## Workshop 1: Geometric and Topological Modeling of Biomolecules

### Organizers

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
Eric Dykeman
Erica Flapan
Mathematics, Pomona College
Alexander Grosberg
Christine Heitsch
Mathematics, Georgia Institute of Technology
Miranda Holmes-Cerfon
Mathematics, Courant Institute of Mathematical Sciences
Giuliana Indelicato
Mathematics, University of Torino
NataÃ¯Â¿Â½a 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
LIX - Ecole Polytechnique, Centre National de la Recherche Scientifique (CNRS)
Alan Rein
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
Istitute of Molecular and Cellular Biology, Architechture et Reactivite de l'ARN
Sarah Woodson
Biophysics, Johns Hopkins University
Kelin Xia
MATHEMATICS, Michigan State University
Roya Zandi
Physics and Astronomy, University of California, Riverside
Peijun Zhang
structural biology, university of pittsburgh
Shan Zhao
Department of Mathematics,
Monday, September 28, 2015
Time Session
07:45 AM

Shuttle to MBI

08:00 AM
08:30 AM

Breakfast

08:30 AM
08:45 AM

Welcome, overview, Introductions: MG

08:45 AM
09:00 AM

Introduction by Workshop Organizers

09:00 AM
09:35 AM
Robijn Bruinsma - Structural Transformations of Viral Shells

Functional protein assemblies frequently undergo spontaneous, large-scale reorganizations driven by the constituent proteins. As an example, the complex sequence of maturation shape transitions of the protein shells of bacteriophage viruses and of the Herpes virus will be discussed. Classical, small-strain elasticity theory is fundamentally unable to address these fascinating events because the proteins composing the aggregate are themselves highly deformed with respect to the stress-free reference state of isolated proteins. Moreover, this stress-free reference state evolves during the maturation process as the proteins are transformed. The talk will discuss how recently developed continuum theories of growing biological tissue combined with finite-element numerical modeling can be adapted to evolving protein aggregates. The theory leads to a simple and natural physical description of the buckling transition that is frequently observed for the bacteriophage viruses during maturation.

09:35 AM
10:10 AM
Alexander Grosberg
10:10 AM
10:50 AM

Break

10:50 AM
11:25 AM
Ileana Streinu
11:25 AM
12:00 PM
Kelin Xia - 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.

12:00 PM
01:30 PM

Lunch Break

01:30 PM
02:05 PM
Eric Dykeman
02:05 PM
02:40 PM
Reidun Twarock
02:40 PM
03:20 PM

Break

03:20 PM
03:55 PM
Miranda Holmes-Cerfon - 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.

03:55 PM
04:30 PM
Giuliana Indelicato
04:30 PM
06:30 PM

Reception and Poster session in MBI Lounge

06:30 PM

Shuttle pick-up from MBI

Tuesday, September 29, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:35 AM
Roya Zandi - Self-assembly of mature conical HIV particles: The role of membrane

Abstract not submitted

09:35 AM
10:10 AM
Alan Rein
10:10 AM
10:50 AM

Break

10:50 AM
11:25 AM
Peijun Zhang - 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.

11:25 AM
12:00 PM

Informal Discussion/daily wrap-up (Twarock moderate)

12:00 PM
01:30 PM

Lunch Break

01:30 PM
02:05 PM
Tamar Schlick
02:05 PM
02:40 PM
Thomas Cheatham
02:40 PM
03:20 PM

Break

03:20 PM
03:55 PM
Neocles Leontis - Challenges in Automating RNA 3D Motif Identification, Extraction, Comparison and Clustering

No abstract has been provided.

03:55 PM
04:30 PM
Karin Musier-Forsyth - Structural insights into retroviral RNA genomes

The 5' untranslated region (5'-UTR) is a highly conserved region of retroviral RNA genomes responsible for regulating many steps of the retroviral lifecycle including viral RNA dimerization, packaging, initiation of reverse transcription, transcriptional regulation, and splicing. A complete understanding of the mechanisms controlling retroviral replication requires structural characterization of this RNA. Unfortunately, its large size and conformational flexibility renders common methods of solving structures, such as X-ray crystallography and NMR exceedingly difficult. Here, we use a solution technique, small-angle X-ray scattering (SAXS), coupled with computational molecular modeling and structure probing, to characterize RNAs (100-350 nucleotides in length) derived from the 5'-UTR of HIV-1 (NL4-3 and MAL isolates), RSV, SIV, and HTLV-1. Similarities and differences in their packaging signals, the presence of tRNA structural mimicry, conformational switches upon dimerization and primer annealing, and length-dependent changes in global conformation will all be discussed.

04:45 PM

Shuttle pick-up from MBI

Wednesday, September 30, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:35 AM
Sarah Woodson - Cooperativity of RNA Folding Landscapes

Abstract not submitted

09:35 AM
10:10 AM
Devarajan (Dave) Thirumalai
10:10 AM
10:50 AM

Break

10:50 AM
11:25 AM
Shan Zhao - 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.

11:25 AM
12:00 PM

Informal Discussion/daily wrap-up (Musier-Forsyth moderate)

12:00 PM
01:30 PM

Lunch Break

01:30 PM
02:05 PM
Konstantin Mischaikow - Measuring Molecules using Persistent Homology

No abstract has been provided.

02:05 PM
02:40 PM
Mariel Vazquez
02:40 PM
03:20 PM

Break

03:20 PM
03:55 PM
Maxim Frank-Kamenetskii
03:55 PM
04:30 PM
Dorothy Buck
04:45 PM

Shuttle pick-up from MBI

Thursday, October 1, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:35 AM
NataÃ¯Â¿Â½a Jonoska - Spatial rigid vertex graphs and RNA-guided DNA rearrangements

We study homologous DNA recombination, in particular, rearrangements guided by RNA templates.

Certain species of ciliates undergo massive DNA rearrangements during their development and are considered model organisms to study these processes. We show that a four-valent rigid vertex graph can provide a physical representation of the DNA at the time of recombination. We associate operations on such graphs with template guided rearrangements and investigate their properties. We show that such an operation leads to the proper order" of the DNA sequence after recombination. Schematically, the braiding process can be represented as a crossing (vertex) in such a graph. The homologous recombination corresponds to removal of the crossings in the graph (called smoothing). We discuss properties of such graphs motivated by DNA assembly, genus ranges, and rearrangement pathways. In particular we analyze these properties and rearrangement patterns for recently sequenced genome of ciliate Oxytricha that contains thousands of scrambled genes.

09:35 AM
10:10 AM
Alexander Vologodskii
10:10 AM
10:50 AM

Break

10:50 AM
11:25 AM
Erica Flapan - 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.

11:25 AM
12:00 PM

TBD

12:00 PM
12:30 PM

Informal Discussion/daily wrap-up (Vologodskii moderate)

12:30 PM
01:30 PM

Lunch Break

01:30 PM
02:05 PM
Douglas Turner - NMR of Small RNAs as Benchmarks for Testing All Atom Predictions of RNA Structure

Less than 5% of the human genome codes for protein, but about 90% codes for transcribed RNA. Structures and functions for much of this RNA are not known. Moreover, it appears to be more difficult to determine and to predict structures of RNAs than structures of proteins. For proteins and RNA, 3D predictions are made by both "knowledge based" and "quantum mechanical based" force fields. NMR experiments on simple RNA systems can provide benchmarks for testing methods to predict 3D structure. Results from NMR experiments and molecular dynamics simulations will be presented for single stranded, unpaired tetramers and for base paired structures of RNA. Comparisons reveal strengths and weaknesses of force fields.

02:05 PM
02:40 PM
Eric Westhof - RNA-Puzzles: a CASP-like collective blind experiment for the evaluation of automatic RNA three-dimensional structure prediction

RNA-Puzzles is a CASP-like collective blind experiment for the evaluation of RNA three-dimensional structure prediction. The primary aims of RNA-Puzzles are (i) to determine the capabilities and limitations of current methods of 3D RNA structure prediction based on sequence, (ii) to find whether and how progress has been made, and (iii) to illustrate whether there are specific bottlenecks that hold back the field. Ten puzzles have been set up and automatic assessments of the agreements with X-ray structures have been performed. Nine groups of modelers around the world participate in this collective effort. Difficulties and progress in RNA structure prediction will be reported.

02:40 PM
03:20 PM

Break

03:20 PM
03:55 PM
David Mathews
03:55 PM
04:30 PM
Christine Heitsch - Geometric combinatorics and computational molecular biology: Branching polytopes for RNA sequences

Abstract not submitted.

04:45 PM

Shuttle pick-up from MBI

06:30 PM
07:00 PM

Cash Bar

07:00 PM
07:00 PM

Banquet in the Fusion Room @ Crowne Plaza Hotel

Friday, October 2, 2015
Time Session
08:00 AM

Shuttle to MBI

08:15 AM
09:00 AM

Breakfast

09:00 AM
09:35 AM
Yann Ponty - Complexity aspects of RNA folding on complex conformation spaces

The prediction of the most stable, prevalent and/or functional structure adopted by an RiboNucleic Acid molecule (RNA) is an old, yet very much ongoing, challenge of computational biology. Currently available computational methods, such as MFold or RNAfold, somehow artificially restrict their search space to tree-like conformations, the secondary structures. However, such a definition intrinsically discards complex topological motifs that are both observed in experimentally-determined structures, essential for the functions performed by the molecule, and conserved throughout the evolution. In this talk, I will review two decades of works aiming at characterizing the complexity of minimizing the free energy of a given RNA molecule, while allowing (limited subsets of) pseudoknots/crossing interactions.

The general hardness of the associated computational problems motivates the development of novel parameterized-complexity approaches and heuristics, as further illustrated by the follow up talk by H Orland.

This is a joint work in collaboration with S. Sheikh (Bloomberg R&D, USA) and R Backofen (Uni. Freiburg, Germany).

09:35 AM
10:10 AM
Henri Orland - 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.

10:10 AM
10:50 AM

Break

10:50 AM
11:30 AM

Informal discussion/daily wrap-up (Musier-Forsyth moderate)

11:30 AM
12:00 PM

Informal discussion/workshop wrap up

12:15 PM

Shuttle pick-up from MBI

Name Email Affiliation
Bramer, David david.s.bramer@gmail.com Mathematics, Michigan State University
Bruinsma, Robijn bruinsma@physics.ucla.edu Department of Physics and Astronomy, Department of Chemistry, University of California, Los Angeles
Buck, Dorothy d.buck@imperial.ac.uk
Bundschuh, Ralf bundschuh@mps.ohio-state.edu Departments of Physics, Chemistry&Biochemistry, Division of Hematology, The Ohio State University
Cang, Zixuan cangzixu@math.msu.edu Department of mathematics, Michigan State University
Cantara, William cantara.2@osu.edu Chemistry and Biochemistry, The Ohio State University
Cao, Yin caoyin@msu.edu Mathematics, Michigan State University
Cermelli, Paolo paolo.cermelli@unito.it
Chen, Duan dchen10@uncc.edu Department of Mathematics, University of North Carolina, Charlotte
Chen, Zhan zchen@georgiasouthern.edu Mathematics, Michigan State University
Dykeman, Eric eric.dykeman@york.ac.uk
Flapan, Erica eflapan@pomona.edu Mathematics, Pomona College
Geng, Weihua wgeng@smu.edu Mathematics, Southern Methodist University
Gong, Xinqi xinqigong@ruc.edu.cn Institute for Mathematical Sciences, Renmin University of China
Gopalan, Venkat gopalan.5@osu.edu Chemistry & Biochemistry, The Ohio State University
Grosberg, Alexander ayg1@nyu.edu
Gulzar, Faisal mfaisalgul33@gmail.com Department of Pharmacology, Faculty of Pharmacy, University of Sargodha
Heitsch, Christine heitsch@math.gatech.edu Mathematics, Georgia Institute of Technology
Holmes-Cerfon, Miranda holmes@cims.nyu.edu Mathematics, Courant Institute of Mathematical Sciences
Indelicato, Giuliana giuliana.indelicato@unito.it Mathematics, University of Torino
Jonoska, Natasha jonoska@math.usf.edu Mathematics and Statistics, University of South Florida
Kurtek, Sebastian skurtek@gmail.com Statistics, The Ohio State University
Leontis, Neocles leontis@bgsu.edu
Mannige, Ranjan rvmannige@lbl.gov
Mathews, David David_Mathews@urmc.rochester.edu
Mischaikow, Konstantin mischaik@math.rutgers.edu Mathematics, Rutgers
Murrugarra, David murrugarra@uky.edu Mathematics, University of Kentucky
Musier-Forsyth, Karin musier@chemistry.ohio-state.edu Chemistry and Biochemistry, Ohio State University
Opron, Kristopher kopron@gmail.com Biochemistry, Michigan State University
Orland, Henri Henri.ORLAND@cea.fr
Ponty, Yann Yann.Ponty@lix.polytechnique.fr LIX - Ecole Polytechnique, Centre National de la Recherche Scientifique (CNRS)
Rabin, Yitzhak rabinserious@gmail.com
Rambo, Robert robert.rambo@diamond.ac.uk
Rein, Alan rein@mail.ncifcrf.gov
Rouzina, Ioulia rouzi002@umn.edu Molecular Biology, Biochemistry and Biophysics, University of Minnesota
Schlick, Tamar ts1@haifa.biomath.nyu.edu Bio/Chem/Bio math, New York University
Streinu, Ileana istreinu@smith.edu
Thirumalai, Devarajan (Dave) thirum@umd.edu IPST, Institute for Physical Sciences and Technology
Turner, Douglas turner@chem.rochester.edu
Twarock, Reidun rt507@york.ac.uk Mathematics and Biology, University of York
Vazquez, Mariel mariel@math.ucdavis.edu
Vologodskii, Alexander alex.vologodskii@nyu.edu Chemistry, New York University
Wang, Chi-Jen cwang463@math.gatech.edu Mathematics, Georgia Institute of Technology
Westhof, Eric e.westhof@ibmc-cnrs.unistra.fr Istitute of Molecular and Cellular Biology, Architechture et Reactivite de l'ARN
Wilson, David David.Wilson@kzoo.edu Physics, Kalamazoo College
Woodson, Sarah swoodson@jhu.edu Biophysics, Johns Hopkins University
Wu, Kedi vettelwu@gmail.com Mathematics, Michigan State University
Wu, Zhongtao ztwu@math.cuhk.edu.hk Mathematics, The Chineses University of Hong Kong
Wu, Jian wu.1495@osu.edu Molecular Genetics, The Ohio State University
Xia, Kelin xiakelin@msu.edu MATHEMATICS, Michigan State University
Zandi, Roya roya.zandi@ucr.edu Physics and Astronomy, University of California, Riverside
Zhang, Peijun pez7@pitt.edu structural biology, university of pittsburgh
Zhao, Shan szhao@bama.ua.edu Department of Mathematics,
Zhou, Yongcheng yzhou@math.colostate.edu Mathematics, Colorado State University
Structural Transformations of Viral Shells

Functional protein assemblies frequently undergo spontaneous, large-scale reorganizations driven by the constituent proteins. As an example, the complex sequence of maturation shape transitions of the protein shells of bacteriophage viruses and of the Herpes virus will be discussed. Classical, small-strain elasticity theory is fundamentally unable to address these fascinating events because the proteins composing the aggregate are themselves highly deformed with respect to the stress-free reference state of isolated proteins. Moreover, this stress-free reference state evolves during the maturation process as the proteins are transformed. The talk will discuss how recently developed continuum theories of growing biological tissue combined with finite-element numerical modeling can be adapted to evolving protein aggregates. The theory leads to a simple and natural physical description of the buckling transition that is frequently observed for the bacteriophage viruses during maturation.

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 MÃ¶bius 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.

Spatial rigid vertex graphs and RNA-guided DNA rearrangements

We study homologous DNA recombination, in particular, rearrangements guided by RNA templates.

Certain species of ciliates undergo massive DNA rearrangements during their development and are considered model organisms to study these processes. We show that a four-valent rigid vertex graph can provide a physical representation of the DNA at the time of recombination. We associate operations on such graphs with template guided rearrangements and investigate their properties. We show that such an operation leads to the proper order" of the DNA sequence after recombination. Schematically, the braiding process can be represented as a crossing (vertex) in such a graph. The homologous recombination corresponds to removal of the crossings in the graph (called smoothing). We discuss properties of such graphs motivated by DNA assembly, genus ranges, and rearrangement pathways. In particular we analyze these properties and rearrangement patterns for recently sequenced genome of ciliate Oxytricha that contains thousands of scrambled genes.

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

The 5' untranslated region (5'-UTR) is a highly conserved region of retroviral RNA genomes responsible for regulating many steps of the retroviral lifecycle including viral RNA dimerization, packaging, initiation of reverse transcription, transcriptional regulation, and splicing. A complete understanding of the mechanisms controlling retroviral replication requires structural characterization of this RNA. Unfortunately, its large size and conformational flexibility renders common methods of solving structures, such as X-ray crystallography and NMR exceedingly difficult. Here, we use a solution technique, small-angle X-ray scattering (SAXS), coupled with computational molecular modeling and structure probing, to characterize RNAs (100-350 nucleotides in length) derived from the 5'-UTR of HIV-1 (NL4-3 and MAL isolates), RSV, SIV, and HTLV-1. Similarities and differences in their packaging signals, the presence of tRNA structural mimicry, conformational switches upon dimerization and primer annealing, and length-dependent changes in global conformation will all be discussed.

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.

Complexity aspects of RNA folding on complex conformation spaces

The prediction of the most stable, prevalent and/or functional structure adopted by an RiboNucleic Acid molecule (RNA) is an old, yet very much ongoing, challenge of computational biology. Currently available computational methods, such as MFold or RNAfold, somehow artificially restrict their search space to tree-like conformations, the secondary structures. However, such a definition intrinsically discards complex topological motifs that are both observed in experimentally-determined structures, essential for the functions performed by the molecule, and conserved throughout the evolution. In this talk, I will review two decades of works aiming at characterizing the complexity of minimizing the free energy of a given RNA molecule, while allowing (limited subsets of) pseudoknots/crossing interactions.

The general hardness of the associated computational problems motivates the development of novel parameterized-complexity approaches and heuristics, as further illustrated by the follow up talk by H Orland.

This is a joint work in collaboration with S. Sheikh (Bloomberg R&D, USA) and R Backofen (Uni. Freiburg, Germany).

NMR of Small RNAs as Benchmarks for Testing All Atom Predictions of RNA Structure

Less than 5% of the human genome codes for protein, but about 90% codes for transcribed RNA. Structures and functions for much of this RNA are not known. Moreover, it appears to be more difficult to determine and to predict structures of RNAs than structures of proteins. For proteins and RNA, 3D predictions are made by both "knowledge based" and "quantum mechanical based" force fields. NMR experiments on simple RNA systems can provide benchmarks for testing methods to predict 3D structure. Results from NMR experiments and molecular dynamics simulations will be presented for single stranded, unpaired tetramers and for base paired structures of RNA. Comparisons reveal strengths and weaknesses of force fields.

RNA-Puzzles: a CASP-like collective blind experiment for the evaluation of automatic RNA three-dimensional structure prediction

RNA-Puzzles is a CASP-like collective blind experiment for the evaluation of RNA three-dimensional structure prediction. The primary aims of RNA-Puzzles are (i) to determine the capabilities and limitations of current methods of 3D RNA structure prediction based on sequence, (ii) to find whether and how progress has been made, and (iii) to illustrate whether there are specific bottlenecks that hold back the field. Ten puzzles have been set up and automatic assessments of the agreements with X-ray structures have been performed. Nine groups of modelers around the world participate in this collective effort. Difficulties and progress in RNA structure prediction will be reported.

Cooperativity of RNA Folding Landscapes

Abstract not submitted

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.

Self-assembly of mature conical HIV particles: The role of membrane

Abstract not submitted

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.

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