Non--Contact Atomic Force Microscopy with CO--functionalized metal tips
(referred to as HR-AFM) provides access to the internal structure of individual
molecules adsorbed on a surface with totally unprecedented resolution. Previous
works have shown that deep learning (DL) models can retrieve the chemical and
structural information encoded in a 3D stack of constant-height HR--AFM images,
leading to molecular identification. In this work, we overcome their
limitations by using a well-established description of the molecular structure
in terms of topological fingerprints, the 1024--bit Extended Connectivity
Chemical Fingerprints of radius 2 (ECFP4), that were developed for substructure
and similarity searching. ECFPs provide local structural information of the
molecule, each bit correlating with a particular substructure within the
molecule. Our DL model is able to extract this optimized structural descriptor
from the 3D HR--AFM stacks and use it, through virtual screening, to identify
molecules from their predicted ECFP4 with a retrieval accuracy on theoretical
images of 95.4\%. Furthermore, this approach, unlike previous DL models,
assigns a confidence score, the Tanimoto similarity, to each of the candidate
molecules, thus providing information on the reliability of the identification.
By construction, the number of times a certain substructure is present in the
molecule is lost during the hashing process, necessary to make them useful for
machine learning applications. We show that it is possible to complement the
fingerprint-based virtual screening with global information provided by another
DL model that predicts from the same HR--AFM stacks the chemical formula,
boosting the identification accuracy up to a 97.6\%. Finally, we perform a
limited test with experimental images, obtaining promising results towards the
application of this pipeline under real conditions

通过使用拓扑指纹描述分子结构并利用深度学习模型进行虚拟筛选，我们能够从三维原子力显微镜堆栈图像中提取最优化的结构描述符，从而实现对分子的识别，识别准确率可达 97.6％。

通过原子力显微镜图像的分子指纹提取进行分子鉴定

Molecular Identification via Molecular Fingerprint extraction from  Atomic Force Microscopy images

Protein function and dynamics are closely related to its sequence and
structure. However prediction of protein function and dynamics from its
sequence and structure is still a fundamental challenge in molecular biology.
Protein classification, which is typically done through measuring the
similarity be- tween proteins based on protein sequence or physical
information, serves as a crucial step toward the understanding of protein
function and dynamics. Persistent homology is a new branch of algebraic
topology that has found its success in the topological data analysis in a
variety of disciplines, including molecular biology. The present work explores
the potential of using persistent homology as an indepen- dent tool for protein
classification. To this end, we propose a molecular topological fingerprint
based support vector machine (MTF-SVM) classifier. Specifically, we construct
machine learning feature vectors solely from protein topological fingerprints,
which are topological invariants generated during the filtration process. To
validate the present MTF-SVM approach, we consider four types of problems.
First, we study protein-drug binding by using the M2 channel protein of
influenza A virus. We achieve 96% accuracy in discriminating drug bound and
unbound M2 channels. Additionally, we examine the use of MTF-SVM for the
classification of hemoglobin molecules in their relaxed and taut forms and
obtain about 80% accuracy. The identification of all alpha, all beta, and
alpha-beta protein domains is carried out in our next study using 900 proteins.
We have found a 85% success in this identifica- tion. Finally, we apply the
present technique to 55 classification tasks of protein superfamilies over 1357
samples. An average accuracy of 82% is attained. The present study establishes
computational topology as an independent and effective alternative for protein
classification.

本研究探讨了使用持久同调作为蛋白质分类的独立工具的潜力，通过构建机器学习特征向量仅基于蛋白质拓扑指纹，提出了一种基于分子拓扑指纹的支持向量机分类器，并取得了较高的分类精度。

蛋白质分类的拓扑学方法

A topological approach for protein classification

Proteins are the most important biomolecules for living organisms. The
understanding of protein structure, function, dynamics and transport is one of
most challenging tasks in biological science. In the present work, persistent
homology is, for the first time, introduced for extracting molecular
topological fingerprints (MTFs) based on the persistence of molecular
topological invariants. MTFs are utilized for protein characterization,
identification and classification. The method of slicing is proposed to track
the geometric origin of protein topological invariants. Both all-atom and
coarse-grained representations of MTFs are constructed. A new cutoff-like
filtration is proposed to shed light on the optimal cutoff distance in elastic
network models. Based on the correlation between protein compactness, rigidity
and connectivity, we propose an accumulated bar length generated from
persistent topological invariants for the quantitative modeling of protein
flexibility. To this end, a correlation matrix based filtration is developed.
This approach gives rise to an accurate prediction of the optimal
characteristic distance used in protein B-factor analysis. Finally, MTFs are
employed to characterize protein topological evolution during protein folding
and quantitatively predict the protein folding stability. An excellent
consistence between our persistent homology prediction and molecular dynamics
simulation is found. This work reveals the topology-function relationship of
proteins.

本研究首次引入持久同调理论以及分子拓扑学概念，基于分子拓扑不变量持久性提出分子拓扑指纹（MTFs），并通过 MTFs 实现了对蛋白质的表征、识别和分类等任务，研究还建议了一种新型的截止距离过滤方法，并提出了基于持久同调不变量的累积条形图用于定量建模蛋白质的柔性，并利用 MTFs 量化预测蛋白质的拓扑演变与折叠稳定性，结果表明，我们的持久同调预测结果与分子动力学模拟结果高度一致，揭示了蛋白质的拓扑 - 功能关系。