Pith. sign in

REVIEW 2 major objections 4 minor 1 cited by

Could Living Cells Use Phase Transitions to Process Information?

T0 review · 2 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

Pith's one-line read A multicomponent phase boundary can act as a decision boundary, turning biomolecular condensation into a physical classifier and controller inside cells.

desk verdict A candid Perspective that maps phase-separation phenomenology onto computing concepts; the ensemble caveat is real but acknowledged, so the paper deserves referee time. read the letter →

arxiv 2507.23384 v1 pith:ATVKOHM5 submitted 2025-07-31 physics.bio-ph cond-mat.dis-nncond-mat.softnlin.AOq-bio.CB

classification physics.bio-phcond-mat.dis-nncond-mat.softnlin.AOq-bio.CB
keywords biomolecularcondensatesphaseseparationphysicalcomputingclassificationdecisionboundariesinformationprocessingneuralnetworkanalogymulticomponentmixtures
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that biomolecular condensation, the same phase-separation physics that forms droplets in cells, can itself process information rather than merely execute it. The central proposal is that a phase boundary in a multicomponent mixture acts as a decision boundary: it separates high-dimensional molecular inputs into discrete output phases, so the cell gets classification for free from its physical interactions. The authors also treat condensation as a control mechanism, since phase coexistence can buffer concentration fluctuations and keep internal conditions stable without a separate sensor, computer, or actuator. They situate these ideas in physical computing, where a system's native nonlinear dynamics, rather than a designed reaction network, performs the computation, and they pose expressivity and learning as the key open questions.

What carries the argument

The load-bearing object is the phase boundary of a multicomponent mixture, read in the grand canonical ensemble: the condensate sits in a reservoir that fixes the concentrations of input species, and crossing a boundary flips the compartment between distinct phases. This boundary is the decision surface, and the matrix $w_{ij}$ of pairwise interaction affinities is the analogue of neural-network weights that positions it. Supporting machinery includes hidden components that modulate apparent input–output interactions like hidden neurons, competitive nucleation that can sharpen or move boundaries beyond equilibrium, Ostwald ripening that encodes temporal information, and driven reactions that shift boundaries and enable spatial control.

What would settle it

In a purified in vitro mixture of several phase-separating components, titrate two input concentrations while holding all other components in large excess as a reservoir: if droplet number and composition always change smoothly rather than jumping sharply along a boundary, the decision-boundary claim fails for that system.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is a reinterpretation: a multicomponent phase-separating system in the grand canonical ensemble is a classifier, with reservoir concentrations of input species as the input vector and the phase that forms as the discrete output. Crossing a phase boundary produces a discontinuous change in droplet structure and composition, which is exactly the sharp switch a decision boundary should make. Because the interaction matrix $w_{ij}$ among molecular species plays the same role as synaptic weights in a neural network, moving phase boundaries is the physical analogue of training. The same physics doubles as control: coexisting phases keep the concentration of a molecule stable inside each phase while the volume fraction adjusts to absorb fluctuations. The authors point to transcriptional condensates, T cell receptor signaling, and stress granules as biological cases where such classification and control may already be at work.

Load-bearing premise

The argument rests on treating a condensate as an open system coupled to a large reservoir that holds the input concentrations fixed, so crossing a phase boundary is a sharp switch; if the cell instead behaves like a closed system with fixed total amounts, the transitions are gradual and the classification becomes ambiguous.

Editorial extensions

If this is right

  • A condensate can convert a high-dimensional molecular environment into a discrete cellular outcome in one physical step, so classification does not require a separate, modular reaction network.
  • Phase coexistence can buffer concentration fluctuations, meaning a single phase-separating system can serve as both sensor and actuator in maintaining homeostasis.
  • Kinetic competition for shared components can sharpen decisions beyond the equilibrium limit, so even closed systems with fixed total concentrations can make unambiguous, winner-take-all choices.
  • Hidden species that are neither inputs nor outputs can renormalize the apparent interaction matrix and thereby expand the set of classification tasks a condensate network can express.
  • Because expression levels and post-translational modifications can move interaction parameters, condensate computation can in principle be retrained on non-genetic timescales.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the decision-boundary reading is right, a condensate's phase diagram becomes a directly measurable description of what the cell 'knows'; mapping the phase diagram of a native condensate would reveal the classification it is wired to make.
  • A concrete test is to reconstitute a multicomponent condensate in vitro, pick two prescribed input conditions, and tune interaction parameters until a phase boundary separates them, then ask whether the boundary generalizes to unseen mixtures the way a trained classifier should.
  • The framework also suggests that evolution may act on phase diagrams as phenotypes, with selection shaping interaction strengths and stoichiometries rather than only reaction-network topology.
  • Fast, reversible reshaping of phase boundaries through component expression offers a candidate mechanism for cellular adaptation that does not require mutation or slow gene-regulatory rewiring.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. This Perspective argues that biomolecular condensates could contribute to cellular information processing through phase transitions, viewed through the lens of physical computing. The authors draw an analogy between phase boundaries in multicomponent phase diagrams and decision boundaries in neural networks, proposing that crossing a phase boundary can classify high-dimensional chemical inputs into discrete outputs. They also discuss control problems, review biological examples (stress granules, transcriptional condensates, T cell activation), introduce computational metrics (sharpness, capacity, expressivity), and outline open questions about physical determinants and learning. The paper is explicitly speculative and concludes with a call for experimental and theoretical work.

Significance. If the proposed framework is substantiated, it would broaden the standard picture of cellular information processing beyond chemical reaction networks, connecting soft matter physics with computation. The paper's strength is its clear organization of open questions and its concrete grounding in published examples, including experimentally demonstrated molecular pattern recognition via phase boundaries (ref. [75]) and theoretical work on multicomponent phase diagrams. The authors are appropriately careful in labeling open questions and limitations, such as the caveat that the reservoir approximation may not hold in cells and that robust buffering may require fine-tuning. For a perspective, the paper provides a useful synthesis that could inspire new experiments at the interface of biophysics and physical computing.

major comments (2)
  1. [II.B and III.B] The central classification analogy in Section II.B relies on the grand canonical ensemble, where a phase boundary is a sharp decision surface. The paper itself acknowledges in Section III.B that in the canonical ensemble, which conserves total material, equilibrium transitions are graded and sharpness must be rescued by kinetic competition. This tension is load-bearing because the sharpness of the decision boundary is the basis of the classification claim. The manuscript should state, even heuristically, under what physical conditions a cellular sub-compartment can be treated as coupled to a large reservoir (e.g., relative size of the surrounding phase, exchange timescales versus decision timescales), and it should explicitly qualify the Fig. 3 claim so that the idealized grand-canonical case is not presented as the default cellular scenario. As written, the reader cannot tell how often the required conditions are met in living cells.
  2. [III.B, 'Nucleation boundaries for higher expressivity'] The text asserts that kinetic decision surfaces are 'known to be more expressive than equilibrium phase boundaries' and cites refs. [75, 90]. Since this claim supports the paper's thesis that phase separation can perform computation in vivo, the mechanism should be briefly explained in the text: for example, in what sense the kinetic boundaries are more expressive and how competition or non-equilibrium effects enlarge the set of achievable input-output maps. Without this argument, the reader has to take the assertion on faith, which weakens the perspective's otherwise carefully reasoned presentation.
minor comments (4)
  1. [Introduction] There is a typo in 'one-dimensionsal' (should be 'one-dimensional').
  2. [II.C] 'an pH sensor' should be 'a pH sensor'; also 'comparments' later in the text should be 'compartments'.
  3. [III.A, Fig. 5] The definition of capacity as the number of distinct phases is clear, but the text could clarify whether the 'expanded' capacity in the canonical ensemble, where multiple phases coexist, corresponds to a useful form of output or merely to a combinatorial bookkeeping device.
  4. [Conclusion] The final paragraph effectively states the main limitation ('requires much experimental and theoretical investigation'), which is appropriate, but it would help to include a brief list of the most decisive experimental tests for the proposed classification-by-phase-transition idea.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the phase-boundary/decision-boundary mapping is an explicitly interpretive analogy, not a derivation from its own inputs.

full rationale

No circular step is present. The paper is a Perspective that maps multicomponent phase separation onto classification and control; the mapping is stated as a reinterpretation ('we re-interpret phase transitions in a multi-component system as classification of high-dimensional chemical compositions'), not as a result derived from a fitted parameter or self-referential definition. There are no fitted quantities, no quantities defined in terms of the target claim, and no derivation in which an output reduces to an input by construction. The self-citations (e.g., refs. 72, 75, 86, 87) serve as supporting examples of hidden-species effects, kinetic competition, and physical computing; they are not invoked as a uniqueness theorem or as the sole justification of the central claim, and the central conceptual content rests on standard phase-equilibrium thermodynamics and independently published results. The main vulnerability—that sharp classification requires the grand canonical reservoir assumption while real cells are closer to the canonical ensemble—is explicitly acknowledged in Sec. III.B ('equilibrium behavior yields more graded transitions' and 'real systems can lie somewhere in between'); this weakens applicability to cells but is an assumption about physical regime, not a circularity. The paper is self-contained as a research agenda and does not claim to have produced a new predictive derivation, so the honest finding is no significant circularity.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No new free parameters are fitted, and no new physical entities are introduced. The paper operates entirely with existing concepts and molecules.

assumptions (4)
  • domain assumption Biomolecular condensates can be described by equilibrium thermodynamics with phase diagrams.
    Used throughout Section II to argue that phase boundaries act as decision boundaries; assumes near-equilibrium behavior for most of the argument.
  • domain assumption Intracellular condensates are coupled to a reservoir that maintains fixed concentrations of components (grand canonical ensemble).
    Core to the sharp phase boundary picture in Section II.B and Figure 3c; acknowledged as an approximation in Section III.B where the canonical ensemble yields graded transitions.
  • domain assumption Interaction parameters w_ij can be tuned by evolution or post-translational modifications to place phase boundaries where needed.
    Necessary for the 'learning' and 'expressivity' arguments in Sections III.B and III.C; the paper suggests but does not demonstrate that such tuning is achievable in cells.
  • ad hoc to paper Physical computing framework applies to molecular systems and can be used to describe cellular information processing.
    The paper adopts the physical computing paradigm as a given, citing analog computing and metamaterial examples; this is a conceptual choice rather than an established fact for biological systems.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Could Living Cells Use Phase Transitions to Process Information?." pith.science (2026). https://pith.science/paper/ATVKOHM5

@misc{pith2026250723384,
  author       = {Pith},
  title        = {Pith review of: Could Living Cells Use Phase Transitions to Process Information?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ATVKOHM5}},
  note         = {Machine review of arXiv:2507.23384}
}
read the original abstract

To maintain homeostasis, living cells process information with networks of interacting molecules. Traditional models for cellular information processing have focused on networks of chemical reactions between molecules. Here, we describe how networks of physical interactions could contribute to the processing of information inside cells. In particular, we focus on the impact of biomolecular condensation, a structural phase transition found in cells. Biomolecular condensation has recently been implicated in diverse cellular processes. Some of these are essentially computational, including classification and control tasks. We place these findings in the broader context of physical computing, an emerging framework for describing how the native dynamics of nonlinear physical systems can be leveraged to perform complex computations. The synthesis of these ideas raises questions about expressivity (the range of problems that cellular phase transitions might be able to solve) and learning (how these systems could adapt and evolve to solve different problems). This emerging area of research presents diverse opportunities across molecular biophysics, soft matter, and physical computing.

Figures

Figures reproduced from arXiv: 2507.23384 by the authors.

Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figures from the paper (1 more)
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Combinatorial decision-making driven by multicomponent surface condensates

    physics.bio-ph 2025-09 conditional novelty 6.0 of 10

    Multicomponent surface condensates can be trained to classify input compositions, with hidden species enabling nonlinear boundaries and reservoir-level tuning enabling task reprogramming.

Reference graph

Works this paper leans on

122 extracted references · 76 canonical work pages · cited by 1 Pith paper

  1. [75]

    C. G. Evans, J. O’Brien, E. Winfree, and A. Murugan, Nature 625, 500 (2024)

  2. [1]

    Desvergne, L

    B. Desvergne, L. Michalik, and W. Wahli, Physiological Reviews 86, 465 (2006)

  3. [2]

    V. W. Wu, N. Thieme, L. B. Huberman, A. Di- etschmann, D. J. Kowbel, J. Lee, S. Calhoun, V. R. Singan, A. Lipzen, Y. Xiong, et al., Proceedings of the National Academy of Sciences 117, 6003 (2020)

  4. [3]

    R. R. Alfieri and P. G. Petronini, Pfl¨ ugers Archiv- European Journal of Physiology 454, 173 (2007)

  5. [4]

    J. M. Raser and E. K. O’Shea, Science 309, 2010 (2005)

  6. [5]

    B. R. Parry, I. V. Surovtsev, M. T. Cabeen, C. S. O’Hern, E. R. Dufresne, and C. Jacobs-Wagner, Cell 156, 183 (2014), publisher: Elsevier

  7. [6]

    O. D. Weiner, Current Opinion in Cell Biology 14, 196 (2002)

  8. [7]

    H. H. Mattingly, K. Kamino, B. B. Machta, and T. Emonet, Nature Physics 17, 1426 (2021), publisher: Nature Publishing Group

Show all 122 references
  1. [8]

    Dongre and R

    A. Dongre and R. A. Weinberg, Nature Reviews Molec- ular Cell Biology 20, 69 (2019)

  2. [9]

    B. L. Bohnsack and K. K. Hirschi, Annu. Rev. Nutr. 24, 433 (2004)

  3. [10]

    D. T. Scadden, Nature 441, 1075 (2006)

  4. [11]

    A. J. Engler, S. Sen, H. L. Sweeney, and D. E. Discher, Cell 126, 677 (2006)

  5. [12]

    A. H. Lang, H. Li, J. J. Collins, and P. Mehta, PLoS computational biology 10, e1003734 (2014)

  6. [13]

    Smart and A

    M. Smart and A. Zilman, Cell Reports Physical Science 4 (2023)

  7. [14]

    Y. E. Antebi, J. M. Linton, H. Klumpe, B. Bintu, M. Gong, C. Su, R. McCardell, and M. B. Elowitz, Cell 170, 1184 (2017)

  8. [15]

    C. J. Su, A. Murugan, J. M. Linton, A. Yeluri, J. Bois, H. Klumpe, M. A. Langley, Y. E. Antebi, and M. B. Elowitz, Cell systems 13, 408 (2022)

  9. [16]

    A. S. Hansen and E. K. O’Shea, Elife 4, e06559 (2015)

  10. [17]

    J. E. Purvis and G. Lahav, Cell 152, 945 (2013)

  11. [18]

    J. A. Papin, T. Hunter, B. O. Palsson, and S. Subra- maniam, Nature Reviews Molecular Cell Biology 6, 99 (2005)

  12. [19]

    T. I. Lee, N. J. Rinaldi, F. Robert, D. T. Odom, Z. Bar- Joseph, G. K. Gerber, N. M. Hannett, C. T. Harbison, C. M. Thompson, I. Simon, et al., Science 298, 799 (2002)

  13. [20]

    M. M. Babu, N. M. Luscombe, L. Aravind, M. Gerstein, and S. A. Teichmann, Current Opinion in Structural Biology 14, 283 (2004)

  14. [21]

    Huelsken and J

    J. Huelsken and J. Behrens, Journal of Cell Science 115, 3977 (2002). 9

  15. [22]

    D. E. Clapham, Cell 131, 1047 (2007)

  16. [23]

    T. J. B¨ oddeker, K. A. Rosowski, D. Berchtold, L. Em- manouilidis, Y. Han, F. H. Allain, R. W. Style, L. Pelk- mans, and E. R. Dufresne, Nature Physics 18, 571 (2022)

  17. [24]

    J.-Y. Youn, B. J. Dyakov, J. Zhang, J. D. Knight, R. M. Vernon, J. D. Forman-Kay, and A.-C. Gingras, Mol. Cell 76, 286 (2019)

  18. [25]

    A. S. Holehouse and B. B. Kragelund, Nat. Rev. Mol. Cell Biol. (2023)

  19. [26]

    J.-M. Choi, A. S. Holehouse, and R. V. Pappu, Annu. Rev. Biophys. 49, 107 (2020)

  20. [27]

    Rostam, S

    N. Rostam, S. Ghosh, C. F. W. Chow, A. Hadarovich, C. Landerer, R. Ghosh, H. Moon, L. Hersemann, D. M. Mitrea, I. A. Klein, A. A. Hyman, and A. Toth- Petroczy, Nat. Methods (2023)

  21. [28]

    S. F. Banani, H. O. Lee, A. A. Hyman, and M. K. Rosen, Nature reviews Molecular cell biology 18, 285 (2017)

  22. [29]

    Ambadi Thody, H

    S. Ambadi Thody, H. D. Clements, H. Baniasadi, A. S. Lyon, M. S. Sigman, and M. K. Rosen, Nature Chem- istry 16, 1794 (2024)

  23. [30]

    A. E. Posey, A. Bremer, N. A. Erkamp, A. Pant, T. P. Knowles, Y. Dai, T. Mittag, and R. V. Pappu, Journal of the American Chemical Society 146, 28268 (2024)

  24. [31]

    Farag, S

    M. Farag, S. R. Cohen, W. M. Borcherds, A. Bremer, T. Mittag, and R. V. Pappu, Nature communications 13, 7722 (2022)

  25. [32]

    Galvanetto, M

    N. Galvanetto, M. T. Ivanovi´ c, A. Chowdhury, A. Sot- tini, M. F. N¨ uesch, D. Nettels, R. B. Best, and B. Schuler, Nature 619, 876 (2023), publisher: Nature Publishing Group

  26. [33]

    Emmanouilidis, L

    L. Emmanouilidis, L. Esteban-Hofer, F. F. Damberger, T. de Vries, C. K. X. Nguyen, L. F. Ib´ a˜ nez, S. Mergen- thal, E. Klotzsch, M. Yulikov, G. Jeschke, and F. H.-T. Allain, Nature Chemical Biology 17, 608 (2021), num- ber: 5 Publisher: Nature Publishing Group

  27. [34]

    C. P. Brangwynne, T. J. Mitchison, and A. A. Hy- man, Proceedings of the National Academy of Sciences 108, 4334 (2011), publisher: Proceedings of the Na- tional Academy of Sciences

  28. [35]

    Jawerth, E

    L. Jawerth, E. Fischer-Friedrich, S. Saha, J. Wang, T. Franzmann, X. Zhang, J. Sachweh, M. Ruer, M. Ijavi, S. Saha, J. Mahamid, A. A. Hyman, and F. J¨ ulicher, Science 370, 1317 (2020)

  29. [36]

    Ijavi, R

    M. Ijavi, R. W. Style, L. Emmanouilidis, A. Kumar, S. M. Meier, A. L. Torzynski, F. H. Allain, Y. Barral, M. O. Steinmetz, and E. R. Dufresne, Soft Matter 17, 1655 (2021), publisher: Royal Society of Chemistry

  30. [37]

    Alshareedah, M

    I. Alshareedah, M. M. Moosa, M. Pham, D. A. Potoyan, and P. R. Banerjee, Nature communications 12, 6620 (2021)

  31. [38]

    Y. Dai, Z. Zhou, W. Yu, Y. Ma, K. Kim, N. Rivera, J. Mohammed, E. Lantelme, H. Hsu-Kim, A. Chilkoti, and L. You, Cell 187, 5951 (2024), publisher: Elsevier

  32. [39]

    M. Zeng, Y. Shang, Y. Araki, T. Guo, R. L. Huganir, and M. Zhang, Cell 166, 1163 (2016)

  33. [40]

    S. A. Shelby, I. Castello-Serrano, K. C. Wisser, I. Leven- tal, and S. L. Veatch, Nat. Chem. Biol. 19, 750 (2023)

  34. [41]

    LeCun, Y

    Y. LeCun, Y. Bengio, and G. Hinton, Nature 521, 436 (2015)

  35. [42]

    Zwicker and L

    D. Zwicker and L. Laan, Proceedings of the National Academy of Sciences 119, e2201250119 (2022), pub- lisher: Proceedings of the National Academy of Sci- ences

  36. [43]

    K. J. ˚Astr¨ om and R. M. Murray,Feedback systems: an introduction for scientists and engineers(Princeton uni- versity press, 2021)

  37. [44]

    Klosin, F

    A. Klosin, F. Oltsch, T. Harmon, A. Honigmann, F. J¨ ulicher, A. A. Hyman, and C. Zechner, Science 367, 464 (2020)

  38. [45]

    Deviri and S

    D. Deviri and S. A. Safran, Proceedings of the National Academy of Sciences 118, e2100099118 (2021)

  39. [46]

    B. R. Sabari, A. Dall’Agnese, A. Boija, I. A. Klein, E. L. Coffey, K. Shrinivas, B. J. Abraham, N. M. Hannett, A. V. Zamudio, J. C. Manteiga, C. H. Li, Y. E. Guo, D. S. Day, J. Schuijers, E. Vasile, S. Malik, D. Hnisz, T. I. Lee, I. I. Cisse, R. G. Roeder, P. A. Sharp, A. K. C...

  40. [47]

    Boija, I

    A. Boija, I. A. Klein, B. R. Sabari, A. Dall’Agnese, E. L. Coffey, A. V. Zamudio, C. H. Li, K. Shrinivas, J. C. Manteiga, N. M. Hannett, B. J. Abraham, L. K. Afeyan, Y. E. Guo, J. K. Rimel, C. B. Fant, J. Schuijers, T. I. Lee, D. J. Taatjes, and R. A. Young, Cell 175, 1842 (2018)

  41. [48]

    X. Su, J. A. Ditlev, E. Hui, W. Xing, S. Banjade, J. Okrut, D. S. King, J. Taunton, M. K. Rosen, and R. D. Vale, Science 352, 595 (2016)

  42. [49]

    S. F. Shimobayashi, P. Ronceray, D. W. Sanders, M. P. Haataja, and C. P. Brangwynne, Nature 599, 503 (2021)

  43. [50]

    H. Yoo, C. Triandafillou, and D. A. Drummond, J. Biol. Chem. 294, 7151 (2019)

  44. [51]

    D. S. Protter and R. Parker, Trends in cell biology 26, 668 (2016)

  45. [52]

    Glauninger, J

    H. Glauninger, J. A. Bard, C. J. W. Hickernell, E. M. Airoldi, W. Li, R. H. Singer, S. Paul, J. Fei, T. R. Sos- nick, E. W. Wallace, and D. A. Drummond, bioRxiv (2024)

  46. [53]

    A. Ali, R. Garde, O. C. Schaffer, J. A. M. Bard, K. Hu- sain, S. K. Kik, K. A. Davis, S. Luengo-Woods, M. G. Igarashi, D. A. Drummond, A. H. Squires, and D. Pin- cus, Nat. Cell Biol. 25, 1691 (2023)

  47. [54]

    C. Hetz, K. Zhang, and R. J. Kaufman, Nat. Rev. Mol. Cell Biol. 21, 421 (2020)

  48. [55]

    Zhang, J

    H. Zhang, J. Wu, D. Fang, and Y. Zhang, Sci. Adv. 7, eabf1966 (2021)

  49. [56]

    Dubˇ cek, D

    T. Dubˇ cek, D. Moreno-Garcia, T. Haag, P. Omidvar, H. R. Thomsen, T. S. Becker, L. Gebraad, C. B¨ arlocher, F. Andersson, S. D. Huber, et al., Advanced Functional Materials , 2311877 (2024)

  50. [57]

    E. W. Dijkstra, in Selected Writings on Computing: A personal Perspective (Springer New York, New York, NY, 1982) pp. 60–66

  51. [58]

    L. H. Hartwell, J. J. Hopfield, S. Leibler, and A. W. Murray, Nature 402, C47 (1999)

  52. [59]

    Endy, Nature 438, 449 (2005)

    D. Endy, Nature 438, 449 (2005)

  53. [60]

    R. A. Brooks, Artif. Intell. 47, 139 (1991)

  54. [61]

    Ulmann, Analog computing (Oldenbourg Wis- senschaftsverlag Verlag, 2013)

    B. Ulmann, Analog computing (Oldenbourg Wis- senschaftsverlag Verlag, 2013)

  55. [62]

    Braitenberg, Vehicles: Experiments in synthetic psy- chology (MIT press, 1986)

    V. Braitenberg, Vehicles: Experiments in synthetic psy- chology (MIT press, 1986)

  56. [63]

    M. S. Bull, L. A. Kroo, and M. Prakash, arXiv preprint arXiv:2107.02930 (2021)

  57. [64]

    Laydevant, L

    J. Laydevant, L. G. Wright, T. Wang, and P. L. McMa- hon, Neuron (2023), 10.1016/j.neuron.2023.11.004

  58. [65]

    Bray, Nature 376, 307 (1995)

    D. Bray, Nature 376, 307 (1995). 10

  59. [66]

    Erbas-Cakmak, S

    S. Erbas-Cakmak, S. Kolemen, A. C. Sedgwick, T. Gunnlaugsson, T. D. James, J. Yoon, and E. U. Akkaya, Chem. Soc. Rev. 47, 2228 (2018)

  60. [67]

    Nandagopal and M

    N. Nandagopal and M. B. Elowitz, Science 333, 1244 (2011)

  61. [68]

    L. Qian, E. Winfree, and J. Bruck, Nature 475, 368 (2011)

  62. [69]

    N. E. Buchler, U. Gerland, and T. Hwa, Proc. Natl. Acad. Sci. U. S. A. 100, 5136 (2003)

  63. [70]

    P. L. McMahon, Nature Reviews Physics 5, 717 (2023)

  64. [71]

    L. G. Wright, T. Onodera, M. M. Stein, T. Wang, D. T. Schachter, Z. Hu, and P. L. McMahon, Nature 601, 549 (2022)

  65. [72]

    Stern, C

    M. Stern, C. Arinze, L. Perez, S. E. Palmer, and A. Mu- rugan, Proceedings of the National Academy of Sciences 117, 14843 (2020)

  66. [73]

    Woods, D

    D. Woods, D. Doty, C. Myhrvold, J. Hui, F. Zhou, P. Yin, and E. Winfree, Nature 567, 366 (2019)

  67. [74]

    Winfree, Algorithmic self-assembly of DNA(Califor- nia Institute of Technology, 1998)

    E. Winfree, Algorithmic self-assembly of DNA(Califor- nia Institute of Technology, 1998)

  68. [76]

    J. J. Hopfield, Proc. Natl. Acad. Sci. U. S. A. 79, 2554 (1982)

  69. [77]

    Krotov and J

    D. Krotov and J. J. Hopfield, in International Confer- ence on Learning Representations(2020)

  70. [78]

    J. A. Hertz, A. S. Krogh, and R. G. Palmer, Introduc- tion to the theory of neural computation, Vol. 1 (Basic Books, 1991)

  71. [79]

    Murugan, Z

    A. Murugan, Z. Zeravcic, M. P. Brenner, and S. Leibler, Proceedings of the National Academy of Sciences 112, 54 (2015)

  72. [80]

    Fink and R

    T. Fink and R. Ball, Phys. Rev. Lett. 87, 198103 (2001)

  73. [81]

    Braz Teixeira, G

    R. Braz Teixeira, G. Carugno, I. Neri, and P. Sartori, Proc. Natl. Acad. Sci. U. S. A.121, e2320504121 (2024)

  74. [82]

    W. M. Jacobs, Phys. Rev. Lett. 126, 258101 (2021)

  75. [83]

    Hornik, M

    K. Hornik, M. Stinchcombe, and H. White, Neural Netw. 2, 359 (1989)

  76. [84]

    Raghu, B

    M. Raghu, B. Poole, J. Kleinberg, S. Ganguli, and J. Sohl-Dickstein, arXiv [stat.ML] (2016), arXiv:1611.08083 [stat.ML]

  77. [85]

    M. J. Kearns and U. Vazirani, An introduction to com- putational learning theory, The MIT Press (MIT Press, London, England, 2019)

  78. [86]

    Parres-Gold, M

    J. Parres-Gold, M. Levine, B. Emert, A. Stuart, and M. B. Elowitz, bioRxiv , 2023.10.30.564854 (2023)

  79. [87]

    Chalk, S

    C. Chalk, S. Buse, K. Shrinivas, A. Murugan, and E. Winfree, in 30th International Conference on DNA Computing and Molecular Programming (DNA 30), Leibniz International Proceedings in Informatics (LIPIcs), Vol. 314, edited by S. Seki and J. M. Stew- art (Schloss Dagstuhl – Lei...

  80. [88]

    Gunawardena, Proc

    J. Gunawardena, Proc. IEEE 110, 590 (2022)

  81. [89]

    Montufar, arXiv [cs.LG] (2018), arXiv:1806.07066 [cs.LG]

    G. Montufar, arXiv [cs.LG] (2018), arXiv:1806.07066 [cs.LG]

  82. [90]

    Zhong, D

    W. Zhong, D. J. Schwab, and A. Murugan, Journal of Statistical Physics 167, 806 (2017)

  83. [91]

    M. S. Heltberg, A. Lucchetti, F.-S. Hsieh, D. P. Minh Nguyen, S. hong Chen, and M. H. Jensen, Cell 185, 4394 (2022)

  84. [92]

    Girard, D

    C. Girard, D. Zwicker, and R. Mercier, Biochem. Soc. Trans. (2023)

  85. [93]

    D. B. McAffee, M. K. O’Dair, J. J. Lin, S. T. Low-Nam, K. B. Wilhelm, S. Kim, S. Morita, and J. T. Groves, Nat. Commun. 13, 7446 (2022)

  86. [94]

    W. Y. C. Huang, S. Alvarez, Y. Kondo, Y. K. Lee, J. K. Chung, H. Y. M. Lam, K. H. Biswas, J. Kuriyan, and J. T. Groves, Science 363, 1098 (2019)

  87. [95]

    W. L. White, H. K. Yirdaw, A. J. Ben-Sasson, J. T. Groves, D. Baker, and H. Y. Kueh, Proc. Natl. Acad. Sci. U. S. A. 122, e2422787122 (2025)

  88. [96]

    Rossetto, G

    R. Rossetto, G. Wellecke, and D. Zwicker, Phys. Rev. Res. 7, 023145 (2025)

  89. [97]

    A. J. Genot, T. Fujii, and Y. Rondelez, Phys. Rev. Lett. 109, 208102 (2012)

  90. [98]

    Kieffer, A

    C. Kieffer, A. J. Genot, Y. Rondelez, and G. Gines, Adv. Biol. (Weinh.) 7, e2200203 (2023)

  91. [99]

    Zwicker, Curr

    D. Zwicker, Curr. Opin. Colloid Interface Sci. 61, 101606 (2022)

  92. [100]

    Ziethen, J

    N. Ziethen, J. Kirschbaum, and D. Zwicker, Phys. Rev. Lett. 130, 248201 (2023)

  93. [101]

    Jambon-Puillet, A

    E. Jambon-Puillet, A. Testa, C. M. Lorenz, R. W. Style, A. Rebane, and E. R. Dufresne, bioRxiv , 2023 (2023)

  94. [102]

    J. D. Wurtz and C. F. Lee, New J. Phys. 20, 045008 (2018)

  95. [103]

    Zwicker, A

    D. Zwicker, A. A. Hyman, and F. J¨ ulicher, Phys. Rev. E 92, 012317 (2015)

  96. [104]

    Soeding, D

    J. Soeding, D. Zwicker, S. Sohrabi-Jahromi, M. Boehn- ing, and J. Kirschbaum, Trends Cell Biol. 30, 4 (2020)

  97. [105]

    Kirschbaum and D

    J. Kirschbaum and D. Zwicker, J. R. Soc. Interface 18, 20210255 (2021)

  98. [106]

    Zwicker, R

    D. Zwicker, R. Seyboldt, C. A. Weber, A. A. Hyman, and F. J¨ ulicher, Nat. Phys.13, 408 (2017)

  99. [107]

    Carati and R

    D. Carati and R. Lefever, Phys. Rev. E 56, 3127 (1997)

  100. [108]

    Aslyamov, F

    T. Aslyamov, F. Avanzini, E. Fodor, and M. Esposito, Phys. Rev. Lett. 131, 138301 (2023)

  101. [109]

    Demarchi, A

    L. Demarchi, A. Goychuk, I. Maryshev, and E. Frey, Phys. Rev. Lett. 130, 128401 (2023)

  102. [110]

    Menou, C

    L. Menou, C. Luo, and D. Zwicker, J. R. Soc. Interface 20, 20230244 (2023)

  103. [111]

    Galstyan, K

    V. Galstyan, K. Husain, F. Xiao, A. Murugan, and R. Phillips, Elife 9 (2020), 10.7554/eLife.60415

  104. [112]

    J. J. Hopfield, Proceedings of the National Academy of Sciences 71, 4135 (1974)

  105. [113]

    Stern and A

    M. Stern and A. Murugan, Annu. Rev. Condens. Matter Phys. 14, 417 (2023)

  106. [114]

    Hofweber and D

    M. Hofweber and D. Dormann, J. Biol. Chem.294, 7137 (2019)

  107. [115]

    Wang, J.-M

    J. Wang, J.-M. Choi, A. S. Holehouse, H. O. Lee, X. Zhang, M. Jahnel, S. Maharana, R. Lemaitre, A. Pozniakovsky, D. Drechsel, I. Poser, R. V. Pappu, S. Alberti, and A. A. Hyman, Cell 174, 688 (2018)

  108. [116]

    R. Zhu, J. M. Del Rio-Salgado, J. Garcia-Ojalvo, and M. B. Elowitz, Science 375, eabg9765 (2022)

  109. [117]

    Alberti, A

    S. Alberti, A. Gladfelter, and T. Mittag, Cell 176, 419 (2019)

  110. [118]

    V. A. Baulin, A. Giacometti, D. A. Fedosov, S. Ebbens, N. R. Varela-Rosales, N. Feliu, M. Chowdhury, M. Hu, R. F¨ uchslin, M. Dijkstra, M. Mussel, R. van Roij, D. Xie, V. Tzanov, M. Zu, S. Hidalgo-Caballero, Y. Yuan, L. Cocconi, C.-M. Ghim, C. Cottin-Bizonne, M. C. Miguel, M. ...

  111. [119]

    J. Gong, N. Tsumura, Y. Sato, and M. Takinoue, Adv. Funct. Mater. 32, 2202322 (2022). 11

  112. [120]

    Takinoue, Interface Focus 13, 20230021 (2023)

    M. Takinoue, Interface Focus 13, 20230021 (2023)

  113. [121]

    Udono, J

    H. Udono, J. Gong, Y. Sato, and M. Takinoue, Adv Biol (Weinh) 7, e2200180 (2023)

  114. [122]

    Fabrini, S

    G. Fabrini, S. P. Nuccio, J. M. Stewart, S. Li, A. Tang, P. W. K. Rothemund, E. Franco, M. Di Antonio, and L. Di Michele, bioRxiv , 2023.10.06.561174 (2023)

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.