Adherent Moving of Polymers in Spherical Confined Binary Semiflexible Ring Polymer Mixtures

Round 1

Reviewer 1 Report

In this manuscript (biophysica-2018621), Zhou et al. use molecular dynamics method to calculate and simulate the semiflexible long ring-semiflexible short ring blended polymers system confined in a fixed hard sphere. When the short ring is L_short<20, the long ring (L_long=50) separated from the blend system and then distributed against the inner wall. The long ring has a random direction of adherent walking behavior on the inner surface of the hard sphere. The research idea and the results are interesting, but there exist some minor errors. Therefore, I can recommend publication in Biophysica after a minor revision:

Minor issues:

• In Introduction: The third paragraph is unclear and I suggest they should reorganize the expression to illustrate the importance of phase separation in biosystem.
• In Introduction: The fourth paragraph needs to be rewritten to clarify that semiflexible ring polymers(SRPs) are common in biological systems and have been extensively studied both theoretically and experimentally.
• In Introduction: confifinement → confinement
• In Introduction: inflfluence → influence
• In Introduction: confifigurations → configurations
• In MM: between two adjacent keys → between two adjacent bonds
• In MM: The comment on units (kBT=1 etc ) should come before the density of the system is discussed, so it is would be clear in what units is expressed.
• In RD: In ”manuscript.pdf” version,there exists format error of figure 3(a). It can be changed to an image format.
• In RD: The authors state on page 7 that "As the simulation time increases, the long SRP gradually detaches from the bulk and eventually adheres to the wall distribution and reaches equilibrium." How did the authors verify that the simulations did not get stuck in metastable states?
• In RD: There exists more than one red chain in figure 6, although they are “possible location at different times”,it is confusing ,the illustration should be deleted.
• In RD: In section 3.2,the discussion about figure 7 can be expanded,especially the existence of oscillation of the particle number density close to the wall.
• Other spelling mistakes such as: saty→ stay etc.

To summarize, to my opinion the work has a potential and contains interesting points, and the manuscript needs a minor improvement before publishable in Biophysica.

Author Response

Please see the attachment

Reviewer 2 Report

The research paper presents the novel work and has potential interest to the researcher in the related field. With some minor corrections, I recommend this manuscript for publication.

Minor comment:

In line 53, please correct the font size “Gomez et. al.”

In line 135, I suggest the author to replace “Table 1’ instead of ‘table 1”. Likewise, replace “figure” with “Figure”

Author Response

Please see the attachment

Reviewer 3 Report

In this work, the authors present a simulation study of a blending system composed of short semiflexible ring polymer (SRP) and long SRP under spherical confinement. The authors show that long SRP tends to move and distribute along the inner wall of the spherical confinement. The authors argue that such non-random distribution of long SRP has an entropic origin. Overall, I find the manuscript needs to be better written. There are many typos, grammar errors, and unclear descriptions of results and methods. I also find that more quantitative analysis and evidence are needed for the main conclusion of the manuscript. Please see the following specific comments:

1. Many sentences needed to be rewritten to correct grammar errors and typos. For instance, line 53, “Gomez et al use” is in a different font from the rest of the text. Line 56, “inflfuence” should be “influence”. Line 64, “system limited to the hard ball, study distribution of long SRP in the binary mixture”. The comma should be replaced with “and”. Line 70, “Our findings provide. The simulation …”. What is the rest of the sentence after “Our findings provide”? There are many more places that need to be rewritten and corrected other than the few examples mentioned here. The authors should perform thorough proofreading before submission.
2. line 25. The authors claim that cyclic polymer systems are ubiquitous in biological systems. This claim lack references. I would argue that cyclic polymers are not ubiquitous in biological systems. For instance, all proteins, chromosomes, and prevalent forms of DNA and RNA in cells are not cyclic (rings).
3. line 36-38, “Experimental results show that there is a partitioning phenomenon in the chromosomal region of fibroblast nuclei, for example, in a simulation system composed of 200 unconnected uncommitted uncombushed rings with a chain length of 1600 monomers”.
   1. first, please provide a reference for the experimental results mentioned here
   2. I don’t see the connection between the simulation in the second half of the sentence and the experimental results in the first half of the sentence
4. The paragraph from line 41 to line 51. I don’t see a point describing the study by Falk et al and how this study is related to the manuscript. The study is about how the attraction between heterochromatin, euchromatin, and lamina contributes to the organization of chromosomes in the nucleus. The polymer model employed in that study is linear chain and copolymer. These features make the study by Falk et al very different from the model studied here.
5. The paragraph from line 52 to line 58. The authors describe the study by Gomez et al on the packing of rubber bands in a cylindrical container. Could the authors provide more discussion on the relevance of Gomez et al to the present study? Because the polymer model studied by the authors is a molecular system where thermal fluctuations play important roles, whereas the system studied by Gomez et al is athermal.
6. Line 70-71, could the authors provide more context on how the present study relates to vesicle-restricted mixed macromolecules?
7. Line 77, “results of this model are consistent with the experimental results”. Reference should be provided. What are the experiments the authors are referring to?
8. Line 84, equation (2). r0 should be r
9. The authors use two different bending energy K_bending for long rings and short rings. Could the authors explain why? Presumably, the ability to bend affect the entropy of chains, hence potentially can affect the distribution of long and short rings. This can have an effect on the main results presented.
10. Line 111, the authors claim that the number of density is set to be \rho=0.5\sigma^{-3}. However, when I used the number provided in Table 1 to calculate \rho, I got \rho~0.429\sigma^{-3}. In addition, L_long * N_long + L_short * N_short in Table 1 has different values for different L_short. The exact and correct number should be specified.
11. Line 148, Eq (6). Definitions for \lambda_1, \lambda_2, and \lambda_3 should be provided
12. Line 154 - 155, the authors claim that SRPs are disk-like. This is not surprising since the authors use a large bending energy K_bending.
13. Line 225. Eq. (9). The explanation of what S(t) is needed. It states “distance S(t)” but the distance between what?
14. Line 226. Eq. (10). The definition of V(t) seems not to be correct. V(t) is infinity according to Eq. (9)
15. Figure 6 plots V versus L_short. However, V is time-dependent according to Eq. (9). Hence, it is unclear what V is in Figure 6.
16. Due to a lack of description of S(t) and V(t), I cannot access the corresponding results.
17. The authors claim that long rings move faster along the inner wall and use Figure 7 as a supporting argument. Figure 7 shows that the density is minimal at the wall. However, there is also a peak in density immediately left to the minimum shown in Figure 7. Hence, it is unclear to me whether the authors’ reasoning is sound.
18. The authors argue that: since the long SRP’s excluded volume overlap with the inner wall’s excluded volume, the entropy of the system increases when the long SRP distribute near the wall. However, it is unclear why such an argument cannot be applied to short SRP. Short SRP’s excluded volume also overlaps with the inner wall’s excluded volume since the underlying monomer is the same for long and short SRP. I suspect that the difference in overlapping is due to the semiflexible nature of the ring. More quantitative analysis and calculation are needed to support the authors’ claim and reasoning.

Author Response

Please see the attachment

Round 2

Reviewer 3 Report

I appreciate the authors' effect in addressing the comments. I am happy with the reply and I confirm that I support the publication of this work.