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
Department of Physics and Astronomy, Department of Chemistry, University of California, Los Angeles
Dorothy Buck
Thomas Cheatham
Eric Dykeman
Erica Flapan
Mathematics, Pomona College
Maxim Frank-Kamenetskii
Alexander Grosberg
Christine Heitsch
Mathematics, Georgia Institute of Technology
Miranda Holmes-Cerfon
Mathematics, Courant Institute of Mathematical Sciences
Giuliana Indelicato
Mathematics, University of Torino
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
Henri Orland
Yann Ponty
Tamar Schlick
Bio/Chem/Bio math, New York University
Ileana Streinu
Devarajan (Dave) Thirumalai
IPST, Institute for Physical Sciences and Technology
Douglas Turner
Mariel Vazquez
Alexander Vologodskii
Chemistry, New York University
Eric Westhof
Sarah Woodson
Biophysics, Johns Hopkins University
Kelin Xia
MATHEMATICS, Michigan State University
Roya Zandi
Peijun Zhang
structural biology, university of pittsburgh
Shan Zhao
Department of Mathematics,
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 Department of Physics and Astronomy, Department of Chemistry, University of California, Los Angeles
Buck, Dorothy
Cang, Zixuan Department of mathematics, Michigan State University
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 Mathematics, Pomona College
Frank-Kamenetskii, Maxim
Geng, Weihua Mathematics, Southern Methodist University
Grosberg, Alexander
Heitsch, Christine Mathematics, Georgia Institute of Technology
Holmes-Cerfon, Miranda Mathematics, Courant Institute of Mathematical Sciences
Indelicato, Giuliana Mathematics, University of Torino
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
Opron, Kristopher Biochemistry, Michigan State University
Orland, Henri
Ponty, Yann
Rabin, Yitzhak
Rambo, Robert
Rein, Alan
Rouzina, Ioulia Molecular Biology, Biochemistry and Biophysics, University of Minnesota
Schlick, Tamar Bio/Chem/Bio math, New York University
Streinu, Ileana
Thirumalai, Devarajan (Dave) IPST, Institute for Physical Sciences and Technology
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 Biophysics, Johns Hopkins University
Xia, Kelin MATHEMATICS, Michigan State University
Zandi, Roya
Zhang, Peijun structural biology, university of pittsburgh
Zhao, Shan Department of Mathematics,
Zhou, Yongcheng Mathematics, Colorado State University
Topological Complexity in Protein Structures

For DNA molecules, topological complexity occurs exclusively as the result of knotting or linking of the polynucleotide backbone. By contrast, while a few knots and links have been found within the polypeptide backbones of some protein structures, non-planarity can also result from the connectivity between a polypeptide chain and inter- and intra-chain linking via cofactors and disulfide bonds. In this talk, we survey the known types of knots, links, and non-planar graphs in protein structures with and without including such bonds and cofactors. Then we present new examples of protein structures containing Möbius ladders and other non-planar graphs as a result of these cofactors. Finally, we propose hypothetical structures illustrating specific disulfide connectivities that would result in the key ring link, the Whitehead link and the 51 knot, the latter two of which have thus far not been identified within protein structures.

Geometric combinatorics and computational molecular biology: Branching polytopes for RNA sequences

Abstract not submitted.

Kinetics of particles with short-range interactions

Particles in soft-matter systems (such as colloids) tend to have very short-range interactions, so traditional theories, that assume the energy landscape is smooth enough, will struggle to capture their dynamics. We propose a new framework to look at such particles, based on taking the limit as the range of the interaction goes to zero. In this limit, the energy landscape is a set of geometrical manifolds plus a single control parameter, while the dynamics on top of the manifolds are given by a hierarchy of Fokker-Planck equations coupled by "sticky" boundary conditions. We show how to compute dynamical quantities such as transition rates between clusters of hard spheres, and then show this agrees quantitatively with experiments on colloids. We hope this framework is useful for modelling other systems with geometrical constraints, such as those that arise in biology.

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.

Structural insights into retroviral RNA genomes

Abstract not submitted.

Searching for Pseudoknot and Knots in RNA

Using the genus as a mean of classification of the topologies of pseudoknots, we propose two algorithms to predict the secondary structure of complex RNAs. In addition, we present a complete study of the search for knots in known RNA structures.

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.

HIV-1 Capsid Assembly, Maturation and Host Cell Interactions by CryoEM

My research program is interested in understanding the structural mechanisms of macromlecular assemblies using an integrated approach by combining three-dimensional cryo-electron microscopy (cryoEM), with biochemical, biophysical, computational methods. With the recent advance in direct electron detection, cryoEM has become a powerful tool for structure determination of protein complexes and assemblies. Our current research efforts are directed to two such large assemblies: HIV-1 viral capsid and bacterial chemotaxis receptor signaling arrays. In this presentation I will focus on HIV-1 capsid assembly, maturation and interaction with host cell factors that modulate viral infectivity. I will also present some of the technologies we developed, in particular the correlative fluorescent light microscopy and cryoEM method (CLEM), to advance our understanding of HIV-1 pathogenesis.

Minimal molecular surface: PDE modeling and fast generation

When an apolar molecule, such as protein, DNA or RNA, is immersed in a polar solvent, the surface free energy minimization naturally leads to the minimal molecular surface (MMS) as the dielectric boundary between biomolecules and the surrounding aqueous environment. Based on the differential geometry, we have generalized the MMS model through the introduction of several potential driven geometric flow PDEs for the molecular surface formation and evolution. For such PDEs, an extra factor is usually added to stabilize the explicit time integration. Two alternating direction implicit (ADI) schemes have been developed based on the scaled form, which involves nonlinear cross derivative terms that have to be evaluated explicitly. This affects the stability and accuracy of these ADI schemes. To overcome these difficulties, we recently propose a new ADI algorithm based on the unscaled divergence form so that cross derivatives are not involved. This new ADI method is found to be unconditionally stable and more accurate than the existing methods. This enables the use of a large time increment in the steady state simulation so that the proposed ADI algorithm is very efficient for biomolecular surface generation.