## 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
Eric Dykeman
Mathematics, University of York
Robert Eisenberg
Molecular Biophysics and Physiology, Rush University Medical Center
Erica Flapan
Mathematics, Pomona College
Alexander Grosberg
Physics, New York University
Christine Heitsch
Mathematics, Georgia Institute of Technology
Miranda Holmes-Cerfon
Mathematics, Courant Institute of Mathematical Sciences
Giuliana Indelicato
Mathematics, University of Torino
Natasa Jonoska
Mathematics and Statistics, University of South Florida
Neocles Leontis
Chemistry Department, Bowling Green State University
David Mathews
Biochemistry and Biophysics, University of Rochester
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
HIV Dynamics and Replication Program, National Institutes of Health (NIH)
Tamar Schlick
Bio/Chem/Bio math, New York University
Ileana Streinu
Computer Science, Smith College
Douglas Turner
Chemistry, University of Rochester
Mariel Vazquez
Mathematics, Microbiology & Molecular Genetics, University of California, Davis
Alexander Vologodskii
Chemistry, New York University
Yusu Wang
Computer Science and Engineering, The Ohio State University
Guowei Wei
Department of Mathematics, Michigan State 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 - Landau Theories of the Assembly of Viruses

We examined the recent application of group theory to the assembly of icosahedral viral shells by Lorman and
Rochal. These authors arrived at the important result that there should be no activation energy barrier. Ultimately
this is a consequence of broken chiral symmetry. Their result conflicts with earlier models for viral assembly that
all find a large energy activation barrier. We extend the work of Lorman and Rochas and find that their result is a
special case of a general family of theories for assembly on icosahedral shells with broken chiral symmetry. Some of
these do and some of these do not have energy activation barriers.

09:35 AM
10:10 AM
Alexander Grosberg - Knots in a Macromolecule

In the talk, I plan to review the current status of the controversial idea that knots in a macromolecule tighten themselves for entropic reasons.

10:10 AM
10:50 AM

Break

10:50 AM
11:25 AM
Ileana Streinu - Rigidity and flexibility of large molecular structures: mathematical and computational challenges

The Protein Databank (PDB) and the Open Crystallography Database (COD) are two large repositories (111 000, resp. 350 000 entries) of known molecular structures, widely used by biochemists and crystallographers. Of particular interest are questions concerning the rigidity and flexibility of these molecules: the answers may reveal intrinsic biological functions or unusual properties of crystalline matter.

I will survey several methods that shed light on these questions., including one based on the mathematics of rigidity theory, as implemented in the web application Kinari developed in my group. Then I will discuss the challenges emerging from making Kinari work with the entire PDB or COD databases, and in particular with extremly large biomolecules such as viruses.

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 - Assembly of ssRNA Viruses I: Identification of packaging signals and their role in assembly

Multiple dispersed sequence/structure motifs in single-stranded RNA genomes termed packaging signals have been shown to play crucial roles in virus assembly. This talk will cover theoretical tools underpinning the discovery of such packaging signals in a wide range of single-stranded RNA viruses, and discuss models demonstrating their impact on virus assembly efficiency and selective genome packaging. We show that graph theoretical tools can be used to better understand the complexity of the assembly process.

02:05 PM
02:40 PM
Reidun Twarock - Assembly of ssRNA viruses II: Consequences of Packaging Signal Mediated Assembly for Viral Evolution

Packaging signals provide an instruction manual for efficient virus assembly and thus place constraints on the evolution of single-stranded RNA genomes. This talk will cover the consequences of packaging signal-mediated assembly for viral evolution. It will discuss the geometry of the implicitly define fitness landscapes underpinning the evolutionary dynamics and the consequences of viral geometry for evolution.

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 - Predicting the geometry of self-assembling nanoparticles

In this talk I will present a mathematical approach to the classification and the prediction of the geometry underlying the arrangements of the polypeptidic building blocks in self-assembling protein nanoparticles.

I will focus on artificially engineered nanoshells made by repeated copies of a single protein or polypeptidic units. I will tackle the problem of the structure determination of such particles given that they do not necessarly conform to the Caspar-Klug theory, which accounts for the arrangement of proteins in icosahedral spherical viruses, and that there is no experimental technique allowing to resolve unambiguously their actual structure.

I will study the topology of the protein network using tools from graph theory and tiling theory. Special attention will be devoted to symmetric particles, which can be fully described and classified.

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

Retroviruses, like all other viruses, contain a protein shell called the capsid that encloses the genetic materials (RNA or DNA). While most viruses adopt spherical shapes, the capsid of mature Human Immunodeficiency Virus (HIV), classified as a retrovirus, self-assembles predominantly into conspicuous conical structures. Despite numerous cryo-electron tomographic studies, the kinetic pathway of assembly of capsid proteins into conical cores is not well understood. To study the impact of genome and surrounding membrane on the formation of HIV shells, we monitor the step by step irreversible growth of HIV capsids. We show that the presence of membrane not only restricts the growth of incomplete capsids, it also induces local stresses on the growing sheet creating the formation of pentamers necessary for the assembly of closed shells. Our results also shed light in the role of genome in the assembly of conical cores. Our findings are consistent with the recent experimental results, emphasizing on the importance of RNA and membrane on the formation of HIV conical shells.

09:35 AM
10:10 AM
Alan Rein - A Conformational Switch in HIV-1 Gag Protein: The Decision to Assemble

Recombinant HIV-1 Gag protein, purified from bacteria, is a soluble protein, but assembles into virus-like particles (VLPs) in a defined in vitro system upon addition of nucleic acid (NA). We have tried to understand how NA-binding promotes assembly. Experiments with Gag-leucine zipper chimeric proteins suggest that when Gag attains a high local concentration, it undergoes a change which primes it for assembly; cooperative NA-binding would be one way it could reach a high local concentration. We have focused on the SP1 region of Gag, which lies between the CA domain (principally responsible for Gag-Gag interactions in VLPs) and the NC domain (principally responsible for NA-binding). Many subtle mutations in SP1 cause drastic disruption of VLP assembly. If the SP1 sequence were folded into an α-helix, the helix would be amphipathic, with a polar face and a hydrophobic face. We have found that a peptide representing SP1 folds into a helix when it is at high concentration; presumably, at these concentrations, helices can aggregate and bury their hydrophobic faces within helix bundles.

We now report that small proteins consisting of SP1 fused to a dimerizing leucine zipper form discrete tetramers in solution. However, many mutations in these SP-zipper chimeras cause them to form dimers rather than tetramers; therefore, SP1-SP1 interactions are responsible for the association of the zipper-induced dimers into tetramers. As these specific mutations also disrupt assembly by Gag, the same SP1-SP1 interactions are also significant in VLP assembly. We hypothesize that folding of SP1 into a helix primes Gag for VLP assembly, perhaps by exposing new interfaces in the CA domain. Information on the structure of these SP1 bundles will be presented.

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 - Multiscale modeling of the chromatin fiber

Understanding chromosome tertiary organization and its role in control of gene expression represents one of the most fundamental open biological challenges. Chromatin structure and gene expression are intimately related because the complex nature and dynamics of protein-bound DNA folding in the living cell regulates gene activity at a large range of spatial and temporal scales. Recent advances in experimental studies of chromatin using nucleosome structure determination, ultra-structural techniques, single-force extension studies, and analysis of chromosomal interactions have revealed important chromatin characteristics under various internal and external conditions. Modeling studies, anchored to high-resolution nucleosome models, have explored many related questions systematically. In this talk, I will describe recent findings regarding chromatin structure and function using a combination of coarse-grained modeling and large-scale all-atom molecular dynamics simulations of chromatin fibers. In particular, I will describe how such multiscale modeling can successfully address questions regarding the effects of epigenetic chemical modifications and the structure of condensed chromosomes in the metaphase cell cycle.

02:05 PM
02:40 PM
Ralf Bundschuh - Protein RNA-binding cooperativity

The interactions between proteins and RNAs are fundamental for gene regulation. Post-transcriptional regulation requires many proteins to bind to RNA. Implementation of combinatorial regulation requires cooperativity between such binding events. In the case of single-stranded RNA binding proteins, a competition emerges between binding by proteins and formation of intramolecular base pairs of the RNA. We show that this competition can be quantitatively modeled and provides a natural mechanism for the required cooperativity between RNA binding proteins.

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
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.

09:35 AM
10:10 AM
Alexander Vologodskii - On Simplification of DNA Topology by Type II DNA Topoisomerases

Type II DNA topoisomerases can change DNA topology by catalyzing the passing of one double-stranded DNA segment through another. In 1997 Rybenkov et al. unexpectedly found that the enzymes can greatly reduce, up to hundred times, the fractions of knotted and linked circular DNA molecules comparing with the corresponding equilibrium values. The phenomenon of topology simplification attracted a lot of attention because it was very difficult to understand how small enzymes could determine topology of large DNA molecules. It seems clear now that the only way for the topoisomerases to achieve topology simplification is to use the fact that the probability of some specific local conformations of DNA segments depends on DNA topology. Although great progress has been made in understanding the phenomenon, some features of it are not explained by the existing models. To eliminate the discrepancy with the experimental data we suggest here a new model of the enzyme action.

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 (Heitsch 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 - Packing, folding and simplifying DNA topology

Cellular processes such as replication, recombination, and packing change the topology of DNA. Controlling these changes is key to ensuring stability inside the cell. We use topological and computational methods to study the action of enzymes that simplify the topology of DNA during replication. I will review these methods and will expand on some thoughts on DNA folding.

02:40 PM
03:20 PM

Break

03:20 PM
03:55 PM
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).

03:55 PM
04:30 PM
David Murrugarra - Molecular Network Control Through Boolean Canalization

Boolean networks are an important class of computational models for molecular interaction networks. Boolean canalization, a type of hierarchical clustering of the inputs of a Boolean function, has been extensively studied in the context of network modeling where each layer of canalization adds a degree of stability in the dynamics of the network. Recently, dynamic network control approaches have been used for the design of new therapeutic interventions and for other applications such as stem cell reprogramming. This talk will discuss the role of canalization in the control of Boolean molecular networks. A method for identifying the potential control edges in the wiring diagram of a network for avoiding undesirable state transitions will be presented. The method is based on identifying appropriate input-output combinations on undesirable transitions that can be modified using the edges in the wiring diagram of the network. Moreover, a method for estimating the number of changed transitions in the state space of the system as a result of an edge deletion in the wiring diagram will be presented. These two complementary methods can help in the selection of appropriate controllers such as for minimizing the side effects resulting from an edge manipulation.

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
Natasa 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
Yusu Wang - Analyzing biological data via topological terrain metaphors

I will talk about the use of topological terrain metaphors for (biological) data visualization and analysis. I will in praticular describe two software we developed: Denali, a generic tool for visualizing tree-like structures (such as clustering trees) using topological terrain metaphors, as well as Ayla, a specialized visual analytic tool for exploring molecular simulation data. This is joint work with J. Eldridge, W. Harvey, M. Belkin, T.-P. Bremer, C. Li, I. Park, V. Pascucci and O. Ruebel.

10:10 AM
10:50 AM

Break

10:50 AM
11:25 AM
Sarah Woodson - Cooperativity of RNA Folding Landscapes

Abstract not submitted

11:25 AM
12:00 PM
Robert Eisenberg - Electrodynamics in Chemical Reactions

Chemical reactions are described and analyzed using conservation of mass and the law of mass action. The conservation of mass does not imply the conservation of electric current, as can easily be seen by in the reaction A •••• B •••• C where IAB ≠ IBC . The two reactions involve different rate constants, that are customarily independent, so the currents cannot be equal under more than one condition! Electric forces are very very much stronger than diffusion forces: one percent change in net charge produces a force large enough to lift the earth; one per cent change in mass has hardly any effect. I argue that chemical models cannot transferable (with one set of parameters) if they do not satisfy conservation of current. I argue that conservation of current must be exact in models of chemical reactions in all conditions, locations, and times because the ‘current’ defined in Maxwell’s equations cannot be stored, at all. My colleagues and I are trying to construct such models, following the lead of colleagues in semiconductor and computational electronics, who have done this for years.

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

The branching of an RNA secondary structure is an important molecular characteristic, yet often difficult to predict correctly by optimizing under the nearest-neighbor thermodynamic model (NNTM).

Prior results for a combinatorial model of RNA folding analyzed the expected degree of branching, and demonstrated that changes in the NNTM parameters can significantly affect this distribution.

This insight was fully developed using methods from geometric combinatorics to give a parametric analysis of the optimal configurations, addressing the dependence of prediction results on the objective function parameters. Furthermore, it is now possible to compute a branching polytope and associated normal fan subdivision of the dual space for any RNA sequence, yielding new insights into the accuracy and robustness of RNA secondary structure prediction.

04:45 PM

Shuttle pick-up from MBI

06:30 PM
07:00 PM

Cash Bar

07:00 PM
09:00 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
Guowei Wei - A multiscale and multiphysical model for molecular self-assembly

Molecular self-assembly is a process for molecules to adopt certain intriguing geometry and topology in the absence of external influence. It is fundamental to the construction of sphere-, rod-, polyhedral- or sheet-like complexes, arrays of nanowires, two-dimensional columnar liquid crystalline lattices, membrane, ribosomes, double helical DNA, viruses and cellular organelles, to mention only a few. The emergence of complexity in self-organizing systems poses fabulous challenges to their quantitative description because of the excessively high dimensionality. A crucial question is how to reduce the number of degrees of freedom, while preserving the fundamental physics in molecular self-assembly. We discuss a multiscale and multiphysics paradigm for molecular self-assembly. In our model, the motion of nano or virual particles is described by coarse-grained molecular mechanics (MM), while the solvent is approximated by a dielectric continuum. The MM is driven by electrostatic and van der Waals interactions among the particles, as well as particle stochastic fluctuations, surface tension, volume effect and solvent-solute interactions. Based on the variational principle, we derive the coupled Laplace-Beltrami Poisson-Boltzmann, and Newton equations for the structure, function, dynamics and transport of molecular self-assembly.

09:35 AM
10:10 AM
Henri Orland
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 (One to airport, and one back to hotel)

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
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 Mathematics, Universita di Torino
Chen, Duan dchen10@uncc.edu Department of Mathematics, University of North Carolina, Charlotte
Chen, Zhan zchen@georgiasouthern.edu Mathematics, Michigan State University
Chen, Tien-Hao chen.3007@osu.edu Chemistry and Biochemistry, The Ohio State University
Dykeman, Eric eric.dykeman@york.ac.uk Mathematics, University of York
Eisenberg, Robert beisenbe@rush.edu Molecular Biophysics and Physiology, Rush University Medical Center
Flapan, Erica eflapan@pomona.edu Mathematics, Pomona College
Foster, Mark foster.281@osu.edu Department of Biochemistry, The Ohio State University
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 Department of Biochemistry, The Ohio State University
Grosberg, Alexander ayg1@nyu.edu Physics, New York University
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 Chemistry Department, Bowling Green State University
Mannige, Ranjan rvmannige@lbl.gov Materials Science Division, Lawrence Berkeley Laboratory
Mathews, David David_Mathews@urmc.rochester.edu Biochemistry and Biophysics, University of Rochester
Mischaikow, Konstantin mischaik@math.rutgers.edu Mathematics, Rutgers
Morleand, Blythe moreland.104@osu.edu Physics, The Ohio State University
Murrugarra, David murrugarra@uky.edu Mathematics, University of Kentucky
Musier-Forsyth, Karin musier@chemistry.ohio-state.edu Chemistry and Biochemistry, Ohio State University
Olson, Erik olson.249@osu.edu Chemistry and Biochemistry, The 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)
Rambo, Robert robert.rambo@diamond.ac.uk Life Sciences, Diamond Light Source
Rein, Alan rein@mail.ncifcrf.gov HIV Dynamics and Replication Program, National Institutes of Health (NIH)
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 Computer Science, Smith College
Thirumalai, Devarajan (Dave) thirum@umd.edu IPST, Institute for Physical Sciences and Technology
Turner, Douglas turner@chem.rochester.edu Chemistry, University of Rochester
Twarock, Reidun rt507@york.ac.uk Mathematics and Biology, University of York
Vazquez, Mariel mariel@math.ucdavis.edu Mathematics, Microbiology & Molecular Genetics, University of California, Davis
Vologodskii, Alexander alex.vologodskii@nyu.edu Chemistry, New York University
Wang, Chi-Jen cwang463@math.gatech.edu Mathematics, Georgia Institute of Technology
Wang, Yusu yusu@cse.ohio-state.edu Computer Science and Engineering, The Ohio State University
Wei, Guowei wei@math.msu.edu Department of Mathematics, Michigan State University
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
Xie, Dexuan dxie@uwm.edu Department of Mathematical Sciences, University of Wisconsin
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,
Zhao, Rundong rdzhao1992@gmail.com Computer Science and Engineering, Michigan State University
Zhou, Yongcheng yzhou@math.colostate.edu Mathematics, Colorado State University
Landau Theories of the Assembly of Viruses

We examined the recent application of group theory to the assembly of icosahedral viral shells by Lorman and
Rochal. These authors arrived at the important result that there should be no activation energy barrier. Ultimately
this is a consequence of broken chiral symmetry. Their result conflicts with earlier models for viral assembly that
all find a large energy activation barrier. We extend the work of Lorman and Rochas and find that their result is a
special case of a general family of theories for assembly on icosahedral shells with broken chiral symmetry. Some of
these do and some of these do not have energy activation barriers.

Protein RNA-binding cooperativity

The interactions between proteins and RNAs are fundamental for gene regulation. Post-transcriptional regulation requires many proteins to bind to RNA. Implementation of combinatorial regulation requires cooperativity between such binding events. In the case of single-stranded RNA binding proteins, a competition emerges between binding by proteins and formation of intramolecular base pairs of the RNA. We show that this competition can be quantitatively modeled and provides a natural mechanism for the required cooperativity between RNA binding proteins.

Assembly of ssRNA Viruses I: Identification of packaging signals and their role in assembly

Multiple dispersed sequence/structure motifs in single-stranded RNA genomes termed packaging signals have been shown to play crucial roles in virus assembly. This talk will cover theoretical tools underpinning the discovery of such packaging signals in a wide range of single-stranded RNA viruses, and discuss models demonstrating their impact on virus assembly efficiency and selective genome packaging. We show that graph theoretical tools can be used to better understand the complexity of the assembly process.

Electrodynamics in Chemical Reactions

Chemical reactions are described and analyzed using conservation of mass and the law of mass action. The conservation of mass does not imply the conservation of electric current, as can easily be seen by in the reaction A â€¢â€¢â€¢â€¢ B â€¢â€¢â€¢â€¢ C where IAB â‰  IBC . The two reactions involve different rate constants, that are customarily independent, so the currents cannot be equal under more than one condition! Electric forces are very very much stronger than diffusion forces: one percent change in net charge produces a force large enough to lift the earth; one per cent change in mass has hardly any effect. I argue that chemical models cannot transferable (with one set of parameters) if they do not satisfy conservation of current. I argue that conservation of current must be exact in models of chemical reactions in all conditions, locations, and times because the â€˜currentâ€™ defined in Maxwellâ€™s equations cannot be stored, at all. My colleagues and I are trying to construct such models, following the lead of colleagues in semiconductor and computational electronics, who have done this for years.

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.

Knots in a Macromolecule

In the talk, I plan to review the current status of the controversial idea that knots in a macromolecule tighten themselves for entropic reasons.

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

The branching of an RNA secondary structure is an important molecular characteristic, yet often difficult to predict correctly by optimizing under the nearest-neighbor thermodynamic model (NNTM).

Prior results for a combinatorial model of RNA folding analyzed the expected degree of branching, and demonstrated that changes in the NNTM parameters can significantly affect this distribution.

This insight was fully developed using methods from geometric combinatorics to give a parametric analysis of the optimal configurations, addressing the dependence of prediction results on the objective function parameters. Furthermore, it is now possible to compute a branching polytope and associated normal fan subdivision of the dual space for any RNA sequence, yielding new insights into the accuracy and robustness of RNA secondary structure prediction.

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.

Predicting the geometry of self-assembling nanoparticles

In this talk I will present a mathematical approach to the classification and the prediction of the geometry underlying the arrangements of the polypeptidic building blocks in self-assembling protein nanoparticles.

I will focus on artificially engineered nanoshells made by repeated copies of a single protein or polypeptidic units. I will tackle the problem of the structure determination of such particles given that they do not necessarly conform to the Caspar-Klug theory, which accounts for the arrangement of proteins in icosahedral spherical viruses, and that there is no experimental technique allowing to resolve unambiguously their actual structure.

I will study the topology of the protein network using tools from graph theory and tiling theory. Special attention will be devoted to symmetric particles, which can be fully described and classified.

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.

Molecular Network Control Through Boolean Canalization

Boolean networks are an important class of computational models for molecular interaction networks. Boolean canalization, a type of hierarchical clustering of the inputs of a Boolean function, has been extensively studied in the context of network modeling where each layer of canalization adds a degree of stability in the dynamics of the network. Recently, dynamic network control approaches have been used for the design of new therapeutic interventions and for other applications such as stem cell reprogramming. This talk will discuss the role of canalization in the control of Boolean molecular networks. A method for identifying the potential control edges in the wiring diagram of a network for avoiding undesirable state transitions will be presented. The method is based on identifying appropriate input-output combinations on undesirable transitions that can be modified using the edges in the wiring diagram of the network. Moreover, a method for estimating the number of changed transitions in the state space of the system as a result of an edge deletion in the wiring diagram will be presented. These two complementary methods can help in the selection of appropriate controllers such as for minimizing the side effects resulting from an edge manipulation.

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).

A Conformational Switch in HIV-1 Gag Protein: The Decision to Assemble

Recombinant HIV-1 Gag protein, purified from bacteria, is a soluble protein, but assembles into virus-like particles (VLPs) in a defined in vitro system upon addition of nucleic acid (NA). We have tried to understand how NA-binding promotes assembly. Experiments with Gag-leucine zipper chimeric proteins suggest that when Gag attains a high local concentration, it undergoes a change which primes it for assembly; cooperative NA-binding would be one way it could reach a high local concentration. We have focused on the SP1 region of Gag, which lies between the CA domain (principally responsible for Gag-Gag interactions in VLPs) and the NC domain (principally responsible for NA-binding). Many subtle mutations in SP1 cause drastic disruption of VLP assembly. If the SP1 sequence were folded into an Î±-helix, the helix would be amphipathic, with a polar face and a hydrophobic face. We have found that a peptide representing SP1 folds into a helix when it is at high concentration; presumably, at these concentrations, helices can aggregate and bury their hydrophobic faces within helix bundles.

We now report that small proteins consisting of SP1 fused to a dimerizing leucine zipper form discrete tetramers in solution. However, many mutations in these SP-zipper chimeras cause them to form dimers rather than tetramers; therefore, SP1-SP1 interactions are responsible for the association of the zipper-induced dimers into tetramers. As these specific mutations also disrupt assembly by Gag, the same SP1-SP1 interactions are also significant in VLP assembly. We hypothesize that folding of SP1 into a helix primes Gag for VLP assembly, perhaps by exposing new interfaces in the CA domain. Information on the structure of these SP1 bundles will be presented.

Multiscale modeling of the chromatin fiber

Understanding chromosome tertiary organization and its role in control of gene expression represents one of the most fundamental open biological challenges. Chromatin structure and gene expression are intimately related because the complex nature and dynamics of protein-bound DNA folding in the living cell regulates gene activity at a large range of spatial and temporal scales. Recent advances in experimental studies of chromatin using nucleosome structure determination, ultra-structural techniques, single-force extension studies, and analysis of chromosomal interactions have revealed important chromatin characteristics under various internal and external conditions. Modeling studies, anchored to high-resolution nucleosome models, have explored many related questions systematically. In this talk, I will describe recent findings regarding chromatin structure and function using a combination of coarse-grained modeling and large-scale all-atom molecular dynamics simulations of chromatin fibers. In particular, I will describe how such multiscale modeling can successfully address questions regarding the effects of epigenetic chemical modifications and the structure of condensed chromosomes in the metaphase cell cycle.

Rigidity and flexibility of large molecular structures: mathematical and computational challenges

The Protein Databank (PDB) and the Open Crystallography Database (COD) are two large repositories (111 000, resp. 350 000 entries) of known molecular structures, widely used by biochemists and crystallographers. Of particular interest are questions concerning the rigidity and flexibility of these molecules: the answers may reveal intrinsic biological functions or unusual properties of crystalline matter.

I will survey several methods that shed light on these questions., including one based on the mathematics of rigidity theory, as implemented in the web application Kinari developed in my group. Then I will discuss the challenges emerging from making Kinari work with the entire PDB or COD databases, and in particular with extremly large biomolecules such as viruses.

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.

Assembly of ssRNA viruses II: Consequences of Packaging Signal Mediated Assembly for Viral Evolution

Packaging signals provide an instruction manual for efficient virus assembly and thus place constraints on the evolution of single-stranded RNA genomes. This talk will cover the consequences of packaging signal-mediated assembly for viral evolution. It will discuss the geometry of the implicitly define fitness landscapes underpinning the evolutionary dynamics and the consequences of viral geometry for evolution.

Packing, folding and simplifying DNA topology

Cellular processes such as replication, recombination, and packing change the topology of DNA. Controlling these changes is key to ensuring stability inside the cell. We use topological and computational methods to study the action of enzymes that simplify the topology of DNA during replication. I will review these methods and will expand on some thoughts on DNA folding.

On Simplification of DNA Topology by Type II DNA Topoisomerases

Type II DNA topoisomerases can change DNA topology by catalyzing the passing of one double-stranded DNA segment through another. In 1997 Rybenkov et al. unexpectedly found that the enzymes can greatly reduce, up to hundred times, the fractions of knotted and linked circular DNA molecules comparing with the corresponding equilibrium values. The phenomenon of topology simplification attracted a lot of attention because it was very difficult to understand how small enzymes could determine topology of large DNA molecules. It seems clear now that the only way for the topoisomerases to achieve topology simplification is to use the fact that the probability of some specific local conformations of DNA segments depends on DNA topology. Although great progress has been made in understanding the phenomenon, some features of it are not explained by the existing models. To eliminate the discrepancy with the experimental data we suggest here a new model of the enzyme action.

Analyzing biological data via topological terrain metaphors

I will talk about the use of topological terrain metaphors for (biological) data visualization and analysis. I will in praticular describe two software we developed: Denali, a generic tool for visualizing tree-like structures (such as clustering trees) using topological terrain metaphors, as well as Ayla, a specialized visual analytic tool for exploring molecular simulation data. This is joint work with J. Eldridge, W. Harvey, M. Belkin, T.-P. Bremer, C. Li, I. Park, V. Pascucci and O. Ruebel.

A multiscale and multiphysical model for molecular self-assembly

Molecular self-assembly is a process for molecules to adopt certain intriguing geometry and topology in the absence of external influence. It is fundamental to the construction of sphere-, rod-, polyhedral- or sheet-like complexes, arrays of nanowires, two-dimensional columnar liquid crystalline lattices, membrane, ribosomes, double helical DNA, viruses and cellular organelles, to mention only a few. The emergence of complexity in self-organizing systems poses fabulous challenges to their quantitative description because of the excessively high dimensionality. A crucial question is how to reduce the number of degrees of freedom, while preserving the fundamental physics in molecular self-assembly. We discuss a multiscale and multiphysics paradigm for molecular self-assembly. In our model, the motion of nano or virual particles is described by coarse-grained molecular mechanics (MM), while the solvent is approximated by a dielectric continuum. The MM is driven by electrostatic and van der Waals interactions among the particles, as well as particle stochastic fluctuations, surface tension, volume effect and solvent-solute interactions. Based on the variational principle, we derive the coupled Laplace-Beltrami Poisson-Boltzmann, and Newton equations for the structure, function, dynamics and transport of molecular self-assembly.

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

Retroviruses, like all other viruses, contain a protein shell called the capsid that encloses the genetic materials (RNA or DNA). While most viruses adopt spherical shapes, the capsid of mature Human Immunodeficiency Virus (HIV), classified as a retrovirus, self-assembles predominantly into conspicuous conical structures. Despite numerous cryo-electron tomographic studies, the kinetic pathway of assembly of capsid proteins into conical cores is not well understood. To study the impact of genome and surrounding membrane on the formation of HIV shells, we monitor the step by step irreversible growth of HIV capsids. We show that the presence of membrane not only restricts the growth of incomplete capsids, it also induces local stresses on the growing sheet creating the formation of pentamers necessary for the assembly of closed shells. Our results also shed light in the role of genome in the assembly of conical cores. Our findings are consistent with the recent experimental results, emphasizing on the importance of RNA and membrane on the formation of HIV conical shells.

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.