Wrapping transition and membrane tension for nanoparticle uptake by asymmetric vesicle under osmotic pressure

1 - A finite area-difference between the monolayers of the lipid bilayer and a finite osmotic concentration of solute in the buffer are relevant for physiological conditions.
2 - The results are novel.
3 - Various aspects of the system are discussed: wrapping diagrams, energy barriers for the transitions, and membrane tensions induced by partially wrapped particles.

1 - The clarity of the manuscript, as well as its general formatting and grammar have to be significantly improved.

In the article "Wrapping transition and membrane tension for nanoparticle uptake by asymmetric vesicle under osmotic pressure", the author studies the wrapping of a particle at a vesicle at finite osmotic concentration and for a lipid-bilayer membrane with an area difference between both monolayers. Using a continuum membrane model, triangulated membranes, and energy minimization, equilibrium states are determined. The numerical method allows the author to extract and interpret the energy contributions due to the bending rigidity of the membrane, the area difference, and the osmotic pressure separately. Wrapping energies and energy barriers for discontinuous wrapping transitions are provided, as well as the membrane tension induced by an (effective) decrease of the vesicle volume because of partially wrapped particles. This study is based on Ref. [40], a previous study by the same author. This new study includes membrane asymmetry, which has not been considered in the original study.

In physiological conditions, both an asymmetry of the lipid-bilayer membrane and a finite osmotic concentration should be taken into account. The topic is very timely, which is also reflected by the Faraday Discussion on "Structural and functional asymmetry of plasma membranes" taking place at the end of next month in London. The results are novel, original, and of interest for readers of SciPost Physics. Furthermore, figures 6-8 hint that the numerical calculations have been performed carefully. However, I cannot recommend the manuscript for publication. The introduction, the interpretation of the results, several figures, and the structure of the manuscript have to be revised before the manuscript can be considered for publication in SciPost Physics. I recommend "reject and resubmit", to give the author the opportunity to significantly revise the presentation of the results.

Here are some issues:
1 - The title mentions an "asymmetric vesicle". This is incorrect. The author studies a vesicle with an asymmetric membrane, a lipid bilayer with two different monolayers.
2 - The abtract is not easy to follow. For example, (i) the fact that the asymmetry is between the monolayers of the lipid bilayers is missing, (ii) it is unclear how the osmotic-pressure difference is induced, and (iii) a "mini-mechanical channel" does not exist.
3 - Line 38, discussing nanoparticle attachment to erythrocytes seems out-of-place.
4 - On page 4, section 2, a discussion of how the integrals in equations (1) and (2) are calculated numerically is entirely missing. The author uses triangulated membranes and energy minimization using Surface Evolver, which should be discussed in a paragraph.
5 - In lines 115 ff., just before equation 3, I am confused about the spontaneous-curvature model being mentioned here because equation 3 does not contain a membrane spontaneous curvature. This is an equation for calculating an energy costs for changing the volume of the vesicle, entirely unrelated to how the deformation energy of the membrane is calculated.
6 - Equation 3 is based on the assumption that an initially spherical vesicle is placed in a buffer with finite osmotic concentration, and that the concentrations inside and outside the vesicle are equal in this state. When the vesicle changes shape upon wrapping a particle, the osmotic concentration within the vesicle increases whereas the osmotic concentration of the (very large volume) of buffer outside the vesicle remains constant. This should be mentioned.
7 - Line 127: It is unclear to me why the assumption of a spherical vesicle for the initial state with fw=0 holds for finite Delta A, see U. Seifert, Adv. Phys. 46, 13 (1997).
8 - Line 129: The "SC model" has not been introduced.
9 - Why are there two different sections on calculating membranes tensions, section 4 and appendix E, and how do they differ?
10 - The formatting of the equations has to be improved. For example, in equations (3) "\frac" should be used, and in equations (4)-(7) the sizes of the brackets should be adjusted (e.g., using "\left" and "\right" in LaTeX).
11 - The first paragraph in the results section 5 should be moved to either the introduction or the conclusions section of the manuscript.
12 - Part of the second paragraph of section 5, how to calculate the wrapping diagrams, should be moved to a methods section. The manuscript does not seem to follow a clear IMRaD structure (Introduction, Methods, Results, and Discussion), which makes is a bit hard to read.
13 - Lines 164-165: The energy barriers do not separate the transitions W1 and W2, stable partially wrapped states separate the two transitions. However, transitions between wrapping states are discontinuous if the corresponding wrapping states are separated by an energy barrier.
14 - Lines 179 ff.: Because this paragraph seems to also be a discussion of figure 2(b), it should be merged with the paragraph starting in line 175.
15 - Because the paragraphs starting in lines 187 and 190 seem to both discuss figure 2(c), they should be merged to a single paragraph.
16 - Line 189: I do not understand what a free-solute system is.
17 - Line 205: "facilitate the stability" should be replaced by "increase the stability"
18 - If line 258, the equation for calculating the membrane tension should not be hidden in an appendix if the corresponding figures are discussed in the main text.
19 - Line 295: It is not an asymmetric vesicle but a vesicle with an asymmetric membrane.
20 - Line 302-304: The wide-to-narrow neck discussion is, in the main text, only mentioned in the conclusions and not in a results section. I do not think that a reader will be able to understand this statement without this aspect having been discussed in one of the previous sections.
21 - As far as I understand, SciPost Physics does not reformat the articles. If so, the figures should be embedded in the main text not be all clustered at the end.
22 - Figure 1 seems inappropriately chosen, because the article discusses membrane asymmetry; the membranes for all snapshots shown in figure 1 are symmetric.
23 - The text in figure 2 overlaps with the data, which should be corrected.
24 - In figure 2, it is unclear to me what "low-solute" and "free-solute" refers to. I do not understand the naming of the terms, and also references to the equations are missing.
25 - In figure 2(b), should there not be a colorful line (and data points) separating the PW and the CW regime in the wrapping diagram? I think that this line is plotted in subfigure 2(c). Would it not be better to combine subfigures (b) and (c) into a single figure?
26 - In subfigure 2(c), the location of the label PW is misleading, because it is (correctly) placed in the parameter regime for partially wrapped states for kappabar/kappa=1.5, but incorrectly placed in the parameter regime for completely wrapped states for kappabar/kappa=4.4.
27 - In figure 2, I cannot see the colorful dashed lines mentioned in the caption in the figure.
28 - It is unclear how the energy barriers in figure 3 have been calculated.
29 - In figure 4, the text overlaps with the data.
30 - In figure 5(a,b), it is unclear how the n^{1/3} scaling regime can be determined without showing data points for this regime.
31 - In figure 5(c,d), I wonder whether it is obvious that for this small osmotic concentration equations E.1 to E.3 hold--and that they would not need to somehow contain the area difference.
32 - In line 337 (and elsewhere), the abbreviation "Equs." should be replaced with "Eqs.".
33 - For an asymmetric membrane, without the presence of a finite osmotic concentration, the vesicle should be non-spherical. Therefore, for fw=0, the reduced volume should be v<1. I do not understand why the reduced volume is smaller than one for high osmotic concentration but 1 for small osmotic concentration. Perhaps the system is stuck in a metastable state?
34 - Figures 1 and 9: The manuscript discusses vesicles with asymmetric membranes. Therefore, I find it very surprising that all vesicle shapes shown in the manuscript seem to be for symmetric membranes only.

Reject