# Exploring Peptide–Solvent Interactions: A Computational Study

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Preparation of XAO and 9-Mer Polypeptides

#### 2.2. MD Simulations

#### 2.3. QM/MM Energy Function

#### 2.4. Calculating Theoretical Scattering Profiles and Effective R${}_{\mathsf{gyr}}$ Values

## 3. Results and Discussion

#### 3.1. Dihedral Angle Distribution

#### 3.2. End-to-End Distance, R${}_{\mathsf{gyr}}$

## 4. Conclusions

## Supplementary Materials

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

QM/MM | quantum mechanics/molecular mechanics |

MD | molecular dynamics |

XAO | X${}_{\mathsf{2}}$A${}_{\mathsf{7}}$O${}_{\mathsf{2}}$, X = diaminobutyric acid, A = alanine, and O = ornithine |

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**Figure 1.**The 11-residue peptide X${}_{\mathsf{2}}$A${}_{\mathsf{7}}$O${}_{\mathsf{2}}$ peptide (XAO), where X, A, and O denote diaminobutyric acid, alanine, and ornithine, respectively, contains seven consecutive alanine residues.

**Figure 2.**The six peptide conformers, C7${}_{\mathsf{eq}}$ ($\mathsf{\Phi}=-{120}^{\circ}$, $\mathsf{\Psi}={50}^{\circ}$) (orange), ${\mathit{\alpha}}_{\mathsf{L}}$ ($\mathsf{\Phi}={65}^{\circ}$, $\mathsf{\Psi}={40}^{\circ}$) (blue), ${\mathit{\alpha}}_{\mathsf{R}}$ ($\mathsf{\Phi}=-{65}^{\circ}$, $\mathsf{\Psi}=-{40}^{\circ}$) (red), 3${}_{\mathsf{10}}$ ($\mathsf{\Phi}=-{60}^{\circ}$, $\mathsf{\Psi}=-{30}^{\circ}$) (green), $\mathit{\beta}$ ($\mathsf{\Phi}=-{120}^{\circ}$, $\mathsf{\Psi}={130}^{\circ}$) (cyan), and P${}_{\mathsf{II}}$ ($\mathsf{\Phi}=-{60}^{\circ}$, $\mathsf{\Psi}={140}^{\circ}$) (gray), that span the Ramachandan space, are depicted schematically for XAO (

**left**) and the 9-mer (

**right**). For these illustrations, all $\mathsf{\Phi}$-$\mathsf{\Psi}$ dihedral angles of the peptide backbones are set to the ideal geometry for each of these six conformers. The peptide backbones are drawn with a ribbon representation to highlight geometric differences. Hydrogen atoms are omitted for clarity.

**Figure 3.**The distribution of $\mathsf{\Phi}$-$\mathsf{\Psi}$ angles sampled by (

**A**) XAO in water (production data collected from 900 ns MD); (

**B**) XAO in vacuo (production data collected from 200 ns MD); and (

**C**) the 9-mer in water (production data collected from 200 ns data) are shown.

**Figure 4.**(

**A**) the QM/MM energy of XAO and ten closest water molecules is plotted for snapshots taken from production data collected over 200 ns of MD. The geometries of XAO and 10 closest water molecules corresponding to high energy, average energy, and low energy states are shown; the lowest-energy conformation (t = 71.4 ns) shows maximum peptide extension; (

**B**) the QM/MM energy of XAO and 40 closest water molecules is plotted for snapshots from production data collected over 200 ns of MD; two representative low-energy geometries are shown.

**Figure 5.**The end-to-end distances of the XAO peptide (blue) and 9-mer (green) are shown for 200 ns MD in aqueous solution. The average XAO end-to-end distance is 22.6 Å (calculated from 900 ns simulation period); the average 9-mer end-to-end distance is 12.4 Å.

**Figure 6.**(

**A**) the R${}_{\mathsf{gyr}}$ [Å] of XAO calculated over the 900 ns of classical MD; (

**B**) the calculated QM/MM energy [kcal/mol] of the XAO peptide is correlated with the R${}_{\mathsf{gyr}}$ [Å]; (

**C**) intensity (arbitrary units) versus scattering (Å${}^{-1}$) is plotted for 100 randomly chosen structures from MD simulations of XAO. Inset shows the Guinier plot of ln(intensity) vs. scattering${}^{2}$.

**Table 1.**The relative populations of XAO geometries from simulations in water are listed for six $\mathsf{\Phi}$-$\mathsf{\Psi}$ geometry basins in Ramachandran plot; populations obtained from simulations in vacuo are listed below in parentheses. Free energy differences [kcal/mol], obtained from a population analysis $F=-{k}_{B}Tln({N}_{b}/{N}_{ref})$, between the six sampled geometries are listed. The last column lists average QM/MM energies [kcal/mol] calculated from snapshots of XAO and the ten nearest water molecules, extracted from the 900 ns MD simulation. The $\mathsf{\Phi}$-$\mathsf{\Psi}$ dihedral angles (given in degrees) correspond to the C${}_{i-1}$–N${}_{i}$–C${}_{\alpha i}$–C${}_{i}$ and N${}_{i}$–C${}_{\alpha i}$–C${}_{i}$–N${}_{i+1}$ atoms, respectively, of adjacent peptide residues.

Geometry | $\mathsf{\Phi}$ | $\mathsf{\Psi}$ | Relative Population (In Vacuo) | Free Energy Difference [kcal/mol] | Average QM/MM Energy [kcal/mol] |
---|---|---|---|---|---|

ine | |||||

P${}_{\mathsf{II}}$ | −180 < $\mathsf{\Phi}$ < 0 | 135 ≤ $\mathsf{\Psi}$ ≤ 180 | 0.534 | 0.00 | −111,479 |

(0.420) | |||||

ine | |||||

$\mathit{\beta}$ | −180 < $\mathsf{\Phi}$ < 0 | 50 ≤ $\mathsf{\Psi}$ < 135 | 0.202 | 0.58 | −111,479 |

(0.147) | |||||

ine | |||||

${\mathit{\alpha}}_{\mathsf{R}}$ | −180 < $\mathsf{\Phi}$ < 0 | −180 ≤$\mathsf{\Psi}$ < −25 | 0.126 | 0.86 | −111,475 |

(0.150) | |||||

ine | |||||

3${}_{\mathsf{10}}$ | −180 < $\mathsf{\Phi}$ < 0 | −25 ≤$\mathsf{\Psi}$ < 0 | 0.062 | 1.28 | −111,475 |

(0.035) | |||||

ine | |||||

${\mathit{\alpha}}_{\mathsf{L}}$ | 0≤ $\mathsf{\Phi}$ < −180 | −180 ≤$\mathsf{\Psi}$≤ 180 | 0.041 | 1.53 | −111,478 |

(0.220) | |||||

ine | |||||

C7${}_{\mathsf{eq}}$ | −180 < $\mathsf{\Phi}$ < 0 | 0 ≤ $\mathsf{\Psi}$ < 50 | 0.035 | 1.62 | −111,478 |

(0.027) |

**Table 2.**The relative populations of 9-mer geometries are listed for six $\mathsf{\Phi}$-$\mathsf{\Psi}$ geometry basins in Ramachandran plot; free energy differences [kcal/mol], obtained from a population analysis $F=-{k}_{B}Tln({N}_{i}/{N}_{ref})$, between the six sampled geometries are listed. The last column lists average QM/MM energies [kcal/mol] calculated from snapshots of the 9-mer and the ten nearest water molecules, extracted from the 200 ns MD simulation. The $\mathsf{\Phi}$-$\mathsf{\Psi}$ dihedral angles (given in degrees) correspond to the C${}_{i-1}$–N${}_{i}$–C${}_{\alpha i}$–C${}_{i}$ and N${}_{i}$–C${}_{\alpha i}$–C${}_{i}$–N${}_{i+1}$ atoms, respectively, of adjacent peptide residues.

Geometry | $\mathsf{\Phi}$ | $\mathsf{\Psi}$ | Relative Population | Free Energy Difference [kcal/mol] | Average QM/MM Energy [kcal/mol] |
---|---|---|---|---|---|

ine | |||||

P${}_{\mathsf{II}}$ | −180 < $\mathsf{\Phi}$ < 0 | 135 ≤ $\mathsf{\Psi}$ ≤ 180 | 0.440 | 0 | −111,092 |

ine | |||||

3${}_{10}$ | −180 < $\mathsf{\Phi}$ < 0 | −25 ≤$\mathsf{\Psi}$ < 0 | 0.167 | 0.58 | −111,101 |

ine | |||||

$\mathit{\beta}$ | −180 < $\mathsf{\Phi}$ < 0 | 50 ≤ $\mathsf{\Psi}$ < 135 | 0.147 | 0.65 | −111,092 |

ine | |||||

${\mathit{\alpha}}_{\mathsf{R}}$ | −180 < $\mathsf{\Phi}$ < 0 | −180 ≤$\mathsf{\Psi}$ < −25 | 0.105 | 0.86 | −111,084 |

ine | |||||

C7${}_{\mathsf{eq}}$ | −180 < $\mathsf{\Phi}$ < 0 | 0 ≤ $\mathsf{\Psi}$ < 50 | 0.099 | 0.89 | −111,096 |

ine | |||||

${\mathit{\alpha}}_{\mathsf{L}}$ | 0≤ $\mathsf{\Phi}$ < −180 | −180 ≤$\mathsf{\Psi}$≤ 180 | 0.042 | 1.41 | −111,078 |

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Elghobashi-Meinhardt, N.
Exploring Peptide–Solvent Interactions: A Computational Study. *Molecules* **2018**, *23*, 2355.
https://doi.org/10.3390/molecules23092355

**AMA Style**

Elghobashi-Meinhardt N.
Exploring Peptide–Solvent Interactions: A Computational Study. *Molecules*. 2018; 23(9):2355.
https://doi.org/10.3390/molecules23092355

**Chicago/Turabian Style**

Elghobashi-Meinhardt, Nadia.
2018. "Exploring Peptide–Solvent Interactions: A Computational Study" *Molecules* 23, no. 9: 2355.
https://doi.org/10.3390/molecules23092355