Pith. sign in

REVIEW 3 major objections 4 minor 76 references

Coarsening model of chromosomal crossover placement

T0 review · 3 major / 4 minor · reviewed 2026-08-04 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that the number and spacing of meiotic crossovers are set by droplet coarsening: crossover precursor droplets (recombination nodules) compete for a shared protein, HEI10, and the survivors become crossovers, with counts fo

desk verdict A serious, carefully written extension of the droplet coarsening model with real scaling laws; the quantitative claims hinge on an unmeasured power-law affinity, but the paper deserves a referee. read the letter →

arxiv 2509.09521 v1 pith:MEQRLSUE submitted 2025-09-11 physics.bio-ph cond-mat.softq-bio.SC

Marcel Ernst , Riccardo Rossetto , David Zwicker This is my paper · ORCID
classification physics.bio-phcond-mat.softq-bio.SC
keywords crossoverplacementcoarseningHEI10synaptonemalcomplexmeiosisscalinglawsinterferenceassurance
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

The paper argues that crossover placement in meiosis is governed by a physical coarsening process: small droplets of the protein HEI10 associated with chromosomes grow and compete for material, and the droplets that survive designate crossovers. It extends an earlier coarsening model by including thermodynamically consistent exchange of HEI10 among droplets, the synaptonemal complex, and the nucleoplasm. From this model it derives scaling laws: crossover count grows linearly with chromosome/SC length when competition is along the SC, and with total HEI10 amount when the SC is absent. These laws are then used to explain crossover counts across species and to reproduce, with one parameter set, the wild-type and zyp1-mutant phenotypes of Arabidopsis thaliana: assurance, interference, heterochiasmy, and homeostasis. If correct, the model gives a single physical explanation for several long-standing observations of crossover patterning.

What carries the argument

The central object is the HEI10 droplet population described as phase-separated recombination nodules coupled to a one-dimensional synaptonemal complex and a well-mixed nucleoplasm. The dynamical core is a thermodynamically consistent exchange-flux description (transition-state theory, detailed balance) with a size-dependent droplet affinity γ_D(V)=γ_0(V/a^3)^-ν. The machinery does the work in two limiting scaling analyses: diffusion-limited coarsening along the SC yields N(t) ~ t^-1/(2+ν) with ν=1/3 giving t^-3/7 and N ~ L; exchange-limited coarsening with or without SC yields N(t) ~ t^-1/(1+ν-ν_N) and N ~ M. These two scaling laws are the quantitative bridge to experimental data across spe

What would settle it

Time-resolved cytological imaging of HEI10 droplets in Arabidopsis thaliana zyp1 mutants: if the droplet count is seen to decrease during pachytene, coarsening is active in the mutant and the paper's conclusion that droplets only grow there (needed to explain the absence of heterochiasmy) would be contradicted. Alternatively, direct measurement of the droplet-affinity size dependence would settle whether ν=1/3 is the right exponent: a measurably different exponent would change the predicted t-scaling and the inferred rate constants.

Watch

Extended reading notes

Core claim

The central claim is that the number of crossovers at pachytene equals the number of surviving HEI10 droplets in a coarsening process. On an intact SC, droplets are coupled by diffusion along the SC and by exchange with the nucleoplasm; in this regime the asymptotic droplet count scales as N ~ L (SC length) while the coarsening exponent is t^-3/7 in the diffusion-limited case. When the SC is absent (zyp1 mutant), droplets exchange only with the nucleoplasm, and N scales with total HEI10 M and as t^-1/(1+ν-ν_N), which for ν=ν_N=1/3 gives t^-1. The same model yields CO assurance from the occupancy probability that every chromosome keeps at least one droplet, CO interference from the spacing th

Load-bearing premise

The entire quantitative structure rests on the assumed power-law size dependence of droplet affinity, γ_D(V) = γ_0(V/a^3)^-ν with ν=1/3 (and ν_S=0 for exchange), which the authors adopt by analogy to surface tension while stating that the biophysical mechanism of HEI10 accumulation is currently unclear; if the real size dependence differs, the predicted exponents and the comparisons to experimental data change.

Editorial extensions

If this is right

  • Crossover count scales linearly with SC length in wild-type organisms, so longer chromosomes get proportionally more class I crossovers beyond the assurance floor.
  • In mutants without the SC, crossover count scales with total HEI10 amount rather than chromosome length, and assurance is reduced because droplets are randomly allocated among chromosomes.
  • Nucleoplasmic exchange can be almost as strong as SC-mediated exchange before CO interference and assurance are lost, so the model tolerates substantial material exchange via the nucleoplasm.
  • CO homeostasis arises because the final count depends on HEI10 line density, not on the number of initiating DSBs or droplets.
  • Heterochiasmy in A. thaliana follows from the linear scaling of CO count with SC length; its disappearance in zyp1 mutants suggests droplets there grow without coarsening.

Reading between the lines

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

  • If the coarsening picture is right, the same scaling laws could be used to predict crossover-count changes in other SC-deficient mutants or in HEI10 dosage variants: the count should track the total available HEI10 raised to a sublinear power.
  • The model's parameter-free character might be tested by measuring the size dependence of HEI10 droplet affinity directly, which would either confirm or replace the assumed ν=1/3.
  • The predicted telomere depletion of crossovers under uniform loading gives a clean, testable contrast with experiments that show elevated telomere crossover frequencies; identifying which heterogeneity resolves the discrepancy would tighten the model.
  • A time-resolved imaging experiment in zyp1 mutants that distinguishes growth-only from coarsening would discriminate the two regimes and, if coarsening were observed, would force a re-examination of the heterochiasmy argument.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper extends a previously proposed coarsening model for crossover placement by incorporating thermodynamically consistent material exchange among HEI10 droplets, the synaptonemal complex (SC), and the nucleoplasm. It derives asymptotic scaling laws for the number of surviving droplets (Eqs. 9, 10, 12), argues that droplet count scales linearly with SC length, and uses these scalings to compare against published crossover counts across species and against A. thaliana wild-type, zyp1, and HEI10oe data. The authors conclude that the extended coarsening model provides a coherent quantitative framework for crossover placement, including CO assurance, interference, heterochiasmy, and homeostasis.

Significance. If the model's constitutive assumptions are accepted, the paper offers a unified, thermodynamically consistent description of crossover patterning that ties together several previously separate observations: linear CO count scaling with chromosome length, CO assurance, CO interference, the effects of SC loss in zyp1 mutants, and reduced heterochiasmy in those mutants. The asymptotic derivations in Appendices A and B are detailed and appear internally consistent with the numerical simulations in Figs. 2–5 and B.3–B.5. The explicit treatment of detailed balance in the exchange fluxes (Eq. 3) is a genuine improvement over earlier coarsening formulations. However, the paper's quantitative data comparisons rest on several parameters and exponents that are either fit to the same data being explained or chosen by analogy without independent measurement, so the strength of the 'coherent explanation' claim is weaker than the text suggests.

major comments (3)
  1. [Section III B and Eq. (9)] The parameter γ_0/γ_S ≈ 10^-4 is obtained by applying the scaling relation (9) to wild-type A. thaliana CO counts, assuming pachytene duration. This makes the model's match to the wild-type total CO count true by construction. The subsequent use of Eq. (9) in Section III C to explain heterochiasmy is a genuine prediction only for the male/female ratio, and only under the untested assumptions that the line density λ and coarsening time are sex-independent. The manuscript should clearly separate fitted predictions from independent predictions. Similarly, γ_S Λ_DN is estimated from zyp1 CO counts using Eq. (12) if coarsening is assumed, and then Section III C uses the lack of heterochiasmy to argue that zyp1 droplets are not coarsening; this reasoning is not circular per se, but the parameter estimate is scenario-dependent and should be flagged as such when drawing conclusions about the mut
  2. [Section II A, Eq. (1c), and Section III B] The quantitative predictions—N∝t^{-3/7}, N∝t^{-1}, N∝L, and N∝M—all derive from the power-law affinity γ_D(V)=γ_0(V/a^3)^{-ν} together with the chosen size-sensitivity exponents ν_N=1/3 and ν_S=0. The paper itself states in Section IV that the biophysical mechanism of HEI10 accumulation is unclear and that active post-translational modifications may be relevant. If the true size dependence differs from ν=1/3, or if ν_N differs, then the asymptotic exponents in Eqs. (9), (10), and (12) change, and the parameter estimates in Section III B (γ_0/γ_S≈10^-4, γ_DN≈10^-1) shift. The manuscript needs a sensitivity analysis, e.g., showing how the data comparisons in Figs. 3, 5, and 6 would change for ν=1/4 (the value used in the earlier model cited in App. B 3 d) or for ν_N=2/3. Without this, the claim of quantitative agreement is not robust.
  3. [Section III A and Fig. 6] The cross-species comparison uses an 'adjusted chromosome length' that is chosen to minimize the root-mean-square error to the theoretical prediction, and the power-law fits in Fig. 6B exclude chromosomes with N<1.2. This amounts to fitting a per-species proportionality factor and does not test the model's predicted absolute CO count. Moreover, many species in Fig. 6B and Fig. B.7 show slopes between 0.5 and 0.8, and some show super-linear slopes, which are not consistent with the model's linear scaling. The statement in Section III A that 'the scaling relation explains experimental data' is therefore overstated. The authors should report the distribution of fitted slopes, provide a statistical test of whether the linear model is preferred after accounting for the plateau, and discuss explicitly how many species are actually consistent with linear scaling.
minor comments (4)
  1. [Throughout] There are numerous typos, including 'droplpet' (Fig. 1 caption), 'exchane' (Fig. 5A), 'conisder' (App. B 3 b), 'teh' (App. B 5), and 'fist-order' (App. B 6). A careful proofread is needed.
  2. [Section II C] The definition κ=γ_S Λ_DS/(D a) is introduced in the text and then used in Fig. 2, but in App. B 3 b it is written as κ=Λ_DS/(aD)=γ_DS/γ_S. The two definitions differ by a factor γ_S; please reconcile notation.
  3. [Section III B] The assumed value γ_S = 10 a^3/V_N is described as 'reasonable results' but no sensitivity of the conclusions to this arbitrary choice is given. Since γ_S affects the estimated γ_DN and γ_DS, a brief discussion of the sensitivity would strengthen the parameter analysis.
  4. [Section II E and Fig. 4] The paper states that the growth regime and coarsening regime cannot be distinguished for zyp1 without time-resolved data, but Section III C later concludes that 'droplets in the A. thaliana zyp1-mutant are not coarsening.' Please make the provisional nature of this conclusion more explicit in the main text.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: model parameters are calibrated, not disguised predictions; scaling-law comparisons and assurance/heterochiasmy checks have independent content.

full rationale

The paper's central derivations are the scaling laws Eqs. (9)–(12), obtained from the stated constitutive assumptions (power-law affinity γ_D(V)=γ_0(V/a^3)^(-ν) and exchange-rate size dependencies). These are model assumptions, not fitted to the data, so the scaling exponents are genuine predictions. The parameters γ_0/γ_S and γ_S Λ_DN are explicitly calibrated in Sec. III B using wild-type and zyp1 CO counts; the paper does not present those same counts as independent predictions. The heterochiasmy ratio in Eq. (15) cancels the fitted exchange rates and affinities, so it is not forced by the calibration. The cross-species linear scaling N∝L is a functional prediction of the coarsening equations, and the 'adjusted chromosome length' in Fig. 6 is a calibration of physical units (Mb→SC length), not a refit of the CO-count slope itself. The CO-assurance prediction in Eq. (14) uses no fitted parameters and is compared to the observed 3/14 failure rate, providing independent support. Self-citations [33,48] supply experimental data and prior model context, but the load-bearing derivation is self-contained in this paper. The acknowledged uncertainty in the biophysical origin of γ_D(V) is a modeling limitation, not circular reasoning.

Assumptions & free parameters 9 free parameters · 8 assumptions · 0 invented entities

The central claim rests on a phenomenological droplet model with several hand-chosen exponents and exchange rates. The most important constants are fit to A. thaliana crossover counts and then used to explain the same data, so the reader pays for these assumptions upstream.

free parameters (9)
  • ν (size-sensitivity exponent of droplet affinity) = 1/3
    Chosen by analogy to surface tension; not measured. Determines the scaling exponents in Eqs. (9), (10), and (12).
  • ν_S (size-sensitivity of droplet-SC exchange) = 0
    Chosen 'for simplicity' in Section III B; affects the exchange-limited scaling exponent 1/(1+ν-ν_S).
  • ν_N (size-sensitivity of droplet-nucleoplasm exchange) = 1/3
    Chosen equal to ν; affects the no-SC coarsening exponent in Eq. (12).
  • γ_0/γ_S = ≈ 10^-4
    Obtained by applying the scaling relation (9) to wild-type A. thaliana CO counts, assuming pachytene lasts 10 h and M ≈ c_D a^3 N. This is a fit, not an independent measurement.
  • γ_S = 10 a^3/V_N = 10 a^3/V_N
    The paper states 'we chose γ_S = 10 a^3/V_N, which produced reasonable results.' No direct experimental constraint is given; it sets the partition between SC and nucleoplasm.
  • γ_DS = γ_S Λ_DS/(D a) = ≈ 0.2
    Estimated from the previous model of the same group and the requirement that γ_S Λ_DS/(D a) > 10^-1 for significant interference and assurance. Order-of-magnitude only.
  • γ_SN = γ_S Λ_SN/(D a) = between 10^-6 and 10^-4
    Lower bound comes from HEI10 loading time ~1 h; upper bound comes from preserving CO interference. Chosen within a range, affecting nucleoplasmic exchange strength.
  • γ_DN = γ_S Λ_DN/(D a) = < 3×10^-2 (growth) or ≈ 10^-1 (coarsening)
    Inferred from zyp1-mutant CO counts via Eq. (11) or Eq. (12). The paper cannot decide which regime applies.
  • M (total HEI10 amount) = ≈ c_D a^3 N, with N = 2 per SC and α_wt ≈ 1
    Assumed most HEI10 ends up in droplets of volume a^3; sets the absolute scale for droplet counts and is estimated from A. thaliana data.
assumptions (8)
  • ad hoc to paper Droplet equilibrium chemical potential μ_α = k_B T ln(γ_α c_α/c_D) with γ_D(V) = γ_0 (V/a^3)^(-ν).
    Postulated in Eq. (1); the size-dependent affinity is a phenomenological device that drives coarsening and sets the scaling exponents.
  • domain assumption Nucleoplasm is well mixed: spatial variations of HEI10 concentration are negligible.
    Stated in Section II A; enables global competition through c_N(t) and underlies the no-SC results.
  • domain assumption Droplets have constant concentration c_D and are fully described by their volume V_j,i.
    Section II A; needed for Eqs. (5); ignores internal droplet structure and wetting interactions with the SC.
  • domain assumption RNs present after a fixed time t become crossovers.
    First paragraph of Section II; this maps surviving droplets to crossover count and is the link between model and data.
  • domain assumption Exchange fluxes follow transition-state theory with detailed balance (Eq. 3).
    Section II A; ensures thermodynamic consistency but is a modeling choice for the kinetics.
  • standard math Asymptotic scaling analysis assumes an infinite system and equal average droplet spacing (mean-field LSW approach).
    Appendices A3-A4; the derivation of Eqs. (9), (10), and (12) rests on this approximation, validated only against the paper's own simulations.
  • domain assumption In the absence of SC, droplet allocation to chromosomes is random (occupancy and coupon-collector statistics).
    Section II E and Appendix A5; used to derive the CO assurance formula Eq. (14).
  • domain assumption In wild-type heterochiasmy, male SCs are ~50% longer with the same line density λ and coarsening time.
    Section III C; the assumption that λ and T_c are sex-independent is not directly measured.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Coarsening model of chromosomal crossover placement." pith.science (2026). https://pith.science/paper/MEQRLSUE

@misc{pith2026250909521,
  author       = {Pith},
  title        = {Pith review of: Coarsening model of chromosomal crossover placement},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MEQRLSUE}},
  note         = {Machine review of arXiv:2509.09521}
}
read the original abstract

Chromosomal crossovers play a crucial role in meiotic cell division, as they ensure proper chromosome segregation and increase genetic variability. Experiments have consistently revealed two key observations across species: (i) the number of crossovers per chromosome is typically small, but at least one, and (ii) crossovers on the same chromosome are subject to interference, i.e., they are more separated than expected by chance. These observations can be explained by a recently proposed coarsening model, where the dynamics of droplets associated with chromosomes designate crossovers. We provide a comprehensive analysis of the coarsening model, which we also extend by including material exchanges between droplets, the synaptonemal complex, and the nucleoplasm. We derive scaling laws for the crossover count, which allows us to analyze data across species. Moreover, our model provides a coherent explanation of experimental data across mutants, including the wild-type and zyp1-mutant of A. thaliana. Consequently, the extended coarsening model provides a solid framework for investigating the underlying mechanisms of crossover placement.

Figures

Figures reproduced from arXiv: 2509.09521 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6 [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

76 extracted references · 1 canonical work pages

  1. [1]

    The one-dimensional compartment has lengthLand an initial line concentrationc(x)

    Relaxation of concentrations in a linear compartment coupled to a bulk We here investigate the relaxation behaviour of an effectively one-dimensional compartment coupled to a large bulk. The one-dimensional compartment has lengthLand an initial line concentrationc(x). We consider diffusion along this compartment with diffusion constantD. Assuming that dif...

  2. [2]

    Stationary profiles between droplets along one-dimensional compartment with bulk-exchange We here analyze the diffusion-limited concentration profile in a one-dimensional compartment with bulk-exchange, where droplets are described by the effective droplet model. Specifically, we consider a bulk with a homogeneous mean-field concentrationc b, a one-dimens...

  3. [3]

    Scaling law for diffusion-limited droplet coarsening along one dimension We here derive an asymptotic solution to diffusion-limited coarsening along an infinite one-dimensional compart- ment. Following the approach of Lifshitz, Slyozov, and Wagner [46, 47], we derive scaling relations for mean droplet growth and the number of remaining droplets as a funct...

  4. [4]

    In particular, we consider an infinite system withN(t) droplets per unit-volume, a droplet size distributionn(V, t), and a bulk that is described by a mean-field concentrationc(t)

    Scaling law of droplet coarsening with generalized exponents In this section we derive the asymptotic scaling relations of a generalized version of the classical diffusion-mediated coarsening [46, 47]. In particular, we consider an infinite system withN(t) droplets per unit-volume, a droplet size distributionn(V, t), and a bulk that is described by a mean...

  5. [5]

    Theoretical approximations of CO assurance In this section we quantify the reduction of CO assurance in mutants with abolished SC. To derive an analytic estimate of CO assurance, we focus on a single chromosome with average droplet count ¯Ni in a cell withNdroplets in total, which are randomly allocated to multiple chromosomes. The probability that this c...

  6. [6]

    To do this, we assumed a null hypothesis (absent CO interference) where COs were independently designated and placed on chromosomes

    Interference length for non-Poissonian total CO count distribution In our recent publication [48], we introduced the interference lengthL int and the normalized interference length Lnorm int to quantify CO interference. To do this, we assumed a null hypothesis (absent CO interference) where COs were independently designated and placed on chromosomes. In t...

  7. [7]

    Non-dimensionalization We simulate the system in non-dimensional units, choosing appropritate length and time scales. Since we discuss various limits of the full model, we cannot use one non-dimensionalization for all cases, and instead introduce two in the following, depening on whether the synaptonemal complex is present or not. a. Non-dimensionalizatio...

  8. [8]

    Relaxation dynamics of HEI10 concentration on a SC in nucleoplasm without droplets We first analyze our model without droplets and for simplicity consider one SC with lengthL=ℓato investigate the time scale of HEI10 loading onto the SC and the relaxation dynamics of non-homogeneous concentration profiles along the SC which are also affected by the exchang...

Show all 76 references
  1. [9]

    Investigation of a coarsening of droplets on a SC without nucleoplasm In this section we consider a system of one SC with droplets that does not exchange HEI10 with the surrounding nucleoplasm, using the non-dimensionalisation description (section B 1 a). 26 a. SC profile in d...

  2. [10]

    thaliana[33, 62]

    Investigation of droplet growth and coarsening without SC In this section, we consider a system without SC which resembles thezyp1-mutant inA. thaliana[33, 62]. Because we assumed fast diffusion in the nucleoplasm, the allocation and positions of individual droplet along chrom...

  3. [11]

    Numerical analysis of full model and comparison to experiments In the following, we consider the full system with all three compartments (the nucleoplasm, the SCs, and droplets) and analyze teh dynamics numerically. a. HEI10 concentration profile along the SC We determine the ...

  4. [12]

    We discretized the concentration field on the SC using equidistant grid points separated by ∆x grid/aand approximated 36 spatial derivatives using finite differences

    Implementation details of numerical simulations The implementation of our model is based on the non-dimensional versions of the equations, which are described in section B 1 a for the model without nucleoplasm and the full model, and section B 1 b for the system without SC. We...

  5. [13]

    L. E. Berchowitz and G. P. Copenhaver, Genetic interference: don’t stand so close to me, Current genomics11, 91 (2010)

    2010

  6. [14]

    S. T. Globus and S. Keeney, The joy of six: how to control your crossovers, Cell149, 11 (2012)

    2012

  7. [15]

    L. K. Anderson, L. D. Lohmiller, X. Tang, D. B. Hammond, L. Javernick, L. Shearer, S. Basu-Roy, O. C. Martin, and M. Falque, Combined fluorescent and electron microscopic imaging unveils the specific properties of two classes of meiotic crossovers, Proceedings of the National ...

    2014

  8. [16]

    S. Wang, D. Zickler, N. Kleckner, and L. Zhang, Meiotic crossover patterns: obligatory crossover, interference and home- ostasis in a single process, Cell cycle (Georgetown, Tex.)14, 305 (2015)

    2015

  9. [17]

    Zickler and N

    D. Zickler and N. Kleckner, A few of our favorite things: Pairing, the bouquet, crossover interference and evolution of meiosis, Seminars in Cell & Developmental Biology54, 135 (2016)

    2016

  10. [18]

    S. P. Otto and B. A. Payseur, Crossover interference: Shedding light on the evolution of recombination, Annual Review of Genetics53, 19 (2019)

    2019

  11. [19]

    G. R. Smith and M. Nambiar, New solutions to old problems: molecular mechanisms of meiotic crossover control, Trends in genetics36, 337 (2020)

    2020

  12. [20]

    Jones, The control of chiasma distribution., inSymposia of the Society for Experimental Biology, Vol

    G. Jones, The control of chiasma distribution., inSymposia of the Society for Experimental Biology, Vol. 38 (1984) pp. 293–320

    1984

  13. [21]

    G. V. B¨ orner, N. Kleckner, and N. Hunter, Crossover/noncrossover differentiation, synaptonemal complex formation, and regulatory surveillance at the leptotene/zygotene transition of meiosis, Cell117, 29 (2004)

    2004

  14. [22]

    von Diezmann and O

    L. von Diezmann and O. Rog, Let’s get physical–mechanisms of crossover interference, Journal of cell science134, jcs255745 (2021)

    2021

  15. [23]

    Lloyd, Crossover patterning in plants, Plant Reproduction 10.1007/s00497-022-00445-4 (2022)

    A. Lloyd, Crossover patterning in plants, Plant Reproduction 10.1007/s00497-022-00445-4 (2022)

    2022 doi

  16. [24]

    Girard, D

    C. Girard, D. Zwicker, and R. Mercier, The regulation of meiotic crossover distribution: a coarse solution to a century-old mystery?, Biochemical Society Transactions51, 1179 (2023)

    2023

  17. [25]

    F. Cole, L. Kauppi, J. Lange, I. Roig, R. Wang, S. Keeney, and M. Jasin, Homeostatic control of recombination is implemented progressively in mouse meiosis, Nature Cell Biology14, 424 (2012)

    2012

  18. [26]

    Zickler and N

    D. Zickler and N. Kleckner, Recombination, pairing, and synapsis of homologs during meiosis, Cold Spring Harbor per- spectives in biology7, a016626 (2015)

    2015

  19. [27]

    J. B. Fernandes, M. S´ egu´ ela-Arnaud, C. Larchevˆ eque, A. H. Lloyd, and R. Mercier, Unleashing meiotic crossovers in hybrid plants, Proceedings of the National Academy of Sciences115, 2431 (2018)

    2018

  20. [28]

    A. H. Sturtevant, The linear arrangement of six sex? linked factors in drosophila, as shown by their mode of association, Journal of experimental zoology14, 43 (1913)

    1913

  21. [29]

    A. H. Sturtevant, The behavior of the chromosomes as studied through linkage, Zeitschrift f¨ ur induktive Abstammungs-und Vererbungslehre13, 234 (1915)

    1915

  22. [30]

    H. J. Muller, The mechanism of crossing-over, The American Naturalist50, 193 (1916)

    1916

  23. [31]

    Kleckner, A

    N. Kleckner, A. Storlazzi, and D. Zickler, Coordinate variation in meiotic pachytene sc length and total crossover/chiasma frequency under conditions of constant dna length, Trends Genet19, 623 (2003)

    2003

  24. [32]

    A. T. Carpenter, Electron microscopy of meiosis in drosophila melanogaster females: I. structure, arrangement, and temporal change of the synaptonemal complex in wild-type, Chromosoma51, 157 (1975)

    1975

  25. [33]

    Zickler and N

    D. Zickler and N. Kleckner, Meiotic chromosomes: integrating structure and function, Annual review of genetics33, 603 (1999). 37

    1999

  26. [34]

    S. L. Page and R. S. Hawley, The genetics and molecular biology of the synaptonemal complex, Annu. Rev. Cell Dev. Biol. 20, 525 (2004)

    2004

  27. [35]

    Capilla-P´ erez, S

    L. Capilla-P´ erez, S. Durand, A. Hurel, Q. Lian, A. Chambon, C. Taochy, V. Solier, M. Grelon, and Raphael, The synap- tonemal complex imposes crossover interference and heterochiasmy in arabidopsis, Proceedings of the National Academy of Sciences118, e2023613118 (2021)

    2021

  28. [36]

    W. T. Stauffer, L. Zhang, and A. Dernburg, Diffusion through a liquid crystalline compartment regulates meiotic recom- bination, Biophysics, Biology and Biophotonics IV: the Crossroads10888, 8 (2019)

    2019

  29. [37]

    O. Rog, S. K¨ ohler, and A. F. Dernburg, The synaptonemal complex has liquid crystalline properties and spatially regulates meiotic recombination factors, Elife6, e21455 (2017)

    2017

  30. [38]

    Neyton, F

    S. Neyton, F. Lespinasse, P. B. Moens, R. Paul, P. Gaudray, V. Paquis-Flucklinger, and S. Santucci-Darmanin, Association between msh4 (muts homologue 4) and the dna strand-exchange rad51 and dmc1 proteins during mammalian meiosis, Molecular human reproduction10, 917 (2004)

    2004

  31. [39]

    Baudat and B

    F. Baudat and B. de Massy, Regulating double-stranded dna break repair towards crossover or non-crossover during mammalian meiosis, Chromosome research15, 565 (2007)

    2007

  32. [40]

    N. M. Hollingsworth and S. J. Brill, The mus81 solution to resolution: generating meiotic crossovers without holliday junctions, Genes & development18, 117 (2004)

    2004

  33. [41]

    Zhang, Z

    L. Zhang, Z. Liang, J. Hutchinson, and N. Kleckner, Crossover patterning by the beam-film model: analysis and implica- tions, PLoS genetics10, e1004042 (2014)

    2014

  34. [42]

    Kleckner, D

    N. Kleckner, D. Zickler, G. H. Jones, J. Dekker, R. Padmore, J. Henle, and J. Hutchinson, A mechanical basis for chromosome function, Proceedings of the National Academy of Sciences101, 12592 (2004)

    2004

  35. [43]

    J. S. King and R. Mortimer, A polymerization model of chiasma interference and corresponding computer simulation., Genetics126, 1127 (1990)

    1990

  36. [44]

    Zhang, S

    L. Zhang, S. K¨ ohler, R. Rillo-Bohn, and A. F. Dernburg, A compartmentalized signaling network mediates crossover control in meiosis, Elife7, e30789 (2018)

    2018

  37. [45]

    Durand, Q

    S. Durand, Q. Lian, J. Jing, M. Ernst, M. Grelon, D. Zwicker, and R. Mercier, Joint control of meiotic crossover patterning by the synaptonemal complex and hei10 dosage, Nature Communications13, 5999 (2022)

    2022

  38. [46]

    Morgan, J

    C. Morgan, J. A. Fozard, M. Hartley, I. R. Henderson, K. Bomblies, and M. Howard, Diffusion-mediated hei10 coarsening can explain meiotic crossover positioning in arabidopsis, Nature Communications12, 4674 (2021)

    2021

  39. [47]

    Zhang, W

    L. Zhang, W. Stauffer, C. Liu, H. Shao, N. Abuzahriyeh, R. Jiang, D. Zwicker, X. Liu, X. Yao, and A. F. Dernburg, Crossover patterning through condensation and coarsening of pro-crossover factors, Nature Cell Biology 10.1038/s41556- 025-01688-9 (2025)

    2025 doi

  40. [48]

    P. A. Ziolkowski, C. J. Underwood, C. Lambing, M. Martinez-Garcia, E. J. Lawrence, L. Ziolkowska, C. Griffin, K. Choi, F. C. H. Franklin, R. A. Martienssen,et al., Natural variation and dosage of the hei10 meiotic e3 ligase control arabidopsis crossover recombination, Genes & ...

    2017

  41. [49]

    Sym and G

    M. Sym and G. Roeder, Crossover interference is abolished in the absence of a synaptonemal complex protein, Cell79, 283 (1994)

    1994

  42. [50]

    J. A. Fozard, C. Morgan, M. Howard, A. Shinohara, and D. Weigel, Coarsening dynamics can explain meiotic crossover patterning in both the presence and absence of the synaptonemal complex, eLife12, e79408 (2023)

    2023

  43. [51]

    Martini, R

    E. Martini, R. L. Diaz, N. Hunter, and S. Keeney, Crossover homeostasis in yeast meiosis, Cell126, 285 (2006)

    2006

  44. [52]

    T. Wang, H. Wang, Q. Lian, Q. Jia, C. You, G. P. Copenhaver, C. Wang, and Y. Wang, Hei10 is subject to phase separation and mediates rpa1a degradation during meiotic interference-sensitive crossover formation, Proceedings of the National Academy of Sciences120, e2310542120 (2023)

    2023

  45. [53]

    H. Kim, J. Kim, N. Son, P. Kuo, C. Morgan, A. Chambon, D. Byun, J. Park, Y. Lee, Y. M. Park,et al., Control of meiotic crossover interference by a proteolytic chaperone network, Nature Plants10, 453 (2024)

    2024

  46. [54]

    C. A. Weber, D. Zwicker, F. J¨ ulicher, and C. F. Lee, Physics of active emulsions, Reports on Progress in Physics82, 064601 (2019)

    2019

  47. [55]

    Zwicker, O

    D. Zwicker, O. W. Paulin, and C. ter Burg, Physics of droplet regulation in biological cells, arXiv e-prints , arXiv (2025)

    2025

  48. [56]

    Zwicker, The intertwined physics of active chemical reactions and phase separation, Current Opinion in Colloid & Interface Science61, 101606 (2022)

    D. Zwicker, The intertwined physics of active chemical reactions and phase separation, Current Opinion in Colloid & Interface Science61, 101606 (2022)

    2022

  49. [57]

    Kirschbaum, Chemical reactions as control mechanisms for biomolecular condensates, PhD Thesis (2022)

    J. Kirschbaum, Chemical reactions as control mechanisms for biomolecular condensates, PhD Thesis (2022)

    2022

  50. [58]

    I. M. Lifshitz and V. V. Slyozov, The kinetics of precipitation from supersaturated solid solutions, Journal of Physics and Chemistry of Solids19, 35 (1961)

    1961

  51. [59]

    C. Wagner, Theorie der alterung von niederschl¨ agen durch uml¨ osen (ostwald-reifung), Zeitschrift f¨ ur Elektrochemie, Berichte der Bunsengesellschaft f¨ ur physikalische Chemie65, 581 (1961)

    1961

  52. [60]

    Ernst, R

    M. Ernst, R. Mercier, and D. Zwicker, Interference length reveals regularity of crossover placement across species, Nature Communications15, 8973 (2024)

    2024

  53. [61]

    A. Hald, A. de Moivre, and B. McClintock, A. de moivre:’de mensura sortis’ or’on the measurement of chance’, International Statistical Review/Revue Internationale de Statistique , 229 (1984)

    1984

  54. [62]

    A. d. Moivre, De mensura sortis, seu, de probabilitate eventuum in ludis a casu fortuito pendentibus, Philosophical transactions of the Royal Society of London27, 213 (1711)

  55. [63]

    Erd˝ os and A

    P. Erd˝ os and A. R´ enyi, On a classical problem of probability theory, Magyar Tud. Akad. Mat. Kutat´ o Int. K¨ ozl6, 215 (1961)

    1961

  56. [64]

    M. A. Prusicki, E. M. Keizer, R. P. van Rosmalen, S. Komaki, F. Seifert, K. M¨ uller, E. Wijnker, C. Fleck, A. Schnittger, C. S. Hardtke, D. C. Bergmann, and J. Feij´ o, Live cell imaging of meiosis in arabidopsis thaliana, eLife8, e42834 (2019). 38

    2019

  57. [65]

    M. A. Prusicki, E. M. Keizer, R. P. van Rosmalen, S. Komaki, F. Seifert, K. M¨ uller, E. Wijnker, C. Fleck, and A. Schnittger, Live cell imaging of meiosis in arabidopsis thaliana, elife8, e42834 (2019)

    2019

  58. [66]

    B. Hu, M. Prusicki, K. Stahlmann, L. Krause, Y. Wang, and A. Schnittger, A cytological framework of female meiosis in arabidopsis, bioRxiv , 2025 (2025)

    2025

  59. [67]

    Ziethen, J

    N. Ziethen, J. Kirschbaum, and D. Zwicker, Nucleation of chemically active droplets, Physical Review Letters130, 248201 (2023)

    2023

  60. [68]

    S. Rosu, D. E. Libuda, and A. M. Villeneuve, Robust crossover assurance and regulated interhomolog access maintain meiotic crossover number, Science334, 1286 (2011)

    2011

  61. [69]

    M. Xue, J. Wang, L. Jiang, M. Wang, S. Wolfe, W. P. Pawlowski, Y. Wang, and Y. He, The number of meiotic double-strand breaks influences crossover distribution in arabidopsis, The Plant Cell30, 2628 (2018)

    2018

  62. [70]

    J. Jing, Q. Lian, S. Durand, and R. Mercier, Maximizing meiotic crossover rates reveals the map of crossover potential, Nature Communications16, 5306 (2025)

    2025

  63. [71]

    Borde and B

    V. Borde and B. de Massy, Programmed induction of dna double strand breaks during meiosis: setting up communication between dna and the chromosome structure, Current opinion in genetics & development23, 147 (2013)

    2013

  64. [72]

    Flajolet, D

    P. Flajolet, D. Gardy, and L. Thimonier, Birthday paradox, coupon collectors, caching algorithms and self-organizing search, Discrete Applied Mathematics39, 207 (1992)

    1992

  65. [73]

    Morgan, M

    C. Morgan, M. A. White, F. C. H. Franklin, D. Zickler, N. Kleckner, and K. Bomblies, Evolution of crossover interference enables stable autopolyploidy by ensuring pairwise partner connections in arabidopsis arenosa, Current Biology31, 4713 (2021)

    2021

  66. [74]

    J. A. Fozard, C. Morgan, and M. Howard, The synaptonemal complex controls cis- versus trans-interference in coarsening- based meiotic crossover patterning, bioRxiv , 2022.04.11.487855 (2022)

    2022

  67. [75]

    A. T. C. Carpenter, Normal synaptonemal complex and abnormal recombination nodules in two alleles of the drosophila meiotic mutant mei-w68, Genetics163, 1337 (2003)

    2003

  68. [76]

    S. Ilie, K. R. Jackson, and W. H. Enright, Adaptive time-stepping for the strong numerical solution of stochastic differential equations, Numerical Algorithms68, 791 (2015)

    2015

Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.