Related papers: Combinatorial RNA Design Designability and Structu…
The primary structure of a ribonucleic acid (RNA) molecule can be represented as a sequence of nucleotides (bases) over the alphabet {A, C, G, U}. The secondary or tertiary structure of an RNA is a set of base pairs which form bonds between…
Data storage in DNA is developing as a possible solution for archival digital data. Recently, to further increase the potential capacity of DNA-based data storage systems, the combinatorial composite DNA synthesis method was suggested. This…
We describe a dynamic programming algorithm for predicting optimal RNA secondary structure, including pseudoknots. The algorithm has a worst case complexity of ${\cal O}(N^6)$ in time and ${\cal O}(N^4)$ in storage. The description of the…
Here we present an approximate analytical theory for the relationship between a protein structure's contact matrix and the shape of its energy spectrum in amino acid sequence space. We demonstrate a dependence of the number of sequences of…
The problem of RNA secondary structure design (also called inverse folding) is the following: given a target secondary structure, one aims to create a sequence that folds into, or is compatible with, a given structure. In several practical…
The field of complex self-assembly is moving toward the design of multi-particle structures consisting of thousands of distinct building blocks. To exploit the potential benefits of structures with such `addressable complexity,' we need to…
We present a base-pairing model of oligonuleotide duplex formation and show in detail its equivalence to the Nearest-Neighbour dimer methods from fits to free energy of duplex formation data for short DNA-DNA and DNA-RNA hybrids containing…
It is the first step for understanding how RNA structure folds from base sequences that to know how its secondary structure is formed. Traditional energy-based algorithms are short of precision, particularly for non-nested sequences, while…
In this paper, we study the combinatorial set of RNA secondary structures of length $n$ with $m$ base-pairs. For a compact representation, we encode an RNA secondary structure by the corresponding Motzkin word. For this combinatorial set,…
We consider systems of recursively defined combinatorial structures. We give algorithms checking that these systems are well founded, computing generating series and providing numerical values. Our framework is an articulation of the…
While artificial intelligence has made remarkable strides in revealing the relationship between biological macromolecules' primary sequence and tertiary structure, designing RNA sequences based on specified tertiary structures remains…
In post-transcriptional regulation, an mRNA molecule is bound by many proteins and/or miRNAs to modulate its function. To enable combinatorial gene regulation, these binding partners of an RNA must communicate with each other, exhibiting…
Designing RNA molecules has garnered recent interest in medicine, synthetic biology, biotechnology and bioinformatics since many functional RNA molecules were shown to be involved in regulatory processes for transcription, epigenetics and…
We propose a model-based, automated, bottom-up approach for design, which is applicable to various physical domains, but in this work we focus on the electrical domain. This bottom-up approach is based on a meta-topology in which each link…
The paper investigates the computational problem of predicting RNA secondary structures. The general belief is that allowing pseudoknots makes the problem hard. Existing polynomial-time algorithms are heuristic algorithms with no…
We investigate block designs, under the A- and MV-criteria, when each treatment can have only one or two replications due to resource constraints, as can happen, for example, in early generation varietal trials. While these are commonly…
The design of multi-stable RNA molecules has important applications in biology, medicine, and biotechnology. Synthetic design approaches profit strongly from effective in-silico methods, which can tremendously impact their cost and…
RNA secondary structure prediction and classification are two important problems in the field of RNA biology. Here, we propose a new permutation based approach to create logical non-disjoint clusters of different secondary structures of a…
We study $T$-designs in the nonbinary Johnson scheme. This scheme generalizes both the Johnson and Hamming schemes and admits a bivariate $Q$-polynomial structure. Zhu (2021) provided a combinatorial characterization of $T$-designs in this…
Recall that Janson showed that if the edges of the complete graph $K_n$ are assigned exponentially distributed independent random weights, then the expected length of a shortest path between a fixed pair of vertices is asymptotically equal…