# Protein Interaction with Dendrimer Monolayers: Energy and Surface Topology

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}O

_{2}. The struggle in designing a GOx-based system is avoiding interactions of dendrimers composing the coating layer with the amino acid chains of the enzyme, which are interactions that direct to enzyme inactivation or diminished activity.

## 2. Materials and Methods

_{22}H

_{48}N

_{10}O

_{4}(G0), C

_{62}H

_{128}N

_{26}O

_{12}(G1), C

_{110}H

_{192}N

_{26}O

_{44}(G1.5), C

_{142}H

_{288}N

_{58}O

_{28}(G2), C

_{302}H

_{512}N

_{122}O

_{60}(G3) and a series of several “zero-generation aromatic” core dendrimers (ZAC) —C

_{16}H

_{28}N

_{2}O

_{4}, C

_{20}H

_{36}N

_{2}O

_{4}, C

_{22}H

_{44}N

_{2}O

_{4}, C

_{24}H

_{45}N

_{3}O

_{6}, C

_{28}H

_{52}N

_{2}O

_{4}. A total of 10 protein-PAMAM complexes were computed. Also free, denaturated 1ATU, and 3D 1ATU were taken into account and compared with the resulting denaturated proteins string. Systems were optimized for normal intravascular conditions (NaCl 0.15 M, temperature 310.15 K, a dielectric solvent constant of 80) with respect to published data. The water effect was taken into account by protonating the system at physiological intravascular conditions. The force field used for all computations was AMBER10 [12].

_{total}= E

_{bond}+ E

_{angle}+ E

_{torsion}+ E

_{electro}+ E

_{vd}, where E

_{total}is the molecule potential energy, E

_{bond}- bond stretch energy, E

_{angle –}angle bend energy, E

_{torsion}- torsion energy, E

_{electro}- electrostatic energy, E

_{vd}- Van der Waals energy, all expressed in kcal/mol. Right equation terms for all protein strings were computed. A polynomial fourth-degree fitting function was used to generate a manifold. Two types of manifold surfaces were generated: a surface base on the representation of the fitting function and a second one based on the integration of the fitting fourth-degree polynomial function. As an example of PAMAM G0 protein string, the expressions used were, respectively:

^{4}− 3790.600 x

^{3}+ 18236 x

^{2}− 35433 x + 23590,

^{4}− 3790.600x

^{3}+ 18236x

^{2}− 35433x + 23590)dx

## 3. Results

_{16}H

_{28}N

_{2}O

_{4}; C

_{20}; C

_{20}H

_{36}N

_{2}o

_{4}; C

_{22}H

_{40}N

_{2}O

_{4}; C

_{24}H

_{45}N

_{3}O

_{6}and C

_{28}H

_{52}N

_{2}O

_{4}, respectively (see Supplementary Materials).

_{22}H

_{4}N

_{2}O

_{4}, respectively (Figure 11).

_{28}decreasing to C

_{16}, and finally by PAMAM G3, G2, G1.5, G1, G0), showing that the G0 protein string “carries” less structural information in comparison with the rest of the series.

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**1ATU system and G1.5 PAMAM. When arbitrary valences are allowed, a protein, i.e., “the string’’ is formed as the expression of forces of the PAMAM layer applied to the protein. (

**a**) Protein 1ATU in its 3D crystallographic determine conformation. (

**b**) Protein string fixed on the G1.5 PAMAM layer.

**Figure 2.**Ramachandran plots for 1ATU free, 1ATUG0, 1ATUG1.5, and 1ATU. Vertical psi (degrees), horizontal phi (degrees). Red core, yellow allowed region, and points outside the contours represent the outlier (see Supplementary Material-S1).

**Figure 3.**Cartesian coordinates of 1ATU after interaction with PAMAM G0 showing variations for each string: X-axis (no. atoms: 1 ATU~3000 atoms); Y-axis (coordinates, in Å); (see Supplementary Materials-S2).

**Figure 4.**1ATU protein strings after interaction with PAMAM dendrimers are represented alone (without the dendrimer monolayer) and named according to their interaction with the type of dendrimer monolayer (from left to right): 1ATUfree, 1ATU G0, 1ATU G1.5, 1ATU 3D, with the dendrimer layer (for the all protein strings, see Supplementary Materials-S2).

**Figure 5.**Surface area and volume of 1ATU protein string in the presence of different dendrimers layers. Ox axis, according with the entries on Table 1: 1—PAMAM generation 0, 2—PAMAM generation 1, 3—PAMAM generation 1.5, 4—PAMAM generation 2, 5—PAMAM generation 3, 6—C

_{16}H

_{28}N

_{2}O

_{4}, 7—C

_{20}H

_{36}N

_{2}O

_{4}, 8—C

_{22}H

_{40}N

_{2}O

_{4}, 9—C

_{24}H

_{45}N

_{3}O

_{6}, 10—C

_{28}H

_{52}N

_{2}O

_{4}, 11—1ATU Free, 12—1ATU 3D. Oy axis: Surface area (Å

^{2}) and Volume (Å

^{3}).

**Figure 6.**Structure of 1ATU (from top to bottom): “native” (top); “free” (with no protein interaction—middle) and G1.5 (with G1.5 PMAM interaction—bottom). Aggregation surface was calculated; all of the Aa domains that may contribute to an aggregation process are represented in red; Aa with the highest score, the chance to produce an aggregation is represented in green. For each protein string, a distinct Aa set is identified accordingly to the string’s geometry.

**Figure 7.**Aggregation score of the native protein, 1 ATU free string, most significant Aa contribution is highlighted (see Supplementary Materials-S3).

**Figure 9.**Manifolds obtained using 1ATU string coordinates equation: (from up to bottom) 1ATU string free, 1ATU G0 (top); 1ATU G1, 1ATU 3D (bottom) (see Supplementary Materials-S5).

**Figure 10.**Manifolds obtained using 1ATU string coordinates equation: (from up to bottom) 1ATU string free, 1ATU G0 (top); 1ATU G1, 1ATU 3D (bottom); see Supplementary Materials-S6.

**Figure 12.**Topological descriptors of protein strings (see Supplementary Materials-S7).

**Figure 13.**Solvation energy of protein strings. In red, the solvation energy for 3D 1ATU crystallographic structure (kcal/mol). Free, computationally denaturated 1ATU energy is represented in orange as a combo graph due to higher dimensionality of data (−26,370,109 kcal/mol).

**Figure 14.**Energy surfaces obtained by the integration of manifold coordinates equations. (

**a**) PAMAM G1.5; (

**b**) 1ATU3D; (

**c**) 1ATU free string.

No. Entry | Protein String | Conformational Energy | Globularity |
---|---|---|---|

1 | PAMAM G 0 | −288.680 | 0.285 |

2 | PAMAM G 1 | −3116.593 | 0.235 |

3 | PAMAM G 1.5 | −2636.470 | 0.244 |

4 | PAMAM G 2 | −2870.539 | 0.239 |

5 | PAMAM G 3 | −2669.584 | 0.233 |

6 | C_{16}H_{28}N_{2}O_{4} | −2714.324 | 0.241 |

7 | C_{20}H_{36}N_{2}O_{4} | −2922.567 | 0.232 |

8 | C_{22}H_{40}N_{2}O_{4} | −2732.875 | 0.229 |

9 | C_{24}H_{45}N_{3}O_{6} | −2854.782 | 0.235 |

10 | C_{28}H_{52}N_{2}O_{4} | −2771.306 | 0.237 |

11 | 1 ATU free | −2338.731 | 0.613 |

12 | 1ATU 3D | −5607.552 | 0.431 |

Protein String | X Coordinate Equation | Y Coordinate Equation | Z Coordinate Equation |
---|---|---|---|

PAMAM G0 | Y = 2.372ln(x) + 71.411 | Y = 0.0107ln(x) + 28.956 | Y = 2.814ln(x) + 29.356 |

PAMAM G1 | Y = −13.610ln(x) + 205.030 | Y = 8.496ln(x) − 30.464 | Y = 4.957ln(x) + 109.780 |

PAMAM G 1.5 | Y = −13.610ln(x) + 156.030 | Y = 8.496ln(x) − 29.864 | Y = 4.957ln(x) − 1.220 |

PAMAM G 2 | Y = –13.610ln(x) + 237.030 | Y = 8.496ln(x) – 29.330 | Y = 4.957ln(x) + 107.780 |

PAMAM G3 | Y = −13.610ln(x) + 154.030 | Y = 8.496ln(x) − 30.813 | Y = 4.957ln(x) + 100.780 |

ZAC C16 | Y = −13.610ln(x) + 202.030 | Y = 8.496ln(x) − 29.707 | Y = 4.957ln(x) + 121.780 |

ZAC C20 | Y = −13.600ln(x) + 140.920 | Y = 8.379ln(x) − 29.030 | Y = 4.968ln(x) + 104.720 |

ZAC 22 | Y = −13.380ln(x) + 178.200 | Y = 8.26ln(x) − 27.706 | Y = 4.789ln(x) + 18.080 |

ZAC 24 | Y = −13.6l0n(x) + 161.970 | Y = 8.469ln(x) − 29.490 | Y = 4.957ln(x) + 64.778 |

ZAC 28 | Y = −13.610ln(x) + 203.030 | Y = 8.496ln(x) − 29.666 | Y = 4.957ln(x) + 114.78 |

1ATU free | Y = 30.216ln(x) − 240.550 | Y = 32.874ln(x) − 325.160 | Y = 49.357ln(x) − 326.08 |

1ATU 3D | Y = 2.9252ln(x) − 49.617 | Y = −0.773ln(x) − 89.669 | Y = −5.266ln(x) + 56.193 |

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**MDPI and ACS Style**

Lungu, C.N.; Füstös, M.E.; Grudziński, I.P.; Olteanu, G.; Putz, M.V.
Protein Interaction with Dendrimer Monolayers: Energy and Surface Topology. *Symmetry* **2020**, *12*, 641.
https://doi.org/10.3390/sym12040641

**AMA Style**

Lungu CN, Füstös ME, Grudziński IP, Olteanu G, Putz MV.
Protein Interaction with Dendrimer Monolayers: Energy and Surface Topology. *Symmetry*. 2020; 12(4):641.
https://doi.org/10.3390/sym12040641

**Chicago/Turabian Style**

Lungu, Claudiu N., Melinda E. Füstös, Ireneusz P. Grudziński, Gabriel Olteanu, and Mihai V. Putz.
2020. "Protein Interaction with Dendrimer Monolayers: Energy and Surface Topology" *Symmetry* 12, no. 4: 641.
https://doi.org/10.3390/sym12040641