Workshop 1: Geometric and Topological Modeling of Biomolecules

(September 28,2015 - October 2,2015 )


Christine Heitsch
Mathematics, Georgia Institute of Technology
Karin Musier-Forsyth
Chemistry and Biochemistry, Ohio State University
Reidun Twarock
Mathematics and Biology, University of York
Alexander Vologodskii
Chemistry, New York University

Modern biological sciences build their foundations on molecular descriptions of DNA, RNA and proteins as essential components. The molecular mechanisms of and the interactions between these components are pivotal to the fundamental secrets of life. Biomolecular structural information can be obtained via a number of experimental techniques, including X-ray crystallography, NMR, EPR, cryo-electron microscopy tomography, multiangle light scattering, confocal laser-scanning microscopy, small angle scattering, and ultra fast laser spectroscopy, to name only a few. However, it is the geometric and topological modeling that interprets and translates such data into three-dimensional structures. In addition to straightforward geometric visualization, geometric modeling bridges the gap between imaging and the mathematical modeling of the structure-function relation, allowing the structural information to be integrated into physical models that shed new light on the molecular mechanisms of life due to the structure-function relation. However, a major challenge in geometric and topological modeling is the handling of the rapidly increasing massive experimental data, often with low signal to noise ratio (SNR) and low fidelity, as in the case of those collected from the structure determination of subcellular structures, organelles and large multiprotein complexes such as viruses. Currently, mean curvature flow, Willmore flow, level set, generalized Laplace-Beltrami operator and partial differential equation transforms are commonly used mathematical techniques for biomolecular geometric and topological modeling, but also applications of group and graph theory have been pioneered in the context of virology. Additionally, wavelets, frames, harmonic analysis and compressive sensing are popular tools for biomolecular visualization and data processing. Moreover, differential geometry, topology and geometric measure theory are powerful approaches for the multiscale modeling of biomolecular structure, dynamics and transport. Finally, persistently stable manifold, topological invariant, Euler characteristic, Frenet frame, and machine learning are vital to the dimensionality reduction of extremely massive biomolecular data. These ideas have been successfully paired with current investigation and discovery of molecular biosciences, and approaches developed in tandem with experiment have demonstrated the power of an interdisciplinary approach. The objective of this workshop is to encourage biologists to outline problems and challenges in experimental data collection and analysis, and mathematicians to come up with new creative and efficient solutions. This program will enable this process to be iterative, with mathematical techniques developed with repeated input and feedback from experimentalists to ensure the real life impact of the work. We plan to enable this by bringing together experts in biomolecular imaging technology and in applied mathematics who share a passion for understanding the molecular mechanism of life on Earth. We expect the workshop to provide a platform for interdisciplinary research collaborations.

Accepted Speakers

Robijn Bruinsma
Dorothy Buck
Thomas Cheatham
Eric Dykeman
Erica Flapan
Maxim Frank-Kamenetskii
Alexander Grosberg
Christine Heitsch
Mathematics, Georgia Institute of Technology
Miranda Holmes-Cerfon
Giuliana Indelicato
Nata�a Jonoska
Mathematics and Statistics, University of South Florida
Neocles Leontis
David Mathews
Konstantin Mischaikow
Mathematics, Rutgers
Karin Musier-Forsyth
Chemistry and Biochemistry, Ohio State University
Sergei Nechaev
Henri Orland
Yann Ponty
Tamar Schlick
Bio/Chem/Bio math, New York University
Ileana Streinu
Devarajan (Dave) Thirumalai
Douglas Turner
Mariel Vazquez
Alexander Vologodskii
Chemistry, New York University
Eric Westhof
Sarah Woodson
Kelin Xia
MATHEMATICS, Michigan State University
Roya Zandi
Peijun Zhang
Shan Zhao
Department of Mathematics, University of Alabama
Monday, September 28, 2015
Time Session
Tuesday, September 29, 2015
Time Session
Wednesday, September 30, 2015
Time Session
Thursday, October 1, 2015
Time Session
Friday, October 2, 2015
Time Session
Name Email Affiliation
Bramer, David Mathematics, Michigan State University
Bruinsma, Robijn
Buck, Dorothy
Cang, Zixuan
Cao, Yin Mathematics, Michigan State University
Cermelli, Paolo
Cheatham, Thomas
Chen, Duan Department of Mathematics, University of North Carolina, Charlotte
Chen, Zhan Mathematics, Michigan State University
Dykeman, Eric
Flapan, Erica
Frank-Kamenetskii, Maxim
Geng, Weihua Mathematics, Southern Methodist University
Grosberg, Alexander
Heitsch, Christine Mathematics, Georgia Institute of Technology
Holmes-Cerfon, Miranda
Indelicato, Giuliana
Jonoska, Natasha Mathematics and Statistics, University of South Florida
Leontis, Neocles
Mannige, Ranjan
Mathews, David
Mischaikow, Konstantin Mathematics, Rutgers
Murrugarra, David Mathematics, University of Kentucky
Musier-Forsyth, Karin Chemistry and Biochemistry, Ohio State University
Nechaev, Sergei
Orland, Henri
Ponty, Yann
Rabin, Yitzhak
Rambo, Robert
Rein, Alan
Rouzina, Ioulia
Schlick, Tamar Bio/Chem/Bio math, New York University
Streinu, Ileana
Thirumalai, Devarajan (Dave)
Turner, Douglas
Twarock, Reidun Mathematics and Biology, University of York
Vazquez, Mariel
Vologodskii, Alexander Chemistry, New York University
Wang, Chi-Jen Mathematics, Georgia Institute of Technology
Westhof, Eric
Wilson, David
Woodson, Sarah
Xia, Kelin MATHEMATICS, Michigan State University
Zandi, Roya
Zhang, Peijun
Zhao, Shan Department of Mathematics, University of Alabama
Zhou, Yongcheng Mathematics, Colorado State University
Challenges in Automating RNA 3D Motif Identification, Extraction, Comparison and Clustering

No abstract has been provided.

Measuring Molecules using Persistent Homology

No abstract has been provided.

Persistent Homology Analysis of Biomolecules

Proteins are the most important biomolecules for living organisms. The understanding of protein structure, function, dynamics, and transport is one of the most challenging tasks in biological science. We have introduced persistent homology for extracting molecular topological fingerprints (MTFs) based on the persistence of molecular topological invariants. MTFs are utilized for protein characterization, identification, and classification. Both all-atom and coarse-grained representations of MTFs are constructed. On the basis of 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.