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.
|Monday, September 28, 2015|
|Tuesday, September 29, 2015|
|Wednesday, September 30, 2015|
|Thursday, October 1, 2015|
|Friday, October 2, 2015|
|Bramer, Davidemail@example.com||Mathematics, Michigan State University|
|Cang, Zixuanfirstname.lastname@example.org||Department of mathematics, Michigan State University|
|Cao, Yinemail@example.com||Mathematics, Michigan State University|
|Chen, Duanfirstname.lastname@example.org||Department of Mathematics, University of North Carolina, Charlotte|
|Chen, Zhanemail@example.com||Mathematics, Michigan State University|
|Flapan, Ericafirstname.lastname@example.org||Mathematics, Pomona College|
|Geng, Weihuaemail@example.com||Mathematics, Southern Methodist University|
|Heitsch, Christinefirstname.lastname@example.org||Mathematics, Georgia Institute of Technology|
|Holmes-Cerfon, Mirandaemail@example.com||Mathematics, Courant Institute of Mathematical Sciences|
|Jonoska, Natashafirstname.lastname@example.org||Mathematics and Statistics, University of South Florida|
|Mischaikow, Konstantinemail@example.com||Mathematics, Rutgers|
|Murrugarra, Davidfirstname.lastname@example.org||Mathematics, University of Kentucky|
|Musier-Forsyth, Karinemail@example.com||Chemistry and Biochemistry, Ohio State University|
|Opron, Kristopherfirstname.lastname@example.org||Biochemistry, Michigan State University|
|Rouzina, Iouliaemail@example.com||Molecular Biology, Biochemistry and Biophysics, University of Minnesota|
|Schlick, Tamar||Bio/Chem/Bio math, New York University|
|Thirumalai, Devarajan (Dave)||firstname.lastname@example.org|
|Twarock, Reidunemail@example.com||Mathematics and Biology, University of York|
|Vologodskii, Alexanderfirstname.lastname@example.org||Chemistry, New York University|
|Wang, Chi-Jenemail@example.com||Mathematics, Georgia Institute of Technology|
|Woodson, Sarahfirstname.lastname@example.org||Biophysics, Johns Hopkins University|
|Xia, Kelinemail@example.com||MATHEMATICS, Michigan State University|
|Zhao, Shanfirstname.lastname@example.org||Department of Mathematics,|
|Zhou, Yongchengemail@example.com||Mathematics, Colorado State University|
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.
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.
No abstract has been provided.
No abstract has been provided.
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.