Pith. sign in

REVIEW 3 major objections 5 minor 84 references

Coupling Anisotropic Curvature and Nematic Order: Mechanisms of Membrane Shape Remodeling

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read Simulations show arc-shaped membrane components pass from pearls to a smooth cylinder as nematic alignment strengthens, while saddle-shaped components stabilize the necks between bare convex vesicle regions.

desk verdict Useful systematic phase maps for arc-shaped CMCs; the saddle-CMC neck claim needs equilibration evidence before it can be trusted as equilibrium. read the letter →

arxiv 2506.14347 v1 pith:OV5MPAFC submitted 2025-06-17 cond-mat.soft physics.bio-ph

Yoav Ravid , Samo Penič , Luka Mesarec , Nir S. Gov , Veronika Kralj-Iglič , Aleš Iglič , Mitja Drab This is my paper · ORCID
classification cond-mat.softphysics.bio-ph PACS 87.16.Dg87.10.Rt
keywords membranecurvaturenematicorderingvesiclemorphologytopologicaldefectsanisotropicinclusionsMonteCarlosimulationdeviatoricreducedvolume
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 claims that two minimal ingredients — an anisotropic intrinsic curvature printed on membrane components and a tendency for neighboring components to align — are enough to account for the variety of shapes closed membranes take. In Monte Carlo simulation, vesicles fully covered with arc-shaped components pass from a chain of pearls to a smooth cylinder as nematic interaction strengthens, and vesicles half covered with saddle-shaped components collect those components in the necks between bare convex regions, holding the neck open. The paper maps these steady-state shapes in the plane of reduced volume and interaction strength, revealing oblate, prolate, boomerang, capped, invaginated, and neck phases, and shows that the in-plane nematic field develops topological defects at high-curvature sites, with total charge matching the Poincaré-Hopf theorem. A sympathetic reader would take this as a candidate minimal mechanism by which BAR-domain proteins and other anisotropic inclusions shape organelles and whole cells.

What carries the argument

The engine of the model is the mismatch-tensor bending energy, written per area as $(2K_1+K_2)(H-H_m)^2 - K_2(D^2 - 2DD_m\cos 2\omega + D_m^2)$, which penalizes both the difference between the membrane's mean and deviatoric curvatures ($H$, $D$) and the component's intrinsic values ($H_m$, $D_m$), and the in-plane rotation angle $\omega$ between the membrane principal frame and the component's principal frame. An arc-shaped component has $H_m = D_m > 0$ (one curved, one flat direction), while a saddle-shaped component has $H_m = 0$, $D_m > 0$ and is frustrated on convex surface. To this are added a nematic (Lebwohl-Lasher / XY-type) coupling between neighboring occupied vertices and a harmonic constraint on the reduced volume $\bar{v} = 6\sqrt{\pi}V/A^{3/2}$. The combined energy is minimized by Monte Carlo moves on a dynamically triangulated, self-avoiding mesh with bond flips, and steady states are classified by the eigenvalues of the gyration tensor and by the local nematic order parameter $S_i = \frac{1}{2}(3\cos^2\theta - 1)$.

What would settle it

Re-run the same reduced-volume and interaction-strength points from several unrelated starting shapes — a random sphere, a pre-formed pearl chain, a ready cylinder — and extend the runs well beyond the 500 Monte Carlo sweeps used here; if the reported neck and invaginated phases appear only for particular starting shapes or dissolve on longer runs, those phases are kinetic transients rather than equilibrium states.

Watch

Extended reading notes

Core claim

The central claim is that coupling the mismatch between a membrane's local curvature tensor and a component's intrinsic curvature tensor to the nematic alignment of neighboring components, under a fixed reduced volume, is sufficient to produce the steady-state phase repertoire reported here. For full coverage with arc-shaped components (nonzero intrinsic mean curvature $H_m$, zero deviator), no nematic interaction yields pearling — a string of near-spheres joined by thin necks in which local nematic order vanishes — and raising the interaction strength $w$ converts the pearls into smooth cylinders whose radius is set by the component curvature. For full coverage with saddle-shaped components ($H_m = 0$, nonzero deviator $D_m$), stronger $w$ first flattens the vesicle and then gives a bow-tie or protrusive shape with a $+1$ defect at the tip and two $+1/2$ defects at its base. On half-covered vesicles, arc components produce oblate, prolate, boomerang, mixed, and capped phases that push the oblate-prolate boundary to lower reduced volume than bare membranes, an entropy effect from components clustering on the oblate rim; saddle components instead stabilize neck phases in which the components aggregate in the negatively curved necks between bare convex caps, persisting even with no volume constraint. The topological defect charge sums to $+2$ throughout, and defects sit where Gaussian curvature is largest.

Load-bearing premise

The load-bearing premise is that the finite Monte Carlo runs reach steady states that represent equilibrium morphologies, when the paper itself reports high metastability and poor reproducibility for the saddle-shaped-CMC transitions, so the neck and invaginated phases could be kinetic artifacts rather than true equilibrium shapes.

Editorial extensions

If this is right

  • Weak nematic coupling among arc-shaped components leaves a fully covered vesicle pearled, so initial curvature sensing requires only weak interactions, while stronger alignment drives full tubulation.
  • Saddle-shaped components stabilize the necks between bare convex regions at concentrations below 10% and even without volume constraints, offering a minimal mechanism for localizing fission sites and connecting tubules.
  • Because arc-shaped components shift the oblate-to-prolate transition to lower reduced volume purely through mixing entropy, anisotropic components can reshape a vesicle even with no direct component-component interaction.
  • The pearl radius and the neck width are set by the component's intrinsic mean and deviatoric curvatures, so the steady-state shape directly encodes the geometry of the components that made it.

Reading between the lines

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

  • A testable prediction follows from the boomerang phase: anisotropic components should generically stabilize an asymmetric intermediate along the oblate-prolate path in experiments on giant unilamellar vesicles with adsorbed anisotropic proteins, something isotropic inclusions would not produce.
  • The paper's reported metastability leaves open that the neck and invaginated phases are kinetically trapped; a simulated-annealing extension that slowly ramps reduced volume or interaction strength could reveal whether the phases are separated by a genuine free-energy barrier.
  • The framework implies a design rule: a protein's intrinsic curvature signature, through the ratio $H_m/D_m$, should predict its morphological role — arc-like components tubulate while saddle-like components clamp necks — a classification that could be tested against measured intrinsic curvatures of BAR and F-BAR domain proteins.
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 / 5 minor

Summary. The manuscript uses Monte Carlo simulations of triangulated vesicles with a deviatoric-elasticity bending energy to study how anisotropic curved membrane components (arc- and saddle-shaped), nematic inter-particle interactions, and volume constraints determine vesicle shape. It reports a pearling-to-cylinder transition for fully arc-covered vesicles, a shift of the oblate-to-prolate transition for half arc-covered vesicles, and neck stabilization by saddle-shaped CMCs. It also analyzes nematic topological defects and compares a fully covered saddle-CMC shape with an axisymmetric calculation. The main evidence is a set of steady-state phase diagrams in the reduced-volume versus interaction-strength plane.

Significance. If the reported phases are true equilibrium morphologies, the work offers a useful framework for anisotropic curvature sensing and membrane remodeling and has clear biological relevance (BAR domains, neck-stabilizing proteins). The manuscript is transparent about its simulation protocol, builds on a well-defined prior theory rather than fitting phase diagrams, and includes a valuable cross-check of defect positions against a fixed-shape axisymmetric calculation. The principal significance risk is that the headline saddle-CMC neck-stabilization claim rests on a phase diagram that the authors themselves label as highly metastable and poorly reproducible, so the thermodynamic reading of the neck phase is not yet supported.

major comments (3)
  1. [Section 4.2.3 and Figure 12] The abstract's distinctive claim that saddle-shaped CMCs 'stabilize necks between the convex regions of bare membrane' is supported only by the neck phase in Figure 12, but the text states that this phase diagram 'features a high degree of metastability, resulting in approximate phases that often coexist for the same v and w' and that the gyration-tensor heatmaps 'cannot reliably distinguish between phases.' No run-to-run statistics, initial-condition independence tests, or convergence traces are reported for the neck or invaginated saddle-CMC states; the convergence checks in Figure 3 cover only three arc-CMC cases. A neck observed in a single finite-length trajectory is not evidence for equilibrium stabilization. Please provide, for representative neck, invaginated, and oblate saddle-CMC parameters: multiple independent runs from distinct initial shapes, longer runs with convergence analysis of energy, volume, and a shape order parameter, and a hysteresis test starting separately from necked and spherical configurations at the same parameters. Without such data, the neck-stabilization claim is not established.
  2. [Section 4.2.1, Figure 9; Section 4.2.3, Figure 12] The phase boundaries in Figures 9 and 12 are drawn by hand from gyration-tensor eigenvalues, but for the saddle-CMC case the text admits that these eigenvalues 'cannot reliably distinguish between phases,' and for the arc-CMC case the separation between boomerang, dumb-bell, and prolate phases is described as 'more qualitative than quantitative.' A hand-drawn boundary based on an order parameter that cannot resolve the phases is not reproducible and does not support the quantitative phase maps. Please define a reproducible classification protocol—for example, thresholds on asphericity and prolateness combined with cluster curvature statistics, or a documented clustering algorithm on shape descriptors—and report the resulting boundaries, including a statement of how robust they are to the chosen thresholds.
  3. [Section 3] The manuscript reports one representative snapshot per phase point but does not state how many independent runs were performed for each parameter set or how representative the displayed shape is. In the metastable regions of Figure 12 this matters directly: a single run cannot establish which phases 'coexist' or their relative probabilities. Please report the number of independent runs per point, the fraction of runs that ended in each phase, and the criterion for selecting the displayed snapshot.
minor comments (5)
  1. [Section 2.3] The symbol E2 is used for both the isotropic binding energy (Eq. 3) and the nematic interaction energy (Eqs. 4-6), which confuses the two distinct mechanisms; please use different symbols such as E_iso and E_nem.
  2. [Section 2.5] The sentence 'uses 8 through a dot product' appears to be a typo for 'uses Eq. (8) through a dot product'; please correct it.
  3. [Figure 12 caption] The caption contains 'stady-state', which should read 'steady-state'.
  4. [Section 8.2.2 and Eq. (23)] The mismatch tensor is first defined in Section 2.1 as M = R Cm R^{-1} - C with an explicit rotation angle omega, but Eq. (23) presents the vertex-level mismatch directly as S minus a diagonal Cm; please clarify how the rotation angle omega enters the discretized computation.
  5. [Section 2.3] The derivation from the Frank energy (Eq. 4) to the Lebwohl-Lasher and XY forms (Eqs. 5-6) should state explicitly which gradient terms are dropped and how the one-constant approximation sets the scale of w relative to k'_G and k'_c.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; model inputs are explicit and phase diagrams are simulation outputs.

full rationale

The paper's energy functional (Eq. 2, from the authors' earlier deviatoric-elasticity theory [33-36]) is an explicit modeling input, not a quantity being predicted. The headline phase results (pearling-to-cylinder for arc CMCs, neck stabilization for saddle CMCs, oblate-prolate acceleration) are obtained by Monte Carlo minimization and are not fits to the same data. The topological-defect claim is checked against the Gauss-Bonnet/Poincare-Hopf theorems, which are external mathematical facts; the total charge +2 is a consistency check rather than a derived prediction. The saddle-CMC/neck affinity is a direct consequence of the model's deviatoric coupling term (Eq. 2: -K2(D^2 - 2DDm cos 2omega + Dm^2)), but the paper presents this as the assumed mechanism, not as an independent derivation; the nontrivial outputs are the global shape transitions and phase boundaries. Section 4.2.3's admission of metastability and poor reproducibility in the saddle-CMC phase diagram (Figure 12) is a correctness/equilibration concern, not a circularity. No fitted parameter is renamed as a prediction, and no load-bearing argument reduces to an unverified self-citation. Score 1 reflects the heavy use of the authors' previous framework while the central claims retain independent simulation content.

Assumptions & free parameters 7 free parameters · 5 assumptions · 0 invented entities

The central claims rest on a standard but same-group-derived anisotropic curvature Hamiltonian (Eqs. 1 and 2), an XY approximation of nematic interactions (Eq. 6), a harmonic volume constraint (Eq. 7), and finite-time Monte Carlo sampling. No new entities are postulated and no parameters are fitted to external data, but many model constants (w, rho, Hm, Dm, v, kv, K2) are scanned or hand-chosen, and the steady-state assumption is weakened by acknowledged metastability.

free parameters (7)
  • w (nematic interaction strength) = scanned 0 to 5 kBT
    Central control parameter in phase diagrams (Figures 2, 7, 9, 12); chosen by hand, not fitted to data.
  • rho (CMC coverage fraction) = 1, 0.5, 0.16, 0.06
    Sets full versus partial coverage; low values show neck aggregation.
  • Hm and Dm (intrinsic mean and deviatoric curvature) = Hm=Dm=0.25; Hm=0 with Dm=0.5, 0.75, 0.98, 1.2 in 1/lmin units
    Define arc versus saddle shapes; determine tube radius and neck width.
  • v (target reduced volume) = scanned approximately 0.3 to 1
    Volume constraint; central to phase diagram axes.
  • kv (volume modulus) = same order as bending terms, exact value not reported
    Controls strength of volume constraint; affects phase boundaries and is not specified numerically.
  • K2 (Gaussian or splay modulus) = varied in Supplementary 8.3.3
    Deviatoric term alone can drive neck ordering at w=0.
  • membrane bending rigidity = 20 kBT
    Fixed simulation scale; results may depend on its value.
assumptions (5)
  • domain assumption The anisotropic bending energy of a membrane patch is captured by the mismatch-tensor expansion E1 = integral (K1/2)(Tr M)^2 + K2 Det M dA, with K1 and K2 as bending and splay moduli.
    Adopted from Kralj-Iglič and Iglič [33-36]; the discrete shape-operator implementation assumes this continuum form is preserved on a triangulated mesh.
  • domain assumption Nematic interactions between CMCs obey a one-constant approximation and can be represented by the XY or Lebwohl-Lasher term E2 approximately -w sum (n_i dot n_j)^2.
    Used for all simulations; ignores splay-twist anisotropy and out-of-plane tilting.
  • domain assumption Finite-length Monte Carlo trajectories converge to steady-state equilibrium shapes.
    Default is 500 MC steps according to the Figure 3 caption; Section 4.2.3 acknowledges metastability and poor reproducibility for saddle-shaped CMCs.
  • standard math The total winding number of the nematic director on a spherical vesicle must be +2 (Gauss-Bonnet and Poincaré-Hopf).
    Used in Section 4.2.4 to interpret defect charges in Figures 14 and 15.
  • domain assumption A dynamically triangulated self-avoiding network with bond flips represents a fluid lipid membrane.
    Standard triangulated-surface model [81,82]; the bond-flip ratio RB=3 sets lateral fluidity.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Coupling Anisotropic Curvature and Nematic Order: Mechanisms of Membrane Shape Remodeling." pith.science (2026). https://pith.science/paper/OV5MPAFC

@misc{pith2026250614347,
  author       = {Pith},
  title        = {Pith review of: Coupling Anisotropic Curvature and Nematic Order: Mechanisms of Membrane Shape Remodeling},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OV5MPAFC}},
  note         = {Machine review of arXiv:2506.14347}
}
read the original abstract

This study theoretically investigates how anisotropic curved membrane components (CMCs) control vesicle morphology through curvature sensing, nematic alignment, topological defects, and volume constraints. By comparing arc-shaped and saddle-shaped CMCs, we identify a rich spectrum of steady-state phases. For fully CMC-covered vesicles, arc-shaped components drive a pearling-to-cylinder transition as nematic interactions strengthen, while on partially CMC-covered vesicles, the saddle-shaped CMCs stabilize necks between the convex regions of bare membrane. We map the steady-state shapes of vesicles partially covered by arc-like and saddle-shaped CMCs, exposing how different vesicle shapes depend on the interplay between nematic interactions and volume constraints, revealing several novel phases. By investigating the in-plane nematic field, we find that topological defects consistently localize to high-curvature regions, revealing how intrinsic and deviatoric curvature effects cooperate in membrane remodeling. These findings establish a unified framework for understanding how proteins and lipid domains with anisotropic intrinsic curvature shape cellular structures -- from organelle morphogenesis to global cell shape.

Figures

Figures reproduced from arXiv: 2506.14347 by the authors.

Figure 1
Figure 1. (a) Example of an arc-shaped CMC with Hm = Dm = 0.25 (C1m = 0.5 and C2m = 0). (b) Example of a saddle-shaped CMC, with Hm = 0, Dm = 0.5. (c) The mismatch between the principle curvatures of a membrane protein and the local curvature of the triangulated membrane. Here, ⃗n is the orientation of the CMC and ⃗t is its perpendicular direction in the local tangent plane. 2.3. Nematic protein-protein interactions Anisotrop… view at source ↗
Figure 20
Figure 20. The membrane deviator is defined for each vertex as [PITH_FULL_IMAGE:figures/full_fig_p015_20.png] view at source ↗
Figure 2
Figure 2. (a) Vesicles fully covered (ρ = 1) with arc-shaped CMCs as function of the nematic interaction energy w and intrinsic mean curvature Hm. Steady-state shapes are generally all cylinders (shapes (B), (C)). The pearling steady-state shapes in (A) arise as a consequence of neighboring CMCs assuming random orientations. Even in the absence of nematic interactions between neighboring CMCs, the membrane conforms to their s… view at source ↗
Figures from the paper (18 more)
Figure 3
Figure 3. Figure 3: Convergence of bending and interaction energy (Eqs. 2 and 6) for the evolution of shapes shown in Figure 2. [PITH_FULL_IMAGE:figures/full_fig_p022_3.png]
Figure 4
Figure 4. Figure 4: As nematic strength w increases from zero, the steady-state shapes go from pearls to cylinders (a). This transition is marked by a steady decrease of not only bending, but also total energy (b). The parameters are the same as in panel (A) of [PITH_FULL_IMAGE:figures/f…
Figure 5
Figure 5. Figure 5: Local nematic order (Eq. 8) and close up of the shapes shown in Figure 2. Also shown is the average [PITH_FULL_IMAGE:figures/full_fig_p022_5.png]
Figure 6
Figure 6. Figure 6: (a) Steady-state equilibrium shapes that are fully covered ( [PITH_FULL_IMAGE:figures/full_fig_p023_6.png]
Figure 7
Figure 7. Figure 7: (a) The curvature-binding strength phase diagram for steady-state shapes with saddle CMCs ( [PITH_FULL_IMAGE:figures/full_fig_p024_7.png]
Figure 8
Figure 8. Figure 8: Nematic order for the steady-state shapes of vesicles covered by saddle-shaped CMC, shown in Figure 7(b). [PITH_FULL_IMAGE:figures/full_fig_p025_8.png]
Figure 9
Figure 9. Figure 9: Reduced volume-binding strength plane for arc-shaped CMCs. (a) Phase diagram as function of [PITH_FULL_IMAGE:figures/full_fig_p026_9.png]
Figure 10
Figure 10. Figure 10: (a) The phase diagram in the space v-E for vesicles with no CMCs shows a familiar sequence of morphologies with increasing v; stomatocytes, oblates and prolates. An interesting intermediate shape transition (ellipsoid) is observed between oblate and prolate shapes, ma…
Figure 11
Figure 11. Figure 11: The oblate-prolate phase transition includes a shift of the inclusion distribution measured from the center [PITH_FULL_IMAGE:figures/full_fig_p027_11.png]
Figure 12
Figure 12. Figure 12: Reduced volume-binding strength plane for saddle-like CMCs. (a) Phase diagram as function of [PITH_FULL_IMAGE:figures/full_fig_p028_12.png]
Figure 13
Figure 13. Figure 13: (a) Anisotropic saddle CMCs (Hm = 0, Dm = 0.98, ρ = 0.16, w = 3, v = 0.54) form necks between empty convex membrane regions. Orange lines show the direction of the principal CMC curvature C1m. (b) The nematic order heatmap and orientation of saddle-like CMCs for the c…
Figure 14
Figure 14. Figure 14: (a) For a fully covered equilibrium steady-state shapes with arc-shaped CMCs ( [PITH_FULL_IMAGE:figures/full_fig_p029_14.png]
Figure 15
Figure 15. Figure 15: Equilibrium orientational ordering profile on a fixed axisymmetric 2D surface that is topologically equivalent [PITH_FULL_IMAGE:figures/full_fig_p030_15.png]
Figure 16
Figure 16. Figure 16: Schematic of a vertex and it’s neighbors. The vertex [PITH_FULL_IMAGE:figures/full_fig_p030_16.png]
Figure 17
Figure 17. Figure 17: (a) Populating an empty cylinder with arc-shaped CMCs ( [PITH_FULL_IMAGE:figures/full_fig_p031_17.png]
Figure 18
Figure 18. Figure 18: (a) With no nematic interaction (w = 0), but increasing K2, the steady-states of vesicles form saddle￾like necks between alternate convex regions and show perfect alignment between neighboring saddle-like CMCs at low concentrations. The x-axis is the constant K2 in Eq…
Figure 19
Figure 19. Figure 19: (a) With no nematic interaction (w = 0), but varying Hm, the steady-states of vesicles gradually change to pearls. (b) Total energy as a function of Hm shows that bending energy initially increaes, but is reduced once the number of pearls is exceeds 2. 32 [PITH_FULL_…
Figure 20
Figure 20. Figure 20: Oblate shapes v = 0.4 at ρ = 0.5 of arc-shaped CMCs (Hm = Dm = 0.25) and three values of w (from 0 to 2). Even with no nematic interaction between CMCs (c), these are not distributed homogenousely over the membrane, but tend to accumulate on the rim, as is reflected i…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

84 extracted references · 80 canonical work pages

  1. [1]

    When physics takes over: BAR proteins and membrane curvature

    Mijo Simunovic et al. “When physics takes over: BAR proteins and membrane curvature”. In: Trends in Cell Biology25.12 (2015), pp. 780–792

    2015

  2. [2]

    Recent developments in membrane curvature sensing and induction by proteins

    Chandra Has and Sovan Lal Das. “Recent developments in membrane curvature sensing and induction by proteins”. In: Biochimica et Biophysica Acta (BBA)-General Subjects1865.10 (2021), p. 129971

    2021

  3. [3]

    Protein–membrane interactions: sensing and generating curvature

    David H Johnson et al. “Protein–membrane interactions: sensing and generating curvature”. In: Trends in Biochemical Sciences(2024)

    2024

  4. [4]

    Insights into membrane curvature sensing and membrane remodeling by intrinsically disordered proteins and protein regions

    Chandra Has, P Sivadas, and Sovan Lal Das. “Insights into membrane curvature sensing and membrane remodeling by intrinsically disordered proteins and protein regions”. In:The Journal of Membrane Biology255.2 (2022), pp. 237–259

    2022

  5. [5]

    Anisotropic membrane cur- vature sensing by amphipathic peptides

    Jordi Gómez-Llobregat, Federico Elıás-Wolff, and Martin Lindén. “Anisotropic membrane cur- vature sensing by amphipathic peptides”. In:Biophysical journal110.1 (2016), pp. 197–204

    work page 2016

  6. [6]

    Curvature in Biological Systems: Its Quantification, Emergence, and Implications across the Scales

    Barbara Schamberger et al. “Curvature in Biological Systems: Its Quantification, Emergence, and Implications across the Scales”. In:Advanced Materials35.13 (2023), p. 2206110

    work page 2023

  7. [7]

    BAR domains and membrane curvature: bringing your curves to the BAR

    Jennifer L Gallop and Harvey T McMahon. “BAR domains and membrane curvature: bringing your curves to the BAR.” In:Biochemical Society Symposia. Vol. 72. Portland Press Limited. 2005, pp. 223–231

    work page 2005

  8. [8]

    Curving cells inside and out: roles of BAR domain proteins in membrane shaping and its cellular implications

    Mijo Simunovic et al. “Curving cells inside and out: roles of BAR domain proteins in membrane shaping and its cellular implications”. In:Annual review of cell and developmental biology35 (2019), pp. 111–129

    work page 2019

Show all 84 references
  1. [9]

    Physical basis of some membrane shaping mechanisms

    Mijo Simunovic et al. “Physical basis of some membrane shaping mechanisms”. In:Philosoph- ical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 374.2072 (2016), p. 20160034

    2016

  2. [10]

    Activated I-BAR IRSp53 clustering controls the formation of VASP- actin–based membrane protrusions

    Feng-Ching Tsai et al. “Activated I-BAR IRSp53 clustering controls the formation of VASP- actin–based membrane protrusions”. In:Science Advances8.41 (2022), eabp8677

    2022

  3. [11]

    Inception mechanisms of tunneling nanotubes

    Mitja Drab et al. “Inception mechanisms of tunneling nanotubes”. In:Cells 8.6 (2019), p. 626

    2019

  4. [12]

    IRSp53 senses negative membrane curvature and phase separates along membrane tubules

    Coline Prévost et al. “IRSp53 senses negative membrane curvature and phase separates along membrane tubules”. In:Nature Communications6.1 (2015), pp. 1–11

    2015

  5. [13]

    Coupling between vesicle shape and the non-homogeneous lateral distribution of membrane constituents in Golgi bodies

    Aleš Iglič et al. “Coupling between vesicle shape and the non-homogeneous lateral distribution of membrane constituents in Golgi bodies”. In:FEBS letters 574.1-3 (2004), pp. 9–12

    2004

  6. [14]

    Rat prominin, like its mouse and human orthologues, is a pentaspan membrane glycoprotein

    Denis Corbeil, Christine A Fargeas, and Wieland B Huttner. “Rat prominin, like its mouse and human orthologues, is a pentaspan membrane glycoprotein”. In:Biochemical and biophysical research communications285.4 (2001), pp. 939–944

    2001

  7. [15]

    Intrinsic curvature properties of photosynthetic proteins in chro- matophores

    Danielle E Chandler et al. “Intrinsic curvature properties of photosynthetic proteins in chro- matophores”. In:Biophysical journal95.6 (2008), pp. 2822–2836

    2008

  8. [16]

    Terasaki spiral ramps in the rough endoplasmic reticulum

    Jemal Guven, Greg Huber, and Dulce Marıá Valencia. “Terasaki spiral ramps in the rough endoplasmic reticulum”. In:Physical review letters113.18 (2014), p. 188101

    2014

  9. [17]

    Endovesicle formation and membrane perturbation induced by polyoxyethyleneglycolalkylethers in human erythrocytes

    Henry Hägerstrand et al. “Endovesicle formation and membrane perturbation induced by polyoxyethyleneglycolalkylethers in human erythrocytes”. In:Biochimica et Biophysica Acta (BBA)-Biomembranes 1665.1-2 (2004), pp. 191–200. 16

    2004

  10. [18]

    Stable tubular microexovesicles of the erythrocyte membrane induced by dimeric amphiphiles

    V Kralj-Iglič et al. “Stable tubular microexovesicles of the erythrocyte membrane induced by dimeric amphiphiles”. In:Physical Review E61.4 (2000), p. 4230

    2000

  11. [19]

    Minimizing isotropic and deviatoric membrane energy - An unifying formation mechanism of different cellular membrane nanovesicle types

    Veronika Kralj-Iglič et al. “Minimizing isotropic and deviatoric membrane energy - An unifying formation mechanism of different cellular membrane nanovesicle types”. In:PloS One 15.12 (Dec. 2020), pp. 1–25.url: https://doi.org/10.1371/journal.pone.0244796

    2020 doi

  12. [20]

    Modelling cellular spreading and emergence of motility in the pres- ence of curved membrane proteins and active cytoskeleton forces

    Raj Kumar Sadhu et al. “Modelling cellular spreading and emergence of motility in the pres- ence of curved membrane proteins and active cytoskeleton forces”. In:The European Physical Journal Plus 136.5 (2021), pp. 1–37

    2021

  13. [21]

    A minimal cell model for lamellipodia-based cellular dynamics and migration

    Raj Kumar Sadhu, Aleš Iglič, and Nir S Gov. “A minimal cell model for lamellipodia-based cellular dynamics and migration”. In:Journal of Cell Science136.14 (2023), jcs260744

    2023

  14. [22]

    A nanostructure platform for live-cell manipulation of membrane curvature

    Xiao Li et al. “A nanostructure platform for live-cell manipulation of membrane curvature”. In: Nature protocols14.6 (2019), pp. 1772–1802

    2019

  15. [23]

    How proteins produce cellular membrane curva- ture

    Joshua Zimmerberg and Michael M Kozlov. “How proteins produce cellular membrane curva- ture”. In:Nature reviews Molecular cell biology7.1 (2006), pp. 9–19

    2006

  16. [24]

    On the role of membrane anisotropy and BAR proteins in the stability of tubular membrane structures

    Doron Kabaso et al. “On the role of membrane anisotropy and BAR proteins in the stability of tubular membrane structures”. In:Journal of Biomechanics45.2 (2012), pp. 231–238

    2012

  17. [25]

    Modeling membrane shaping by proteins: focus on EHD2 and N-BAR domains

    Felix Campelo et al. “Modeling membrane shaping by proteins: focus on EHD2 and N-BAR domains”. In:FEBS letters 584.9 (2010), pp. 1830–1839

    2010

  18. [26]

    Interactions between model inclusions on closed lipid bilayer membranes

    Timon Idema and Daniela J Kraft. “Interactions between model inclusions on closed lipid bilayer membranes”. In:Current Opinion in Colloid & Interface Science40 (2019), pp. 58–69

    2019

  19. [27]

    Free energy of closed membrane with anisotropic inclusions

    Veronika Kralj-Iglič et al. “Free energy of closed membrane with anisotropic inclusions”. In: The European Physical Journal B-Condensed Matter and Complex Systems10 (1999), pp. 5–8

    1999

  20. [28]

    Membrane remodeling due to a mixture of multiple types of curvature proteins

    Gaurav Kumar and Anand Srivastava. “Membrane remodeling due to a mixture of multiple types of curvature proteins”. In:Journal of Chemical Theory and Computation18.9 (2022), pp. 5659–5671

    2022

  21. [29]

    Mesoscale computational stud- ies of membrane bilayer remodeling by curvature-inducing proteins

    N Ramakrishnan, PB Sunil Kumar, and Ravi Radhakrishnan. “Mesoscale computational stud- ies of membrane bilayer remodeling by curvature-inducing proteins”. In:Physics reports543.1 (2014), pp. 1–60

    2014

  22. [30]

    Mesoscale simulation of biomembranes with FreeDTS

    Weria Pezeshkian and John H Ipsen. “Mesoscale simulation of biomembranes with FreeDTS”. In: Nature Communications15.1 (2024), p. 548

    2024

  23. [31]

    Numerical studies of triangulated vesicles with anisotropic membrane in- clusions

    Yoav Ravid et al. “Numerical studies of triangulated vesicles with anisotropic membrane in- clusions”. In:Advances in Biomembranes and Lipid Self-Assembly. 2024, pp. 21–40

    2024

  24. [32]

    The influence of anisotropic membrane inclusions on curvature elastic properties of lipid membranes

    Miha Fošnaric et al. “The influence of anisotropic membrane inclusions on curvature elastic properties of lipid membranes”. In:Journal of chemical information and modeling45.6 (2005), pp. 1652–1661

    2005

  25. [33]

    Elastic properties of biological membranes influenced by attached proteins

    Aleš Iglič, Tomaž Slivnik, and Veronika Kralj-Iglič. “Elastic properties of biological membranes influenced by attached proteins”. In:Journal of Biomechanics40.11 (2007), pp. 2492–2500

    2007

  26. [34]

    On the role of membrane anisotropy in the beading transition of undulated tubular membrane structures

    Aleš Iglič et al. “On the role of membrane anisotropy in the beading transition of undulated tubular membrane structures”. In: Journal of Physics A: Mathematical and General 38.40 (2005), p. 8527

    2005

  27. [35]

    Deviatoric elasticity as a possible physical mechanism explaining collapse of inorganic micro and nanotubes

    V Kralj-Iglič et al. “Deviatoric elasticity as a possible physical mechanism explaining collapse of inorganic micro and nanotubes”. In:Physics Letters A296.2 (2002), pp. 151–155. 17

    2002

  28. [36]

    Stability of membranous nanostructures: a possible key mechanism in cancer progression

    Veronika Kralj-Iglic. “Stability of membranous nanostructures: a possible key mechanism in cancer progression”. In:International journal of nanomedicine(2012), pp. 3579–3596

    2012

  29. [37]

    Shapes of bilayer vesicles with membrane embedded molecules

    Veronika Kralj-Iglič, Sasa Svetina, and B Žekž. “Shapes of bilayer vesicles with membrane embedded molecules”. In:European Biophysics Journal24 (1996), pp. 311–321

    1996

  30. [38]

    Elastic properties of lipid bilayers: theory and possible experiments

    Wolfgang Helfrich. “Elastic properties of lipid bilayers: theory and possible experiments”. In: Zeitschrift für Naturforschung C28.11-12 (1973), pp. 693–703

    1973

  31. [39]

    A review of mechanics- based mesoscopic membrane remodeling methods: capturing both the physics and the chemical diversity

    Gaurav Kumar, Satya Chaithanya Duggisetty, and Anand Srivastava. “A review of mechanics- based mesoscopic membrane remodeling methods: capturing both the physics and the chemical diversity”. In:The Journal of Membrane Biology255.6 (2022), pp. 757–777

    2022

  32. [40]

    Interaction of surfactin with membranes: a computational approach

    Magali Deleu et al. “Interaction of surfactin with membranes: a computational approach”. In: Langmuir 19.8 (2003), pp. 3377–3385

    2003

  33. [41]

    Theoretical study of vesicle shapes driven by coupling curved proteins and active cytoskeletal forces

    Miha Fošnarič et al. “Theoretical study of vesicle shapes driven by coupling curved proteins and active cytoskeletal forces”. In:Soft Matter (2019)

    2019

  34. [42]

    I. Liquid crystals. On the theory of liquid crystals

    Frederick C Frank. “I. Liquid crystals. On the theory of liquid crystals”. In:Discussions of the Faraday Society25 (1958), pp. 19–28

    1958

  35. [43]

    Monte Carlo results for a discrete-lattice model of nematic ordering

    Gordon Lasher. “Monte Carlo results for a discrete-lattice model of nematic ordering”. In: Physical Review A5.3 (1972), p. 1350

    1972

  36. [44]

    Monte Carlo simulations of fluid vesicles with in-plane orientational ordering

    Netasan Ramakrishnan, PB Sunil Kumar, and John H Ipsen. “Monte Carlo simulations of fluid vesicles with in-plane orientational ordering”. In:Physical Review E81.4 (2010), p. 041922

    2010

  37. [45]

    Shape of unperturbed linear polymers: polypropy- lene

    Doros N Theodorou and Ulrich W Suter. “Shape of unperturbed linear polymers: polypropy- lene”. In:Macromolecules 18.6 (1985), pp. 1206–1214

    1985

  38. [46]

    Theoretical model of membrane protrusions driven by curved active pro- teins

    Yoav Ravid et al. “Theoretical model of membrane protrusions driven by curved active pro- teins”. In:Frontiers in Molecular Biosciences10 (2023), p. 1153420

    2023

  39. [47]

    Shape transformations of vesicles: Phase diagram for spontaneous-curvature and bilayer-coupling models

    Udo Seifert, Karin Berndl, and Reinhard Lipowsky. “Shape transformations of vesicles: Phase diagram for spontaneous-curvature and bilayer-coupling models”. In:Physical review A44.2 (1991), p. 1182

    1991

  40. [48]

    The existence of non-axisymmetric bilayer vesicle shapes predicted by the bilayer couple model

    Vera Kralj-Iglič, Saša Svetina, and Boštjan Žekš. “The existence of non-axisymmetric bilayer vesicle shapes predicted by the bilayer couple model”. In: European biophysics journal 22 (1993), pp. 97–103

    1993

  41. [49]

    The topological theory of defects in ordered media

    N David Mermin. “The topological theory of defects in ordered media”. In:Reviews of Modern Physics 51.3 (1979), p. 591

    1979

  42. [50]

    Effective topological charge cancelation mechanism

    Luka Mesarec et al. “Effective topological charge cancelation mechanism”. In:Scientific reports 6.1 (2016), p. 27117

    2016

  43. [51]

    Curvature-induced defect unbinding in toroidal geometries

    Mark Bowick, David R Nelson, and Alex Travesset. “Curvature-induced defect unbinding in toroidal geometries”. In:Physical Review E—Statistical, Nonlinear, and Soft Matter Physics 69.4 (2004), p. 041102

    2004

  44. [52]

    Anomalous coupling between topological defects and curvature

    Vincenzo Vitelli and Ari M Turner. “Anomalous coupling between topological defects and curvature”. In:Physical review letters93.21 (2004), p. 215301

    2004

  45. [53]

    Coupling of nematic in-plane orientational ordering and equilibrium shapes of closed flexible nematic shells

    Luka Mesarec et al. “Coupling of nematic in-plane orientational ordering and equilibrium shapes of closed flexible nematic shells”. In:Scientific reports13.1 (2023), p. 10663

    2023

  46. [54]

    Topologicaldefectsindispersedwordsandworldsaroundliquidcrystals, or liquid crystal drops

    OlegDLavrentovich.“Topologicaldefectsindispersedwordsandworldsaroundliquidcrystals, or liquid crystal drops”. In:Liquid crystals 24.1 (1998), pp. 117–126. 18

    1998

  47. [55]

    Sur les courbes définies par les équations différentielles

    Henri Poincaré. “Sur les courbes définies par les équations différentielles”. In:Journal de math- ématiques pures et appliquées1 (1885), pp. 167–244

  48. [56]

    The geometry of soft materials: a primer

    Randall D Kamien. “The geometry of soft materials: a primer”. In:Reviews of Modern physics 74.4 (2002), p. 953

    2002

  49. [57]

    Extrinsic curvature effects on nematic shells

    Gaetano Napoli and Luigi Vergori. “Extrinsic curvature effects on nematic shells”. In:Physical review letters108.20 (2012), p. 207803

    2012

  50. [58]

    Monte Carlo studies of the XY model on two-dimensional curved surfaces

    Robin L Blumberg Selinger et al. “Monte Carlo studies of the XY model on two-dimensional curved surfaces”. In:The Journal of Physical Chemistry B115.48 (2011), pp. 13989–13993

    2011

  51. [59]

    Quadrupolar ordering of phospholipid molecules in narrow necks of phospholipid vesicles

    Veronika Kralj-Iglič et al. “Quadrupolar ordering of phospholipid molecules in narrow necks of phospholipid vesicles”. In:Journal of statistical physics125 (2006), pp. 727–752

    2006

  52. [60]

    Theoretical study of vesicle shapes driven by coupling curved proteins and active cytoskeletal forces

    Miha Fošnarič et al. “Theoretical study of vesicle shapes driven by coupling curved proteins and active cytoskeletal forces”. In:Soft Matter 15.26 (2019), pp. 5319–5330

    2019

  53. [61]

    Surfactin molecules with a cone-like structure promote the formation of membrane domains with negative spontaneous curvature and induce membrane invaginations

    Žiga Pandur et al. “Surfactin molecules with a cone-like structure promote the formation of membrane domains with negative spontaneous curvature and induce membrane invaginations”. In: Journal of colloid and interface science650 (2023), pp. 1193–1200

    2023

  54. [62]

    On Gaussian curvature and membrane fission

    Mara Denisse Rueda-Contreras et al. “On Gaussian curvature and membrane fission”. In: Scientific Reports11.1 (2021), p. 9562

    2021

  55. [63]

    On the role of anisotropy of membrane components in formation and stabilization of tubular structures in multicomponent membranes

    Nataliya Bobrovska et al. “On the role of anisotropy of membrane components in formation and stabilization of tubular structures in multicomponent membranes”. In:PloS One 8.9 (2013), e73941

    2013

  56. [64]

    Lipid-Composition-Mediated Forces Can Stabilize Tubular Assemblies of I-BAR Proteins

    Zack Jarin et al. “Lipid-Composition-Mediated Forces Can Stabilize Tubular Assemblies of I-BAR Proteins”. In:Biophysical Journal120 (2021), pp. 46–54

    2021

  57. [65]

    Curvature-sensing and generation of membrane proteins: a review

    Hiroshi Noguchi. “Curvature-sensing and generation of membrane proteins: a review”. In:DOI: 10.1039/D5SM00101C (2025)

    2025 doi

  58. [66]

    Drp1 polymerization stabilizes curved tubular membranes similar to those of constricted mitochondria

    Begoña Ugarte-Uribe et al. “Drp1 polymerization stabilizes curved tubular membranes similar to those of constricted mitochondria”. In:Journal of cell science132.4 (2019), jcs208603

    2019

  59. [67]

    Weaving the web of ER tubules

    Junjie Hu, William A Prinz, and Tom A Rapoport. “Weaving the web of ER tubules”. In:Cell 147.6 (2011), pp. 1226–1231

    2011

  60. [68]

    Shape variation of bilayer membrane daughter vesicles induced by anisotropic membrane inclusions

    Klemen Bohinc et al. “Shape variation of bilayer membrane daughter vesicles induced by anisotropic membrane inclusions”. In:Cellular & Molecular Biology Letters11 (2006), pp. 90– 101

    2006

  61. [69]

    Stabilization of pores in lipid bilayers by anisotropic inclusions

    Miha Fošnaričˇ et al. “Stabilization of pores in lipid bilayers by anisotropic inclusions”. In:The Journal of Physical Chemistry B107.45 (2003), pp. 12519–12526

    2003

  62. [70]

    Aleš Iglič and Veronika Kralj-Iglič.Stabilization of Hydrophilic Pores in Charged Lipid Bilayers by Anisotropic Membrane Inclusions. 2008

    2008

  63. [71]

    On the role of anisotropy of membrane constituents in formation of a mem- brane neck during budding of a multicomponent membrane

    Aleš Iglič et al. “On the role of anisotropy of membrane constituents in formation of a mem- brane neck during budding of a multicomponent membrane”. In:Journal of biomechanics40.3 (2007), pp. 579–585

    2007

  64. [72]

    Curvature-dependent lateral distribution of raft markers in the human erythrocyte membrane

    Henry Hägerstrand et al. “Curvature-dependent lateral distribution of raft markers in the human erythrocyte membrane”. In:Molecular membrane biology23.3 (2006), pp. 277–288

    2006

  65. [73]

    Tubulationpatternofmembranevesicles coated with biofilaments

    GauravKumar,NRamakrishnan,andAnirbanSain.“Tubulationpatternofmembranevesicles coated with biofilaments”. In:Physical Review E99.2 (2019), p. 022414. 19

    2019

  66. [74]

    Deformation of membrane vesicles due to chiral surface proteins

    Arabinda Behera et al. “Deformation of membrane vesicles due to chiral surface proteins”. In: Soft Matter 17.34 (2021), pp. 7953–7962

    2021

  67. [75]

    Role of disclinations in determining the morphology of deformable fluid interfaces

    N Ramakrishnan, John H Ipsen, and PB Sunil Kumar. “Role of disclinations in determining the morphology of deformable fluid interfaces”. In:Soft Matter 8.11 (2012), pp. 3058–3061

    2012

  68. [76]

    Sorting of proteins with shape and curvature anisotropy on a lipid bilayer tube

    Pranav Vyas, PB Sunil Kumar, and Sovan Lal Das. “Sorting of proteins with shape and curvature anisotropy on a lipid bilayer tube”. In:Soft Matter 18.8 (2022), pp. 1653–1665

    2022

  69. [77]

    Membrane-mediated aggregation of curvature-inducing nematogens and membrane tubulation

    N Ramakrishnan, PB Sunil Kumar, and John H Ipsen. “Membrane-mediated aggregation of curvature-inducing nematogens and membrane tubulation”. In:Biophysical journal 104.5 (2013), pp. 1018–1028

    2013

  70. [78]

    Anisotropic spontaneous curvatures in lipid membranes

    Nikhil Walani, Jennifer Torres, and Ashutosh Agrawal. “Anisotropic spontaneous curvatures in lipid membranes”. In:Physical Review E89.6 (2014), p. 062715

    2014

  71. [79]

    Vesiculation mechanisms mediated by anisotropic pro- teins

    Ke Xiao, Chen-Xu Wu, and Rui Ma. “Vesiculation mechanisms mediated by anisotropic pro- teins”. In:Physical Review Research5.2 (2023), p. 023176

    2023

  72. [80]

    Essential cell biology

    Bruce Alberts et al. Essential cell biology. Garland Science, 2015

    2015

  73. [81]

    Random surface discretizations and the renormalization of the bending rigidity

    G Gompper and DM Kroll. “Random surface discretizations and the renormalization of the bending rigidity”. In:Journal de Physique I6.10 (1996), pp. 1305–1320

    1996

  74. [82]

    Triangulated-surface models of fluctuating membranes

    G Gompper and DM Kroll. “Triangulated-surface models of fluctuating membranes”. In:Sta- tistical Mechanics of Membranes and Surfaces(2004), pp. 359–426

    2004

  75. [83]

    Bending elasticity of vesicle membranes studied by Monte Carlo simulations of vesicle thermal shape fluctuations

    Samo Penič et al. “Bending elasticity of vesicle membranes studied by Monte Carlo simulations of vesicle thermal shape fluctuations”. In:Soft Matter 11 (25 2015), pp. 5004–5009.doi: 10. 1039/C5SM00431D. url: http://dx.doi.org/10.1039/C5SM00431D

    2015 doi

  76. [84]

    Minimizing isotropic and deviatoric membrane energy–An unifying formation mechanism of different cellular membrane nanovesicle types

    Veronika Kralj-Iglič et al. “Minimizing isotropic and deviatoric membrane energy–An unifying formation mechanism of different cellular membrane nanovesicle types”. In:PloS one 15.12 (2020), e0244796. 20 Figure 2: (a) Vesicles fully covered (ρ = 1) with arc-shaped CMCs as funct...

    2020

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.