Biomathematics afternoon in Ljubljana, 2016

Wednesday 17 Feb 2016, 14:00 → 22:00 Europe/Ljubljana

2.05 (University of Ljubljana, FMF)

A meeting to present and exchange the uses of various mathematical notions (such as topology) in the bio-sciences.

Topics also include designing/predicting RNA, DNA and proteins.

14:30 → 15:00 Coffee, Tea, Posters

15:00 → 16:20 First session

15:00 Bernhard Thiel (TBI) - Integrating Cryo-EM with Coarse Grained RNA 3D Structure Prediction in ERNWIN

Ernwin (Kerpedjiev 2015) is program that performs a Metropolis-Rosenbluth like Monte Carlo sampling of coarse grained RNA 3D structures. Lokal conformations are sampled directly from possible conformations found in crystal structures or structures predicted with very accurate methods. An energy function used in the accept-reject step of the sampling procedure accounts for long-range interactions and directs the global structure in the desired way. Single molecule Cryo Electron Microscopy and Atomic Force Microscopy images can show large-scale properties of RNA molecules projected to a 2D plane. We compare such images to mathematically generated projections of predicted RNA 3D structures to improve our structure prediction model and to draw conclusions about the observed RNA.

15:20 Roman Jerala (KI) - Design principles for rapid folding of knotted DNA

Knots are some of the most remarkable topological features in nature. Self-assembly of knotted polymers without breaking or forming covalent bonds is challenging, as the chain needs to be steered through the previously formed loops in a predefined order. Here we describe principles to guide the folding of highly knotted single-chain DNA nanostructures as demonstrated on a nano-sized square pyramid. Folding of knots is encoded by the arrangement of modules of different stability based on derived topological and kinetic rules. Among DNA designs composed of the same modules and encoding the same topology only the one with the folding pathway designed according to the “free-end” rule folded efficiently into the target structure. Besides high folding yields upon slow annealing, this design also folded rapidly upon temperature quenching and dilution from chemical denaturant. We anticipate that this strategy could be used to design the folding of other knotted programmable molecules.

15:40 Ronny Lorenz (TBI) Constraints in RNA secondary structure predixction

Background: A large class of RNA secondary structure prediction programs uses an elaborate energy model grounded in extensive thermodynamic measurements and exact dynamic programming algorithms. External experimental evidence can be in principle be incorporated by means of hard constraints that restrict the search space or by mean of soft constraints that distort the energy model. In particular recent advances in coupling chemical and enzymatic probing with sequencing techniques but also comparative approaches provide an increasing amount experimental data to be combined with secondary structure prediction. Results: Responding to the increasing needs for a versatile and user-friendly inclusion of external evidence into diverse flavours RNA secondary structure prediction tools we implemented a generic layer of constraint handling into the ViennaRNA package. It makes explicit use of the conceptual separation of the "folding grammar" defining the search space and the actual energy evalution, which allows constraints to be interleaved in a natural way between recursion steps and evaluation of the standard energy function. Conclusions: The extension of the ViennaRNA package provides a generic way to include diverse types of constraints into RNA folding algorithms. The computational overhead incurred is negligible in practice. A wide variety of application scenarios can be accomodated by the new framework, including the incorporation of structure probing data, non-standard base pairs and chemical modifications, as well as structure-dependent ligand binding.

16:00 Ajasja Ljubetič (KI) - Designing, modelling and folding protein polyhedra

Protein origami is an exciting emerging field, inspired by the success of DNA origami. Proteins however, unlike DNA, have a large number of weak long range interactions which are very difficult to predict and even more to design. This problem can be elegantly solved by using modular components with exactly defined binding partners of which coiled coils are an excellent example (Kočar et al., WIREs, 2014). The topology of where the interacting building blocks are located in the sequence determines the final three dimensional shape of such TOPOFOLD proteins. As an example, a topofold tetrahedron has recently been constructed out of six coiled coil pairs (Gradišar et al., NatChemBiol 2013). The folding pathway is often critical for the correct structure and function of proteins. In contrast to natural proteins, topofold proteins do not possess a compact hydrophobic core and the folding pathway is therefore determined by the topology of building blocks and the order in which these building blocks assemble. Here we present a short overview of the methodology used to design arbitrary protein polyhedra. The folding pathway of a topofold protein tetrahedron is presented in detail. In particular we have examined the folding using all-atom structure based (Go) simulations. We are using these simulations to test how different arrangements of building blocks in the protein sequence affect its folding pathway. This allows us to design optimized versions of topofold proteins with smooth folding pathways in order to avoid misfolding and aggregation. We have also examined the folding pathways using stop-flow techniques. The chevron plot shows a weak dependence on denaturant concentration, which is compatible with multistate folding pathways observed in Go simulations.

16:20 → 16:40 Cofee, tea

16:40 → 18:00 Second session

16:40 Andrea Tanzer (TBI) RNA secondary structure prediction - a case study

17:00 Jernej Rus (Abelium, FMF) - Strong traces as a model for self-assembly polypeptide nanostructures

In 2011 Gradišar et al. presented a novel self-assembly strategy for polypeptide nanostructure design that could lead to significant developments in biotechnology. We will talk about strong traces (closed walk which traverse every edge exactly twice and for every vertex $v$, there is no subset $N$ of its neighbors, with $1 \leq |N| < d(v)$, such that every time the walk enters $v$ from $N$, it also exits to a vertex in $N$), which were introduced to serve as an appropriate mathematical description for this biotechnological research. Among other, we will show how strong traces are connected to graph embeddings. Some derivations, such as parallel strong traces, antiparallel strong traces, and $d$-stable traces will also be mentioned.

17:20 Peter Stadler (Univ. Leipzig) Trees

17:40 Tomaž Pisanski (UL FMF) - Crossings in polyhedral self-assembly

In this talk we will present a model for single strand or multiple strand polyhredral self-assembly. In particular we will consider the problem of crossings and self-crossings of strands at polyhedral vertices. The model uses the methods of topological graph theory, i.e. embeddings of graphs in surfaces. This is work in progress in BioOrigami project in connection with the Roman Jerala group from National Institute of Chemistry. It is also related to the bilateral US-SVN project with Egon Schulte.

18:00 → 18:30 Coffee, Tea, Posters

19:00 → 22:00 Conference dinner

Gostilna Čad http://www.gostilna-cad.si/gb/index.html (each pays for himself/herself).