Particle swarm optimization for finding RNA secondary structures

Abstract

This paper proposes a Particle Swarm Optimization (PSO) algorithm called HelixPSO for finding RNA secondary structures that have a low energy and are similar to the native structure. HelixPSO is compared to the recent algorithms RnaPredict, SARNA-Predict, SetPSO, and RNAfold. For a set of standard RNA test sequences it is shown that HelixPSO obtains a better average sensitivity than SARNA-Predict and SetPSO and is as good as RNA-Predict and RNAfold. When best values for different measures (e.g., number of correctly predicted base pairs, false positives, and sensitivity) over several runs are compared, HelixPSO performs better than RNAfold, similar to RNA-Predict, and is outperformed by SARNA-Predict. It is shown that HelixPSO complements Rna-Predict and SARNA-Predict well since the algorithms show often very different behavior on the same sequence. Furthermore, a parallel version of the HelixPSO is proposed and it is shown that good speedup values can be obtained for small to medium size PC clusters.

dPSO‐Vis: Topology‐based Visualization of Discrete Particle Swarm Optimization

“…The set of base pairs represents the secondary structure. Typically, base pairs occur only between G and C, or A and U, or G and U (for additional restrictions and details see, e.g., [GM11]).…”

“…The secondary structure determines the free energy of the molecule and its stability. The RNA secondary prediction problem is to find a secondary structure, i.e., a feasible set of base pairs, with maximum free energy (with respect to some energy model, for details see [GM11]). To reduce the problem size, maximal sets of two or more adjacent base pairs that form a ladder‐like structure, called helices, can be considered as the main elements of an RNA secondary structure.…”

“…Another optimization is the usage of 1‐elitism, i.e., after each simulation step the worst particle is reset to the position of the best particle without altering its target vector (e‐SA‐HelixPSO). For details see [Gei08, GM11].…”

“…In order to evaluate dPSO‐Vis, we analyzed HelixPSO for three example RNAs that are listed in Table 2 with corresponding numbers that characterize the size of their search space and configuration space. The largest example is an RNA from E. coli, which has been used in the original evaluation of HelixPSO [GM11]. Figure 5 shows the resulting images.…”

“…The formulation of PSO is based on vector mathematics and thus requires the optimization domain to be a continuous vector space. Nevertheless, many PSO algorithms have also been proposed for problems with a discrete search space in recent years, among them HelixPSO [GM07, Gei08, GM11]. There exist mainly three approaches: i) map the discrete search space into a continuous search space and use a standard PSO (positions of particles are then mapped to the closest position that corresponds to a point in the discrete search space), ii) particles move within a multidimensional probability space and a particle creates a solution randomly such that its position determines the probabilities for choosing the different values in the discrete space, iii) the particles move directly within the search space and the movement is influenced by so called target positions from the search space.…”