# Analyzing Fluctuation Properties in Protein Elastic Networks with Sequence-Specific and Distance-Dependent Interactions

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## Abstract

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## 1. Introduction

## 2. Elastic Network Normal Mode Analysis

#### 2.1. Comparison to Experiments

#### 2.2. Set of PDB Structures

#### 2.3. Data Analysis

## 3. Results

## 4. Discussion

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

#### Appendix A.1. Tables of Stiffness Constants

#### Appendix A.2. Set of PDB Crystal Structures (Additional Information)

#### Appendix A.3. Analysis of NMR Protein Data and Comparison with Model Prediction

#### Appendix A.4. Set of PDB Solution NMR Protein Structures

#### Appendix A.5. Data Analysis

**Figure A1.**Fluctuation dynamics in studied proteins. B-factor profiles for two kinesin protein structures are shown; the motor domain of (

**a**) kinesin KIF1A and of (

**b**) human kinesin. Model predictions are displayed as red and blue lines; corresponding experimental data is shown in black. In the B-factor profiles, positions where model estimates are significantly poor were marked for each protein. The corresponding regions in the respective protein structure are also indicated.

**Figure A2.**Extensive analysis of predictions by ENM variants. The error in MSF prediction for a set of more than 2000 protein structures is shown (in logarithmic scale). Each data point represents the absolute deviation of predicted and experimental MSF obtained for a single residue bead in a protein elastic network, as a function of its relative degree. (

**a**) Red dots are obtained for ANM${}_{10}$ and blue dots correspond to sANM${}_{10}$ predictions. (

**b**) ANM${}_{13}$ is compared with sANM${}_{13}$. In both plots, the average absolute errors are indicated as black lines for sANMs and as green lines for ANMs.

**Figure A3.**Extensive analysis of predictions by ENM variants. The error in MSF prediction for a set of more than 2000 protein structures is shown. Each data point represents the deviation of predicted and experimental MSF obtained for a single residue bead in a protein elastic network, as a function of its relative degree. (

**a**) Red dots are obtained for ANM${}_{16}$ and blue dots correspond to sdANM predictions. (

**b**) ANM${}_{13}$ is compared with sANM${}_{13}$. In both plots, the average errors are indicated as black lines for sANMs and as green lines for ANMs.

**Figure A4.**Analysis of predictions by ENM variants for the NMR structural data set. (

**a**) The correlation coefficient averaged over all considered proteins is shown for all models (top row). The averaged absolute deviation in MSF predictions for residue beads from groups with different chemical specificity (hydrophobic, polar, and charged) is shown for all models. Also shown is the averaged absolute error for residue beads categorized into different secondary structural elements. In (

**b**,

**c**), corresponding graphs are shown. Solid lines correspond to sANM data, where values for sdANM are displayed at interaction radius abscissa position 16 Å. Dashed lines are used for ANM data.

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**Figure 1.**Fluctuation dynamics in studied proteins. (

**a**) Table of correlation coefficients for protein structures obtained from the considered model variants. For each of the two identified groups, four examples are shown. In the second group, bold numbers indicate for each protein the highest correlation of experiment and model predictions. (

**b**–

**e**) B-factor profiles for four protein structures are shown. Model predictions are displayed as red and blue lines; corresponding experimental data is shown in black. In the B-factor profiles, positions where model estimates are significantly poor were marked for each protein. The corresponding regions in the respective protein structure are also indicated.

**Figure 2.**Extensive analysis of predictions by ENM variants. The error in MSF prediction for a set of more than 2000 protein structures is shown (in logarithmic scale). Each data point represents the absolute deviation of predicted and experimental MSF obtained for a single residue bead in a protein elastic network, as a function of its relative degree. (

**a**) Red dots are obtained for ANM${}_{16}$ and blue dots correspond to sdANM predictions. (

**b**) ANM${}_{10}$ is compared with sdANM. In both plots, the average absolute errors are indicated as black lines for sdANM and as green lines for ANMs.

**Figure 3.**Extensive analysis of predictions by ENM variants. (

**a**) The correlation coefficient averaged over all considered structures is shown for all models (top row). The averaged absolute deviation in MSF predictions for residue beads from groups with different chemical specificity (hydrophobic, polar, and charged) is shown for all models. Also shown is the averaged absolute error for residue beads categorized into different secondary structural elements. In (

**b**,

**c**), corresponding graphs are shown. Solid lines correspond to sANM data, where values for sdANM are displayed at interaction radius abscissa position 16 Å. Dashed lines are used for ANM data.

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**MDPI and ACS Style**

Amyot, R.; Togashi, Y.; Flechsig, H.
Analyzing Fluctuation Properties in Protein Elastic Networks with Sequence-Specific and Distance-Dependent Interactions. *Biomolecules* **2019**, *9*, 549.
https://doi.org/10.3390/biom9100549

**AMA Style**

Amyot R, Togashi Y, Flechsig H.
Analyzing Fluctuation Properties in Protein Elastic Networks with Sequence-Specific and Distance-Dependent Interactions. *Biomolecules*. 2019; 9(10):549.
https://doi.org/10.3390/biom9100549

**Chicago/Turabian Style**

Amyot, Romain, Yuichi Togashi, and Holger Flechsig.
2019. "Analyzing Fluctuation Properties in Protein Elastic Networks with Sequence-Specific and Distance-Dependent Interactions" *Biomolecules* 9, no. 10: 549.
https://doi.org/10.3390/biom9100549