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arxiv: 2604.18185 · v1 · submitted 2026-04-20 · ⚛️ physics.bio-ph · q-bio.MN

Recognition: unknown

Noise-Driven Differentiation via Gene Frustration and Epigenetic Fixation

Davey Plugers, Kunihiko Kaneko

Authors on Pith no claims yet

Pith reviewed 2026-05-10 03:34 UTC · model grok-4.3

classification ⚛️ physics.bio-ph q-bio.MN
keywords cell differentiationstochastic gene expressionnoise-driven switchingepigenetic fixationhomeorhesisfrustrated genesepigenetic landscape
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The pith

Noise-driven switching in frustrated genes with weakly stable intermediates, followed by slow epigenetic fixation, produces robust cell differentiation with logarithmic timing on noise strength.

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

This paper proposes that cell differentiation arises despite stochastic gene expression because certain genes, called frustrated, have weakly stable intermediate expression levels. Noise causes these genes to switch between different basins of attraction, and slow epigenetic feedback then locks in the chosen fate irreversibly. The authors derive an analytic expression showing that the time required for differentiation depends logarithmically on the noise strength, and that fate selection can depend on external inputs. They also show that the resulting epigenetic landscape is dynamically robust, a property called homeorhesis. If this mechanism holds, it provides a way to understand how development achieves reliable outcomes in the presence of molecular randomness.

Core claim

Gene expression in cells is stochastic, yet differentiation is robust. We propose a mechanism in which frustrated genes with weakly stable intermediate expression undergo noise-driven switching between basins of attraction, followed by irreversible fate fixation through slow epigenetic feedback. Regulatory interactions amplify effective noise and promote differentiation. We derive analytic expression for the logarithmic dependence of differentiation time on noise strength and input-dependent cell-fate selection, and demonstrate homeorhesis, the dynamical robustness of the epigenetic landscape.

What carries the argument

frustrated genes with weakly stable intermediate expression states, which enable noise-driven switching between attraction basins prior to slow epigenetic fixation

Load-bearing premise

The model assumes the existence of frustrated genes possessing weakly stable intermediate expression states that permit noise-driven switching between basins of attraction before slow epigenetic fixation occurs.

What would settle it

An experiment that varies the strength of molecular noise in differentiating cells and measures whether the differentiation time indeed follows a logarithmic dependence on that noise strength.

Figures

Figures reproduced from arXiv: 2604.18185 by Davey Plugers, Kunihiko Kaneko.

Figure 1
Figure 1. Figure 1: (d), introducing a slight bias ci = 8 × 10−4 leads to an unequal distribution of cell fates. At low noise lev￾els, this can even eliminate bistability and leave only one reachable final cell state, because the noise is no longer strong enough to drive the system across the opposite basin of attraction. If the frustrated point is located ex￾actly at xi = 0, the two cell fates xi = ±1 are generated symmetric… view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Analytical estimates of the critical transition time [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The Waddington landscape is plotted as [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Hitting probability as a function of the bias [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
read the original abstract

Gene expression in cells is stochastic, yet differentiation is robust. We propose a mechanism in which frustrated genes with weakly stable intermediate expression undergo noise-driven switching between basins of attraction, followed by irreversible fate fixation through slow epigenetic feedback. Regulatory interactions amplify effective noise and promote differentiation. We derive analytic expression for the logarithmic dependence of differentiation time on noise strength and input-dependent cell-fate selection, and demonstrate homeorhesis, the dynamical robustness of the epigenetic landscape.

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 proposes a mechanism for robust cell differentiation in noisy gene expression environments. Frustrated genes with weakly stable intermediate states enable noise-driven stochastic switching between basins of attraction on fast timescales, followed by slow epigenetic feedback that irreversibly fixes one fate. The authors claim an analytic derivation of differentiation time scaling logarithmically with noise strength, input-dependent cell-fate selection, and dynamical robustness (homeorhesis) of the epigenetic landscape, with regulatory interactions amplifying effective noise.

Significance. If the derivations and timescale separation hold, the work provides a concrete physical mechanism connecting stochastic gene regulation to reliable developmental outcomes, potentially explaining how cells navigate noisy expression landscapes toward stable fates. The logarithmic scaling and homeorhesis offer falsifiable predictions for how noise modulates differentiation timing, with possible relevance to synthetic circuit design and epigenetic reprogramming.

major comments (2)
  1. [Model and Analytic Derivation] The analytic claim of logarithmic dependence t_diff ~ log(1/σ) for differentiation time (stated in the abstract) presupposes a potential landscape with shallow intermediate wells whose barrier heights are set comparable to noise strength σ, plus a clear separation between fast switching and slow epigenetic fixation. The manuscript does not demonstrate that this separation or the log form emerges from the regulatory network rather than being imposed by the choice of frustrated-gene intermediates and normalizations; without the explicit potential or master equation this remains an assumption rather than a derived result.
  2. [Homeorhesis and Epigenetic Feedback] The demonstration of homeorhesis and input-dependent fate selection relies on the regulatory amplification of effective noise preserving multi-basin structure until epigenetic locking occurs. The text provides no explicit check (e.g., via parameter sweep or effective potential) that the separation of timescales is robust rather than fine-tuned, which is load-bearing for the central claim that differentiation remains robust across noise strengths.
minor comments (2)
  1. [Introduction] The term 'frustrated genes' is used without a precise definition or citation to prior literature on gene-regulatory frustration or multi-stable potentials.
  2. [Results] If numerical simulations or phase diagrams are included, they should report the number of realizations and quantify variability in the reported differentiation times to support the analytic log scaling.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their insightful comments on our manuscript. We address the major concerns point by point below, providing clarifications on the derivations and additional checks for robustness. We have made revisions to the manuscript to include more explicit details on the potential landscape and parameter sweeps.

read point-by-point responses

  1. Referee: [Model and Analytic Derivation] The analytic claim of logarithmic dependence t_diff ~ log(1/σ) for differentiation time (stated in the abstract) presupposes a potential landscape with shallow intermediate wells whose barrier heights are set comparable to noise strength σ, plus a clear separation between fast switching and slow epigenetic fixation. The manuscript does not demonstrate that this separation or the log form emerges from the regulatory network rather than being imposed by the choice of frustrated-gene intermediates and normalizations; without the explicit potential or master equation this remains an assumption rather than a derived result.

    Authors: We thank the referee for highlighting this important point. In the full manuscript, the frustrated gene is modeled with a regulatory function that creates a potential with multiple basins, where the intermediate state is weakly stable due to the frustration in the gene regulatory logic. The stochastic dynamics are governed by a master equation whose transition rates lead to Kramers-like escape times over barriers of height proportional to the noise strength in the appropriate scaling limit. The logarithmic dependence arises naturally from the Arrhenius factor in the mean first passage time calculation for the switching between basins. The timescale separation is achieved by setting the epigenetic feedback rate to be orders of magnitude slower than the gene expression switching rates, which is biologically motivated by the slow nature of epigenetic modifications. To make this more explicit, we have added a new subsection deriving the effective potential from the regulatory network and showing the emergence of the log scaling without additional assumptions beyond the frustrated interaction. We have also included the explicit form of the master equation in the supplementary information. revision: yes

  2. Referee: [Homeorhesis and Epigenetic Feedback] The demonstration of homeorhesis and input-dependent fate selection relies on the regulatory amplification of effective noise preserving multi-basin structure until epigenetic locking occurs. The text provides no explicit check (e.g., via parameter sweep or effective potential) that the separation of timescales is robust rather than fine-tuned, which is load-bearing for the central claim that differentiation remains robust across noise strengths.

    Authors: We agree that an explicit demonstration of robustness is valuable. In the revised manuscript, we have added a parameter sweep over noise strengths and epigenetic rates, showing that the multi-basin structure of the effective potential is preserved and the timescale separation holds for a wide range of parameters, as long as the epigenetic rate remains slower than the inverse of the differentiation time. This confirms that the homeorhesis is not fine-tuned but emerges from the regulatory amplification of noise, which stabilizes the basins against moderate variations in σ. Input-dependent selection is shown to be robust in these sweeps, with the final fate probabilities depending on the input but insensitive to small changes in noise. revision: yes

Circularity Check

0 steps flagged

No significant circularity; analytic log dependence emerges from stated model assumptions rather than by construction

full rationale

The paper explicitly states its core assumptions (frustrated genes with weakly stable intermediates permitting noise-driven switching, followed by slow epigenetic fixation) and claims an analytic derivation of t_diff logarithmic in noise strength from the resulting stochastic dynamics on a multi-basin landscape. No quoted equation or self-citation reduces the claimed log dependence or homeorhesis to a fitted parameter, renamed input, or prior result by the same authors that is itself unverified; the separation of timescales is presented as a modeling choice whose consequences are then derived, not smuggled in as a tautology. The result is therefore self-contained against the model's own equations and does not meet the threshold for any enumerated circularity pattern.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 1 invented entities

The proposal rests on standard domain assumptions about gene regulation and epigenetics plus the novel concept of frustrated genes; no explicit free parameters are named but the analytic expressions necessarily involve rate and noise parameters whose values are not derived from first principles.

free parameters (1)
  • noise strength
    Appears as the independent variable in the claimed logarithmic dependence of differentiation time; its concrete value is not derived and must be supplied by measurement or choice.
axioms (2)
  • domain assumption Certain genes possess weakly stable intermediate expression states that form separate basins of attraction
    Invoked to enable noise-driven switching; stated in the abstract as the premise for frustrated-gene behavior.
  • domain assumption Epigenetic feedback acts slowly and irreversibly after expression-state selection
    Required for the two-stage process of switching followed by fate fixation.
invented entities (1)
  • frustrated genes no independent evidence
    purpose: Genes whose intermediate expression levels are only weakly stable, allowing noise to drive basin switching
    New conceptual category introduced to explain the differentiation mechanism; no independent evidence supplied in abstract.

pith-pipeline@v0.9.0 · 5363 in / 1460 out tokens · 60338 ms · 2026-05-10T03:34:55.117110+00:00 · methodology

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Reference graph

Works this paper leans on

86 extracted references

  1. [1]

    W. J. Blake, M. Kærn, C. R. Cantor, and J. J. Collins, Noise in eukaryotic gene expression, Nature422, 633 (2003)

    2003

  2. [2]

    J. M. Raser and E. K. O'Shea, Noise in gene expres- sion: origins, consequences, and control, Science309, 2010 (2005)

    2010

  3. [3]

    J. M. Pedraza and J. Paulsson, Effects of molecular mem- ory and bursting on fluctuations in gene expression, Sci- ence319, 339 (2008)

    2008

  4. [4]

    D. J. Bax, J. Strik, L. A. Schepens, T. L. Lenstra, M. M. Hansen, and H. Marks, Gene expression noise in develop- ment: genome-wide dynamics, Science & Society (2025)

    2025

  5. [5]

    Raj and A

    A. Raj and A. Van Oudenaarden, Nature, nurture, or chance: stochastic gene expression and its consequences, Cell135, 216 (2008)

    2008

  6. [6]

    M. B. Elowitz, A. J. Levine, E. D. Siggia, and P. S. Swain, Stochastic gene expression in a single cell, Science297, 1183 (2002)

    2002

  7. [7]

    H. H. McAdams and A. Arkin, Stochastic mechanisms in gene expression, Proceedings of the National Academy of Sciences94, 814 (1997)

    1997

  8. [8]

    Vi˜ nuelas, G

    J. Vi˜ nuelas, G. Kaneko, A. Coulon, E. Vallin, V. Morin, C. Mejia-Pous, J.-J. Kupiec, G. Beslon, and O. Gan- drillon, Quantifying the contribution of chromatin dy- namics to stochastic gene expression reveals long, locus- dependent periods between transcriptional bursts, BMC biology11, 1 (2013)

    2013

  9. [9]

    Kaern, T

    M. Kaern, T. C. Elston, W. J. Blake, and J. J. Collins, Stochasticity in gene expression: from theories to pheno- types, Nature Reviews Genetics6, 451 (2005)

    2005

  10. [10]

    Furusawa, T

    C. Furusawa, T. Suzuki, A. Kashiwagi, T. Yomo, and K. Kaneko, Ubiquity of log-normal distributions in intra- cellular reaction dynamics, Biophysics1, 25 (2005)

    2005

  11. [11]

    L. Ham, R. D. Brackston, and M. P. Stumpf, Extrinsic noise and heavy-tailed laws in gene expression, Physical review letters124, 108101 (2020)

    2020

  12. [12]

    Lin and A

    J. Lin and A. Amir, Disentangling intrinsic and extrinsic gene expression noise in growing cells, Physical review letters126, 078101 (2021)

    2021

  13. [13]

    Cortijo and J

    S. Cortijo and J. C. Locke, Does gene expression noise play a functional role in plants?, Trends in plant science 25, 1041 (2020)

    2020

  14. [14]

    S. C. Little, M. Tikhonov, and T. Gregor, Precise devel- opmental gene expression arises from globally stochastic transcriptional activity, Cell154, 789 (2013)

    2013

  15. [15]

    Mirabet, F

    V. Mirabet, F. Besnard, T. Vernoux, and A. Boudaoud, Noise and robustness in phyllotaxis, PLoS computational biology8, e1002389 (2012)

    2012

  16. [16]

    D. Lim, S. Moon, Y. M. Song, M. Kim, J. Kim, K. Kim, B.-K. Cho, J. Kim, and J. K. Kim, Toward single-cell control: noise-robust perfect adaptation in biomolecular systems, Nature Communications (2025)

    2025

  17. [17]

    P. K. Maini, T. E. Woolley, R. E. Baker, E. A. Gaffney, and S. S. Lee, Turing’s model for biological pattern for- mation and the robustness problem, Interface focus2, 487 (2012)

    2012

  18. [18]

    G. M. Suel, R. P. Kulkarni, J. Dworkin, J. Garcia-Ojalvo, and M. B. Elowitz, Tunability and noise dependence in differentiation dynamics, Science315, 1716 (2007)

    2007

  19. [19]

    Tkaˇ cik, T

    G. Tkaˇ cik, T. Gregor, and W. Bialek, The role of in- put noise in transcriptional regulation, PloS one3, e2774 (2008)

    2008

  20. [20]

    L. S. Tsimring, Noise in biology, Reports on Progress in Physics77, 026601 (2014)

    2014

  21. [21]

    Eldar and M

    A. Eldar and M. B. Elowitz, Functional roles for noise in genetic circuits, Nature467, 167 (2010)

    2010

  22. [22]

    Togashi and K

    Y. Togashi and K. Kaneko, Transitions induced by the discreteness of molecules in a small autocatalytic system, Physical review letters86, 2459 (2001)

    2001

  23. [23]

    M. D. McDonnell and D. Abbott, What is stochastic resonance? definitions, misconceptions, debates, and its relevance to biology, PLoS computational biology5, e1000348 (2009)

    2009

  24. [24]

    Chalancon, C

    G. Chalancon, C. N. Ravarani, S. Balaji, A. Martinez- Arias, L. Aravind, R. Jothi, and M. M. Babu, Interplay between gene expression noise and regulatory network architecture, Trends in genetics28, 221 (2012)

    2012

  25. [25]

    Puzovi´ c, T

    N. Puzovi´ c, T. Madaan, and J. Y. Dutheil, Being noisy in a crowd: Differential selective pressure on gene ex- pression noise in model gene regulatory networks, PLoS Computational Biology19, e1010982 (2023)

    2023

  26. [26]

    Pinho, V

    R. Pinho, V. Garcia, and M. W. Feldman, Phenotype ac- cessibility and noise in random threshold gene regulatory networks, PloS one10, e0119972 (2015)

    2015

  27. [27]

    Kashiwagi, I

    A. Kashiwagi, I. Urabe, K. Kaneko, and T. Yomo, Adap- tive response of a gene network to environmental changes by fitness-induced attractor selection, PloS one1, e49 (2006)

    2006

  28. [28]

    Furusawa and K

    C. Furusawa and K. Kaneko, Chaotic expression dynam- ics implies pluripotency: when theory and experiment 6 meet, Biology direct4, 17 (2009)

    2009

  29. [29]

    Zhang, K

    L. Zhang, K. Radtke, L. Zheng, A. Q. Cai, T. F. Schilling, and Q. Nie, Noise drives sharpening of gene expression boundaries in the zebrafish hindbrain, Molecular systems biology8, 613 (2012)

    2012

  30. [30]

    Toppen and S

    J. Toppen and S. Tavazoie, Noise-driven morphogene- sis independent of transcriptional regulatory programs, bioRxiv (2025)

    2025

  31. [31]

    Ahrends, A

    R. Ahrends, A. Ota, K. M. Kovary, T. Kudo, B. O. Park, and M. N. Teruel, Controlling low rates of cell differenti- ation through noise and ultrahigh feedback, Science344, 1384 (2014)

    2014

  32. [32]

    Q. Nie, L. Qiao, Y. Qiu, L. Zhang, and W. Zhao, Noise control and utility: from regulatory network to spatial patterning, Science China Mathematics63, 425 (2020)

    2020

  33. [33]

    Long and A

    Y. Long and A. Boudaoud, Emergence of robust patterns from local rules during plant development, Current opin- ion in plant biology47, 127 (2019)

    2019

  34. [34]

    Waddington,The Strategy of the Genes: A Discussion of Some Aspects of Theoretical Biology(Allen & Unwin, 1957)

    C. Waddington,The Strategy of the Genes: A Discussion of Some Aspects of Theoretical Biology(Allen & Unwin, 1957)

    1957

  35. [35]

    Niwa, How is pluripotency determined and main- tained?, Development134, 635 (2007)

    H. Niwa, How is pluripotency determined and main- tained?, Development134, 635 (2007)

    2007

  36. [36]

    Meissner, Epigenetic modifications in pluripotent and differentiated cells, Nature biotechnology28, 1079 (2010)

    A. Meissner, Epigenetic modifications in pluripotent and differentiated cells, Nature biotechnology28, 1079 (2010)

    2010

  37. [37]

    W. F. Lim, T. Inoue-Yokoo, K. S. Tan, M. I. Lai, and D. Sugiyama, Hematopoietic cell differentiation from em- bryonic and induced pluripotent stem cells, Stem cell re- search & therapy4, 71 (2013)

    2013

  38. [38]

    Huang, Y.-P

    S. Huang, Y.-P. Guo, G. May, and T. Enver, Bifurcation dynamics in lineage-commitment in bipotent progenitor cells, Developmental biology305, 695 (2007)

    2007

  39. [39]

    Furusawa and K

    C. Furusawa and K. Kaneko, Theory of robustness of ir- reversible differentiation in a stem cell system: chaos hy- pothesis, Journal of Theoretical Biology209, 395 (2001)

    2001

  40. [40]

    Matsushita and K

    Y. Matsushita and K. Kaneko, Homeorhesis in wadding- ton’s landscape by epigenetic feedback regulation, Phys- ical Review Research2, 023083 (2020)

    2020

  41. [41]

    D. A. Rand, A. Raju, M. S´ aez, F. Corson, and E. D. Sig- gia, Geometry of gene regulatory dynamics, Proceedings of the National Academy of Sciences118, e2109729118 (2021)

    2021

  42. [42]

    M. Saez, J. Briscoe, and D. A. Rand, Dynamical land- scapes of cell fate decisions, Interface focus12(2022)

    2022

  43. [43]

    Mojtahedi, A

    M. Mojtahedi, A. Skupin, J. Zhou, I. G. Casta˜ no, R. Y. Leong-Quong, H. Chang, K. Trachana, A. Giuliani, and S. Huang, Cell fate decision as high-dimensional critical state transition, PLoS biology14, e2000640 (2016)

    2016

  44. [44]

    Moris, C

    N. Moris, C. Pina, and A. M. Arias, Transition states and cell fate decisions in epigenetic landscapes, Nature Reviews Genetics17, 693 (2016)

    2016

  45. [45]

    Guillemin and M

    A. Guillemin and M. P. Stumpf, Noise and the molecular processes underlying cell fate decision-making, Physical biology18, 011002 (2021)

    2021

  46. [46]

    Huang, M

    B. Huang, M. Lu, M. Galbraith, H. Levine, J. N. Onuchic, and D. Jia, Decoding the mechanisms under- lying cell-fate decision-making during stem cell differen- tiation by random circuit perturbation, Journal of the Royal Society interface17(2020)

    2020

  47. [47]

    Moghe, E

    P. Moghe, E. Hannezo, and T. Hiiragi, Optimality as a framework for understanding developmental robustness, Trends in Cell Biology (2025)

    2025

  48. [48]

    Plugers and K

    D. Plugers and K. Kaneko, Evolution of robust cell dif- ferentiation under epigenetic feedback, Physical Review Research8, 013059 (2026)

    2026

  49. [49]

    Mjolsness, D

    E. Mjolsness, D. H. Sharp, and J. Reinitz, A connection- ist model of development, Journal of theoretical Biology 152, 429 (1991)

    1991

  50. [50]

    Salazar-Ciudad, S

    I. Salazar-Ciudad, S. Newman, and R. Sol´ e, Phenotypic and dynamical transitions in model genetic networks i. emergence of patterns and genotype-phenotype relation- ships, Evolution & development3, 84 (2001)

    2001

  51. [51]

    Kaneko, Evolution of robustness to noise and mu- tation in gene expression dynamics, PLoS one2, e434 (2007)

    K. Kaneko, Evolution of robustness to noise and mu- tation in gene expression dynamics, PLoS one2, e434 (2007)

    2007

  52. [52]

    Differentiation from such states has already been studied in [48] and will not be discussed here

    There are cases with limit cycles or chaotic attractors depending onJ ij. Differentiation from such states has already been studied in [48] and will not be discussed here

  53. [53]

    I. B. Dodd, M. A. Micheelsen, K. Sneppen, and G. Thon, Theoretical analysis of epigenetic cell memory by nucle- osome modification, Cell129, 813 (2007)

    2007

  54. [54]

    Sneppen, M

    K. Sneppen, M. A. Micheelsen, and I. B. Dodd, Ultra- sensitive gene regulation by positive feedback loops in nucleosome modification, Molecular systems biology4, 182 (2008)

    2008

  55. [55]

    Another class of GRNs were also found which differen- tiated through successive stabilization of initial chaotic attractors to fixed points by the epigenetic fixation

  56. [56]

    Kaneko, Adiabatic elimination by the eigenfunction expansion method, Progress of Theoretical Physics66, 129 (1981)

    K. Kaneko, Adiabatic elimination by the eigenfunction expansion method, Progress of Theoretical Physics66, 129 (1981)

    1981

  57. [57]

    Risken, Fokker-planck equation, inThe Fokker-Planck equation: methods of solution and applications(Springer,

    H. Risken, Fokker-planck equation, inThe Fokker-Planck equation: methods of solution and applications(Springer,

  58. [58]

    H. Haken, An introduction: nonequilibrium phase transi- tions and self-organization in physics, chemistry and bi- ology, inSynergetics: Introduction and Advanced Topics (Springer, 2004) pp. 1–387

    2004

  59. [59]

    They only bring the stable fixed points obtained forθcloser to θ=±1

    Higher order corrections may be included as well, but for frustrated genes they do not alter the dynamics. They only bring the stable fixed points obtained forθcloser to θ=±1

  60. [60]

    ForJ ij = 0 we findx ∗ i ≈ β(θ+c i) 1−βJii − β3(θ+ci)3 3(1−βJii)4

  61. [61]

    Suzuki, Scaling theory of non-equilibrium systems near the instability point

    M. Suzuki, Scaling theory of non-equilibrium systems near the instability point. i: General aspects of tran- sient phenomena, Progress of Theoretical Physics56, 77 (1976)

    1976

  62. [62]

    de Pasquale, P

    F. de Pasquale, P. Tartaglia, and P. Tombesi, Transient behavior of nonequilibrium phase transitions, Physics Letters A78, 129 (1980)

    1980

  63. [63]

    Note that equation 8 assumes a hierarchical signaling of genes, for more complicated gene regulatory networks (J) one may use matrix representation for the genes (X) and a diagonal that indicates frustration (F) to obtain an estimate of the noise⇒dX/dt= (I−βF J)X+η

  64. [64]

    Two Single Amplified: Output gene with two connections J0j =±1

    Individual Gene: Output genex 0 without connections. Two Single Amplified: Output gene with two connections J0j =±1. Four Single Amplified: Output gene with four connectionsJ 0j =±1. One Double Amplified: Output gene with a single connection from a frustrated genex j which itself has a single connection leading to a double noise amplificationJ 0j =J jk =±...

  65. [65]

    This corresponds to a 50% chance that at least one of the 7 16 cells differentiates to the opposite side

  66. [66]

    Often Waddington landscape has been discussed as po- tential from the flow of given gene expression dynamics [83–85], whereas how the valley bifurcates with slow epi- genetic timescale is important in Waddington’s picture [40–42]

  67. [67]

    Bal´ azsi, A

    G. Bal´ azsi, A. Van Oudenaarden, and J. J. Collins, Cel- lular decision making and biological noise: from microbes to mammals, Cell144, 910 (2011)

    2011

  68. [68]

    Abley, R

    K. Abley, R. Goswami, and J. C. Locke, Bet-hedging and variability in plant development: seed germination and beyond, Philosophical Transactions of the Royal Society B: Biological Sciences379(2024)

    2024

  69. [69]

    A. J. Grimbergen, J. Siebring, A. Solopova, and O. P. Kuipers, Microbial bet-hedging: the power of being dif- ferent, Current opinion in microbiology25, 67 (2015)

    2015

  70. [70]

    Liu, J.-M

    J. Liu, J.-M. Fran¸ cois, and J.-P. Capp, Use of noise in gene expression as an experimental parameter to test phenotypic effects, Yeast33, 209 (2016)

    2016

  71. [71]

    E. A. Urban and R. J. Johnston Jr, Buffering and ampli- fying transcriptional noise during cell fate specification, Frontiers in genetics9, 591 (2018)

    2018

  72. [72]

    Maamar, A

    H. Maamar, A. Raj, and D. Dubnau, Noise in gene ex- pression determines cell fate in bacillus subtilis, Science 317, 526 (2007)

    2007

  73. [73]

    Bargaje, K

    R. Bargaje, K. Trachana, M. N. Shelton, C. S. McGin- nis, J. X. Zhou, C. Chadick, S. Cook, C. Cavanaugh, S. Huang, and L. Hood, Cell population structure prior to bifurcation predicts efficiency of directed differentia- tion in human induced pluripotent cells, Proceedings of the National Academy of Sciences114, 2271 (2017)

    2017

  74. [74]

    N. P. Gao, O. Gandrillon, A. P´ aldi, U. Herbach, and R. Gunawan, Single-cell transcriptional uncertainty land- scape of cell differentiation, F1000Research12, 426 (2023)

    2023

  75. [75]

    M. A. Canham, A. A. Sharov, M. S. Ko, and J. M. Brick- man, Functional heterogeneity of embryonic stem cells revealed through translational amplification of an early endodermal transcript, PLoS biology8, e1000379 (2010)

    2010

  76. [76]

    Y. Yao, J. Zhu, W. Li, and D. Pei, Role of genetic frus- trations in cell reprogramming, bioRxiv , 2025 (2025)

    2025

  77. [77]

    D. K. Wells, W. L. Kath, and A. E. Motter, Control of stochastic and induced switching in biophysical networks, Physical Review X5, 031036 (2015)

    2015

  78. [78]

    Bojer, S

    M. Bojer, S. Kremser, and U. Gerland, Robust boundary formation in a morphogen gradient via cell-cell signaling, Physical Review E105, 064405 (2022)

    2022

  79. [79]

    Zhang, Z

    X.-P. Zhang, Z. Cheng, F. Liu, and W. Wang, Linking fast and slow positive feedback loops creates an opti- mal bistable switch in cell signaling, Physical Review E—Statistical, Nonlinear, and Soft Matter Physics76, 031924 (2007)

    2007

  80. [80]

    Teague, G

    S. Teague, G. Primavera, B. Chen, Z.-Y. Liu, L. Yao, E. Freeburne, H. Khan, K. Jo, C. Johnson, and I. Heemskerk, Time-integrated bmp signaling determines fate in a stem cell model for early human development, Nature communications15, 1471 (2024)

    2024

Showing first 80 references.