# The Roles of Electrostatic Interactions in Capsid Assembly Mechanisms of Giant Viruses

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## Abstract

**:**

## 1. Introduction

## 2. Results and Discussion

#### 2.1. Electrostatic Potential for the Capsomers

#### 2.1.1. Single Capsomer

#### 2.1.2. Interaction between Capsomers

#### 2.1.3. Salt Bridges Contribute to the Electrostatic Interaction between Capsomers

#### 2.2. Electrostatic Binding Force between Capsomers

#### 2.3. Binding Energy Calculation Results from Molecular Mechanics with Poisson–Boltzmann and Surface Area Solvation (MM/PBSA) Analyses

#### 2.4. T-Number and Total Contribution of Each Mode in the Virion of Giant Viruses

^{2}+ h∙k + k

^{2}. For example, the T-number of PBCV-1 is 169 (h = 7, k = 8; T = 7

^{2}+ 7 × 8 + 8

^{2}) (Figure 1c). It is noteworthy that all giant viruses have their h number equal to 7 and have the same size pentasymmetrons with 31 capsomers: one pentameric capsomer located at the 5-fold axis and 30 (5 × 6) pseudohexameric capsomers [8]. Each asymmetric unit (triangular area encircled by white dotted lines in Figure 1c) inside the pentasymmetron has six capsomers in three layers radiating from the 5-fold axis, one in the first layer (closest to the 5-fold axis), two in the second layer, and three in the third layer. Therefore, the h number includes three steps in the pentasymmetron, three steps in the trisymmetron, and one more step to align with the pentameric capsomers (Figure 1c). The size difference among giant viruses only appears on their various sizes of trisymmetron [8]. The size of trisymmetron is linked to the k in the T-number. If the equilateral trisymmetron has n capsomers on its edge, because of the same three layers in a pentasymmetron asymmetric unit, n will be k plus 3 (Figure 1c and Figure 3).

## 3. Methods

#### 3.1. Capsid Structure Preparation

#### 3.2. DelPhi Calculations of Electrostatic Potential

#### 3.3. Capsomer Manipulations to Simulate Capsid Assembly

#### 3.4. Electrostatic Binding Forces between Capsomers

#### 3.5. Molecular Dynamic (MD) Simulations for Capsomer Pairs

#### 3.6. Binding Energy Calculations Using MM/PBSA

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgement

## Conflicts of Interest

## References

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**Figure 1.**Paramecium bursaria Chlorella virus-1 (PBCV-1) capsomer structures and arrangements. (

**a**) A ribbon diagram of the PBCV-1 major capsid protein (MCP) Vp54 (PDB ID 5TIP). The two jelly-rolls are colored in yellow (J1) and cyan (J2), respectively; (

**b**) a ribbon diagram of the PBCV-1 capsomer displaying a pseudo-hexagonal shape. Individual double jelly-roll MCPs are color-coded with pink, jade green, and azure; (

**c**) Isosurface rendering of PBCV-1 cryo-EM map (EMD 5378). Capsomers are colored based on their orientation in red, blue, green, cyan, and orange. The boundaries of one trisymmetron and one pentasymmetron are outlined in white. One asymmetric unit within one pentasymmetron is outlined in dashed white lines. The yellow dots present the steps for calculating the triangulation number (T number) with the h and k numbers labeled in yellow. One set of icosahedral symmetry symbols are labeled in red; (

**d**) The magnified icosahedral 2-fold surface areas (outlined in yellow dashed line in (

**c**)) and three selected capsomers (A, B, and C). To show their orientations, these three capsomers are labeled by yellow triangles where the vertices of the triangle point to the three higher jelly-roll surface loops; (

**e**) A schematic diagram of showing the three selected capsomers in (

**d**) for highlighting their orientations, charge distributions, and binding modes. The outlines of the capsomer are colored as the same color in (

**b**) with J1 and J2 labeled. Three binding modes are labeled by 1, 2, and 3, close to the corresponding interfaces. Two side views of PBCV-1 capsomer electrostatic surfaces are presented on the sides of capsomer C pointing to their corresponding surface. The electrostatic surfaces are rendered by Chimera with a color scale from −1.0 to 1.0 kT/Å. Negatively and positively charged areas are colored in red and blue, respectively. (

**f**) The electrostatic potential field lines between three selected PBCV-1 capsomers rendered by Visual Molecular Dynamics (VMD). Negatively and positively charged capsomer surface areas are colored with a scale from −1.0 to 1.0 kT/Å.

**Figure 2.**Binding forces of modes 1, 2, and 3 scanned by all four operations. The magnitudes of binding forces are presented as vertical histogram bars for each binding mode (panels in each column). Binding forces of each mode are scanned by four different operations (panels in each row). For example, the panels in the first column are binding forces of mode 1 scanned by (

**a1**) shifting away 5 to 40 Å, (

**b1**) shifting perpendicular 5 to 60 Å up and down, (

**c1**) spinning −60° to 60°, and (

**d1**) rotating around −30° to 30°. Similarly, the panels in the second column (

**a2**,

**b2**,

**c2**,

**d2**) and that in the third column (

**a3**,

**b3**,

**c3**,

**d3**) are binding forces of mode2 and mode3, respectively. Positive forces indicate the attractive force while the negative forces are the repulsive forces. Black arrows on each panel point to the native position.

**Figure 3.**Schematic demonstration of the trisymmetron for calculating the population of all 3 binding modes. Each black dot represents one capsomer. Different types of lines represent different binding mode between two capsomers (dots). Within the trisymmetron, n (for PBCV-1, n = 11) rows of capsomers were connected by binding mode 1 (solid line). At the bottom edge, extra row of dots (capsomers) from neighboring trisymmetrons are shown connected by a dashed line and dotted lines, representing binding modes 2 and 3, respectively. The capsomer numbers along one edge are labeled by their number of n.

**Figure 4.**Simulating capsomer assembly operations. In each of the four operations, the capsomer on the left (shown in electrostatic colored surface) is fixed, whereas the capsomer on the right (in grey) is manipulated by (

**a**) shifting away 5 to 40 Å, (

**b**) shifting perpendicular 5 to 60 Å up and down, (

**c**) spinning −60° to 60°, and (

**d**) rotating around −30° to 30°. The binding forces are presented by yellow arrows. The tail of each arrow is located at the mass center of the manipulated capsomer when it was displaced in the corresponding locations. In order to differentiate the binding force from different spinning degree in (

**c**), the force arrows are translated by 40 Å onto a circle where the spinning degrees are represented by the angle theta (θ). Additional diagrams for the direction of binding force are shown in Figure S3.

Binding Mode | Polar Solvation Energy (kcal/mol) | Non-Polar Solvation Energy (kcal/mol) | Van der Waals Energy (kcal/mol) | Coulombic Energy (kcal/mol) | Total Binding Energy (kcal/mol) | |||||
---|---|---|---|---|---|---|---|---|---|---|

Mean | SD ^{[a]} | Mean | SD | Mean | SD | Mean | SD | Mean | SD | |

1 | 99.41 | 19.46 | −14.58 | 0.73 | −80.80 | 6.50 | −64.89 | 25.22 | −60.85 | 8.05 |

2 | 208.20 | 28.27 | −19.17 | 1.05 | −119.74 | 10.25 | −167.72 | 32.72 | −98.43 | 9.83 |

3 | 8.42 | 16.23 | −9.67 | 0.71 | −46.25 | 5.59 | 23.69 | 16.67 | −23.81 | 5.65 |

^{[a]}Standard deviation.

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**MDPI and ACS Style**

Xian, Y.; Karki, C.B.; Silva, S.M.; Li, L.; Xiao, C.
The Roles of Electrostatic Interactions in Capsid Assembly Mechanisms of Giant Viruses. *Int. J. Mol. Sci.* **2019**, *20*, 1876.
https://doi.org/10.3390/ijms20081876

**AMA Style**

Xian Y, Karki CB, Silva SM, Li L, Xiao C.
The Roles of Electrostatic Interactions in Capsid Assembly Mechanisms of Giant Viruses. *International Journal of Molecular Sciences*. 2019; 20(8):1876.
https://doi.org/10.3390/ijms20081876

**Chicago/Turabian Style**

Xian, Yuejiao, Chitra B. Karki, Sebastian Miki Silva, Lin Li, and Chuan Xiao.
2019. "The Roles of Electrostatic Interactions in Capsid Assembly Mechanisms of Giant Viruses" *International Journal of Molecular Sciences* 20, no. 8: 1876.
https://doi.org/10.3390/ijms20081876