Fast and anisotropic flexibility-rigidity index for protein flexibility and fluctuation analysis

The Journal of Chemical Physics

Zhao

Guo

2015

Self Cite

Although persistent homology has emerged as a promising tool for the topological simplification of complex data, it is computationally intractable for large datasets. We introduce multiresolution persistent homology to handle excessively large datasets. We match the resolution with the scale of interest so as to represent large scale datasets with appropriate resolution. We utilize flexibilityrigidity index to access the topological connectivity of the data set and define a rigidity density for the filtration analysis. By appropriately tuning the resolution of the rigidity density, we are able to focus the topological lens on the scale of interest. The proposed multiresolution topological analysis is validated by a hexagonal fractal image which has three distinct scales. We further demonstrate the proposed method for extracting topological fingerprints from DNA molecules. In particular, the topological persistence of a virus capsid with 273 780 atoms is successfully analyzed which would otherwise be inaccessible to the normal point cloud method and unreliable by using coarse-grained multiscale persistent homology. The proposed method has also been successfully applied to the protein domain classification, which is the first time that persistent homology is used for practical protein domain analysis, to our knowledge. The proposed multiresolution topological method has potential applications in arbitrary data sets, such as social networks, biological networks, and graphs. C 2015 AIP Publishing LLC. [http://dx

“…We construct the multiresolution geometric representation by using the FRI method, 23,24,35 which converts the point cloud data into a matrix or a density FIG. 1.…”

Section: Methods and Algorithmmentioning

confidence: 99%

“…FRI 23,24,35 was originally invented for the flexibility analysis of biomolecules. It provides an excellent prediction of macromolecular Debye-Waller factors or B-factors.…”

Section: A Multiresolution Geometric Analysismentioning

confidence: 99%

Section: Conclusion Remarksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multiresolution persistent homology for excessively large biomolecular datasets

The Journal of Chemical Physics

Zhao

Guo

2015

Self Cite

“…In terms of B-factor prediction, GNM is typically more accurate than ANM. 35,37 Therefore, GNM has been widely used in the study of biomolecular structure, dynamics, and functions. 7,32,41,60 It has demonstrated its utilities in stability analysis, 31 docking simulation, 15 viral capsids 39,42 and domain motions of hemoglobin, 58 F1 ATPase, 8,63 chaperonin GroEL, 23,62 and the ribosome.…”

Section: Introductionmentioning

confidence: 99%

Multiscale Gaussian network model (mGNM) and multiscale anisotropic network model (mANM)

The Journal of Chemical Physics

Opron

Wei

2015

Self Cite

Gaussian network model (GNM) and anisotropic network model (ANM) are some of the most popular methods for the study of protein flexibility and related functions. In this work, we propose generalized GNM (gGNM) and ANM methods and show that the GNM Kirchhoff matrix can be built from the ideal low-pass filter, which is a special case of a wide class of correlation functions underpinning the linear scaling flexibility-rigidity index (FRI) method. Based on the mathematical structure of correlation functions, we propose a unified framework to construct generalized Kirchhoff matrices whose matrix inverse leads to gGNMs, whereas, the direct inverse of its diagonal elements gives rise to FRI method. With this connection, we further introduce two multiscale elastic network models, namely, multiscale GNM (mGNM) and multiscale ANM (mANM), which are able to incorporate different scales into the generalized Kirchhoff matrices or generalized Hessian matrices. We validate our new multiscale methods with extensive numerical experiments. We illustrate that gGNMs outperform the original GNM method in the B-factor prediction of a set of 364 proteins. We demonstrate that for a given correlation function, FRI and gGNM methods provide essentially identical B-factor predictions when the scale value in the correlation function is sufficiently large. More importantly, we reveal intrinsic multiscale behavior in protein structures. The proposed mGNM and mANM are able to capture this multiscale behavior and thus give rise to a significant improvement of more than 11% in B-factor predictions over the original GNM and ANM methods. We further demonstrate the benefits of our mGNM through the B-factor predictions of many proteins that fail the original GNM method. We show that the proposed mGNM can also be used to analyze protein domain separations. Finally, we showcase the ability of our mANM for the analysis of protein collective motions. C 2015 AIP Publishing LLC. [http://dx

Persistent topology for cryo‐EM data analysis

Numer Methods Biomed Eng

Guo

2015

Self Cite

In this work, we introduce persistent homology for the analysis of cryo-electron microscopy (cryo-EM) density maps. We identify the topological fingerprint or topological signature of noise, which is widespread in cryo-EM data. For low signal to noise ratio (SNR) volumetric data, intrinsic topological features of biomolecular structures are indistinguishable from noise. To remove noise, we employ geometric flows which are found to preserve the intrinsic topological fingerprints of cryo-EM structures and diminish the topological signature of noise. In particular, persistent homology enables us to visualize the gradual separation of the topological fingerprints of cryo-EM structures from those of noise during the denoising process, which gives rise to a practical procedure for prescribing a noise threshold to extract cryo-EM structure information from noise contaminated data after certain iterations of the geometric flow equation. To further demonstrate the utility of persistent homology for cryo-EM data analysis, we consider a microtubule intermediate structure (EMD-1129). Three helix models, an alpha-tubulin monomer model, an alphaand beta-tubulin model, and an alpha-and beta-tubulin dimer model, are constructed to fit the cryo-EM data. The least square fitting leads to similarly high correlation coefficients, which indicates that structure determination via optimization is an ill-posed inverse problem. However, these models have dramatically different topological fingerprints. Especially, linkages or connectivities that discriminate one model from another one, play little role in the traditional density fitting or optimization, but are very sensitive and crucial to topological fingerprints. The intrinsic topological features of the microtubule data are identified after topological denoising. By a comparison of the topological fingerprints of the original data and those of three models, we found that the third model is topologically favored. The present work offers persistent homology based new strategies for topological denoising and for resolving ill-posed inverse problems.