Persistent homology analysis of protein structure, flexibility and folding
arXiv:1412.2779 · doi:10.1002/cnm.2655
Abstract
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.
arXiv comment22 figures, 82 references
References in corpus (4)
Cited by in corpus (48)
- A roadmap for the computation of persistent homology
- What are higher-order networks?
- TopologyNet: Topology based deep convolutional neural networks for biomolecular property predictions
- Representability of algebraic topology for biomolecules in machine learning based scoring and virtual screening
- Persistent homology of time-dependent functional networks constructed from coupled time series
- Persistence weighted Gaussian kernel for topological data analysis
- Advances of Machine Learning in Materials Science: Ideas and Techniques
- A review of mathematical representations of biomolecules
- Construction of and efficient sampling from the simplicial configuration model
- Finding cosmic voids and filament loops using topological data analysis
- Quantitative and Interpretable Order Parameters for Phase Transitions from Persistent Homology
- Topological data analysis distinguishes parameter regimes in the Anderson-Chaplain model of angiogenesis
- Multiscale Gaussian network model (mGNM) and multiscale anisotropic network model (mANM)
- Quantum algorithm for persistent Betti numbers and topological data analysis
- Spatial Applications of Topological Data Analysis: Cities, Snowflakes, Random Structures, and Spiders Spinning Under the Influence
- Simplicial degree in complex networks. Applications of Topological Data Analysis to Network Science
- Fractal Dimension Estimation with Persistent Homology: A Comparative Study
- Dirac signal processing of higher-order topological signals
- Protein folding analysis using features obtained by persistent homology
- Persistent homology analysis of ion aggregation and hydrogen-bonding network
- Blind prediction of protein B-factor and flexibility
- Minimal Cycle Representatives in Persistent Homology using Linear Programming: an Empirical Study with User's Guide
- Representations of Energy Landscapes by Sublevelset Persistent Homology: An Example With n-Alkanes
- Topological Learning for Brain Networks
- DTM-based Filtrations
- Persistent homology analysis of osmolyte molecular aggregation and their hydrogen-bonding networks
- Rips filtrations for quasi-metric spaces and asymmetric functions with stability results
- Evolutionary homology on coupled dynamical systems
- STruD: Truss Decomposition of Simplicial Complexes
- Higher-order Connection Laplacians for Directed Simplicial Complexes
- FreSCo: Mining Frequent Patterns in Simplicial Complexes
- Persistent cohomology for data with multicomponent heterogeneous information
- Topological estimation of the latent geometry of a complex network
- Tight basis cycle representatives for persistent homology of large data sets
- Sequence-based Multiscale Model (SeqMM) for High-throughput chromosome conformation capture (Hi-C) data analysis
- MathDL: Mathematical deep learning for D3R Grand Challenge 4
- Time series analysis using persistent homology of distance matrix
- Fast Topological Clustering with Wasserstein Distance
- A torus model for optical flow
- A Primer on Persistent Homology of Finite Metric Spaces
- Persistent homology and the shape of evolutionary games
- Weighted persistent homology for osmolyte molecular aggregation and hydrogen-bonding network analysis
- Metrics for Learning in Topological Persistence
- Detection of Small Holes by the Scale-Invariant Robust Density-Aware Distance (RDAD) Filtration
- A Unified Topological Approach to Data Science
- Exact Probability Landscapes of Stochastic Phenotype Switching in Feed-Forward Loops: Phase Diagrams of Multimodality
- Visualization of AE's Training on Credit Card Transactions with Persistent Homology
- A Domain-Oblivious Approach for Learning Concise Representations of Filtered Topological Spaces for Clustering