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Characterization of phospholipid-cholesterol bilayers as self-assembled amphiphile block polymers that contain headgroups

T0 review · 4 major / 8 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read The paper argues that modeling a phospholipid–cholesterol bilayer as two diblock copolymers, with cholesterol given an explicit headgroup, makes the tilted gel phase the free-energy minimum and quantitatively reproduces cholesterol's…

desk verdict A plausible headgroup-aware SCFT model that recovers cholesterol's condensation and chemical-potential trends, but only establishes phase stability at zero cholesterol and overstates the quantitative match. read the letter →

arxiv 2505.12726 v2 pith:EC4OG2VD submitted 2025-05-19 cond-mat.soft physics.bio-ph

Xiaoyuan Wang , Fredric S. Cohen , Shixin Xu , Yongqiang Cai This is my paper · ORCID
classification cond-mat.softphysics.bio-ph
keywords BilayermembraneSelf-assemblyCholesterolLipidPolymerSelf-consistentfieldtheoryCondensationeffectTiltedgelphase
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

This paper tries to show that a phospholipid–cholesterol bilayer can be accurately described as a self-assembled mixture of two diblock copolymers in water: one polymer with a flexible head and rigid tail for the lipid, and one with a small flexible head and rigid rod for cholesterol. When cholesterol carries an explicit headgroup, the model's lowest-free-energy state is a tilted gel phase, like the experimentally observed $L_{\beta'}$ phase of DPPC. From that state, with a fixed parameter set, the model reproduces four established cholesterol effects: area condensation, membrane thickening, a fall in lipid tilt from about $43^\circ$ toward near zero, and a chemical potential that rises linearly with cholesterol concentration between 37% and 50%. This matters because the same field-theoretic machinery could then be used to compute structural and thermodynamic properties of biomimetic polymer–lipid membranes and to design vesicle platforms for drug delivery.

What carries the argument

The machinery that carries the argument is self-consistent field theory for a canonical ensemble of three polymers in one spatial dimension: water as a flexible A homopolymer, the phospholipid as a BC rod–coil diblock with flexible head B and rigid tail C, and cholesterol as a DE rod–coil diblock with small flexible head D and rigid rod E. The free energy combines Flory–Huggins isotropic interactions among all five species, a Maier–Saupe orientational term that aligns the rigid rods through the tensor $\mathbf{S}$, and coil stretching entropy. The new element relative to the authors' earlier model is the explicit D headgroup on cholesterol, whose small volume ratio $f_D:f_B = 1:10$ forces the phospholipid headgroups to stretch sideways to shield the hydrophobic E rod from water. The equilibrium state is selected by minimizing the free energy with respect to the computational-domain length $l$, which for the pure bilayer places the tilted $C_s$ phase below both the interdigitated and non-interdigitated untilted phases; tilt is read from the spectral decomposition of the orientational density tensor of the C rods.

What would settle it

Re-run the SCFT calculations with cholesterol's rigid E rod shorter than the lipid tail (for example $f_E = 0.65$ with $f_C = 0.75$) while keeping every interaction parameter at the paper's default values; if the tilted $C_s$ phase no longer is the free-energy minimum or the 37–50% linear chemical-potential regime disappears, the central claims are tied to the assumed $f_E=f_C$ geometry.

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Extended reading notes

Core claim

In its own terms, this paper establishes that a diblock-copolymer SCFT model in which cholesterol is given a small explicit headgroup can account for the main structural and thermodynamic effects of cholesterol in saturated phospholipid bilayers. With volume fractions and chain lengths chosen to match DPPC and cholesterol ($f_B=0.25$, $f_D=0.025$, $f_C=f_E=0.75$, $\beta_C=\beta_E=4$), the tilted $C_s$ phase—lipids tilted away from the bilayer normal, as in the experimentally observed $L_{\beta'}$ gel phase—is the global free-energy minimum, with an equilibrium tilt of about $43^\circ$ at $l^*/R_g = 16.6$, below the metastable interdigitated and non-interdigitated untilted phases. As cholesterol concentration rises from 0 to 50%, the model produces a monotonic decrease in average area per molecule (the condensation effect), an increase in bilayer thickness from about $4.16R_g$ toward $5.64R_g$, a drop in lipid tilt from $43^\circ$ to below $10^\circ$, and a cholesterol chemical potential that increases linearly with concentration between 37% and 50%, in agreement with liposome experiments. The mechanism asserted is that phospholipid headgroups redistribute and stretch tangentially to shield cholesterol's small headgroup from water; the enthalpic gain from improved interactions, dominated by the Maier–Saupe orientational term, more than compensates the headgroup stretching entropy loss. The paper also claims that among headgroup interactions, the phospholipid headgroup–solvent term $\chi_{AB}N$ is the dominant control on tilt and chemical potential, while cholesterol headgroup interactions have negligible influence.

Load-bearing premise

The load-bearing premise is that the ten interaction-energy parameters and the single rod-alignment parameter, most taken from an earlier headless-cholesterol model and a few chosen by hand, together with the assumption that cholesterol's rigid part is exactly as long as the lipid tail, truly represent how cholesterol and phospholipids interact; if those choices are wrong, the predicted phase ordering and the agreement with experiments would not follow.

Editorial extensions

If this is right

  • In a pure lipid bilayer, the equilibrium is the tilted gel phase $C_s$, with free energy lower than both interdigitated and non-interdigitated untilted phases; the model therefore gives an SCFT route to the $L_{\beta'}$ phase of DPPC without hand-placing molecular orientations.
  • Adding cholesterol reduces the average area per molecule (condensation), increases bilayer thickness, and lowers lipid tilt, with structural changes saturating near 37–50% cholesterol; the theory attributes this to headgroup stretching that shields cholesterol from water.
  • Cholesterol's chemical potential rises monotonically and linearly in the 37–50% concentration range, in agreement with liposome measurements, and this curve is computed rather than fitted.
  • Varying phospholipid tail length changes tilt and the cholesterol concentration at which thickness saturates: longer tails keep the bilayer in the tilted phase at higher cholesterol content.
  • In headgroup interaction sweeps, the phospholipid headgroup–water interaction $\chi_{AB}N$ is the dominant control on tilt and cholesterol chemical potential, while cholesterol headgroup interactions have little effect.

Reading between the lines

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

  • Relaxing the geometric choice $f_E=f_C$ (cholesterol's rigid rod as long as the lipid tail) is the most direct calculation the paper leaves open; if shortening or lengthening the E rod breaks the 37–50% linear chemical-potential window, that window would be an artifact of the chosen geometry rather than a robust consequence of the headgroup mechanism.
  • If the $C_s$-phase ordering is robust to reasonable variation of the interaction parameters, the same machinery could predict how changing phospholipid headgroup size or hydrophilicity shifts the condensation percentage, since the paper only reports that quantity for one geometry.
  • The model's headgroup-shielding account of condensation is a quantitative realization of the umbrella picture; applied to lipids with different headgroup volumes, it would predict that the condensation effect weakens as cholesterol's headgroup becomes larger relative to the lipid headgroup.
  • Because the SCFT chemical potential is computed directly at each concentration, a natural next application is two-lipid mixtures, where the same computation could predict how cholesterol partitions between coexisting liquid-ordered and liquid-disordered domains without additional thermodynamic assumptions.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 8 minor

Summary. This paper develops a self-consistent field theory (SCFT) model of phospholipid/cholesterol bilayers, representing the phospholipid as a rod-coil diblock copolymer (flexible headgroup B and rigid tail C) and cholesterol as a second rod-coil diblock copolymer with an explicit flexible headgroup D and rigid hydrophobic block E, immersed in a solvent A. The authors fix model parameters from geometric considerations and from their prior headless-cholesterol SCFT study [31], compare three candidate phases (A_c, A_s, C_s), and report that the tilted C_s phase has the lowest free energy for cholesterol-free bilayers. They then compute, on the C_s branch, the cholesterol chemical potential, area condensation, bilayer thickness, and lipid tilt as functions of cholesterol concentration, finding a linear chemical potential regime at high cholesterol concentration, a condensation effect, and decreasing tilt with increasing cholesterol. They also study the influence of headgroup volume fraction, hydrophobic length, and headgroup interaction parameters. The main claims are that the model identifies a tilted gel phase as the equilibrium configuration and captures the experimentally known condensation, thickening, and reduced-tilt trends, with quantitative agreement for the cholesterol chemical potential.

Significance. If the central claims are substantiated, this is a useful contribution to coarse-grained modeling of lipid-cholesterol bilayers. The explicit representation of the cholesterol headgroup is an advance over the authors' earlier headless-cholesterol model, and the SCFT framework is standard and the numerics appear carefully executed. The model yields several falsifiable predictions (e.g., the linear high-concentration chemical potential, the unit-area reduction, and the tilt reduction) that can be compared with experiments, and it offers a practical route to designing biomimetic polymer membranes. The authors are honest in the conclusion about the model's limitations, including the qualitative nature of the structural predictions and the unknown mapping between polymer deformation and real molecular interactions. However, the abstract overstates the quantitative character of the condensation result, and the phase stability of the C_s state at finite cholesterol concentration is not established, which undermines the equilibrium claim at the concentrations where the main predictions are made.

major comments (4)
  1. [Sections 3.1 and 3.2, Figs. 4-6] The stability of the C_s phase is established only for cholesterol-free bilayers (φ_DE = 0) in Fig. 4(a). All finite-cholesterol results in Section 3.2—chemical potential, condensation, thickness, and tilt—are computed on the C_s branch without a free-energy comparison against the A_c and A_s phases at the same cholesterol concentration. The paper itself states in Section 3.2.3 that at φ_DE = 0.5 'the bilayer structure approaches that of the A_s-phase' and in Section 3.3.2 refers to a 'structural transition from the C-phase to the A-phase.' If the A_s or A_c free energy is lower at φ_DE = 0.2, 0.375, or 0.5, then the C_s-branch curves in Figs. 5 and 6 describe a metastable state, and the abstract's assertion that the simulations identify a minimum free-energy configuration is not supported at the concentrations where the main predictions are made. Please report the free energies of all three phases as functions of φ_DE, or explicitly delimit the stability window of the C_s phase.
  2. [Abstract vs. Section 4, Section 3.2.2] The abstract claims the model 'quantitatively captures the well-known area condensation effect,' but Section 3.2.2 (Fig. 6(a)) presents no quantitative comparison to experimental area data; the text only states that the predictions are 'consistent with experimental measurements [23].' Section 4 explicitly limits structural agreement to 'qualitatively reproduces structural trends' and restricts quantitative agreement to the chemical potential. This is an internal inconsistency. Please either add a quantitative overlay of model and experimental areas (e.g., data from Ref. [23]) with an error metric, or revise the abstract to say, for example, 'qualitatively captures' the condensation effect.
  3. [Section 3.1, Table 1] The interaction parameters χ_BD N = −30, χ_CD N = χ_DE N = 40, χ_CE N = 0, and η N = 30 are assigned by hand based on 'previous studies [1,31]' and on qualitative reasoning such as 'we chose a moderate interaction parameter' (Section 3.1). The central predictions—condensation magnitude, tilt angle, and chemical potential slope—depend on these values, yet no sensitivity analysis is provided for χ_CE, χ_BD, or η; the parameter variations in Sections 3.3 and 3.4 concern headgroup volume ratios and headgroup interaction parameters only. Because the paper claims quantitative agreement for the chemical potential and the abstract claims quantitative capture of the condensation effect, please include a sensitivity study for these key parameters or otherwise justify their transferability from the headless-cholesterol model of Ref. [31] to the present model with an explicit cholesterol headgroup.
  4. [Section 3.1] The model sets the cholesterol hydrophobic rod length equal to the lipid tail length: f_E = f_C and L_E = L_C = f_C β_C. This geometric assumption is introduced without justification, although in reality the rigid hydrophobic portion of cholesterol is shorter than a DPPC acyl chain. The tail-length study in Section 3.3.2 varies L_C while keeping L_E fixed, so the equal-length assumption is never tested against the physically more plausible L_E < L_C case. Since the tilt and thickness predictions are likely sensitive to the relative rod lengths, please test at least one case with L_E < L_C or provide a geometric/conceptual justification for the equal-length choice.
minor comments (8)
  1. [Section 3.1] The text states L_B = 2√(f_B R_g); this is dimensionally incorrect. The intended expression is L_B = 2√(f_B) R_g (since R_B^g = √(f_B) R_g).
  2. [Table 1] The table row reading 'χ_AB N = χ_AD N = χ_BE = 0' appears to contain a typo: the text sets χ_AB N = χ_AD N = χ_BD N = 0, and χ_BE is not otherwise defined in the paper. Please correct.
  3. [References [47] and [48]] The DOIs for references [47] and [48] appear to be swapped: [47] (JACS 2005) is assigned 10.1021/nn3023602 and [48] (ACS Nano 2012) is assigned 10.1021/ja043600x. Please verify and correct these DOIs.
  4. [Figure 5 caption] The caption lists several fitted curves with R^2 values from Ref. [24] but does not identify which curve is the SCFT result; a legend or explicit labeling of the SCFT curve would make the comparison clear.
  5. [Section 3.2.2] The sentence 'the density distribution of phospholipid headgroups also increases along the tangential direction of the bilayer membrane interface' is confusing because the model is solved in a one-dimensional normal direction; consider rewording to refer to the areal density or lateral packing density.
  6. [General] There are several typographical errors, including 'weuseself-consistentfieldtheory' in the abstract, 'Shownsisthe tilt' in the Fig. 4 caption, 'examble' in Section 3.3.2, and an unmatched parenthesis in Section 3.2.3 after the Maier-Saupe energy comparison. Please copyedit.
  7. [Section 2.1] The text says the BC and DE copolymers 'were preassembled into bilayer membranes' while elsewhere the system is described as self-assembled; clarifying that the preassembled structure is only the initial condition for the SCFT minimization would remove the apparent inconsistency.
  8. [Section 3.3.2] The two hydrophobic-length cases are written as 'L_C = f_C β_C = 0.75 * 4 = 3 R_g and L_C = f_C β_C = 0.800625 * 4.1 = 3.2826 R_g'; the second expression is a new value of L_C, so the text should say something like 'and for the longer tail, L_C = f_C β_C = 0.800625 × 4.1 = 3.2826 R_g' for clarity.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: SCFT predictions are generated from fixed geometric and interaction parameters and benchmarked against external experiments; self-citations supply parameters, not the target results.

full rationale

The central claims (C_s equilibrium tilt, condensation, membrane thickening, reduced tilt, and chemical-potential linearity) are outputs of SCFT free-energy minimization, not fits to the experimental quantities. Section 3.1 sets volume fractions from DPPC/cholesterol geometry (f_B=0.25, f_D=0.025, f_C=f_E=0.75) and interaction parameters from prior work [1,31] plus explicit modeling choices (e.g., chi_BD N = -30); these are inputs, and the paper then compares the resulting predictions to independent experimental data (Refs. [23,24,28,34,35]). The tilt is extracted from the computed orientational order parameter in Appendix A.4, not imposed as a target. The chemical potential is obtained by differentiating the SCFT free energy in Appendix A.3 and is compared to external measurements [24] after only a vertical offset at 30% concentration. Although Ref. [31] is a self-citation and supplies parameter values, the prior headless-cholesterol model was explicitly unable to produce the condensation effect, so the current condensation, tilt, thickening, and chemical-potential results are not imported from that citation. The uniaxial assumption used to define tilt is cited to Ref. [1], but it is a standard modeling convention for interpreting the orientational tensor, not a result that already contains the paper's predictions. The lack of a C_s-versus-A_s free-energy comparison at finite cholesterol is a potential metastability and correctness concern, not a circularity. No fitted parameter is renamed as a prediction, and no equation in the derivation reduces to its input by construction. The condensation claim is presented as a unit-area decrease rather than an excess-area calculation, which weakens the comparison to the classical definition but does not constitute circular reasoning.

Assumptions & free parameters 8 free parameters · 6 assumptions · 0 invented entities

The model introduces no new physical particles or forces; its polymer blocks are standard coarse-grained representations. The free parameters are interaction strengths and geometric ratios chosen by hand or from prior studies, and the axioms are the standard SCFT mean-field assumptions plus specific structural simplifications.

free parameters (8)
  • chi_BD * N = -30
    Attraction between phospholipid and cholesterol headgroups; chosen by hand, central to condensation effect and tilt changes (Section 3.1, Table 1).
  • chi_CD * N = chi_DE * N = 40
    Repulsion involving cholesterol headgroup set high due to its small volume fraction (Section 3.1).
  • chi_AC * N = chi_AE * N = 30
    Water-tail repulsion inherited from prior SCFT studies [1,31].
  • chi_CE * N = 0
    Chosen as a moderate interaction; no experimental determination (Section 3.1).
  • eta * N = 30
    Maier-Saupe orientational interaction strength; set to reflect strong liquid crystalline order (Section 3.1).
  • beta_C = beta_E = 4
    Rod asymmetry parameters; geometric choices tied to tail length (Section 3.1).
  • Volume fractions f_B, f_C, f_D, f_E = 0.25, 0.75, 0.025, 0.75
    Set from phospholipid headgroup-to-tail volume ratio 1:3 and cholesterol headgroup volume ratio 1:10 relative to phospholipid headgroup (Section 3.1).
  • n_A = 2
    Number of solvent polymers per lipid; no explicit justification (Table 1).
assumptions (6)
  • domain assumption Self-consistent mean-field approximation captures equilibrium bilayer structure.
    The entire free energy is computed at mean-field level; fluctuations are neglected.
  • domain assumption The bilayer is planar and translational invariant in lateral directions; a 1D computation domain over a period l is sufficient, with l optimized.
    Used in all simulations, with the optimal domain l* chosen to minimize free energy (Appendix A.2).
  • domain assumption Local incompressibility sum_i phi_i = 1.
    Standard SCFT constraint used in Eq. (1).
  • ad hoc to paper Phospholipid two acyl chains are represented by a single rigid rod, and cholesterol is a rigid rod of the same length as the lipid tail.
    Section 2.1 and 3.1; a strong geometric simplification that affects tilt and thickness predictions.
  • domain assumption Maier-Saupe interaction form for orientational order.
    Standard liquid crystal model used for rigid rods (Section 2.1).
  • ad hoc to paper Interaction parameters from prior work [1,31] and hand choices are transferable to the new cholesterol-headgroup model.
    Section 3.1; the mapping between polymer parameters and molecular interactions is stated as not fully understood in the Conclusion.

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Pith. "Pith review of Characterization of phospholipid-cholesterol bilayers as self-assembled amphiphile block polymers that contain headgroups." pith.science (2026). https://pith.science/paper/EC4OG2VD

@misc{pith2026250512726,
  author       = {Pith},
  title        = {Pith review of: Characterization of phospholipid-cholesterol bilayers as self-assembled amphiphile block polymers that contain headgroups},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EC4OG2VD}},
  note         = {Machine review of arXiv:2505.12726}
}
read the original abstract

Cholesterol is known to modulate the structure and function of biological membranes. In this study, we use self-consistent field theory (SCFT) to investigate phospholipid/cholesterol bilayer membranes modeled with two types of diblock copolymers. These copolymer-based bilayers serve as biomimetic platforms with applications in areas such as drug delivery. Our simulations identify a minimum free energy configuration characterized by phospholipid tails tilted relative to the membrane normal. The model quantitatively captures the well-known area condensation effect as cholesterol concentration increases, along with membrane thickening and reduced tilt angle. Thermodynamically, we observe a linear dependence between cholesterol's chemical potential and its concentration within the 37-50% range, consistent with experimental results. Additionally, we analyze the effects of block copolymer length and headgroup interactions on bilayer structure. Interactions between phospholipid headgroups and the solvent emerge as the most influential. This work provides a theoretical framework for understanding cholesterol's regulatory role in membrane structure and mechanics.

Figures

Figures reproduced from arXiv: 2505.12726 by the authors.

Figure 1
Figure 1. Schematic diagrams of polymer structures: (a) Homopolymer A-Coil with degree of polymerization 𝑁𝐴 . (b) Diblock copolymer BC-Rod-Coil with total degree of polymer￾ization 𝑁𝐵 + 𝑁𝐶 . (c) Diblock copolymer DE-Rod-Coil with total degree of polymerization 𝑁𝐷 + 𝑁𝐸 . The arrows indicate the directions that we used to solve the propagators. A, B, C, D, and E blocks are represented as ̃𝑎, 𝑏̃, ̃𝑐, 𝑑̃, and ̃𝑒, respectively. Th… view at source ↗
Figure 2
Figure 2. Polymer size diagram with 𝑓𝐵 = 0.25, 𝑓𝐷 = 0.025, 𝑓𝐶 = 𝑓𝐸 = 0.75, 𝛽𝐶 = 𝛽𝐸 = 4. A-Coil simulates water, BC-Rod-Coil simulates saturated phospholipids, and DE-Rod-Coil simulates cholesterol. The unit length is 𝑅𝑔 . The red circle (B-Coil) and black circle (D-Coil) represent the headgroups of phospholipids and cholesterol, respectively. The blue rectangle (C-Rod) and green rectangle (E-Rod) represent the hydrophobic reg… view at source ↗
Figure 3
Figure 3. The initial states used for simulating phospholipid￾cholesterol bilayer membranes are a self-assembled Rod￾Coil/Coil self-assembled system as described below, where 𝐧 represents the normal direction of the bilayer membrane: (a) In the 𝐴𝑐 phase bilayer membrane, the tails of the bilayer membrane are interdigitated, while the Rod molecules maintain their average orientation parallel to the normal direction of the bila… view at source ↗
Figures from the paper (8 more)
Figure 5
Figure 5. Figure 5: Comparison of chemical potentials. The parameters for the chemical potentials obtained from self-consistent field simulations are listed in [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]
Figure 4
Figure 4. Figure 4: (a) The free energy ̃ (left ordinate) of the liquid crystal A-phase bilayer and C-phase bilayer as functions of the computation domain 𝑙 in the canonical ensemble. Showns is the tilt 𝜃 (right ordinate) of the C-Rod (i.e., phospholipid tails) in the C-phase bilayer as …
Figure 6
Figure 6. Figure 6: (c) illustrates phospholipid tilt and bilayer thick￾ness as a function of cholesterol concentration. As the [PITH_FULL_IMAGE:figures/full_fig_p006_6.png]
Figure 8
Figure 8. Figure 8: The tilt 𝜃 (left ordinate, solid curve) of the C-Rod and the bilayer thickness Ω (right ordinate, dashed curve) as a function of the cholesterol concentration 𝜑𝐷𝐸 for two phospholipid acyl chain lengths 𝐿𝐶 = 3𝑅𝑔 (𝑓𝐶 = 0.75, 𝛽𝐶 = 4𝑅𝑔 ), or 3.2826𝑅𝑔 (𝑓𝐶 = 0.800625, 𝛽𝐶 = …
Figure 7
Figure 7. Figure 7: The density distributions of a bilayer for two choles￾terol concentrations. (a) 𝜑𝐷𝐸 = 0.3333, and (b) 𝜑𝐷𝐸 = 0.5. (c) The cholesterol chemical potential 𝜇𝐷𝐸 of the bilayer under different volume fractions (𝑓𝐷 ∶ 𝑓𝐵 = 1 ∶ 10, 𝑓𝐷 ∶ 𝑓𝐵 = 1 ∶ 5, and 𝑓𝐷 ∶ 𝑓𝐵 = 1 ∶ 4) as funct…
Figure 9
Figure 9. Figure 9: (a) The tilt 𝜃 of lipids as functions of interactions 𝜒𝐴𝐵𝑁 with cholesterol concentrations 𝜑𝐷𝐸 = 0, 0.2, 0.4. (b) The tilt 𝜃 of lipids as functions of interactions 𝜒𝐴𝐷𝑁 with cholesterol concentrations 𝜑𝐷𝐸 = 0.2, 0.4. (c) The tilt 𝜃 of lipids as functions of interaction…
Figure 10
Figure 10. Figure 10: The density concentration 𝜙 of the phospholipid for different values of 𝜒𝐴𝐵 = 0 (dotted curve), −10 (dashed curve), −20 (solid curve) at cholesterol concentrations of 𝜑𝐷𝐸 = 0 (a), 𝜑𝐷𝐸 = 0.2 (b), and 𝜑𝐷𝐸 = 0.4 (c). The density concentration 𝜙 of the cholesterol headgro…
Figure 11
Figure 11. Figure 11: The density concentration of the bilayer for different values of 𝜒𝐴𝐷 = 0 (dotted curve), −10 (dashed curve), −20 (dash-dotted curve), −30 (solid curve) at cholesterol concentrations of 𝜑𝐷𝐸 = 0.2 (a) and 𝜑𝐷𝐸 = 0.4 (b). The inset in (b) zooms into the density concentrat…

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Works this paper leans on

63 extracted references · 59 canonical work pages

  1. [31]

    Mimicking effects of cholesterol in lipid bilayer membranes by self-assembled am- phiphilic block copolymers[J]

    Wang X, Xu S, Cohen F S, Zhang J, Cai Y. Mimicking effects of cholesterol in lipid bilayer membranes by self-assembled am- phiphilic block copolymers[J]. Soft matter, 2023, 19(29): 5487-

    work page 2023

  2. [23]

    https://doi.org/10.1529/biophysj.106.099234

    HungW-C,LeeM-T,ChenF-Y,HuangHW.Thecondensingeffect ofcholesterolinlipidbilayers[J].Biophysicaljournal,2007,92(11): 3960-3967. https://doi.org/10.1529/biophysj.106.099234

    work page doi:10.1529/biophysj.106.099234 2007

  3. [1]

    Liquid crystalline bilayers self-assembled from rod–coil diblock copolymers[J]

    Cai Y, Zhang P, Shi A C. Liquid crystalline bilayers self-assembled from rod–coil diblock copolymers[J]. Soft Matter, 2017, 13(26): 4607-4615. https://doi.org/10.1039/C7SM00354D

    work page doi:10.1039/c7sm00354d 2017

  4. [2]

    Eine einfache molekulare Theorie des ne- matischen kristallinfl"ussigen Zustandes[J]

    Maier W, Saupe A. Eine einfache molekulare Theorie des ne- matischen kristallinfl"ussigen Zustandes[J]. Zeitschrift für Natur- forschung A, 1958, 13(7): 564-566. https://doi.org/10.1515/zna- 1958-0716

    doi:10.1515/zna- 1958

  5. [3]

    The chemical potential of plasma membrane cholesterol: implications for cell biology[J]

    Ayuyan A G, Cohen F S. The chemical potential of plasma membrane cholesterol: implications for cell biology[J]. Biophysical journal, 2018, 114(4): 904-918. https://doi.org/10.1016/j.bpj.2017.12.042

    work page doi:10.1016/j.bpj.2017.12.042 2018

  6. [4]

    https://doi.org/10.1021/ma302026a

    SongW,TangP,QiuF,YangY,ShiAC.Phasebehaviorofrod–coil diblock copolymer and homopolymer blends from self-consistent fieldtheory[J].TheJournalofPhysicalChemistryB,2011,115(26): 8390-8400. https://doi.org/10.1021/ma302026a

    work page doi:10.1021/ma302026a 2011

  7. [5]

    Principles of polymer chemistry[M]

    Flory P J. Principles of polymer chemistry[M]. Cornell university press, 1953. doi: http://doi.org/10.1007/978-1-4614-2212-9. Figure 12: The density concentration of the bilayer for different values of 𝜒𝐵𝐷 = 0 (dotted curve), −10 (dashed curve), −20 (dash-dotted curve), −30 (solid curve) at cholesterol concentrations of 𝜑𝐷𝐸 = 0.2 (a) and 𝜑𝐷𝐸 = 0.4 (b). Th...

    doi:10.1007/978-1-4614-2212-9 1953

  8. [6]

    Self-consistent mean- field model based on molecular dynamics: Application to lipid- cholesterol bilayers[J]

    Khelashvili G A, Pandit S A, Scott H L. Self-consistent mean- field model based on molecular dynamics: Application to lipid- cholesterol bilayers[J]. The Journal of chemical physics, 2005, 123(3): 034910. doi: https://doi.org/10.1063/1.1943412

    work page doi:10.1063/1.1943412 2005

Show all 63 references
  1. [7]

    Interaction of cholesterol- like molecules in polyunsaturated phosphatidylcholine lipid bilayers as revealed by a self-consistent field theory[J]

    Leermakers F A M, Rabinovich A L. Interaction of cholesterol- like molecules in polyunsaturated phosphatidylcholine lipid bilayers as revealed by a self-consistent field theory[J]. Physical Review E, 2007, 76(3): 031904. doi: https://doi.org/10.1103/PhysRevE.76.031904

    2007 doi

  2. [8]

    Equilibrium morphology of block copoly- mer melts[J]

    Ohta T, Kawasaki K. Equilibrium morphology of block copoly- mer melts[J]. Macromolecules, 1986, 19(10): 2621-2632. doi: https://doi.org/10.1021/ma00219a022

    1986 doi

  3. [9]

    Variational Methods in Molecular Modeling[M]

    Wu J. Variational Methods in Molecular Modeling[M]. Springer,

  4. [10]

    Phase separation of satu- ratedandmono-unsaturatedlipidsasdeterminedfromamicroscopic model[J]

    Elliott R, Katsov K, Schick M, Szleifer I. Phase separation of satu- ratedandmono-unsaturatedlipidsasdeterminedfromamicroscopic model[J]. The Journal of chemical physics, 2005, 122(4): 044904. doi: https://doi.org/10.1063/1.1836753

    2005 doi

  5. [12]

    Mesoscopic simulation of cell mem- brane damage, morphology change and rupture by nonionic surfactants[J]

    Groot R D, Rabone K L. Mesoscopic simulation of cell mem- brane damage, morphology change and rupture by nonionic surfactants[J]. Biophysical journal, 2001, 81(2): 725-736. doi: https://doi.org/10.1016/S0006-3495(01)75737-2

    2001 doi

  6. [13]

    Molecular simulation of the DMPC-cholesterol phase diagram[J]

    de Meyer F J-M, Benjamini A, Rodgers J M, Misteli Y, Smit B. Molecular simulation of the DMPC-cholesterol phase diagram[J]. The Journal of Physical Chemistry B, 2010, 114(32): 10451-10461. doi: https://doi.org/10.1021/jp103903s

    2010 doi

  7. [14]

    Phase transitions in semiflexible-rod diblock copolymers: A self-consistent field theory[J]

    Li S, Jiang Y, Chen J Z Y. Phase transitions in semiflexible-rod diblock copolymers: A self-consistent field theory[J]. Soft Matter, 2014, 10(44): 8932-8944. https://doi.org/10.1039/C4SM01884B

    2014 doi

  8. [15]

    Lipid composition of rat liver plasma membranes[J]

    Ray T K, Skipski V P, Barclay M, Essner E, Archibald F M. Lipid composition of rat liver plasma membranes[J]. Journal of Biological Chemistry, 1969, 244(20): 5528-5536. https://doi.org/10.1016/S0021-9258(18)63595-1

    1969 doi

  9. [16]

    Plasma membranes contain half the phospholipid and 90% of the cholesterol and sphingomyelin in cultured human fibroblasts[J]

    Lange Y, Swaisgood M H, Ramos B V, Steck T L. Plasma membranes contain half the phospholipid and 90% of the cholesterol and sphingomyelin in cultured human fibroblasts[J]. Journal of Biological Chemistry, 1989, 264(7): 3786-3793. https://doi.org/10.1016/S0021-9258(19)84918-9

    1989 doi

  10. [17]

    Physical biology of the cell[M]

    Phillips R, Kondev J, Theriot J, Garcia H. Physical biology of the cell[M]. Garland Science, 2012. https://doi.org/10.1201/9781134111589

    2012 doi

  11. [18]

    Cholesterol in phospholipid bi- layers: positions and orientations inside membranes with dif- ferent unsaturation degrees[J]

    Ermilova I, Lyubartsev A P. Cholesterol in phospholipid bi- layers: positions and orientations inside membranes with dif- ferent unsaturation degrees[J]. Soft Matter, 2019, 15(1): 78-93. https://doi.org/10.1039/C8SM01937A

    2019 doi

  12. [19]

    Detailed molecular dynamics simulations of model biological membranes containing cholesterol[J]

    Berkowitz M L. Detailed molecular dynamics simulations of model biological membranes containing cholesterol[J]. Biochimica et Biophysica Acta (BBA)-Biomembranes, 2009, 1788(1): 86-96. https://doi.org/10.1016/j.bbamem.2008.09.009

    2009 doi

  13. [20]

    Structure of cholesterol in lipid rafts[J]

    Toppozini L, Meinhardt S, Armstrong C L, Yamani Z, Kučerka N, Schmid F, Rheinst"adter M C. Structure of cholesterol in lipid rafts[J]. Physical review letters, 2014, 113(22): 228101. https://doi.org/10.1103/PhysRevLett.113.228101

    2014 doi

  14. [21]

    The influence of cholesterol on membrane protein structure, function, and dynam- ics studied by molecular dynamics simulations[J]

    Grouleff J, Irudayam S J, Skeby K K, Schiøtt B. The influence of cholesterol on membrane protein structure, function, and dynam- ics studied by molecular dynamics simulations[J]. Biochimica et BiophysicaActa(BBA)-Biomembranes,2015,1848(9):1783-1795. https://doi.org/10.1016/j.b...

    2015 doi

  15. [22]

    Modulation of lipid vesi- cle–membrane interactions by cholesterol[J]

    Chng C-P, Hsia K J, Huang C. Modulation of lipid vesi- cle–membrane interactions by cholesterol[J]. Soft Matter, 2022, 18(40): 7752-7761. https://doi.org/10.1039/D2SM00693F

    2022 doi

  16. [24]

    Chemical potential measurements constrain models of cholesterol-phosphatidylcholine interactions[J]

    Shaw T R, Wisser K, Schaffner T A, Gaffney A, Machta B, Veatch S L. Chemical potential measurements constrain models of cholesterol-phosphatidylcholine interactions[J]. Biophysical Journal, 2023, 122(6): 1105-1117. https://doi.org/10.1016/j.bpj.2023.02.009

    2023 doi

  17. [25]

    Self-Assembled Aggregates of Rod- Coil Block Copolymers and Their Solubilization and Encapsu- lation of Fullerenes[J]

    Jenekhe S A, Chen X L. Self-Assembled Aggregates of Rod- Coil Block Copolymers and Their Solubilization and Encapsu- lation of Fullerenes[J]. Science, 1998, 279(5358): 1903-1907. https://doi.org/10.1126/science.279.5358.1903

    1998

  18. [26]

    Croonian Lectures ON THE RôLE OF FATS IN VITAL PHENOMENA[J]

    Leathes J B. Croonian Lectures ON THE RôLE OF FATS IN VITAL PHENOMENA[J]. The Lancet, 1925, 205(5303): 803-807. https://doi.org/10.1016/S0140-6736(01)22310-1

    1925 doi

  19. [27]

    The standard Gaussian model for block copolymer melts[J]

    Matsen M W. The standard Gaussian model for block copolymer melts[J]. Journal of Physics: Condensed Matter, 2001, 14(2): R21. https://doi.org/10.1088/0953-8984/14/2/201

    2001 doi

  20. [28]

    Cholesterol per- turbs lipid bilayers nonuniversally[J]

    Pan J, Mills T T, Tristram-Nagle S, Nagle J F. Cholesterol per- turbs lipid bilayers nonuniversally[J]. Physical review letters, 2008, 100(19): 198103. https://doi.org/10.1103/PhysRevLett.100.198103

    2008 doi

  21. [29]

    Component volumes ofunsaturatedphosphatidylcholinesinfluidbilayers:adensitometric study[J]

    Uhr’ıkov’a D, Ryb’ar P, Hianik T, Balgav‘y P. Component volumes ofunsaturatedphosphatidylcholinesinfluidbilayers:adensitometric study[J]. Chemistry and physics of lipids, 2007, 145(2): 97-105. https://doi.org/10.1016/j.chemphyslip.2006.11.004

    2007 doi

  22. [30]

    A detailed analysis of partial molecular volumes in DPPC/cholesterol binary bilayers[J]

    Miyoshi T, L"onnfors M, Slotte J P, Kato S. A detailed analysis of partial molecular volumes in DPPC/cholesterol binary bilayers[J]. Biochimica et Biophysica Acta (BBA)-Biomembranes, 2014, 1838(12): 3069-3077. https://doi.org/10.1016/j.bbamem.2014.07.004

    2014 doi

  23. [32]

    Advances in block copolymer- phospholipid hybrid vesicles: from physical-chemical properties to applications[J]

    Brodszkij E, St"adler B. Advances in block copolymer- phospholipid hybrid vesicles: from physical-chemical properties to applications[J]. Chemical Science, 2024. https://doi.org/10.1039/D4SC01444H

    2024 doi

  24. [33]

    Bioin- spired polymer vesicles and membranes for biological and medical applications[J]

    Palivan C G, Goers R, Najer A, Zhang X, Car A, Meier W. Bioin- spired polymer vesicles and membranes for biological and medical applications[J]. Chemical Society Reviews, 2016, 45(2): 377-411. https://doi.org/10.1039/C5CS00569H

    2016 doi

  25. [34]

    Fatty-acid chain tilt angles and directions in dipalmitoyl phosphatidylcholine bilayers[J]

    Katsaras J, Yang D S, Epand R M. Fatty-acid chain tilt angles and directions in dipalmitoyl phosphatidylcholine bilayers[J]. Biophysi- caljournal,1992,63(4):1170-1175.https://doi.org/10.1016/S0006- 3495(92)81680-6

    1992 doi

  26. [35]

    Order and disor- der in fully hydrated unoriented bilayers of gel-phase dipalmi- toylphosphatidylcholine[J]

    Sun W-J, Suter R M, Knewtson M A, Worthington C R, Tristram-Nagle S, Zhang R, Nagle J F. Order and disor- der in fully hydrated unoriented bilayers of gel-phase dipalmi- toylphosphatidylcholine[J]. Physical Review E, 1994, 49(5): 4665. https://doi.org/10.1103/PhysRevE.49.4665

    1994 doi

  27. [36]

    Simulation of gel phase formation and melting in lipid bilayers using a coarse-grained model[J]

    Marrink S J, Risselada J, Mark A E. Simulation of gel phase formation and melting in lipid bilayers using a coarse-grained model[J]. Chemistry and physics of lipids, 2005, 135(2): 223-244. https://doi.org/10.1016/j.chemphyslip.2005.03.001

    2005 doi

  28. [37]

    The Journal of Physical Chemistry B, 2012, 116(51): 14829-14838

    Pan J, Cheng X, Heberle F A, Mostofian B, Kučerka N, Drazba P, KatsarasJ.Interactionsbetweenetherphospholipidsandcholesterol asdeterminedbyscatteringandmoleculardynamicssimulations[J]. The Journal of Physical Chemistry B, 2012, 116(51): 14829-14838. https://doi.org/10.1021/jp310345j

    2012 doi

  29. [38]

    Effect of cholesterol on the rigidity of saturated and unsaturated membranes: fluctuation and electrodeformation analysis of giant vesicles[J]

    Gracia R S, Bezlyepkina N, Knorr R L, Lipowsky R, Dimova R. Effect of cholesterol on the rigidity of saturated and unsaturated membranes: fluctuation and electrodeformation analysis of giant vesicles[J]. Soft Matter, 2010, 6(7): 1472-1482

    2010

  30. [39]

    Electromechanical limits of polymersomes[J]

    Aranda-Espinoza H, Bermudez H, Bates F S, Discher D E. Electromechanical limits of polymersomes[J]. Physical review letters, 2001, 87(20): 208301. https://doi.org/10.1103/PhysRevLett.87.208301

    2001 doi

  31. [40]

    Molecular organization and dynamics in polymersome membranes: A lateral diffusion study[J]

    Itel F, Chami M, Najer A, L"orcher S, Wu D, Dinu I A, Meier W. Molecular organization and dynamics in polymersome membranes: A lateral diffusion study[J]. Macromolecules, 2014, 47(21): 7588-

    2014

  32. [41]

    Influence of cholesterol on phospholipid bilayer structure and dynamics[J]

    Boughter C T, Monje-Galvan V, Im W, Klauda J B. Influence of cholesterol on phospholipid bilayer structure and dynamics[J]. The Journal of Physical Chemistry B, 2016, 120(45): 11761-11772. https://doi.org/10.1021/acs.jpcb.6b08574

    2016 doi

  33. [42]

    Cholesterol effects on the phos- pholipid condensation and packing in the bilayer: a molecu- lar simulation study[J]

    R’og T, Pasenkiewicz-Gierula M. Cholesterol effects on the phos- pholipid condensation and packing in the bilayer: a molecu- lar simulation study[J]. FEBS letters, 2001, 502(1-2): 68-71. https://doi.org/10.1016/S0014-5793(01)02668-0

    2001 doi

  34. [43]

    Characterization of cholesterol-sphingomyelin domains and their dynamics in bi- layer membranes[J]

    Samsonov A V, Mihalyov I, Cohen F S. Characterization of cholesterol-sphingomyelin domains and their dynamics in bi- layer membranes[J]. Biophysical journal, 2001, 81(3): 1486-1500. https://doi.org/10.1016/S0006-3495(01)75803-1

    2001 doi

  35. [44]

    Block copolymer vesicles—using concepts from polymer chemistry to mimic biomembranes[J]

    Kita-Tokarczyk K, Grumelard J, Haefele T, Meier W. Block copolymer vesicles—using concepts from polymer chemistry to mimic biomembranes[J]. Polymer, 2005, 46(11): 3540-3563. https://doi.org/10.1016/j.polymer.2005.02.083

    2005 doi

  36. [45]

    Thinking the future of membranes: Perspec- tives for advanced and new membrane materials and manufacturing processes[J]

    Nunes S P, Culfaz-Emecen P Z, Ramon G Z, Visser T, Koops G H, Jin W, Ulbricht M. Thinking the future of membranes: Perspec- tives for advanced and new membrane materials and manufacturing processes[J]. Journal of Membrane Science, 2020, 598: 117761. https://doi.org/10.1016/j.m...

    2020

  37. [46]

    Self-supporting, dou- ble stimuli-responsive porous membranes from polystyrene-block- poly (N, N-dimethylaminoethyl methacrylate) diblock copoly- mers[J]

    Schacher F, Ulbricht M, M"uller A H E. Self-supporting, dou- ble stimuli-responsive porous membranes from polystyrene-block- poly (N, N-dimethylaminoethyl methacrylate) diblock copoly- mers[J]. Advanced Functional Materials, 2009, 19(7): 1040-1045. https://doi.org/10.1002/adfm...

    2009 doi

  38. [47]

    Hybrid nanocapsules: Interactions of ABA block copolymers with liposomes[J]

    Ruysschaert T, Sonnen A F P, Haefele T, Meier W, Winterhalter M, Fournier D. Hybrid nanocapsules: Interactions of ABA block copolymers with liposomes[J]. Journal of the American Chemical Society, 2005, 127(17): 6242-6247. https://doi.org/10.1021/nn3023602

    2005 doi

  39. [48]

    Controlling the localization of polymer-functionalized nanoparticles in mixed lipid/polymer membranes[J]

    Olubummo A, Schulz M, Lechner B-D, Scholtysek P, Ba- cia K, Blume A, Kressler J, Binder W H. Controlling the localization of polymer-functionalized nanoparticles in mixed lipid/polymer membranes[J]. ACS nano, 2012, 6(10): 8713-8727. https://doi.org/10.1021/ja043600x

    2012 doi

  40. [49]

    Chimeric lipid/block copolymer nanovesicles:Physico-chemicalandbio-compatibilityevaluation[J]

    Pippa N, Stellas D, Skandalis A, Pispas S, Demetzos C, Libera M, Marcinkowski A, Trzebicka B. Chimeric lipid/block copolymer nanovesicles:Physico-chemicalandbio-compatibilityevaluation[J]. European Journal of Pharmaceutics and Biopharmaceutics, 2016, 107: 295-309. https://doi....

    2016 doi

  41. [50]

    Bilayer-domain forma- tion of thermoresponsive amphiphilic block copolymers in hybrid liposomes for synthetic molecular channels[J]

    Ozawa N, Kosaka S, Fujii S, Nishimura T. Bilayer-domain forma- tion of thermoresponsive amphiphilic block copolymers in hybrid liposomes for synthetic molecular channels[J]. Polymer Chemistry, 2023, 14(18): 2198-2204. https://doi.org/10.1039/D3PY00223C

    2023 doi

  42. [51]

    Substrate-sorting nanoreactors based on permeable peptide polymer vesicles and hybrid liposomes with synthetic macromolecular channels[J]

    Nishimura T, Hirose S, Sasaki Y, Akiyoshi K. Substrate-sorting nanoreactors based on permeable peptide polymer vesicles and hybrid liposomes with synthetic macromolecular channels[J]. Jour- nal of the American Chemical Society, 2019, 142(1): 154-161. https://doi.org/10.1021/ja...

    2019 doi

  43. [52]

    Evaluation of hybrid vesicles in an intestinal cell model based on structured paper chips[J]

    De Dios Andres P, Westensee I N, Brodszkij E, Ramos- Docampo M A, Gal N, Stadler B. Evaluation of hybrid vesicles in an intestinal cell model based on structured paper chips[J]. Biomacromolecules, 2021, 22(9): 3860-3872. https://doi.org/10.1021/acs.biomac.1c00686

    2021 doi

  44. [53]

    Advanced functional polymer mem- branes[J]

    Ulbricht M. Advanced functional polymer mem- branes[J]. Polymer, 2006, 47(7): 2217-2262. https://doi.org/10.1016/j.polymer.2006.01.084

    2006 doi

  45. [54]

    Mixing block copolymers with phospholipids at the nanoscale: from hybrid polymer/lipid wormlike micelles to vesicles pre- senting lipid nanodomains[J]

    Dao T P Tuyen, Brûlet A, Fernandes F, Er-Rafik M, Ferji K, Schweins R, Chapel J-P, Fedorov A, Schmutz M, Prieto M, others. Mixing block copolymers with phospholipids at the nanoscale: from hybrid polymer/lipid wormlike micelles to vesicles pre- senting lipid nanodomains[J]. La...

    2017 doi

  46. [55]

    On the assembly of zwitterionic block copolymers with phos- pholipids[J]

    Spanjers J M, Brodszkij E, Gal N, Pedersen J S, St"adler B. On the assembly of zwitterionic block copolymers with phos- pholipids[J]. European Polymer Journal, 2022, 180: 111612. https://doi.org/10.1016/j.eurpolymj.2022.111612

    2022

  47. [56]

    Functionalized poly- mersomesforbiomedicalapplications[J].PolymerChemistry,2013, 4(11): 3160-3176

    Pawar P V, Gohil S V, Jain J P, Kumar N. Functionalized poly- mersomesforbiomedicalapplications[J].PolymerChemistry,2013, 4(11): 3160-3176. https://doi.org/10.1039/C3PY00023K

    2013 doi

  48. [57]

    Multicompartmen- talized polymeric systems: towards biomimetic cellular structure and function[J]

    Marguet M, Bonduelle C, Lecommandoux S. Multicompartmen- talized polymeric systems: towards biomimetic cellular structure and function[J]. Chemical Society Reviews, 2013, 42(2): 512-529. https://doi.org/10.1039/C2CS35312A

    2013 doi

  49. [58]

    Protein–polymer nanoreactors for medical applications[J]

    Palivan C G, Fischer-Onaca O, Delcea M, Itel F, Meier W. Protein–polymer nanoreactors for medical applications[J]. Chemical Society Reviews, 2012, 41(7): 2800-2823. https://doi.org/10.1039/C1CS15240H

    2012 doi

  50. [59]

    Novel aspects of encapsulation and delivery using polymersomes[J]

    Messager L’ea, Gaitzsch J, Chierico L, Battaglia G. Novel aspects of encapsulation and delivery using polymersomes[J]. Current opinion in pharmacology, 2014, 18: 104-111. https://doi.org/10.1016/j.coph.2014.09.017

    2014 doi

  51. [60]

    Polymer nanocompartments in broad-spectrum medical applications[J]

    Najer A, Wu D, Vasquez D, Palivan C G, Meier W. Polymer nanocompartments in broad-spectrum medical applications[J]. Nanomedicine, 2013, 8(3): 425-447. https://doi.org/10.2217/nnm.13.11

    2013 doi

  52. [61]

    PEO-b-PCL–DPPC chimeric nanocarriers: Self-assembly aspects in aqueous and bio- logical media and drug incorporation[J]

    Pippa N, Kaditi E, Pispas S, Demetzos C. PEO-b-PCL–DPPC chimeric nanocarriers: Self-assembly aspects in aqueous and bio- logical media and drug incorporation[J]. Soft Matter, 2013, 9(15): 4073-4082. https://doi.org/10.1039/C3SM27447K. Page 14 of 14

    2013 doi

  53. [2016]

    doi: https://doi.org/10.1007/978-981-10-2502-0

    doi

  54. [5501]

    https://doi.org/10.1039/D3SM00804E

    doi

  55. [7596]

    https://doi.org/10.1021/ma5015403

    doi

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.