Abstract
We introduce a Firefly-inspired algorithmic approach for protein structure prediction over two different lattice models in three-dimensional space. In particular, we consider three-dimensional cubic and three-dimensional face-centred-cubic (FCC) lattices. The underlying energy models are the Hydrophobic-Polar (H-P) model, the Miyazawa–Jernigan (M-J) model and a related matrix model. The implementation of our approach is tested on ten H-P benchmark problems of a length of 48 and ten M-J benchmark problems of a length ranging from 48 until 61. The key complexity parameter we investigate is the total number of objective function evaluations required to achieve the optimum energy values for the H-P model or competitive results in comparison to published values for the M-J model. For H-P instances and cubic lattices, where data for comparison are available, we obtain an average speed-up over eight instances of 2.1, leaving out two extreme values (otherwise, 8.8). For six M-J instances, data for comparison are available for cubic lattices and runs with a population size of 100, where, a priori, the minimum free energy is a termination criterion. The average speed-up over four instances is 1.2 (leaving out two extreme values, otherwise 1.1), which is achieved for a population size of only eight instances. The present study is a test case with initial results for ad hoc parameter settings, with the aim of justifying future research on larger instances within lattice model settings, eventually leading to the ultimate goal of implementations for off-lattice models.
Highlights
Research on protein structure and folding has a long history, dating back to the seminal work by Pauling and Corey [1]; see [2,3,4,5]
By selecting such a small value of T, we try to avoid that conformations different from Sbest do not move for too many steps structurally towards a conformation that is no longer the best with respect to the energy value
We presented the initial results of protein structure prediction in lattice models by using simplified energy function and a new Firefly-inspired heuristic with ad hoc parameter settings
Summary
Research on protein structure and folding has a long history, dating back to the seminal work by Pauling and Corey [1]; see [2,3,4,5]. Lattice models have been shown to be useful for the study of globular proteins [17,19], of the conformational space induced by (simplified) protein sequences [4,20] and for the analysis of a number of other features important in protein structure prediction, such as long-range interactions in proteins [23]. In the centre of the present paper is the adaptation of a brand new population-based method to protein structure prediction, namely, the Firefly Algorithm (FA). For the H-P model and face-centred-cubic (FCC) lattices, a new tabu search heuristic is applied in [30] to 21 sequences of a length between 90 and 279. The results encourage us to analyse further larger instances for the H-P model and to adapt the approach to off-lattice models
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