# “Dividing and Conquering” and “Caching” in Molecular Modeling

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## Abstract

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## 1. Introduction

## 2. Challenges in Molecular Modeling

#### 2.1. Accurate Description of Molecular Interactions

#### 2.2. Inherent Low Efficiency in Sampling of Configurational Space

## 3. DC and “Caching” in Traditional Molecular Modeling

#### 3.1. Coarse Graining, a Partially Transferable “Caching” Strategy

#### 3.2. Enhanced Sampling, a Nontransferable in Resolution DC and “Caching” Strategy

## 4. Machine Learning Improves “Caching”

#### 4.1. Toward Ab Initio Accuracy of Molecular Simulation Potentials

#### 4.2. Machine Learning and Coarse Graining

#### 4.3. Machine Learning in Searching for RC/CVs and Construction of MSM

## 5. The Local Free Energy Landscape Approach

## 6. More on Connections among CG, ES and LFEL Approach

## 7. Conclusions and Prospect

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic illustration of time scale separation issue in CG. (

**A**,

**B**) show two situations with ${C}_{\alpha}$ distances between two amino acids GLU and ALA being R, but with GLU have different conformations. If ${C}_{\alpha}$ atoms were defined as CG site, then these two relative conformation with distinct interactions would be treated as the same. In (

**A**,

**B**), CG site distance in both (

**A**,

**B**) are R, but many other pairs of atoms have distinct distances as exemplified by ${r}_{1}$ and ${r}_{2}$. Such treatment would only be true if for any small amount of displacement of ${C}_{\alpha}$, side chains accomplished many rotations and thus may be accurately represented by averaging (i.e., with good time scale separation). This issue is apparently not limited to the specific definition of ${C}_{\alpha}$ being CG site, but rather general for essentially all CG development.

**Figure 2.**Schematic illustration of the LFEL approach in contrast to present mainstream FF framework. FF parameterization is the foundation for present classical computational molecular science. Training of neural network for “caching” LFEL is the foundation for LFEL approach, the source data can be either of experimental or computational origin. In FF framework, simulation (with or without ES) is driven by FF, in LFEL approach, propagation of molecular systems to minimize free energy (or maximize joint probability) is driven by compromise among many LFELs. Expensive repetitive local sampling in FF framework is substituted by differentiation w.r.t. LFELs.

**Figure 3.**Schematic illustration of essential features for enhanced sampling by metadynamics and MSM. (

**A**) The “S” shape grey line represents the unknown manifold in the configurational space (represented by the square) of a molecular system. (

**B**) Small circles connected by blue arrows represent computed (guessed) RC/CVs for the molecular system, which is utilized to conduct metadynamics simulations. (

**C**) The FEL of the molecular system along the computed/selected RC/CV in (

**B**,

**D**) “Caching” of the LFEL by bias potentials (gaussians represented by blue bell shaped lines) accumulated in the course of metadynamics simulations. (

**E**) Distribution of the molecular system to the whole configurational space at the start of a MSM simulation, small circles represent initial start points for short MSM trajectories. (

**F**) Sampling results of short MSM trajectories fall mainly near the manifold, distinct “states” are represented by different colors. (

**G**) Establishment of transition matrix by transition counts between “states” obtained from short trajectories.

**Figure 4.**Schematic illustration of difference between CG and GSFE implementation of LFEL using protein as an example. (

**A**) Target molecular systems in physical space. Due to the goal of constructing partially transferable models and/or force fields, usually many different but similar molecular systems are considered. (

**B**) Selection of local atom/particle clusters to be represented as one particle in CG model. (

**C**) Selection of CG sites. (

**D**) Comparison between atomistic (or higher resolution) simulation results and CG (lower resolution) results. (

**E**) Adjust of CG FF parameter according to comparison from (

**D**). (

**F**) Definition of solvent region for each solute unit. (

**G**) Feature extraction for each solute. (

**H**) “Caching” of LFEL with neural network by training with prepared data sets.

Key Words | Number of Publications |
---|---|

Molecular dynamics simulation | 241,748 |

Monte Carlo simulation | 189,550 |

QM-MM (quantum mechanical—molecular mechanical) simulation | 9907 |

Dissipative particle dynamics simulation | 3693 |

Langevin dynamics simulation | 3893 |

Molecular modeling | 2,072,091 |

All of the above | 2,243,182 |

Algorithm | Coarse Graining | Enhanced Sampling | LFEL Approach |
---|---|---|---|

Resolution | Lower | In | In |

Transferable? | Partial | No | Partial |

Dividing space | Physical | Configurational | Physical |

Free energy unit | Partially Specified | Specified | Arbitrary |

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Cao, X.; Tian, P.
“Dividing and Conquering” and “Caching” in Molecular Modeling. *Int. J. Mol. Sci.* **2021**, *22*, 5053.
https://doi.org/10.3390/ijms22095053

**AMA Style**

Cao X, Tian P.
“Dividing and Conquering” and “Caching” in Molecular Modeling. *International Journal of Molecular Sciences*. 2021; 22(9):5053.
https://doi.org/10.3390/ijms22095053

**Chicago/Turabian Style**

Cao, Xiaoyong, and Pu Tian.
2021. "“Dividing and Conquering” and “Caching” in Molecular Modeling" *International Journal of Molecular Sciences* 22, no. 9: 5053.
https://doi.org/10.3390/ijms22095053