models. Thus our work highlights the importance of the three-dimensional surface topography in bacterial surface exploration.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript uses multi-particle collision dynamics (MPCD) simulations of a non-tumbling E. coli model (rigid spherocylindrical body plus Kirchhoff-rod flagella) to examine motility near sinusoidal no-slip surfaces. It reports that low curvature produces persistent clockwise near-surface swimming, intermediate curvature permits escape near ridges, and high curvature induces oscillatory groove-parallel swimming that enhances trapping by reversing rotation sense from clockwise to counter-clockwise; the reversal is additionally illustrated with two minimal models.

Significance. If the reported reversal and trapping enhancement are robust, the work extends flat-wall hydrodynamic studies to three-dimensional topography and supplies both numerical evidence and mechanistic insight via minimal models, with relevance to bacterial surface colonization and biofilm initiation.

major comments (2)
  1. [Simulation Setup] Simulation Setup section: the manuscript notes consistency with known flat-wall behavior but supplies no quantitative benchmark (e.g., resistive-force theory or boundary-element comparison) for the curvature-induced reversal itself; because the central claim that surface geometry reverses rotation sense rests on this hydrodynamic feature, the absence of such validation is load-bearing.
  2. [Results] Results, high-curvature regime: the oscillatory swimming and reduced escape at larger curvatures are reported from MPCD runs, yet no grid-convergence study, collision-rule sensitivity test, or parameter sweep on the Kirchhoff-rod stiffnesses is presented for the reversal; this leaves open whether the effect is a robust Stokes-flow feature or an artifact of the mesoscale discretization.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'two minimal models' is used without naming or briefly characterizing them; adding one sentence would improve readability.
  2. [Figures] Figure captions and trajectory plots: ensure that clockwise versus counter-clockwise sense is unambiguously labeled (arrows or color coding) so that the reported reversal is immediately visible to readers.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and valuable comments on our manuscript. We provide point-by-point responses below and will revise the manuscript accordingly where appropriate.

read point-by-point responses

  1. Referee: [Simulation Setup] Simulation Setup section: the manuscript notes consistency with known flat-wall behavior but supplies no quantitative benchmark (e.g., resistive-force theory or boundary-element comparison) for the curvature-induced reversal itself; because the central claim that surface geometry reverses rotation sense rests on this hydrodynamic feature, the absence of such validation is load-bearing.

    Authors: We appreciate this point. While the manuscript demonstrates consistency with flat-wall behavior, we acknowledge the lack of a specific quantitative benchmark for the reversal. In the revised manuscript, we will add a comparison to resistive-force theory for the flat case and explain how the minimal models validate the hydrodynamic reversal mechanism independently of the MPCD discretization. We believe this addresses the load-bearing aspect of the claim. revision: yes

  2. Referee: [Results] Results, high-curvature regime: the oscillatory swimming and reduced escape at larger curvatures are reported from MPCD runs, yet no grid-convergence study, collision-rule sensitivity test, or parameter sweep on the Kirchhoff-rod stiffnesses is presented for the reversal; this leaves open whether the effect is a robust Stokes-flow feature or an artifact of the mesoscale discretization.

    Authors: We agree that additional tests would enhance confidence in the results. In the revision, we will include a grid-convergence study and a parameter sweep on the Kirchhoff-rod stiffnesses to demonstrate that the reversal is robust and not an artifact of the discretization. Collision-rule sensitivity will also be discussed. revision: yes

Circularity Check

0 steps flagged

No significant circularity in simulation-based results

full rationale

The paper reports numerical outcomes from MPCD fluid simulations coupled to a Kirchhoff-rod flagellar model. All reported behaviors (persistent CW swimming at low curvature, escape at intermediate curvature, oscillatory groove swimming and CW-to-CCW reversal at high curvature) are direct simulation outputs rather than algebraic derivations, fitted parameters renamed as predictions, or self-citation chains. No equations, ansatzes, or uniqueness theorems are invoked that reduce to the inputs by construction. The reader's assessment of score 1.0 is consistent with the absence of any load-bearing circular step.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The claims depend on the accuracy of the chosen hydrodynamic simulation method and the non-tumbling assumption for the model bacterium, which are domain-standard but introduce free parameters in the flagellar and surface models.

free parameters (2)
  • surface curvature amplitude
    Varied across low to high values to identify transitions in escape and trapping behavior.
  • flagella mechanical parameters
    Stiffness and length parameters in the Kirchhoff rod model chosen to represent E. coli flagella.
axioms (2)
  • domain assumption The fluid is modeled as incompressible with no-slip boundary conditions on the surface.
    Standard assumption in hydrodynamic simulations of bacteria near walls.
  • domain assumption The model bacterium is non-tumbling.
    Explicitly stated as a non-tumbling E. coli in the simulation setup.

pith-pipeline@v0.9.1-grok · 5761 in / 1564 out tokens · 38367 ms · 2026-06-26T15:36:07.923839+00:00 · methodology

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Reference graph

Works this paper leans on

66 extracted references

  1. [1]

    planar part

    We use them to define the parameters in our simulations. The particle density is set toρ=10m 0/a3 0 and the time step is∆t=0.05τ 0, which yields a viscosityη=7.5η 0. 52 Finally , at room temperature kBT0 =4.13 pN nm. To incorporate theE. colimodel into the MPCD simulations, we choosea 0 =h=0.1µm. Thus, the discretization of the flagellar filament is chose...

  2. [2]

    Most importantly , we apply a torque|T rot|=3000k BT0 alongu 3, so that the rod rotates around its main axis

    Similarly , we apply a confinement torqueT conf =−K(u 3 ×e y)to keep the rod axisu 3 aligned with the y-direction and setK=1×10 5 kBT0. Most importantly , we apply a torque|T rot|=3000k BT0 alongu 3, so that the rod rotates around its main axis. Note that the torque roughly agrees with the total 8 Figure 9Simulated confinement forceF x conf for a rotating...

  3. [3]

    R. M. Donlan,Emerg. Infect. Dis., 2002,8, 881

    2002

  4. [4]

    Hall-Stoodley , J

    L. Hall-Stoodley , J. W. Costerton and P. Stoodley ,Nat. Rev. Microbiol., 2004,2, 95–108

    2004

  5. [5]

    H. H. Tuson and D. B. Weibel,Soft Matter, 2013,9, 4368– 4380

    2013

  6. [6]

    T. E. P. Kimkes and M. Heinemann,FEMS Microbiol. Rev., 2020,44, 106–122

    2020

  7. [7]

    Sharma, J

    S. Sharma, J. Mohler, S. D. Mahajan, S. A. Schwartz, L. Bruggemann and R. Aalinkeel,Microorganisms, 2023,11, 1614

    2023

  8. [8]

    H. Y. Liu, E. L. Prentice and M. A. Webber,NPJ Antimicrob. Resist., 2024,2, 27

    2024

  9. [9]

    Zheng, M

    S. Zheng, M. Bawazir, A. Dhall, H.-E. Kim, L. He, J. Heo and G. Hwang,Front. Bioeng. Biotechnol., 2021,9, 643722

    2021

  10. [10]

    H. C. Berg,E. coli in Motion, Springer, 1st edn, 2004

    2004

  11. [11]

    Turner, W

    L. Turner, W. S. Ryu and H. C. Berg,J. Bacteriol., 2000,182, 2793–2801

    2000

  12. [12]

    Lauga,Annu

    E. Lauga,Annu. Rev. Fluid Mech., 2016,48, 105–130

    2016

  13. [13]

    H. C. Berg,Annu. Rev. of Biochem., 2003,72, 19–54

    2003

  14. [14]

    N. C. Darnton, L. Turner, S. Rojevsky and H. C. Berg,J. Bac- teriol., 2007,189, 1756–1764

    2007

  15. [15]

    Bianchi, F

    S. Bianchi, F. Saglimbeni, G. Frangipane, M. C. Cannarsa and R. Di Leonardo,PRX Life, 2023,1, 013016

    2023

  16. [16]

    Lauga and T

    E. Lauga and T. R. Powers,Rep. Prog. Phys., 2009,72, 096601

    2009

  17. [17]

    S. E. Spagnolie and E. Lauga,J. Fluid Mech., 2012,700, 105– 147

    2012

  18. [18]

    Drescher, J

    K. Drescher, J. Dunkel, L. H. Cisneros, S. Ganguly , R. E. Gold- stein, R. E. G. Designed and R. E. G. Performed,PNAS, 2011, 108, 10940–10945

    2011

  19. [19]

    Schaar, A

    K. Schaar, A. Zöttl and H. Stark,Phys. Rev. Lett., 2015,115, 038101

    2015

  20. [20]

    Junot, T

    G. Junot, T. Darnige, A. Lindner, V. A. Martinez, J. Arlt, A. Dawson, W. C. K. Poon, H. Auradou and E. Clément,Phys. Rev. Lett., 2022,128, 248101

    2022

  21. [21]

    Bianchi, F

    S. Bianchi, F. Saglimbeni and R. Di Leonardo,Phys. Rev. X, 2017,7, 011010

    2017

  22. [22]

    A. P. Berke, L. Turner, H. C. Berg and E. Lauga,Phys. Rev. Lett., 2008,101, 038102

    2008

  23. [23]

    Giacché, T

    D. Giacché, T. Ishikawa and T. Yamaguchi,Phys. Rev. E, 2010, 82, 056309

    2010

  24. [24]

    Lauga, W

    E. Lauga, W. R. DiLuzio, G. M. Whitesides and H. A. Stone, Biophys. J., 2006,90, 400–412

    2006

  25. [25]

    S. M. Mousavi, G. Gompper and R. G. Winkler,Soft Matter, 2020,16, 4866–4875

    2020

  26. [26]

    Lemelle, J

    L. Lemelle, J. F. Palierne, E. Chatre and C. Place,J. Bacteriol., 2010,192, 6307–6308

    2010

  27. [27]

    J. Hu, A. Wysocki, R. G. Winkler and G. Gompper,Sci. Rep., 2015,5, 9586

    2015

  28. [28]

    Vizsnyiczai, G

    G. Vizsnyiczai, G. Frangipane, S. Bianchi, F. Saglimbeni, D. Dell’Arciprete and R. Di Leonardo,Nat. Commun., 2020, 11, 2340

    2020

  29. [29]

    Acemoglu and S

    A. Acemoglu and S. Yesilyurt,Biophys. J., 2014,106, 1537– 1547

    2014

  30. [30]

    B. Liu, K. S. Breuer and T. R. Powers,Phys. Fluids, 2014,26, 011701

    2014

  31. [31]

    Yoshioka, Y

    A. Yoshioka, Y. Y. Shimada, T. Omori, N. A. Uemura, K. Takeshita, K. Ishigami, H. Morimura, M. Furubayashi, T. Kan, H. Wada, Y. Kikuchi and D. Nakane,Nat. Commun., 2026,17, 713

    2026

  32. [32]

    J. B. Lynch, N. James, M. McFall-Ngai, E. G. Ruby , S. Shin and D. Takagi,Biophys. J., 2022,121, 2653–2662

    2022

  33. [33]

    Sipos, K

    O. Sipos, K. Nagy , R. Di Leonardo and P. Galajda,Phys. Rev. Lett., 2015,114, 258104

    2015

  34. [34]

    Takaha and D

    Y. Takaha and D. Nishiguchi,Phys. Rev. E, 2023,107, 014602

    2023

  35. [35]

    Kurzthaler and H

    C. Kurzthaler and H. A. Stone,Soft Matter, 2021,17, 3322– 3332

    2021

  36. [36]

    Pérez-Estay , M

    B. Pérez-Estay , M. L. Cordero, N. Sepúlveda and R. Soto, Phys. Rev. E, 2024,109, 054601

    2024

  37. [37]

    R. Mok, J. Dunkel and V. Kantsler,Phys. Rev. E, 2019,99, 052607

    2019

  38. [38]

    Das and A

    S. Das and A. Cacciuto,Soft Matter, 2019,15, 8290–8301

    2019

  39. [39]

    Kuron, P

    M. Kuron, P. Stärk, C. Holm and J. De Graaf,Soft Matter, 2019,15, 5908–5920

    2019

  40. [40]

    Vogel and H

    R. Vogel and H. Stark,Eur . Phys. J. E, 2010,33, 259–271

    2010

  41. [41]

    Vogel and H

    R. Vogel and H. Stark,Phys. Rev. Lett., 2013,110, 1–5

    2013

  42. [42]

    T. C. Adhyapak and H. Stark,Phys. Rev. E, 2015,92, 052701

    2015

  43. [43]

    T. C. Adhyapak and H. Stark,Soft Matter, 2016,12, 5621– 5629

    2016

  44. [44]

    Martin, T

    P. Martin, T. C. Adhyapak and H. Stark,Soft Matter, 2025, 21, 5921–5934. 13

    2025

  45. [45]

    A. W. Zantop and H. Stark,Soft Matter, 2020,16, 6400–6412

    2020

  46. [46]

    Malevanets,J

    A. Malevanets,J. Chem. Phys., 1999,110, 8605–8613

    1999

  47. [47]

    Noguchi, N

    H. Noguchi, N. Kikuchi and G. Gompper,Europhys. Lett., 2007,78, 10005

    2007

  48. [48]

    J. Hu, M. Yang, G. Gompper and R. G. Winkler,Soft Matter, 2015,11, 7867–7876

    2015

  49. [49]

    Zöttl and H

    A. Zöttl and H. Stark,Eur . Phys. J. E, 2018,41, 61

    2018

  50. [50]

    Zöttl and J

    A. Zöttl and J. M. Yeomans,Nat. Phys., 2019,15, 554–558

    2019

  51. [51]

    T. Kato, F. Makino, T. Miyata, P. Horváth and K. Namba,Nat. Commun., 2019,10, 5295

    2019

  52. [52]

    Gompper, T

    G. Gompper, T. Ihle, D. M. Kroll and R. G. Winkler,J. Chem. Phys, 2008, 1–87

    2008

  53. [53]

    I. O. Götze, H. Noguchi and G. Gompper,Phys. Rev. E, 2007, 76, 046705

    2007

  54. [54]

    Noguchi and G

    H. Noguchi and G. Gompper,Phys. Rev. E, 2008,78, 016706

    2008

  55. [55]

    Ripoll, K

    M. Ripoll, K. Mussawisade, R. G. Winkler and G. Gompper, Phys. Rev. E, 2005,72, 016701

    2005

  56. [56]

    N. C. Darnton and H. C. Berg,Biophys. J., 2007,92, 2230– 2236

    2007

  57. [57]

    Bianchi, F

    S. Bianchi, F. Saglimbeni, G. Frangipane, D. Dell’Arciprete and R. Di Leonardo,Soft Matter, 2019,15, 3397–3406

    2019

  58. [58]

    W. F. Cope,Proc. R. Soc. Lond. A Math. Phys. Sci., 1949,197, 201–217

    1949

  59. [59]

    G. C. Antunes, P. Malgaretti, J. Harting and S. Dietrich,Phys. Rev. Lett., 2022,129, 188003

    2022

  60. [60]

    G. C. Antunes, P. Malgaretti and J. Harting,J. Chem. Phys., 2023,159, 134903

    2023

  61. [61]

    G. C. Antunes, M. Jiménez-Sánchez, P. Malgaretti, J. Bach- mann and J. Harting,J. Chem. Phys., 2024,161, 124708

    2024

  62. [62]

    Malgaretti, I

    P. Malgaretti, I. Pagonabarraga and J. M. Rubi,Phys. Rev. Lett., 2014,113, 128301

    2014

  63. [63]

    Richter, P

    T. Richter, P. Malgaretti, T. M. Koller and J. Harting,Adv. Mater . Interfaces, 2025,12, 2400835

    2025

  64. [64]

    Richter, P

    T. Richter, P. Malgaretti and J. Harting,Phys. Fluids, 2025, 37, 072019

    2025

  65. [65]

    Thiele and E

    U. Thiele and E. Knobloch,Physica D: Nonlinear Phenomena, 2004,190, 213–248

    2004

  66. [66]

    Diekmann and U

    J. Diekmann and U. Thiele,Phys. Rev. Fluids, 2025,10, 024002. 14

    2025