LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

Computational Design and Experimental Validation of Functional Ribonucleic Acid Nanostructures

In living cells, two major classes of ribonucleic acid (RNA) molecules can be found. The first class called the messenger RNA (mRNA) contains the genetic information that allows the ribosome to read and translate it into proteins. The second class called non-coding RNA (ncRNA), do not code for proteins and are involved with key cellular processes, such as gene expression regulation, splicing, differentiation, and development. NcRNAs fold into an ensemble of thermodynamically stable secondary structures, which will eventually lead the molecule to fold into a specific 3D structure. It is widely known that ncRNAs carry their functions via their 3D structures as well as their molecular composition. The secondary structure of ncRNAs is composed of different types of structural elements (motifs) such as stacking base pairs, internal loops, hairpin loops and pseudoknots. Pseudoknots are specifically difficult to model, are abundant in nature and known to stabilize the functional form of the molecule. Due to the diverse range of functions of ncRNAs, their computational design and analysis have numerous applications in nano-technology, therapeutics, synthetic biology, and materials engineering. The RNA design problem is to find novel RNA sequences that are predicted to fold into target structure(s) while satisfying specific qualitative characteristics and constraints. RNA design can be modeled as a combinatorial optimization problem (COP) and is known to be computationally challenging or more precisely NP-hard. Numerous algorithms to solve the RNA design problem have been developed over the past two decades, however mostly ignore pseudoknots and therefore limit application to only a slice of real-world modeling and design problems. Moreover, the few existing pseudoknot designer methods which were developed only recently, do not provide any evidence about the applicability of their proposed design methodology in biological contexts. The two objectives of this thesis are set to address these two shortcomings. First, we are interested in developing an efficient computational method for the design of RNA secondary structures including pseudoknots that show significantly improved in-silico quality characteristics than the state of the art. Second, we are interested in showing the real-world worthiness of the proposed method by validating it experimentally. More precisely, our aim is to design instances of certain types of RNA enzymes (i.e. ribozymes) and demonstrate that they are functionally active. This would likely only happen if their predicted folding matched their actual folding in the in-vitro experiments. In this thesis, we present four contributions. First, we propose a novel adaptive defect weighted sampling algorithm to efficiently solve the RNA secondary structure design problem where pseudoknots are included. We compare the performance of our design algorithm with the state of the art and show that our method generates molecules that are thermodynamically more stable and less defective than those generated by state of the art methods. Moreover, we show when the effect of fitness evaluation is decoupled from the search and optimization process, our optimization method converges faster than the non-dominated sorting genetic algorithm (NSGA II) and the ant colony optimization (ACO) algorithm do. Second, we use our algorithmic development to implement an RNA design pipeline called Enzymer and make it available as an open source package useful for wet lab practitioners and RNA bioinformaticians. Enzymer uses multiple sequence alignment (MSA) data to generate initial design templates for further optimization. Our design pipeline can then be used to re-engineer naturally occurring RNA enzymes such as ribozymes and riboswitches. Our first and second contributions are published in the RNA section of the Journal of Frontiers in Genetics. Third, we use Enzymer to reengineer three different species of pseudoknotted ribozymes: a hammerhead ribozyme from the mouse gut metagenome, a hammerhead ribozyme from Yarrowia lipolytica and a glmS ribozyme from Thermoanaerobacter tengcogensis. We designed a total of 18 ribozyme sequences and showed the 16 of them were active in-vitro. Our experimental results have been submitted to the RNA journal and strongly suggest that Enzymer is a reliable tool to design pseudoknotted ncRNAs with desired secondary structure. Finally, we propose a novel architecture for a new ribozyme-based gene regulatory network where a hammerhead ribozyme modulates expression of a reporter gene when an external stimulus IPTG is present. Our in-vivo results show expected results in 7 out of 12 cases

Large bichromatic point sets admit empty monochromatic 4-gons

We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES(k) such that any set S of at least fES(k) points in general position in the plane has a subset of k points that are the vertices of a convex k-gon. In our setting the points of S are colored, and we say that a (not necessarily convex) spanned polygon is monochromatic if all its vertices have the same color. Moreover, a polygon is called empty if it does not contain any points of S in its interior. We show that any bichromatic set of n ≥ 5044 points in R2 in general position determines at least one empty, monochromatic quadrilateral (and thus linearly many).Postprint (published version

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum