# Interaction of Macromolecular Chain with Phospholipid Membranes in Solutions: A Dissipative Particle Dynamics Simulation Study

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## Abstract

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## 1. Introduction

## 2. Results

#### 2.1. Pulling Forces along the Direction Parallel to Membrane Surfaces

#### 2.1.1. Conformations of Polymer Chains under Weak Adsorption

#### 2.1.2. Conformations of Polymer Chains under Strong Adsorption

#### 2.1.3. Variance of Bead Number in Membrane

#### 2.2. Pulling Forces Perpendicular to Membrane Surfaces

#### 2.2.1. Conformations of Polymer Chains under Weak Adsorption

#### 2.2.2. Conformations of Polymer Chains under Strong Adsorption

#### 2.2.3. Order Parameters of Phospholipid Molecules

## 3. Model and Method

#### 3.1. Methodology

#### 3.2. Model

#### 3.3. Simulation Parameters

**F**to each bead of the polymer chains, that is, along the x direction in the parallel pulling case and the z direction in the perpendicular pulling case. These pulling forces can be implemented to mimic the effect of an external electric field in electrolyte experiments [86,87]. It is worthwhile to relate the force unit $\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$ to the unit commonly used in the experiments. Here, we consider a 5000 bp dsDNA chain with the total mass of $M\approx 5.3\times {10}^{-21}\phantom{\rule{4pt}{0ex}}\mathrm{kg}$ and then coarse-grain this dsDNA sequence into a chain with N DPD beads, where $N=500$. Thus, one DPD bead has a mass of $m\approx 1.06\times {10}^{-23}\phantom{\rule{4pt}{0ex}}\mathrm{kg}$ since the time unit $\tau $ and length unit ${r}_{\mathrm{c}}$ are approximately $\tau =1.88\phantom{\rule{4pt}{0ex}}\mathrm{ns}$ and ${r}_{\mathrm{c}}=0.5\phantom{\rule{4pt}{0ex}}\mathrm{nm}$ [71]. This yeilds $m{r}_{\mathrm{c}}/{\tau}^{2\phantom{\rule{4pt}{0ex}}}=1.3\times {10}^{-3}\phantom{\rule{4pt}{0ex}}\mathrm{pN}$. Therefore, the total pulling forces acting on the whole polymer chain with 500 DPD beads (5000 bp dsDNA) can be expressed as $F=N{F}_{x}=500\times 2.0\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2\phantom{\rule{4pt}{0ex}}}=1.3\phantom{\rule{4pt}{0ex}}\mathrm{pN}$ when ${F}_{x}=2.0\phantom{\rule{4pt}{0ex}}\phantom{\rule{4pt}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2\phantom{\rule{4pt}{0ex}}}$. This is the same order of magnitude as the pulling force acting on a dsDNA chain in single-molecule experiments [45,88].

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Variation of gyration radius $\u2329{R}_{\mathrm{g}}\u232a$ for the polymer chains in the weak adsorption cases of ${a}_{{}_{\mathrm{PH}}}=-5$. The pulling forces applied to the polymer chain are along the x direction as (

**a**) ${F}_{x}=0.5\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, (

**b**) ${F}_{x}=1.0\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, (

**c**) ${F}_{x}=1.5\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, and (

**d**) ${F}_{x}=2.0\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$. The red dotted lines denote the values of gyration radius for the polymer with coil conformation. The black dashed lines show the variation trends.

**Figure 2.**Variation of shape factor $\u2329\delta \u232a$ for the polymer chains in the weak adsorption cases of ${a}_{{}_{\mathrm{PH}}}=-5$. The pulling force applied to the polymer chain is along the x direction as (

**a**) ${F}_{x}=0.5\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, (

**b**) ${F}_{x}=1.0\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, (

**c**) ${F}_{x}=1.5\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, and (

**d**) ${F}_{x}=2.0\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$. The black dashed lines show the variation trends. The typical conformations are also inserted.

**Figure 3.**Variation of gyration radius $\u2329{R}_{\mathrm{g}}\u232a$ for the polymer chains in the strong adsorption cases of ${a}_{{}_{\mathrm{PH}}}=-20$. The pulling force applied to the polymer chain is along the x direction as (

**a**) ${F}_{x}=0.5\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, (

**b**) ${F}_{x}=1.0\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, (

**c**) ${F}_{x}=1.5\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$ and (

**d**) ${F}_{x}=2.0\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$.

**Figure 4.**Variation of shape factor $\u2329\delta \u232a$ for the polymer chains in the strong adsorption cases of ${a}_{{}_{\mathrm{PH}}}=-20$. The pulling force applied to the polymer chain is along the x direction as (

**a**) ${F}_{x}=0.5\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, (

**b**) ${F}_{x}=1.0\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, (

**c**) ${F}_{x}=1.5\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, and (

**d**) ${F}_{x}=2.0\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$. The black dashed lines show the variation trends. The typical conformations are also inserted.

**Figure 5.**The number of hydrophilic phospholipid molecules that lie in the range $z=10\phantom{\rule{0.222222em}{0ex}}{r}_{\mathrm{c}}-15\phantom{\rule{0.222222em}{0ex}}{r}_{\mathrm{c}}$ as functions of the pulling time in the cases of (

**a**) weak adsorption ${a}_{{}_{\mathrm{PH}}}=-5$ and weak pulling force ${F}_{x}=0.5\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, (

**b**) weak adsorption ${a}_{{}_{\mathrm{PH}}}=-5$ and strong pulling force ${F}_{x}=2.0\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, (

**c**) strong adsorption ${a}_{{}_{\mathrm{PH}}}=-20$ and weak pulling force ${F}_{x}=0.5\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, and (

**d**) strong adsorption ${a}_{{}_{\mathrm{PH}}}=-20$ and strong pulling force ${F}_{x}=2.0\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$. The black dashed lines show the variation trends.

**Figure 6.**Variation of shape factor $\u2329\delta \u232a$ for the polymer chains in the weak adsorption cases of ${a}_{{}_{\mathrm{PH}}}=-5$. The pulling force applied to the polymer chain is along the z direction as (

**a**) ${F}_{z}=0.5\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, (

**b**) ${F}_{z}=1.0\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, (

**c**) ${F}_{z}=1.5\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, and (

**d**) ${F}_{z}=2.0\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$. The black dashed lines show the variation trends. The typical conformations are also inserted.

**Figure 7.**The rod–coil transition period as a function of pulling force applied along the z direction in the weak adsorption cases of ${a}_{{}_{\mathrm{PH}}}=-5$. The error bars are also shown.

**Figure 8.**Variation of shape factor $\u2329\delta \u232a$ for the polymer chains in the strong adsorption cases of ${a}_{{}_{\mathrm{PH}}}=-20$. The pulling force applied to the polymer chain is along the z direction as (

**a**) ${F}_{z}=0.5\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, (

**b**) ${F}_{z}=1.0\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, (

**c**) ${F}_{z}=1.5\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, and (

**d**) ${F}_{z}=2.0\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$. The black dashed lines show the variation trends. The typical conformations are also inserted.

**Figure 9.**The rod–coil transition period as a function of pulling force applied along the z direction in the strong adsorption cases of ${a}_{{}_{\mathrm{PH}}}=-20$. The error bars are also shown.

**Figure 10.**Order parameter profiles of phospholipid films in the cases of (

**a**) weak adsorption ${a}_{{}_{\mathrm{PH}}}=-5$ and weak pulling force ${F}_{z}=0.5\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, (

**b**) weak adsorption ${a}_{{}_{\mathrm{PH}}}=-5$ and strong pulling force ${F}_{z}=2.0\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, (

**c**) strong adsorption ${a}_{{}_{\mathrm{PH}}}=-20$ and weak pulling force ${F}_{z}=0.5\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$, and (

**d**) strong adsorption ${a}_{{}_{\mathrm{PH}}}=-20$ and strong pulling force ${F}_{z}=2.0\phantom{\rule{0.222222em}{0ex}}m{r}_{\mathrm{c}}/{\tau}^{2}$. The black curve corresponds to the moment when the polymer chain is about to separate from the phospholipid membrane, and the red curve corresponds to the moment when the phospholipid membrane changes more significantly at the end of the action.

**Figure 11.**Schematic diagram of the phospholipid membrane and linear polymer model. The phospholipid membrane consists of one hydrophilic chain (pink head beads) and two hydrophobic chains (blue tail beads). The linear polymer (red beads) interacts with the hydrophilic head chains on the upper surface of the phospholipid membrane. (

**a**) The pulling force applied to the polymer chain is along the x-direction. (

**b**) The pulling force applied to the polymer chain is along the z-direction.

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## Share and Cite

**MDPI and ACS Style**

Wang, Y.; Mou, X.; Ji, Y.; Pan, F.; Li, S.
Interaction of Macromolecular Chain with Phospholipid Membranes in Solutions: A Dissipative Particle Dynamics Simulation Study. *Molecules* **2023**, *28*, 5790.
https://doi.org/10.3390/molecules28155790

**AMA Style**

Wang Y, Mou X, Ji Y, Pan F, Li S.
Interaction of Macromolecular Chain with Phospholipid Membranes in Solutions: A Dissipative Particle Dynamics Simulation Study. *Molecules*. 2023; 28(15):5790.
https://doi.org/10.3390/molecules28155790

**Chicago/Turabian Style**

Wang, Yuane, Xuankang Mou, Yongyun Ji, Fan Pan, and Shiben Li.
2023. "Interaction of Macromolecular Chain with Phospholipid Membranes in Solutions: A Dissipative Particle Dynamics Simulation Study" *Molecules* 28, no. 15: 5790.
https://doi.org/10.3390/molecules28155790