# Exploring Successful Parameter Region for Coarse-Grained Simulation of Biomolecules by Bayesian Optimization and Active Learning

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Machine Learning Based Region Search of Successful Parameters

#### 2.1.1. Parameter Sampling By Bo

#### 2.1.2. Parameter Sampling by Us

#### 2.1.3. Combination of BO and US

#### 2.2. F1-Motor and CG-MD Simulation

#### 2.3. Simulation Dynamics and Sampled Parameter Space

#### 2.4. Definition of Success Rate for the Rotation of $\gamma $ Subunit in F1-Motor

## 3. Results

#### 3.1. Sampling Performances for F1-Motor Simulations Using Newtonian Dynamics

#### 3.2. Sampling Performance of F1-Motor Simulations Using Langevin Dynamics

## 4. Discussion

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Flowcharts of efficient region search of successful parameters by using Bayesian optimization (

**a**) and uncertainty sampling (

**b**). (

**c**) The combination of Bayesian optimization (BO) and uncertainty sampling (US) (BOUS) for successful parameter region search.

**Figure 2.**(

**a**) Structure of F${}_{1}$-ATPase motor and counterclockwise rotation angle $\theta $ from initial structure. The red part corresponds to $\gamma $-subunit, and the blue and green parts correspond to the $\beta $ and $\alpha $ subunits, respectively. (

**b**) Example of time-series of the rotation angle $\theta $. Black lines indicate the switched angle, referred to as the reference angle of the gamma-subunit in coarse-grained (CG)-molecular dynamics (MD) simulations. The light-green region shows the proper angle region, which is referred to as the tolerance angle. The goodness score of F1-motor rotation is defined as the ratio of the angle $\theta $s in the tolerance range.

**Figure 3.**(

**a**) Success rate distribution of F1-motor rotation based on Newtonian dynamics simulations in the parameter space. (a-1) and (a-2) show examples trajectories of F1-motor rotations in (

**a**). The success rates were 1 and 0.2, respectively. (

**b**) Regions of successful parameters changing the criteria (success threshold $\tau $) to ensure success. The yellow and blue grids are “success” and “failure” parameters in each threshold $\tau $, respectively. (

**c**–

**f**) are typical examples of successful parameter search using BOUS, US, BO, and RS. The numbers of sampled parameters were 41 for BOUS and 80 for US, BO, and random sampling (RS).

**Figure 4.**Performance of successful parameter search for Newtonian dynamics simulations using BOUS, US, BO, and RS. The success thresholds were 1.0 (

**a**), 0.9 (

**b**), 0.8 (

**c**), 0.7 (

**d**), and 0.6 (

**e**), respectively. The dashed blue line shows the total number of successful parameters for each threshold. (

**f**) shows the efficiency of the search for best parameter detection using BO and RS with $\tau =1.0$.

**Figure 5.**Results of Langevin dynamics simulations. (

**a**) Success rate distribution in the parameter space. (

**b**) Successful parameter region (yellow) with $\tau =0.8$. (

**c**–

**g**) show performances of parameter region search using BOUS, US, BO, and RS. The success thresholds are 0.9 (

**c**), 0.8 (

**d**), 0.7 (

**e**), 0.6 (

**f**), and 0.5 (

**g**), respectively. (

**h**) shows the performance of BO and RS for the best parameter search.

**Table 1.**Numbers of samplings required to detect all successful parameters with a probability of 95% or higher using BOUS, US, BO, and RS. SP indicates the number of successful parameters. The values in parentheses indicate the ratios of the number of calculations in the exhaustive search. The total number of parameter candidates was 252.

$\mathit{\tau}$ | SP | BOUS | US | BO | RS |
---|---|---|---|---|---|

1.0 | 5 (1.98%) | 31 (12.3%) | 115 (45.6%) | 67 (26.6%) | 237 (94.0%) |

0.9 | 8 (3.17%) | 36 (14.3%) | 90 (35.7%) | 100 (39.7%) | 241 (95.6%) |

0.8 | 15 (5.95%) | 45 (17.9%) | 56 (22.2%) | 114 (45.2%) | 242 (96.0%) |

0.7 | 22 (8.73%) | 60 (23.8%) | 65 (25.8%) | 129 (51.2%) | 238 (94.4%) |

0.6 | 29 (11.5%) | 80 (31.7%) | 82 (32.5%) | 146 (57.9%) | 241 (95.6%) |

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**MDPI and ACS Style**

Kanada, R.; Tokuhisa, A.; Tsuda, K.; Okuno, Y.; Terayama, K.
Exploring Successful Parameter Region for Coarse-Grained Simulation of Biomolecules by Bayesian Optimization and Active Learning. *Biomolecules* **2020**, *10*, 482.
https://doi.org/10.3390/biom10030482

**AMA Style**

Kanada R, Tokuhisa A, Tsuda K, Okuno Y, Terayama K.
Exploring Successful Parameter Region for Coarse-Grained Simulation of Biomolecules by Bayesian Optimization and Active Learning. *Biomolecules*. 2020; 10(3):482.
https://doi.org/10.3390/biom10030482

**Chicago/Turabian Style**

Kanada, Ryo, Atsushi Tokuhisa, Koji Tsuda, Yasushi Okuno, and Kei Terayama.
2020. "Exploring Successful Parameter Region for Coarse-Grained Simulation of Biomolecules by Bayesian Optimization and Active Learning" *Biomolecules* 10, no. 3: 482.
https://doi.org/10.3390/biom10030482