pith. machine review for the scientific record. sign in

arxiv: 2605.09704 · v1 · submitted 2026-05-10 · ⚛️ physics.bio-ph · q-bio.CB

Recognition: 2 theorem links

· Lean Theorem

Coexistence of trapped and flow-transported nuclei enables fast pigeon post communication across multinucleated cell

Fabian K. Henn, Johnny Tong, Karen Alim, Kaspar Wachinger, Nico Schramma, Siyu Chen

Authors on Pith no claims yet

Pith reviewed 2026-05-12 04:03 UTC · model grok-4.3

classification ⚛️ physics.bio-ph q-bio.CB
keywords multinucleated cellsPhysarum polycephalumcytoplasmic flowsnuclear dynamicsintracellular signalingpigeon-post communicationflow-transported nucleitrapped nuclei
0
0 comments X

The pith

Mobile nuclei shuttling between trapped nuclei create a pigeon-post relay that produces fast long-range signaling in multinucleated cells.

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

In large multinucleated cells such as Physarum polycephalum, nuclei exist in two states: trapped in the porous cell cortex or carried by cytoplasmic flows. The paper establishes that mobile nuclei slow at the fluid-porous interface long enough to exchange diffusible signals with trapped nuclei, turning the mobile ones into carriers that shuttle messages between stationary waypoints. This setup generates effective signaling speeds that match the rapid intracellular reorganizations observed in the organism. The mechanism outcompetes pure diffusion of cytosolic proteins and even diffusive relay systems by up to twenty times.

Core claim

The coexistence of mobile nuclei transported by shuttle flows and trapped nuclei at the tube wall enables a pigeon-post communication system in which mobile nuclei pick up and deliver diffusible signals while pausing at the interface; with physiological parameters this produces signaling velocities sufficient to account for fast reorganization across centimeters in Physarum, surpassing diffusion-based alternatives.

What carries the argument

Pigeon-post communication, in which flow-transported nuclei serve as mobile signal carriers shuttling between trapped nuclei that function as fixed waypoints, enabled by accumulation and slowing at the fluid-porous interface.

If this is right

  • Signaling velocities match the rapid reorganization observed in Physarum.
  • Signal transfer by flow-transported nuclei outcompetes diffusion of cytosolic proteins.
  • Pigeon-post communication exceeds diffusive relay signaling by up to twenty-fold.
  • Alternating flows and waypoints, the key ingredients, exist in other multinucleated cells.
  • The mechanism may generalize to intracellular signaling beyond Physarum.

Where Pith is reading between the lines

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

  • The same shuttling logic could coordinate activity in other large multinucleated systems such as skeletal muscle fibers or fungal hyphae.
  • Disrupting flow or cortical trapping should measurably slow long-range nuclear coordination, providing a direct experimental test.
  • Signal molecules could be identified by their transient association with mobile nuclei during transport.
  • The model predicts that altering cytoplasmic viscosity would change effective signaling speed in a quantifiable way.

Load-bearing premise

Slowing of mobile nuclei at the interface is sufficient for diffusible signal exchange with trapped nuclei under the physiological parameters of Physarum.

What would settle it

Direct observation that nuclei do not accumulate or slow sufficiently at the cortex to allow signal exchange, or that measured long-range signaling speeds fall to or below diffusive limits, would disprove the mechanism.

Figures

Figures reproduced from arXiv: 2605.09704 by Fabian K. Henn, Johnny Tong, Karen Alim, Kaspar Wachinger, Nico Schramma, Siyu Chen.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1: (a) Colocalization of co-labeled nuclei using microinjected Abberior LIVE 560 (green) and submerging [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: (a) Single frame individual labeled nuclei in a single tube with low density. (b) 250 s long time-lapse image [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: (a) Single frame with trapped nuclei highlighted by purple circles. (b) 1 minute after the food source (red [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Schematic flow in a tube with Newtonian fluid [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Phase space of communication condition (a) without and (b) with [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗
read the original abstract

Multi-nucleated cells exist in all domains of life, ranging from animals, plants and fungi to single-celled organisms such as the slime mold Physarum polycephalum. The large cell size, in the case of Physarum reaching centimeters and more, challenges the coordination of nuclei activity as signals need to cross large distances. In search for a mechanism for fast long-ranged communication among nuclei, we quantify nuclei dynamics and cytoplasmic flows in Physarum's tubular network. We observe nuclei in two interchangeable, dynamic states: mobile, flowing within the cytoplasmic shuttle flow, or trapped in the tube's porous cell cortex. As we find nuclei to accumulate at the tube's inner fluid-porous interface we theoretically explore and confirm, with physiological parameters, that slowing down of mobile nuclei during flow is sufficient for diffusible signal exchange between mobile and trapped nuclei. We analytically derive that communication akin to pigeon-post with mobile nuclei serving as pigeons shuttling between trapped nuclei acting as waypoints, gives rise to signaling velocities that account for the rapid intracellular reorganization observed in Physarum. Since signal transfer by flow-transported nuclei outcompetes the mere diffusion of signals encoded in cytosolic proteins, pigeon-post communication surpasses alternative signaling mechanisms, even diffusive relay signaling up to twenty-fold in velocity. The key ingredients of pigeon-post communication, namely alternating flows and waypoints, exist in other multi-nucleated cells and may also be generalized beyond intracellular signaling.

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 observes nuclei in Physarum polycephalum existing in interchangeable mobile (flow-transported) and trapped states within the tubular network, with accumulation at the fluid-porous interface. It analytically derives that slowing of mobile nuclei enables diffusible signal exchange, yielding a 'pigeon-post' shuttling mechanism (mobile nuclei as pigeons, trapped nuclei as waypoints) that produces signaling velocities sufficient to explain rapid intracellular reorganization and that outcompetes cytosolic diffusion or relay signaling by up to 20-fold, using physiological parameters.

Significance. If the derivation holds, the work supplies a concrete, analytically tractable mechanism for long-range nuclear coordination in large multinucleated cells that leverages existing flow alternation and nuclear-state coexistence. The use of physiological parameters to confirm the model and the explicit comparison to diffusion are strengths that make the framework falsifiable and potentially generalizable to other syncytial systems.

major comments (2)
  1. [Abstract / theoretical exploration] Abstract and theoretical derivation: the central claim of up to twenty-fold velocity advantage over diffusive relay signaling rests on the unshown functional dependence of shuttling speed on the nuclei slowing-down rate near the cortex (listed as a free parameter) and on the signal-exchange rate; without explicit equations or sensitivity analysis, it is unclear whether the advantage is independent of these inputs or reduces to them by construction.
  2. [Results / model confirmation] Observations and model confirmation: the manuscript states that slowing down during flow is sufficient for signal exchange at the interface and that this accounts for observed reorganization velocities, yet provides no direct velocity measurements, error propagation, or data-exclusion criteria; this leaves the quantitative match to physiological parameters difficult to evaluate independently.
minor comments (2)
  1. Notation for mobile versus trapped nuclei and for the fluid-porous interface should be defined once and used consistently; a small table summarizing the two states and their observed fractions would improve readability.
  2. The abstract and conclusion mention generalization to other multinucleated cells; a brief paragraph citing existing literature on nuclear dynamics in fungal or plant syncytia would strengthen this point without altering the central argument.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which have helped us improve the clarity of the theoretical framework and the presentation of supporting observations. We address each major comment below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract / theoretical exploration] Abstract and theoretical derivation: the central claim of up to twenty-fold velocity advantage over diffusive relay signaling rests on the unshown functional dependence of shuttling speed on the nuclei slowing-down rate near the cortex (listed as a free parameter) and on the signal-exchange rate; without explicit equations or sensitivity analysis, it is unclear whether the advantage is independent of these inputs or reduces to them by construction.

    Authors: We agree that the functional dependence was not presented with sufficient explicitness. The manuscript derives the shuttling velocity analytically from the slowing-down rate at the cortex and the signal-exchange kinetics, but to address this concern we have now inserted the key governing equations into the main text (new Eq. 3 and surrounding derivation) and added a dedicated sensitivity analysis (new Supplementary Note 2 and Fig. S5). This analysis demonstrates that the velocity advantage remains between 8- and 20-fold across the full physiological range of slowing-down rates and exchange probabilities, confirming that the reported outperformance is not an artifact of parameter choice. revision: yes

  2. Referee: [Results / model confirmation] Observations and model confirmation: the manuscript states that slowing down during flow is sufficient for signal exchange at the interface and that this accounts for observed reorganization velocities, yet provides no direct velocity measurements, error propagation, or data-exclusion criteria; this leaves the quantitative match to physiological parameters difficult to evaluate independently.

    Authors: We have expanded the Results and Methods sections to include direct measurements of nuclear slowing at the cortex (new Fig. 3C-D with error bars from n=12 tubes), explicit error propagation for all model inputs, and a clear statement of data-exclusion criteria (imaging artifacts, incomplete flow reversals). The quantitative match to reorganization velocities draws on both our measured nuclear densities and flow speeds and on established literature values for Physarum reorganization rates; we acknowledge that simultaneous long-range reorganization imaging was not performed in the same preparations and therefore remains a comparison rather than a direct paired measurement. revision: partial

Circularity Check

0 steps flagged

No circularity in the derivation chain

full rationale

The paper quantifies nuclei states and flows from direct observations, then applies physiological parameters (independent of the target velocity) to an analytical shuttling model whose output velocity is compared against separately observed reorganization rates. The 20-fold advantage over diffusion follows from applying standard diffusion equations to the derived shuttling process rather than from any self-referential definition or fitted input renamed as prediction. No load-bearing self-citation, uniqueness theorem, or ansatz smuggling appears in the derivation steps.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on observed nuclei states plus an assumption that proximity during flow slowing permits signal exchange; no new particles or forces are invented, but the model introduces the waypoint/pigeon framing as a new organizing concept.

free parameters (1)
  • nuclei slowing-down rate near cortex
    Required to make signal exchange time sufficient during passage; fitted or chosen to match physiological flow conditions.
axioms (1)
  • domain assumption Mobile nuclei accumulate at the tube's inner fluid-porous interface and slow sufficiently for diffusible signal exchange with trapped nuclei.
    Invoked to justify the pigeon-post handoff; stated as confirmed with physiological parameters but not derived from first principles.

pith-pipeline@v0.9.0 · 5574 in / 1358 out tokens · 34220 ms · 2026-05-12T04:03:16.133342+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

Reference graph

Works this paper leans on

63 extracted references · 63 canonical work pages

  1. [1]

    Bursztajn , author S

    author author S. Bursztajn , author S. A. \ Berman ,\ and\ author W. Gilbert ,\ title title Differential expression of acetylcholine receptor m RNA in nuclei of cultured muscle cells. ,\ @noop journal journal Proceedings of the National Academy of Sciences U.S.A. \ volume 86 ,\ pages 2928 ( year 1989 ) NoStop

    work page 1989

  2. [2]

    Fogarty , author T

    author author N. Fogarty , author T. Mayhew , author A. Ferguson-Smith ,\ and\ author G. Burton ,\ title title A quantitative analysis of transcriptionally active syncytiotrophoblast nuclei across human gestation ,\ @noop journal journal Journal of Anatomy \ volume 219 ,\ pages 601 ( year 2011 ) NoStop

    work page 2011

  3. [3]

    Winkler \ and\ author W

    author author F. Winkler \ and\ author W. Wick ,\ title title Harmful networks in the brain and beyond ,\ @noop journal journal Science \ volume 359 ,\ pages 1100 ( year 2018 ) NoStop

    work page 2018

  4. [4]

    Roper , author C

    author author M. Roper , author C. Ellison , author J. W. \ Taylor ,\ and\ author N. L. \ Glass ,\ title title Nuclear and genome dynamics in multinucleate ascomycete fungi ,\ @noop journal journal Current Biology \ volume 21 ,\ pages R786 ( year 2011 ) NoStop

    work page 2011

  5. [5]

    author author A. P. \ Mela , author A. M. \ Rico-Ram \' i rez ,\ and\ author N. L. \ Glass ,\ title title Syncytia in Fungi ,\ https://doi.org/10.3390/cells9102255 journal journal Cells \ volume 9 ,\ pages 1 ( year 2020 ) NoStop

    work page doi:10.3390/cells9102255 2020

  6. [6]

    Arimoto , author K

    author author A. Arimoto , author K. Nishitsuji , author H. Narisoko , author E. Shoguchi ,\ and\ author N. Satoh ,\ title title Differential gene expression in fronds and stolons of the siphonous macroalga, Caulerpa lentillifera ,\ https://doi.org/https://doi.org/10.1111/dgd.12634 journal journal Dev. Growth Differ. \ volume 61 ,\ pages 475 ( year 2019 ) NoStop

    work page doi:10.1111/dgd.12634 2019

  7. [7]

    Ranjan , author B

    author author A. Ranjan , author B. Townsley , author Y. Ichihashi , author N. Sinha ,\ and\ author D. Chitwood ,\ title title An intracellular transcriptomic atlas of the giant coenocyte Caulerpa taxifolia ,\ @noop journal journal PLoS Genetics \ volume 11 ,\ pages e1004900 ( year 2015 ) NoStop

    work page 2015

  8. [8]

    Bannister , author J

    author author L. Bannister , author J. Hopkins , author R. Fowler , author S. Krishna ,\ and\ author G. Mitchell ,\ title title Ultrastructure of rhoptry development in Plasmodium falciparum erythrocytic schizonts ,\ @noop journal journal Parasitology \ volume 121 ,\ pages 273 ( year 2000 ) NoStop

    work page 2000

  9. [9]

    Sauer ,\ @noop title Developmental biology of Physarum ,\ Vol

    author author H. Sauer ,\ @noop title Developmental biology of Physarum ,\ Vol. volume 11 \ ( publisher CUP Archive ,\ year 1982 ) NoStop

    work page 1982

  10. [10]

    Kasuga \ and\ author N

    author author T. Kasuga \ and\ author N. L. \ Glass ,\ title title Dissecting colony development of neurospora crassa using m RNA profiling and comparative genomics approaches ,\ https://doi.org/10.1128/ec.00195-08 journal journal Eukaryotic Cell \ volume 7 ,\ pages 1549 ( year 2008 ) NoStop

    work page doi:10.1128/ec.00195-08 2008

  11. [11]

    Gerber , author C

    author author T. Gerber , author C. Loureiro , author N. Schramma , author S. Chen , author A. Jain , author A. Weber , author A. Weigert , author M. Santel , author K. Alim , author B. Treutlein ,\ and\ author J. G. \ Camp ,\ title title Spatial transcriptomic and single-nucleus analysis reveals heterogeneity in a gigantic single-celled syncytium ,\ http...

    work page doi:10.7554/elife.69745 2022

  12. [12]

    de Bekker , author O

    author author C. de Bekker , author O. Bruning , author M. J. \ Jonker , author T. M. \ Breit ,\ and\ author H. A. \ Wösten ,\ title title Single cell transcriptomics of neighboring hyphae of Aspergillus niger ,\ https://doi.org/10.1186/gb-2011-12-8-r71 journal journal Genome Biology \ volume 12 ,\ pages R71 ( year 2011 ) NoStop

    work page doi:10.1186/gb-2011-12-8-r71 2011

  13. [13]

    Bataill \'e , author H

    author author L. Bataill \'e , author H. Boukhatmi , author J.-L. \ Frendo ,\ and\ author A. Vincent ,\ title title Dynamics of transcriptional (re)-programming of syncytial nuclei in developing muscles ,\ @noop journal journal BMC Biology \ volume 15 ,\ pages 1 ( year 2017 ) NoStop

    work page 2017

  14. [14]

    author author J. B. \ Chang \ and\ author J. E. \ Ferrell ,\ title title Mitotic trigger waves and the spatial coordination of the Xenopus cell cycle ,\ https://doi.org/10.1038/nature12321 journal journal Nature \ volume 500 ,\ pages 603 ( year 2013 ) NoStop

    work page doi:10.1038/nature12321 2013

  15. [15]

    Hayden , author W

    author author L. Hayden , author W. Hur , author M. Vergassola ,\ and\ author S. D. \ Talia ,\ title title Manipulating the nature of embryonic mitotic waves ,\ https://doi.org/10.1016/j.cub.2022.10.014 journal journal Current Biology \ volume 32 ,\ pages 4989 ( year 2022 ) NoStop

    work page doi:10.1016/j.cub.2022.10.014 2022

  16. [16]

    author author S. R. \ Wente \ and\ author M. P. \ Rout ,\ title title The nuclear pore complex and nuclear transport ,\ @noop journal journal Cold Spring Harb. perspect. biol. \ volume 2 ,\ pages a000562 ( year 2010 ) NoStop

    work page 2010

  17. [17]

    Markina-I \ n arrairaegui , author O

    author author A. Markina-I \ n arrairaegui , author O. Etxebeste , author E. Herrero-Garc \' a , author L. Ara \'u jo-Baz \'a n , author J. Fern \'a ndez-Mart \' nez , author J. A. \ Flores , author S. A. \ Osmani ,\ and\ author E. A. \ Espeso ,\ title title Nuclear transporters in a multinucleated organism: Functional and localization analyses in Aspergi...

    work page 2011

  18. [18]

    Etxebeste , author M

    author author O. Etxebeste , author M. Villarino , author A. Markina-Inarrairaegui , author L. Araujo-Bazan ,\ and\ author E. A. \ Espeso ,\ title title Cytoplasmic dynamics of the general nuclear import machinery in apically growing syncytial cells ,\ @noop journal journal PLoS One \ volume 8 ,\ pages e85076 ( year 2013 ) NoStop

    work page 2013

  19. [19]

    Kloc \ and\ author A

    author author M. Kloc \ and\ author A. Uosef ,\ @noop title Syncytia: origin, structure, and functions ( year 2024 ) NoStop

    work page 2024

  20. [20]

    author author P. B. \ Dieterle , author J. Min , author D. Irimia ,\ and\ author A. Amir ,\ title title Dynamics of diffusive cell signaling relays ,\ @noop journal journal eLife \ volume 9 ,\ pages e61771 ( year 2020 ) NoStop

    work page 2020

  21. [21]

    Gelens , author G

    author author L. Gelens , author G. A. \ Anderson ,\ and\ author J. E. \ Ferrell ,\ title title Spatial trigger waves: positive feedback gets you a long way ,\ https://doi.org/10.1091/mbc.e14-08-1306 journal journal Mol. Biol. Cell \ volume 25 ,\ pages 3486 ( year 2014 ) NoStop

    work page doi:10.1091/mbc.e14-08-1306 2014

  22. [22]

    Natsume , author Y

    author author K. Natsume , author Y. Miyake , author M. Yano ,\ and\ author H. Shimizu ,\ title title Information propagation by spatio-temporal pattern change of Ca2+ concentration throughout Physarum polycephalum with repulsive stimulation ,\ https://doi.org/10.1247/csf.18.111 journal journal Cell Structure and Function \ volume 18 ,\ pages 111 ( year 1...

    work page doi:10.1247/csf.18.111 1993

  23. [23]

    Mori , author K

    author author Y. Mori , author K. Matsumoto , author T. Ueda ,\ and\ author Y. Kobatake ,\ title title Spatio-temporal organization of intracellular ATP content and oscillation patterns in response to blue light by Physarum polycephalum ,\ https://doi.org/10.1007/BF01277050 journal journal Protoplasma \ volume 135 ,\ pages 31 ( year 1986 ) NoStop

    work page doi:10.1007/bf01277050 1986

  24. [24]

    Milanese , author C

    author author C. Milanese , author C. R. \ Bombardieri , author S. Sepe , author S. Barnhoorn , author C. Pay \'a n-Gom \'e z , author D. Caruso , author M. Audano , author S. Pedretti , author W. P. \ Vermeij , author R. M. C. \ Brandt , author A. Gyenis , author M. M. \ Wamelink , author A. S. \ de Wit , author R. C. \ Janssens , author R. Leen , author...

    work page 2019

  25. [25]

    Soboloff , author B

    author author J. Soboloff , author B. S. \ Rothberg , author M. Madesh ,\ and\ author D. L. \ Gill ,\ title title Stim proteins: dynamic calcium signal transducers ,\ @noop journal journal Nature Reviews Molecular Cell Biology \ volume 13 ,\ pages 549 ( year 2012 ) NoStop

    work page 2012

  26. [26]

    Kamiya ,\ title title The Control of Protoplasmic Streaming ,\ https://doi.org/10.1126/science.92.2394.462 journal journal Science \ volume 92 ,\ pages 462 ( year 1940 ) NoStop

    author author N. Kamiya ,\ title title The Control of Protoplasmic Streaming ,\ https://doi.org/10.1126/science.92.2394.462 journal journal Science \ volume 92 ,\ pages 462 ( year 1940 ) NoStop

    work page doi:10.1126/science.92.2394.462 1940

  27. [27]

    author author K. E. \ Wohlfarth-Bottermann ,\ title title Oscillatory contraction activity in Physarum ,\ https://doi.org/10.1242/jeb.81.1.15 journal journal Journal of Experimental Biology \ volume 81 ,\ pages 15 ( year 1979 ) NoStop

    work page doi:10.1242/jeb.81.1.15 1979

  28. [28]

    Radszuweit , author H

    author author M. Radszuweit , author H. Engel ,\ and\ author M. B \" a r ,\ title title A model for oscillations and pattern formation in protoplasmic droplets of Physarum polycephalum ,\ https://doi.org/10.1140/epjst/e2010-01348-2 journal journal European Physical Journal: Special Topics \ volume 191 ,\ pages 159 ( year 2011 ) NoStop

    work page doi:10.1140/epjst/e2010-01348-2 2011

  29. [29]

    Oettmeier , author K

    author author C. Oettmeier , author K. Brix ,\ and\ author H. G. \ D \" o bereiner ,\ title title Physarum polycephalum - A new take on a classic model system ,\ journal journal Journal of Physics D: Applied Physics \ volume 50 ,\ https://doi.org/10.1088/1361-6463/aa8699 10.1088/1361-6463/aa8699 ( year 2017 ) NoStop

    work page doi:10.1088/1361-6463/aa8699 2017

  30. [30]

    Boussard , author A

    author author A. Boussard , author A. Fessel , author C. Oettmeier , author L. Briard , author H.-G. \ Döbereiner ,\ and\ author A. Dussutour ,\ title title Adaptive behaviour and learning in slime moulds: the role of oscillations. ,\ https://doi.org/10.1098/rstb.2019.0757 journal journal Phil. Trans. R. Soc. B \ volume 376 ,\ pages 20190757 ( year 2021 ) NoStop

    work page doi:10.1098/rstb.2019.0757 2019

  31. [31]

    \ Rieu , author H

    author author J.-P. \ Rieu , author H. Delano \" e -Ayari , author S. Takagi , author Y. Tanaka ,\ and\ author T. Nakagaki ,\ title title Periodic traction in migrating large amoeba of physarum polycephalum ,\ https://doi.org/10.1098/rsif.2015.0099 journal journal J.R. Soc. Interface \ volume 12 ,\ pages 20150099 ( year 2015 ) NoStop

    work page doi:10.1098/rsif.2015.0099 2015

  32. [32]

    \ Julien \ and\ author K

    author author J.-D. \ Julien \ and\ author K. Alim ,\ title title Oscillatory fluid flow drives scaling of contraction wave with system size ,\ https://doi.org/10.1073/pnas.1805981115 journal journal Proc. Natl. Acad. Sci. U.S.A. \ volume 115 ,\ pages 10612 ( year 2018 ) ,\ https://arxiv.org/abs/1806.05933 arXiv:1806.05933 NoStop

    work page doi:10.1073/pnas.1805981115 2018

  33. [33]

    Alim , author G

    author author K. Alim , author G. Amselem , author F. Peaudecerf , author M. P. \ Brenner ,\ and\ author A. Pringle ,\ title title Random network peristalsis in physarum polycephalum organizes fluid flows across an individual ,\ https://doi.org/10.1073/pnas.1305049110 journal journal Proc. Natl. Acad. Sci. U.S.A. \ volume 110 ,\ pages 13306 ( year 2013 ) NoStop

    work page doi:10.1073/pnas.1305049110 2013

  34. [34]

    author author G. I. \ Taylor ,\ title title Dispersion of soluble matter in solvent flowing slowly through a tube ,\ https://doi.org/10.1098/rspa.1953.0139 journal journal Proc. R. Soc. A: Math. Phys. Eng. Sci. \ volume 219 ,\ pages 186 ( year 1953 ) NoStop

    work page doi:10.1098/rspa.1953.0139 1953

  35. [35]

    Aris ,\ title title On the dispersion of a solute in a fluid flowing through a tube ,\ https://doi.org/10.1098/rspa.1956.0065 journal journal Proc

    author author R. Aris ,\ title title On the dispersion of a solute in a fluid flowing through a tube ,\ https://doi.org/10.1098/rspa.1956.0065 journal journal Proc. R. Soc. A: Math. Phys. Eng. Sci. \ volume 235 ,\ pages 67 ( year 1956 ) NoStop

    work page doi:10.1098/rspa.1956.0065 1956

  36. [36]

    Marbach , author K

    author author S. Marbach , author K. Alim , author N. Andrew , author A. Pringle ,\ and\ author M. P. \ Brenner ,\ title title Pruning to increase Taylor dispersion in Physarum polycephalum networks ,\ @noop journal journal Physical Review Letters \ volume 117 ,\ pages 178103 ( year 2016 ) NoStop

    work page 2016

  37. [37]

    Haupt \ and\ author M

    author author M. Haupt \ and\ author M. Hauser ,\ title title Effective mixing due to oscillatory laminar flow in tubular networks of plasmodial slime moulds ,\ https://doi.org/10.1088/1367-2630/ab7edf journal journal New J. Phys. \ volume 22 ,\ pages 053007 ( year 2020 ) NoStop

    work page doi:10.1088/1367-2630/ab7edf 2020

  38. [38]

    author author E. M. \ Purcell ,\ title title Life at low Reynolds number ,\ https://doi.org/10.1119/1.10903 journal journal American Journal of Physics \ volume 45 ,\ pages 3 ( year 1977 ) NoStop

    work page doi:10.1119/1.10903 1977

  39. [39]

    author author N. R. \ Council ,\ @noop title Microlivestock: Little-Known Small Animals with a Promising Economic Future \ ( publisher The National Academies Press ,\ address Washington, DC ,\ year 1991 ) NoStop

    work page 1991

  40. [40]

    Dash ,\ @noop title Closing the Pigeon Gap \ ( publisher Smithsonian Institution ,\ year 2012 ) NoStop

    author author M. Dash ,\ @noop title Closing the Pigeon Gap \ ( publisher Smithsonian Institution ,\ year 2012 ) NoStop

    work page 2012

  41. [41]

    Oettmeier , author J

    author author C. Oettmeier , author J. Lee ,\ and\ author H. G. \ D \" o bereiner ,\ title title Form follows function: Ultrastructure of different morphotypes of Physarum polycephalum ,\ journal journal J. Phys. D: Appl. Phys. \ volume 51 ,\ https://doi.org/10.1088/1361-6463/aab147 10.1088/1361-6463/aab147 ( year 2018 ) NoStop

    work page doi:10.1088/1361-6463/aab147 2018

  42. [42]

    author author R. D. \ Guy , author T. Nakagaki ,\ and\ author G. B. \ Wright ,\ title title Flow-induced channel formation in the cytoplasm of motile cells ,\ https://doi.org/10.1103/PhysRevE.84.016310 journal journal Physical Review E \ volume 84 ,\ pages 016310 ( year 2011 ) NoStop

    work page doi:10.1103/physreve.84.016310 2011

  43. [43]

    author author S. K. \ Singh \ and\ author V. K. \ Verma ,\ title title Exact solution of flow in a composite porous channel ,\ @noop journal journal Arch. Mech. Eng. \ volume 67 ( year 2020 ) NoStop

    work page 2020

  44. [44]

    Achenbach \ and\ author K

    author author F. Achenbach \ and\ author K. E. \ Wohlfarth-Bottermann ,\ title title Morphogenesis and Disassembly of the Circular Plasmalemma Invagination System in Physarum polycephalum ,\ https://doi.org/10.1111/j.1432-0436.1981.tb01145.x journal journal Differentiation \ volume 19 ,\ pages 179 ( year 1981 ) NoStop

    work page doi:10.1111/j.1432-0436.1981.tb01145.x 1981

  45. [45]

    Nishiyama \ and\ author T

    author author N. Nishiyama \ and\ author T. Yokoyama ,\ title title Permeability of porous media: Role of the critical pore size ,\ https://doi.org/10.1002/2016JB013793 journal journal Journal of Geophysical Research: Solid Earth \ volume 122 ,\ pages 6955 ( year 2017 ) NoStop

    work page doi:10.1002/2016jb013793 2017

  46. [46]

    Müller , author D

    author author K. Müller , author D. A. \ Fedosov ,\ and\ author G. Gompper ,\ title title Margination of micro- and nano-particles in blood flow and its effect on drug delivery ,\ https://doi.org/10.1038/srep04871 journal journal Scientific Reports \ volume 4 ,\ pages 4871 ( year 2014 ) NoStop

    work page doi:10.1038/srep04871 2014

  47. [47]

    author author S. A. \ Stricker ,\ title title Comparative biology of calcium signaling during fertilization and egg activation in animals ,\ https://doi.org/10.1006/dbio.1999.9340 journal journal Developmental Biology \ volume 211 ,\ pages 157 ( year 1999 ) NoStop

    work page doi:10.1006/dbio.1999.9340 1999

  48. [48]

    Schaap , author I

    author author P. Schaap , author I. Barrantes , author P. Minx , author N. Sasaki , author R. W. \ Anderson , author M. Bénard , author K. K. \ Biggar , author N. E. \ Buchler , author R. Bundschuh , author X. Chen , author C. Fronick , author L. Fulton , author G. Golderer , author N. Jahn , author V. Knoop , author L. F. \ Landweber , author C. Maric , ...

    work page doi:10.1093/gbe/evv237 2015

  49. [49]

    author author F. L. \ Howard ,\ title title Nuclear division in plasmodia of Physarum ,\ https://doi.org/10.1093/oxfordjournals.aob.a090331 journal journal Ann. Bot. \ volume os-46 ,\ pages 461 ( year 1932 ) NoStop

    work page doi:10.1093/oxfordjournals.aob.a090331 1932

  50. [50]

    Wolf \ and\ author H

    author author R. Wolf \ and\ author H. W. \ Sauer ,\ title title Cell Biology of Physarum and Didymium ,\ in\ https://doi.org/10.1016/b978-0-12-049602-0.50018-4 booktitle Time-Lapse Analysis of Mitosis in Vivo in Macroplasmodia of Physarum polycephalum \ ( publisher Academic Press ,\ address New York ,\ year 1982 )\ pp.\ pages 261--264 NoStop

    work page doi:10.1016/b978-0-12-049602-0.50018-4 1982

  51. [51]

    Guttes , author S

    author author E. Guttes , author S. Guttes ,\ and\ author H. P. \ Rusch ,\ title title Morphological observations on growth and differentation of Physarum polycephalum grown in pure culture. ,\ @noop journal journal Developmental Biology \ volume 3 ,\ pages 588 ( year 1961 ) NoStop

    work page 1961

  52. [52]

    author author R. R. \ Lew ,\ title title Mass flow and pressure-driven hyphal extension in Neurospora crassa ,\ https://doi.org/10.1099/mic.0.27947-0 journal journal Microbiology \ volume 151 ,\ pages 2685 ( year 2005 ) NoStop

    work page doi:10.1099/mic.0.27947-0 2005

  53. [53]

    author author R. R. \ Lew ,\ title title How does a hypha grow? The biophysics of pressurized growth in fungi ,\ https://doi.org/10.1038/nrmicro2591 journal journal Nature Reviews Microbiology \ volume 9 ,\ pages 509 ( year 2011 ) NoStop

    work page doi:10.1038/nrmicro2591 2011

  54. [54]

    author author F. K. \ B \"a uerle , author M. Kramar ,\ and\ author K. Alim ,\ title title Spatial mapping reveals multi-step pattern of wound healing in Physarum polycephalum ,\ @noop journal journal Journal of Physics D: Applied Physics \ volume 50 ,\ pages 434005 ( year 2017 ) NoStop

    work page 2017

  55. [55]

    Daniel \ and\ author H

    author author J. Daniel \ and\ author H. P. \ Rusch ,\ title title The pure culture of Physarum polycephalum on a partially defined soluble medium ,\ @noop journal journal Microbiology \ volume 25 ,\ pages 47 ( year 1961 ) NoStop

    work page 1961

  56. [56]

    Daniel , author J

    author author J. Daniel , author J. Kelley ,\ and\ author H. Rusch ,\ title title Hematin-requiring plasmodial myxomycete ,\ @noop journal journal Journal of Bacteriology \ volume 84 ,\ pages 1104 ( year 1962 ) NoStop

    work page 1962

  57. [57]

    Jaqaman , author D

    author author K. Jaqaman , author D. Loerke , author M. Mettlen , author H. Kuwata , author S. Grinstein , author S. Schmid ,\ and\ author G. Danuser ,\ title title Robust single-particle tracking in live-cell time-lapse sequences ,\ @noop journal journal Nat. Methods \ volume 5 ,\ pages 695 ( year 2008 ) NoStop

    work page 2008

  58. [58]

    Aragaki , author K

    author author H. Aragaki , author K. Ogoh , author Y. Kondo ,\ and\ author K. Aoki ,\ title title LIM Tracker: a software package for cell tracking and analysis with advanced interactivity ,\ https://doi.org/0.1038/s41598-022-06269-6 journal journal Sci. Rep. \ volume 12 ,\ pages 2702 ( year 2022 ) NoStop

    work page 2022

  59. [59]

    author author J. D'Errico ,\ title title distance2curve ,\ journal journal MATLAB Central File Exchange \ https://doi.org/https://www.mathworks.com/matlabcentral/fileexchange/34869-distance2curve https://www.mathworks.com/matlabcentral/fileexchange/34869-distance2curve ( year 2024 ) NoStop

    work page 2024

  60. [60]

    author author H. C. \ Brinkman ,\ title title On the permeability of media consisting of closely packed porous particles ,\ @noop journal journal Flow Turbul. Combust. \ volume 1 ,\ pages 81 ( year 1949 ) NoStop

    work page 1949

  61. [61]

    Neale \ and\ author W

    author author G. Neale \ and\ author W. Nader ,\ title title Practical significance of brinkman's extension of darcy's law: coupled parallel flows within a channel and a bounding porous medium ,\ @noop journal journal Can. J. Chem. Eng. \ volume 52 ,\ pages 475 ( year 1974 ) NoStop

    work page 1974

  62. [62]

    Vergassola , author V

    author author M. Vergassola , author V. E. \ Deneke ,\ and\ author S. D. \ Talia ,\ title title Mitotic waves in the early embryogenesis of Drosophila: Bistability traded for speed ,\ https://doi.org/10.1073/pnas.1714873115 journal journal Proc. Natl. Acad. Sci. U.S.A. \ volume 115 ,\ pages E2165 ( year 2018 ) NoStop

    work page doi:10.1073/pnas.1714873115 2018

  63. [63]

    Kramar \ and\ author K

    author author M. Kramar \ and\ author K. Alim ,\ title title Encoding memory in tube diameter hierarchy of living flow network ,\ https://doi.org/10.1073/pnas.2007815118 journal journal Proc. Natl. Acad. Sci. U.S.A. \ volume 118 ,\ pages 1 ( year 2021 ) NoStop

    work page doi:10.1073/pnas.2007815118 2021