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Bernd Burghardt

Publications and source records attributed to Bernd Burghardt.

4 recordsLinked to original sources
arXiv2006

RNA secondary structure design

We consider the inverse-folding problem for RNA secondary structures: for a given (pseudo-knot-free) secondary structure find a sequence that has that structure as its ground state. If such a sequence exists, the structure is called designable. We implemented a branch-and-bound algorithm that is able to do an exhaustive search within the sequence space, i.e., gives an exact answer whether such a sequence exists. The bound required by the branch-and-bound algorithm are calculated by a dynamic programming algorithm. We consider different alphabet sizes and an ensemble of random structures, which we want to design. We find that for two letters almost none of these structures are designable. The designability improves for the three-letter case, but still a significant fraction of structures is undesignable. This changes when we look at the natural four-letter case with two pairs of complementary bases: undesignable structures are the exception, although they still exist. Finally, we also study the relation between designability and the algorithmic complexity of the branch-and-bound algorithm. Within the ensemble of structures, a high average degree of undesignability is correlated to a long time to prove that a given structure is (un-)designable. In the four-letter case, where the designability is high everywhere, the algorithmic complexity is highest in the region of naturally occurring RNA.

physics.bio-ph↗
arXiv2006

What do we learn from correlations of local and global network properties?

In complex networks a common task is to identify the most important or "central" nodes. There are several definitions, often called centrality measures, which often lead to different results. Here we study extensively correlations between four local and global measures namely the degree, the shortest-path-betweenness, the random-walk betweenness and the subgraph centrality on different random-network models like Erdos-Renyi, Small-World and Barabasi-Albert as well as on different real networks like metabolic pathways, social collaborations and computer networks. Correlations are quite different between the real networks and the model networks questioning whether the models really reflect all important properties of the real world.

physics.soc-ph↗
arXiv2004

Dependence of RNA secondary structure on the energy model

We analyze a microscopic RNA model, which includes two widely used models as limiting cases, namely it contains terms for bond as well as for stacking energies. We numerically investigate possible changes in the qualitative and quantitative behaviour while going from one model to the other; in particular we test, whether a transition occurs, when continuously moving from one model to the other. For this we calculate various thermodynamic quantities, both at zero temperature as well as at finite temperatures. All calculations can be done efficiently in polynomial time by a dynamic programming algorithm. We do not find a sign for transition between the models, but the critical exponent $ν$ of the correlation length, describing the phase transition in all models to an ordered low-temperature phase, seems to depend continuously on the model. Finally, we apply the epsilon-Coupling method, to study low excitations. The exponent $θ$ describing the energy-scaling of the excitations seems to depend not much on the energy model.

q-bio.QM↗